PhysRevA.103.053114.nb

(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 12.3' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[    121279,       2882]
NotebookOptionsPosition[    118766,       2836]
NotebookOutlinePosition[    119211,       2854]
CellTagsIndexPosition[    119168,       2851]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[TextData[StyleBox["Reaching high laser intensity by a radiating \
electron", "Title",
 FontWeight->"Regular",
 FontColor->RGBColor[
  0.2964217593652247, 0.6292210269321736, 0.2727702754253452]]], "Text",
 CellChangeTimes->{{3.822636147120782*^9, 3.822636149053595*^9}, {
   3.822636240732341*^9, 3.82263625191656*^9}, {3.822637212068983*^9, 
   3.822637212721833*^9}, {3.822893489756895*^9, 3.822893491949749*^9}, {
   3.832321238753117*^9, 3.832321249383651*^9}, {3.8323245292762823`*^9, 
   3.8323245340020647`*^9}, 3.832906798222391*^9, {3.83303920946581*^9, 
   3.8330392125191813`*^9}, 
   3.833465389390917*^9},ExpressionUUID->"47d4fbe3-762d-4eb1-bac4-\
7015f4eb338f"],

Cell[TextData[{
 StyleBox[ButtonBox["M. Jirka, et al, Phys. Rev. A 103, 053114",
  BaseStyle->"Hyperlink",
  ButtonData->{
    URL["https://journals.aps.org/pra/abstract/10.1103/PhysRevA.103.053114"], 
    None},
  ButtonNote->
   "https://journals.aps.org/pra/abstract/10.1103/PhysRevA.103.053114"], 
  "Section",
  FontSize->24,
  FontColor->GrayLevel[0]],
 StyleBox["\nN", "Section",
  FontSize->24,
  FontColor->GrayLevel[0]],
 StyleBox[ButtonBox["otebook",
  BaseStyle->"Hyperlink",
  ButtonData->{
    URL["https://journals.aps.org/pra/abstract/10.1103/PhysRevA.103.053114"], 
    None},
  ButtonNote->
   "https://journals.aps.org/pra/abstract/10.1103/PhysRevA.103.053114"], 
  "Section",
  FontSize->24,
  FontColor->GrayLevel[0]],
 StyleBox[": \[CapitalOAcute]scar Amaro, June 2021/Jan 2022 @", "Section",
  FontSize->24,
  FontColor->GrayLevel[0]],
 StyleBox[ButtonBox[" ",
  BaseStyle->"Hyperlink",
  ButtonData->{
    URL["http://epp.ist.utl.pt/"], None},
  ButtonNote->"http://epp.ist.utl.pt/"], "Section",
  FontSize->24,
  FontColor->GrayLevel[0]],
 StyleBox[ButtonBox["GoLP-EPP",
  BaseStyle->"Hyperlink",
  ButtonData->{
    URL["http://epp.ist.utl.pt/"], None},
  ButtonNote->"http://epp.ist.utl.pt/"], "Section",
  FontSize->24,
  FontVariations->{"Underline"->True},
  FontColor->GrayLevel[0]]
}], "Text",
 CellChangeTimes->{{3.8226362283387003`*^9, 3.822636334723393*^9}, 
   3.822636391632341*^9, {3.8226372468331547`*^9, 3.822637246833611*^9}, {
   3.832321233277671*^9, 3.8323212337519627`*^9}, {3.832906767931561*^9, 
   3.832906784631399*^9}, {3.833039215806007*^9, 3.83303921638756*^9}, {
   3.833465334543377*^9, 3.833465371077303*^9}, {3.852220855259931*^9, 
   3.8522208579871063`*^9}, 3.852221706794441*^9},
 FontSize->14,ExpressionUUID->"5811daa7-a200-478a-ab40-602e7a80d388"],

Cell[TextData[{
 StyleBox["Figure 1", "Section",
  FontSize->24,
  FontWeight->"Bold",
  FontColor->GrayLevel[0]],
 StyleBox["\nProblem: what is the definition of T(\[Tau])? By inspection it\
\[CloseCurlyQuote]s possible to determine an approximate relation, though it \
does not seem to be explicit in the text.", "Section",
  FontSize->24,
  FontColor->GrayLevel[0]]
}], "Text",
 CellChangeTimes->{{3.8226362283387003`*^9, 3.822636334723393*^9}, {
  3.822636391632341*^9, 3.8226364148286*^9}, {3.822636632459257*^9, 
  3.82263666754714*^9}, {3.8226367225529222`*^9, 3.822636739164402*^9}, {
  3.822893500475507*^9, 3.822893523209238*^9}, {3.8323245369078817`*^9, 
  3.832324665848118*^9}, {3.83290680301472*^9, 3.832906868114419*^9}, {
  3.833039222269853*^9, 3.8330392572797956`*^9}, {3.833465392675682*^9, 
  3.833465398403303*^9}, {3.8522207715900583`*^9, 3.852220814025341*^9}},
 FontSize->14,ExpressionUUID->"b42d87dc-c063-4fc7-9791-3433843c7cd8"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Clear", "[", 
   RowBox[{
   "\[Chi]e", ",", "\[ScriptCapitalE]e", ",", "\[Gamma]e", ",", "W\[Gamma]", 
    ",", "pc", ",", "tc", ",", "\[Omega]0", ",", "E0", ",", 
    "\[ScriptCapitalE]c", ",", "me", ",", "c", ",", "e", ",", "\[Alpha]", ",",
     "\[HBar]", ",", "T", ",", "ES", ",", "\[Lambda]\[Mu]m", ",", "\[Tau]"}], 
   "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[Chi]e", "=", 
   RowBox[{"2", "\[Gamma]e", " ", 
    RowBox[{"E0", "/", "ES"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[Gamma]e", "=", 
   RowBox[{"\[ScriptCapitalE]e", "/", 
    RowBox[{"(", 
     RowBox[{"me", " ", 
      RowBox[{"c", "^", "2"}]}], ")"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"W\[Gamma]", "=", 
   RowBox[{
    RowBox[{"3", "^", 
     RowBox[{"(", 
      RowBox[{"2", "/", "3"}], ")"}]}], " ", "28", " ", 
    RowBox[{"Gamma", "[", 
     RowBox[{"2", "/", "3"}], "]"}], " ", "\[Alpha]", " ", 
    RowBox[{"me", "^", "2"}], " ", 
    RowBox[{"c", "^", "4"}], 
    RowBox[{
     RowBox[{"\[Chi]e", "^", 
      RowBox[{"(", 
       RowBox[{"2", "/", "3"}], ")"}]}], "  ", "/", 
     RowBox[{"(", 
      RowBox[{"54", " ", "\[HBar]", " ", "\[ScriptCapitalE]e"}], ")"}]}]}]}], 
  " ", ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"pc", " ", "=", " ", 
   RowBox[{"W\[Gamma]", " ", "tc"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"tc", "=", 
   RowBox[{"\[Tau]", "/", 
    RowBox[{"(", 
     RowBox[{"2", 
      RowBox[{"Sqrt", "[", 
       RowBox[{"2", 
        RowBox[{"Log", "[", "2", "]"}]}], "]"}]}], ")"}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[Omega]0", "=", 
   RowBox[{"2", "\[Pi]", " ", 
    RowBox[{"c", "/", 
     RowBox[{"(", 
      RowBox[{"\[Lambda]\[Mu]m", " ", 
       RowBox[{"10", "^", 
        RowBox[{"-", "6"}]}]}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"E0", "=", 
    RowBox[{"0.855", " ", "\[Lambda]\[Mu]m", "  ", 
     RowBox[{"Sqrt", "[", 
      RowBox[{"I0", " ", 
       RowBox[{"10", "^", 
        RowBox[{"-", "18"}]}]}], "]"}], " ", "me", " ", "\[Omega]0", " ", 
     RowBox[{"c", "/", "e"}]}]}], ";"}], "\[IndentingNewLine]", 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[ScriptCapitalE]c", "=", 
   RowBox[{
    RowBox[{
     RowBox[{"(", 
      RowBox[{"1", "-", 
       RowBox[{"16", "/", "63"}]}], ")"}], "^", "pc"}], "  ", 
    "\[ScriptCapitalE]e"}]}], " ", 
  RowBox[{"(*", 
   RowBox[{
    RowBox[{"Refine", "[", 
     RowBox[{
      RowBox[{"//", "Simplify"}], ",", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"c", ">", "0"}], ",", 
        RowBox[{"me", ">", "0"}], ",", 
        RowBox[{"E0", ">", "0"}], ",", 
        RowBox[{"ES", ">", "0"}], ",", 
        RowBox[{"\[HBar]", ">", "0"}], ",", 
        RowBox[{"\[ScriptCapitalE]e", ">", "0"}], ",", 
        RowBox[{"\[Tau]", ">", "0"}]}], "}"}]}], "]"}], "//", 
    "FullSimplify"}], "*)"}], "\[IndentingNewLine]", 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"me", "=", 
    RowBox[{"9.11", " ", 
     RowBox[{"10", "^", 
      RowBox[{"-", "31"}]}]}]}], ";"}], 
  RowBox[{"(*", 
   RowBox[{"[", "Kg", "]"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"c", "=", " ", "299792458"}], ";"}], " ", 
  RowBox[{"(*", 
   RowBox[{"[", 
    RowBox[{"m", "/", "s"}], "]"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"e", "=", 
    RowBox[{"1.602176634", " ", 
     RowBox[{"10", "^", 
      RowBox[{"-", "19"}]}]}]}], ";"}], " ", 
  RowBox[{"(*", 
   RowBox[{"[", "C", "]"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"\[Alpha]", "=", 
    RowBox[{"1", "/", "137"}]}], ";"}], " ", 
  RowBox[{"(*", 
   RowBox[{"[", "]"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"\[HBar]", "=", 
    RowBox[{"1.054571817", " ", 
     RowBox[{"10", "^", 
      RowBox[{"-", "34"}]}]}]}], ";"}], 
  RowBox[{"(*", 
   RowBox[{"[", 
    RowBox[{"J", " ", "s"}], "]"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"T", "=", 
   RowBox[{"0.67", 
    FractionBox[
     RowBox[{"\[Lambda]\[Mu]m", " ", 
      RowBox[{"10", "^", 
       RowBox[{"-", "6"}]}]}], "c"]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"ES", "=", 
    RowBox[{
     RowBox[{"me", "^", "2"}], " ", 
     RowBox[{
      RowBox[{"c", "^", "3"}], "/", 
      RowBox[{"(", 
       RowBox[{"e", " ", "\[HBar]"}], ")"}]}]}]}], ";"}], 
  RowBox[{"(*", 
   RowBox[{"[", 
    RowBox[{"V", "/", "m"}], "]"}], "*)"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{"LogLinearPlot", "[", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{
      RowBox[{"(", 
       SuperscriptBox[
        RowBox[{"(", 
         FractionBox["47", "63"], ")"}], 
        FractionBox[
         RowBox[{"0.030199136711634034`", " ", 
          SuperscriptBox["c", "4"], " ", 
          SuperscriptBox["me", "2"], " ", 
          SuperscriptBox[
           RowBox[{"(", 
            FractionBox[
             RowBox[{
              SqrtBox["I0"], " ", "\[ScriptCapitalE]e"}], 
             RowBox[{"e", " ", "ES"}]], ")"}], 
           RowBox[{"2", "/", "3"}]], " ", "\[Alpha]", " ", "\[Tau]"}], 
         RowBox[{"\[ScriptCapitalE]e", " ", "\[HBar]"}]]], ")"}], "//.", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"\[ScriptCapitalE]e", "->", 
         RowBox[{"100", " ", 
          RowBox[{"10", "^", "9"}], " ", "e"}]}], ",", 
        RowBox[{"\[Tau]", "->", "T"}], ",", 
        RowBox[{"\[Lambda]\[Mu]m", "->", "0.25"}]}], "}"}]}], ",", 
     RowBox[{
      RowBox[{"(", 
       SuperscriptBox[
        RowBox[{"(", 
         FractionBox["47", "63"], ")"}], 
        FractionBox[
         RowBox[{"0.030199136711634034`", " ", 
          SuperscriptBox["c", "4"], " ", 
          SuperscriptBox["me", "2"], " ", 
          SuperscriptBox[
           RowBox[{"(", 
            FractionBox[
             RowBox[{
              SqrtBox["I0"], " ", "\[ScriptCapitalE]e"}], 
             RowBox[{"e", " ", "ES"}]], ")"}], 
           RowBox[{"2", "/", "3"}]], " ", "\[Alpha]", " ", "\[Tau]"}], 
         RowBox[{"\[ScriptCapitalE]e", " ", "\[HBar]"}]]], ")"}], "//.", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"\[ScriptCapitalE]e", "->", 
         RowBox[{"100", " ", 
          RowBox[{"10", "^", "9"}], " ", "e"}]}], ",", 
        RowBox[{"\[Tau]", "->", "T"}], ",", 
        RowBox[{"\[Lambda]\[Mu]m", "->", "0.5"}]}], "}"}]}], ",", 
     RowBox[{
      RowBox[{"(", 
       SuperscriptBox[
        RowBox[{"(", 
         FractionBox["47", "63"], ")"}], 
        FractionBox[
         RowBox[{"0.030199136711634034`", " ", 
          SuperscriptBox["c", "4"], " ", 
          SuperscriptBox["me", "2"], " ", 
          SuperscriptBox[
           RowBox[{"(", 
            FractionBox[
             RowBox[{
              SqrtBox["I0"], " ", "\[ScriptCapitalE]e"}], 
             RowBox[{"e", " ", "ES"}]], ")"}], 
           RowBox[{"2", "/", "3"}]], " ", "\[Alpha]", " ", "\[Tau]"}], 
         RowBox[{"\[ScriptCapitalE]e", " ", "\[HBar]"}]]], ")"}], "//.", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"\[ScriptCapitalE]e", "->", 
         RowBox[{"100", " ", 
          RowBox[{"10", "^", "9"}], " ", "e"}]}], ",", 
        RowBox[{"\[Tau]", "->", "T"}], ",", 
        RowBox[{"\[Lambda]\[Mu]m", "->", "1"}]}], "}"}]}], ",", 
     RowBox[{
      RowBox[{"(", 
       SuperscriptBox[
        RowBox[{"(", 
         FractionBox["47", "63"], ")"}], 
        FractionBox[
         RowBox[{"0.030199136711634034`", " ", 
          SuperscriptBox["c", "4"], " ", 
          SuperscriptBox["me", "2"], " ", 
          SuperscriptBox[
           RowBox[{"(", 
            FractionBox[
             RowBox[{
              SqrtBox["I0"], " ", "\[ScriptCapitalE]e"}], 
             RowBox[{"e", " ", "ES"}]], ")"}], 
           RowBox[{"2", "/", "3"}]], " ", "\[Alpha]", " ", "\[Tau]"}], 
         RowBox[{"\[ScriptCapitalE]e", " ", "\[HBar]"}]]], ")"}], "//.", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"\[ScriptCapitalE]e", "->", 
         RowBox[{"50", " ", 
          RowBox[{"10", "^", "9"}], " ", "e"}]}], ",", 
        RowBox[{"\[Tau]", "->", "T"}], ",", 
        RowBox[{"\[Lambda]\[Mu]m", "->", "1"}]}], "}"}]}], ",", 
     RowBox[{
      RowBox[{"(", 
       SuperscriptBox[
        RowBox[{"(", 
         FractionBox["47", "63"], ")"}], 
        FractionBox[
         RowBox[{"0.030199136711634034`", " ", 
          SuperscriptBox["c", "4"], " ", 
          SuperscriptBox["me", "2"], " ", 
          SuperscriptBox[
           RowBox[{"(", 
            FractionBox[
             RowBox[{
              SqrtBox["I0"], " ", "\[ScriptCapitalE]e"}], 
             RowBox[{"e", " ", "ES"}]], ")"}], 
           RowBox[{"2", "/", "3"}]], " ", "\[Alpha]", " ", "\[Tau]"}], 
         RowBox[{"\[ScriptCapitalE]e", " ", "\[HBar]"}]]], ")"}], "//.", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"\[ScriptCapitalE]e", "->", 
         RowBox[{"30", " ", 
          RowBox[{"10", "^", "9"}], " ", "e"}]}], ",", 
        RowBox[{"\[Tau]", "->", "T"}], ",", 
        RowBox[{"\[Lambda]\[Mu]m", "->", "1"}]}], "}"}]}], ",", 
     RowBox[{
      RowBox[{"(", 
       SuperscriptBox[
        RowBox[{"(", 
         FractionBox["47", "63"], ")"}], 
        FractionBox[
         RowBox[{"0.030199136711634034`", " ", 
          SuperscriptBox["c", "4"], " ", 
          SuperscriptBox["me", "2"], " ", 
          SuperscriptBox[
           RowBox[{"(", 
            FractionBox[
             RowBox[{
              SqrtBox["I0"], " ", "\[ScriptCapitalE]e"}], 
             RowBox[{"e", " ", "ES"}]], ")"}], 
           RowBox[{"2", "/", "3"}]], " ", "\[Alpha]", " ", "\[Tau]"}], 
         RowBox[{"\[ScriptCapitalE]e", " ", "\[HBar]"}]]], ")"}], "//.", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"\[ScriptCapitalE]e", "->", 
         RowBox[{"100", " ", 
          RowBox[{"10", "^", "9"}], " ", "e"}]}], ",", 
        RowBox[{"\[Tau]", "->", 
         RowBox[{"2", "T"}]}], ",", 
        RowBox[{"\[Lambda]\[Mu]m", "->", "1"}]}], "}"}]}], ",", 
     RowBox[{
      RowBox[{"(", 
       SuperscriptBox[
        RowBox[{"(", 
         FractionBox["47", "63"], ")"}], 
        FractionBox[
         RowBox[{"0.030199136711634034`", " ", 
          SuperscriptBox["c", "4"], " ", 
          SuperscriptBox["me", "2"], " ", 
          SuperscriptBox[
           RowBox[{"(", 
            FractionBox[
             RowBox[{
              SqrtBox["I0"], " ", "\[ScriptCapitalE]e"}], 
             RowBox[{"e", " ", "ES"}]], ")"}], 
           RowBox[{"2", "/", "3"}]], " ", "\[Alpha]", " ", "\[Tau]"}], 
         RowBox[{"\[ScriptCapitalE]e", " ", "\[HBar]"}]]], ")"}], "//.", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"\[ScriptCapitalE]e", "->", 
         RowBox[{"50", " ", 
          RowBox[{"10", "^", "9"}], " ", "e"}]}], ",", 
        RowBox[{"\[Tau]", "->", 
         RowBox[{"2", "T"}]}], ",", 
        RowBox[{"\[Lambda]\[Mu]m", "->", "1"}]}], "}"}]}], ",", 
     RowBox[{
      RowBox[{"(", 
       SuperscriptBox[
        RowBox[{"(", 
         FractionBox["47", "63"], ")"}], 
        FractionBox[
         RowBox[{"0.030199136711634034`", " ", 
          SuperscriptBox["c", "4"], " ", 
          SuperscriptBox["me", "2"], " ", 
          SuperscriptBox[
           RowBox[{"(", 
            FractionBox[
             RowBox[{
              SqrtBox["I0"], " ", "\[ScriptCapitalE]e"}], 
             RowBox[{"e", " ", "ES"}]], ")"}], 
           RowBox[{"2", "/", "3"}]], " ", "\[Alpha]", " ", "\[Tau]"}], 
         RowBox[{"\[ScriptCapitalE]e", " ", "\[HBar]"}]]], ")"}], "//.", 
      RowBox[{"{", 
       RowBox[{
        RowBox[{"\[ScriptCapitalE]e", "->", 
         RowBox[{"30", " ", 
          RowBox[{"10", "^", "9"}], " ", "e"}]}], ",", 
        RowBox[{"\[Tau]", "->", 
         RowBox[{"2", "T"}]}], ",", 
        RowBox[{"\[Lambda]\[Mu]m", "->", "1"}]}], "}"}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"I0", ",", 
     RowBox[{"10", "^", "23"}], ",", 
     RowBox[{"10", "^", "25"}]}], "}"}], ",", 
   RowBox[{"PlotRange", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{
        RowBox[{"10", "^", "23"}], ",", 
        RowBox[{"10", "^", "25"}]}], "}"}], ",", 
      RowBox[{"{", 
       RowBox[{"0", ",", "1"}], "}"}]}], "}"}]}], ",", 
   RowBox[{"Frame", "\[Rule]", "True"}], ",", 
   RowBox[{"GridLines", "\[Rule]", "Automatic"}], ",", 
   RowBox[{"ImageSize", "\[Rule]", "400"}], ",", 
   RowBox[{"FrameLabel", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
     "\"\<\!\(\*SubscriptBox[\(I\), \(0\)]\)[W/\!\(\*SuperscriptBox[\(cm\), \
\(2\)]\)]\>\"", ",", 
      "\"\<\!\(\*SubsuperscriptBox[\(\[ScriptCapitalE]\), \(c\), \
\(e\)]\)/\!\(\*SubscriptBox[\(\[ScriptCapitalE]\), \(c\)]\)\>\""}], "}"}]}], 
   ",", 
   RowBox[{"PlotStyle", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"Directive", "[", 
       RowBox[{"Black", ",", "Dashed"}], "]"}], ",", 
      RowBox[{"Directive", "[", 
       RowBox[{"Black", ",", "DotDashed"}], "]"}], ",", 
      RowBox[{"Directive", "[", "Black", "]"}], ",", 
      RowBox[{"Directive", "[", 
       RowBox[{"Darker", "[", "Blue", "]"}], "]"}], ",", 
      RowBox[{"Directive", "[", 
       RowBox[{"Lighter", "[", "Blue", "]"}], "]"}], ",", " ", 
      RowBox[{"Directive", "[", 
       RowBox[{"Darker", "[", "Green", "]"}], "]"}], ",", 
      RowBox[{"Directive", "[", 
       RowBox[{"Darker", "[", "Yellow", "]"}], "]"}], ",", 
      RowBox[{"Directive", "[", "Yellow", "]"}]}], "}"}]}]}], "]"}]}], "Input",\

 CellChangeTimes->{{3.852201445048253*^9, 3.85220160364121*^9}, {
   3.852201639233583*^9, 3.852201733145811*^9}, {3.852201916762659*^9, 
   3.852201966434247*^9}, {3.852202007358787*^9, 3.85220211749953*^9}, {
   3.852219071077714*^9, 3.85221928634422*^9}, {3.852219320577791*^9, 
   3.8522193752394667`*^9}, {3.8522194106553497`*^9, 3.852219796484385*^9}, {
   3.852219834180423*^9, 3.8522198379613543`*^9}, {3.852219873338623*^9, 
   3.852220058704288*^9}, 3.8522201108013897`*^9, {3.852220231659902*^9, 
   3.85222031342881*^9}, {3.852220602018907*^9, 3.852220719173004*^9}, {
   3.852221521889414*^9, 3.852221525262611*^9}, {3.8606503405392733`*^9, 
   3.8606503701676483`*^9}, {3.860650411447089*^9, 3.860650608133498*^9}},
 CellLabel->"In[1]:=",ExpressionUUID->"ea4d5d8c-6a7f-4e75-8b06-1a39586fce4c"],

Cell[BoxData[
 RowBox[{
  SuperscriptBox[
   RowBox[{"(", 
    FractionBox["47", "63"], ")"}], 
   FractionBox[
    RowBox[{"0.030199136711634034`", " ", 
     SuperscriptBox["c", "4"], " ", 
     SuperscriptBox["me", "2"], " ", 
     SuperscriptBox[
      RowBox[{"(", 
       FractionBox[
        RowBox[{
         SqrtBox["I0"], " ", "\[ScriptCapitalE]e"}], 
        RowBox[{"e", " ", "ES"}]], ")"}], 
      RowBox[{"2", "/", "3"}]], " ", "\[Alpha]", " ", "\[Tau]"}], 
    RowBox[{"\[ScriptCapitalE]e", " ", "\[HBar]"}]]], " ", 
  "\[ScriptCapitalE]e"}]], "Output",
 CellChangeTimes->{{3.852202081681612*^9, 3.8522021183132*^9}, {
   3.852219112547639*^9, 3.852219117050993*^9}, {3.852219151272949*^9, 
   3.852219153689378*^9}, 3.852219183784604*^9, {3.852219255202034*^9, 
   3.8522192867049637`*^9}, 3.852219336380186*^9, 3.852219375670068*^9, {
   3.852219421277276*^9, 3.852219464462943*^9}, {3.852219540453817*^9, 
   3.852219589527915*^9}, 3.852219650224058*^9, 3.8522196916367702`*^9, {
   3.852219728372415*^9, 3.852219796807857*^9}, 3.852219838314179*^9, 
   3.852219877945146*^9, {3.852219997173564*^9, 3.852220059165745*^9}, 
   3.852220111171113*^9, {3.852220232073709*^9, 3.852220235321628*^9}, {
   3.852220265936089*^9, 3.85222031384394*^9}, {3.852220667565275*^9, 
   3.852220719515216*^9}, 3.852221525745352*^9, 3.86065019782732*^9, 
   3.860650342938959*^9, {3.860650457695031*^9, 3.860650608399665*^9}, 
   3.860661803963689*^9},
 CellLabel->"Out[9]=",ExpressionUUID->"20ff20a4-af8b-4b39-8fd9-c1fa188d18f6"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {GrayLevel[0], AbsoluteThickness[1.6], Opacity[1.], 
      Dashing[{Small, Small}], LineBox[CompressedData["
1:eJwVzXs01AkUB3CVar2VR7bHmlRSS48xUWm7t6L0+/0svVRIcrLWKySMBplE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       "]]},
     Annotation[#, "Charting`Private`Tag$7366#1"]& ], 
    TagBox[
     {GrayLevel[0], AbsoluteThickness[1.6], Opacity[1.], 
      Dashing[{0, Small, Small, Small}], LineBox[CompressedData["
1:eJwVz3s01AkUB/BJbTIblSKlKLWMWIVprMe6Vyn1+/1araQtmtRhbShrWyk0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       "]]},
     Annotation[#, "Charting`Private`Tag$7366#2"]& ], 
    TagBox[
     {GrayLevel[0], AbsoluteThickness[1.6], Opacity[1.], 
      LineBox[CompressedData["
1:eJwVz3s0VAkcB/BJbTJqNo/a2E0RnVFWpyiU9fsppHuvVLbdRjXpYW2D9KKp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       "]]},
     Annotation[#, "Charting`Private`Tag$7366#3"]& ], 
    TagBox[
     {RGBColor[0, 0, 
       NCache[
        Rational[2, 3], 0.6666666666666666]], AbsoluteThickness[1.6], Opacity[
      1.], LineBox[CompressedData["
1:eJwVy3s0lAkcxvGpdivXJJW1FbXVDtm2QWmN/H65FO/7llah0XEtp40ssoN2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       "]]},
     Annotation[#, "Charting`Private`Tag$7366#4"]& ], 
    TagBox[
     {RGBColor[
       NCache[
        Rational[1, 3], 0.3333333333333333], 
       NCache[
        Rational[1, 3], 0.3333333333333333], 1], AbsoluteThickness[1.6], 
      Opacity[1.], LineBox[CompressedData["
1:eJwVz3s0lAkcxvGptcllNRKn66xbhZTcmkL9fhWl930zlW3dNlFsG1FyiYZB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       "]]},
     Annotation[#, "Charting`Private`Tag$7366#5"]& ], 
    TagBox[
     {RGBColor[0, 
       NCache[
        Rational[2, 3], 0.6666666666666666], 0], AbsoluteThickness[1.6], 
      Opacity[1.], LineBox[CompressedData["
1:eJwVx3081AccwPHj1dJdqCQrofLQKCUPnRbz/dbk4ff7YYVW6aXoQXqSJJrH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       "]]},
     Annotation[#, "Charting`Private`Tag$7366#6"]& ], 
    TagBox[
     {RGBColor[
       NCache[
        Rational[2, 3], 0.6666666666666666], 
       NCache[
        Rational[2, 3], 0.6666666666666666], 0], AbsoluteThickness[1.6], 
      Opacity[1.], LineBox[CompressedData["
1:eJwVzXk8lAkcx3FkXZVVojtHxTiqdRQl8/vRSJ7n0WzYyhFpa7vNDJFMSGXK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       "]]},
     Annotation[#, "Charting`Private`Tag$7366#7"]& ], 
    TagBox[
     {RGBColor[1, 1, 0], AbsoluteThickness[1.6], Opacity[1.], 
      LineBox[CompressedData["
1:eJwVz3s0lAkYBvBJLaGsLnQXswklxZC21PtqKb7vs6J2xjSFOpySteoUYVyz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       "]]},
     Annotation[#, "Charting`Private`Tag$7366#8"]& ]}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{52.95945713886305, 0},
  CoordinatesToolOptions:>{"DisplayFunction" -> ({
      Exp[
       Part[#, 1]], 
      Part[#, 2]}& ), "CopiedValueFunction" -> ({
      Exp[
       Part[#, 1]], 
      Part[#, 2]}& )},
  DisplayFunction->Identity,
  Frame->{{True, True}, {True, True}},
  FrameLabel->{{
     FormBox[
     "\"\\!\\(\\*SubsuperscriptBox[\\(\[ScriptCapitalE]\\), \\(c\\), \\(e\\)]\
\\)/\\!\\(\\*SubscriptBox[\\(\[ScriptCapitalE]\\), \\(c\\)]\\)\"", 
      TraditionalForm], None}, {
     FormBox[
     "\"\\!\\(\\*SubscriptBox[\\(I\\), \\(0\\)]\\)[W/\\!\\(\\*SuperscriptBox[\
\\(cm\\), \\(2\\)]\\)]\"", TraditionalForm], None}},
  FrameTicks->FrontEndValueCache[{{Automatic, Automatic}, {Quiet[
       Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& , 
      Charting`ScaledFrameTicks[{Log, Exp}]}}, {{
     Automatic, Automatic}, {{{52.95945713886305, 
        FormBox[
         TemplateBox[{"\[Times]", "\"\[Times]\"", "1", 
           
           TemplateBox[{"10", "23"}, "Superscript", SyntaxForm -> 
            SuperscriptBox]}, "RowWithSeparators"], TraditionalForm], {0.01, 
        0.}}, {54.568895051297154`, 
        FormBox[
         TemplateBox[{"\[Times]", "\"\[Times]\"", "5", 
           
           TemplateBox[{"10", "23"}, "Superscript", SyntaxForm -> 
            SuperscriptBox]}, "RowWithSeparators"], TraditionalForm], {0.01, 
        0.}}, {55.262042231857095`, 
        FormBox[
         TemplateBox[{"\[Times]", "\"\[Times]\"", "1", 
           
           TemplateBox[{"10", "24"}, "Superscript", SyntaxForm -> 
            SuperscriptBox]}, "RowWithSeparators"], TraditionalForm], {0.01, 
        0.}}, {56.8714801442912, 
        FormBox[
         TemplateBox[{"\[Times]", "\"\[Times]\"", "5", 
           
           TemplateBox[{"10", "24"}, "Superscript", SyntaxForm -> 
            SuperscriptBox]}, "RowWithSeparators"], TraditionalForm], {0.01, 
        0.}}, {57.564627324851145`, 
        FormBox[
         TemplateBox[{"\[Times]", "\"\[Times]\"", "1", 
           
           TemplateBox[{"10", "25"}, "Superscript", SyntaxForm -> 
            SuperscriptBox]}, "RowWithSeparators"], TraditionalForm], {0.01, 
        0.}}, {52.266309958303104`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       52.44863151509706, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       52.602782194924316`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       52.73631358754884, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       52.85409662320522, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       53.652604319423, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       54.05806942753116, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       54.34575149998294, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       54.751216608091106`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       54.90536728791837, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       55.038898680542886`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       55.15668171619927, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       55.95518941241704, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       56.36065452052521, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       56.64833659297699, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       57.05380170108515, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       57.20795238091241, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       57.34148377353693, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       57.459266809193316`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       58.257774505411085`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       58.66323961351925, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       58.95092168597103, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       59.17406523728524, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       59.3563867940792, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       59.51053747390645, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       59.64406886653098, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       59.76185190218736, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       59.86721241784519, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}}, {{
       52.95945713886305, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.01, 0.}}, {
       54.568895051297154`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.01, 0.}}, {
       55.262042231857095`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.01, 0.}}, {
       56.8714801442912, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.01, 0.}}, {
       57.564627324851145`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.01, 0.}}, {
       52.266309958303104`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       52.44863151509706, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       52.602782194924316`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       52.73631358754884, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       52.85409662320522, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       53.652604319423, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       54.05806942753116, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       54.34575149998294, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       54.751216608091106`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       54.90536728791837, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       55.038898680542886`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       55.15668171619927, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       55.95518941241704, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       56.36065452052521, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       56.64833659297699, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       57.05380170108515, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       57.20795238091241, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       57.34148377353693, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       57.459266809193316`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       58.257774505411085`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       58.66323961351925, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       58.95092168597103, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       59.17406523728524, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       59.3563867940792, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       59.51053747390645, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       59.64406886653098, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       59.76185190218736, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       59.86721241784519, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}}}}],
  
  GridLines->{{52.95945713886305, 54.568895051297154`, 55.262042231857095`, 
    56.8714801442912, 57.564627324851145`}, Automatic},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  ImageSize->400,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, 
    "DefaultGraphicsInteraction" -> {
     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
      "Effects" -> {
       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
        "Droplines" -> {
         "freeformCursorMode" -> True, 
          "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None},
  PlotRange->NCache[{{
      Log[100000000000000000000000], 
      Log[10000000000000000000000000]}, {0, 1}}, {{52.95945713886305, 
     57.564627324851145`}, {0, 1}}],
  PlotRangeClipping->True,
  PlotRangePadding->{{0, 0}, {0, 0}},
  Ticks->{Quiet[
     Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& , 
    Automatic}]], "Output",
 CellChangeTimes->{{3.852202081681612*^9, 3.8522021183132*^9}, {
   3.852219112547639*^9, 3.852219117050993*^9}, {3.852219151272949*^9, 
   3.852219153689378*^9}, 3.852219183784604*^9, {3.852219255202034*^9, 
   3.8522192867049637`*^9}, 3.852219336380186*^9, 3.852219375670068*^9, {
   3.852219421277276*^9, 3.852219464462943*^9}, {3.852219540453817*^9, 
   3.852219589527915*^9}, 3.852219650224058*^9, 3.8522196916367702`*^9, {
   3.852219728372415*^9, 3.852219796807857*^9}, 3.852219838314179*^9, 
   3.852219877945146*^9, {3.852219997173564*^9, 3.852220059165745*^9}, 
   3.852220111171113*^9, {3.852220232073709*^9, 3.852220235321628*^9}, {
   3.852220265936089*^9, 3.85222031384394*^9}, {3.852220667565275*^9, 
   3.852220719515216*^9}, 3.852221525745352*^9, 3.86065019782732*^9, 
   3.860650342938959*^9, {3.860650457695031*^9, 3.860650608399665*^9}, 
   3.860661804480062*^9},
 CellLabel->"Out[17]=",ExpressionUUID->"c139e6f2-848c-4247-9352-7cedd5b0bf8e"]
}, Open  ]],

Cell[TextData[{
 StyleBox["Figure 2", "Section",
  FontSize->24,
  FontWeight->"Bold",
  FontColor->GrayLevel[0]],
 StyleBox["\nConfirm with figure", "Section",
  FontSize->24,
  FontColor->GrayLevel[0]]
}], "Text",
 CellChangeTimes->{{3.8226362283387003`*^9, 3.822636334723393*^9}, {
  3.822636391632341*^9, 3.8226364148286*^9}, {3.822636632459257*^9, 
  3.82263666754714*^9}, {3.8226367225529222`*^9, 3.822636739164402*^9}, {
  3.822893500475507*^9, 3.822893523209238*^9}, {3.8323245369078817`*^9, 
  3.832324665848118*^9}, {3.83290680301472*^9, 3.832906868114419*^9}, {
  3.833039222269853*^9, 3.8330392572797956`*^9}, {3.833465392675682*^9, 
  3.833465398403303*^9}, {3.8522207715900583`*^9, 3.852220814025341*^9}, {
  3.852220900774466*^9, 3.852220910798373*^9}, {3.852221204774682*^9, 
  3.852221216475109*^9}},
 FontSize->14,ExpressionUUID->"36734f63-26d2-4abf-a77e-4a5741f54431"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Clear", "[", 
   RowBox[{
   "\[Chi]e", ",", "\[ScriptCapitalE]e", ",", "\[Gamma]e", ",", "W\[Gamma]", 
    ",", "pc", ",", "tc", ",", "tf", ",", "\[Omega]0", ",", "E0", ",", 
    "\[ScriptCapitalE]c", ",", "me", ",", "c", ",", "e", ",", "\[Alpha]", ",",
     "\[HBar]", ",", "T", ",", "ES", ",", "\[Lambda]\[Mu]m", ",", "\[Tau]"}], 
   "]"}], "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[Chi]e", "=", 
   RowBox[{"2", "\[Gamma]e", " ", 
    RowBox[{"E0", "/", "ES"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[Gamma]e", "=", 
   RowBox[{"\[ScriptCapitalE]e", "/", 
    RowBox[{"(", 
     RowBox[{"me", " ", 
      RowBox[{"c", "^", "2"}]}], ")"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"W\[Gamma]", "=", 
   RowBox[{
    RowBox[{"3", "^", 
     RowBox[{"(", 
      RowBox[{"2", "/", "3"}], ")"}]}], " ", "28", " ", 
    RowBox[{"Gamma", "[", 
     RowBox[{"2", "/", "3"}], "]"}], " ", "\[Alpha]", " ", 
    RowBox[{"me", "^", "2"}], " ", 
    RowBox[{"c", "^", "4"}], 
    RowBox[{
     RowBox[{"\[Chi]e", "^", 
      RowBox[{"(", 
       RowBox[{"2", "/", "3"}], ")"}]}], "  ", "/", 
     RowBox[{"(", 
      RowBox[{"54", " ", "\[HBar]", " ", "\[ScriptCapitalE]e"}], ")"}]}]}]}], 
  " ", ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"tc", "=", 
   RowBox[{"\[Tau]", "/", 
    RowBox[{"(", 
     RowBox[{"2", 
      RowBox[{"Sqrt", "[", 
       RowBox[{"2", 
        RowBox[{"Log", "[", "2", "]"}]}], "]"}]}], ")"}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"tf", "=", 
   RowBox[{"\[Tau]", "/", 
    RowBox[{"(", 
     RowBox[{"Sqrt", "[", 
      RowBox[{"2", 
       RowBox[{"Log", "[", "2", "]"}]}], "]"}], ")"}]}]}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"pc", " ", "=", " ", 
   RowBox[{"W\[Gamma]", " ", "tc"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"pf", " ", "=", " ", 
   RowBox[{"W\[Gamma]", " ", "tf"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[Omega]0", "=", 
   RowBox[{"2", "\[Pi]", " ", 
    RowBox[{"c", "/", 
     RowBox[{"(", 
      RowBox[{"\[Lambda]\[Mu]m", " ", 
       RowBox[{"10", "^", 
        RowBox[{"-", "6"}]}]}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"E0", "=", 
    RowBox[{"0.855", " ", "\[Lambda]\[Mu]m", "  ", 
     RowBox[{"Sqrt", "[", 
      RowBox[{"I0", " ", 
       RowBox[{"10", "^", 
        RowBox[{"-", "18"}]}]}], "]"}], " ", "me", " ", "\[Omega]0", " ", 
     RowBox[{"c", "/", "e"}]}]}], ";"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"me", "=", 
    RowBox[{"9.11", " ", 
     RowBox[{"10", "^", 
      RowBox[{"-", "31"}]}]}]}], ";"}], 
  RowBox[{"(*", 
   RowBox[{"[", "Kg", "]"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"c", "=", " ", "299792458"}], ";"}], " ", 
  RowBox[{"(*", 
   RowBox[{"[", 
    RowBox[{"m", "/", "s"}], "]"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"e", "=", 
    RowBox[{"1.602176634", " ", 
     RowBox[{"10", "^", 
      RowBox[{"-", "19"}]}]}]}], ";"}], " ", 
  RowBox[{"(*", 
   RowBox[{"[", "C", "]"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"\[Alpha]", "=", 
    RowBox[{"1", "/", "137"}]}], ";"}], " ", 
  RowBox[{"(*", 
   RowBox[{"[", "]"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"\[HBar]", "=", 
    RowBox[{"1.054571817", " ", 
     RowBox[{"10", "^", 
      RowBox[{"-", "34"}]}]}]}], ";"}], 
  RowBox[{"(*", 
   RowBox[{"[", 
    RowBox[{"J", " ", "s"}], "]"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"T", "=", 
   RowBox[{"0.67", 
    FractionBox[
     RowBox[{"\[Lambda]\[Mu]m", " ", 
      RowBox[{"10", "^", 
       RowBox[{"-", "6"}]}]}], "c"]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"ES", "=", 
    RowBox[{
     RowBox[{"me", "^", "2"}], " ", 
     RowBox[{
      RowBox[{"c", "^", "3"}], "/", 
      RowBox[{"(", 
       RowBox[{"e", " ", "\[HBar]"}], ")"}]}]}]}], ";"}], 
  RowBox[{"(*", 
   RowBox[{"[", 
    RowBox[{"V", "/", "m"}], "]"}], "*)"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"I0", "=", 
   RowBox[{"10", "^", "24"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[ScriptCapitalE]e", "=", 
   RowBox[{"50", " ", 
    RowBox[{"10", "^", "9"}], " ", "e"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[Tau]", "=", "T"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"\[Lambda]\[Mu]m", "=", "1"}], ";"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[ScriptCapitalE]c", "=", 
   RowBox[{
    RowBox[{
     RowBox[{"(", 
      RowBox[{"1", "-", 
       RowBox[{"16", "/", "63"}]}], ")"}], "^", "pc"}], "  ", 
    "\[ScriptCapitalE]e"}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[Gamma]ec", "=", 
   RowBox[{"\[ScriptCapitalE]c", "/", 
    RowBox[{"(", 
     RowBox[{"me", "  ", 
      RowBox[{"c", "^", "2"}]}], ")"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"\[ScriptCapitalE]f", "=", 
    RowBox[{
     RowBox[{
      RowBox[{"(", 
       RowBox[{"1", "-", 
        RowBox[{"16", "/", "63"}]}], ")"}], "^", "pf"}], "  ", 
     "\[ScriptCapitalE]e"}]}], ";"}], "\[IndentingNewLine]", 
  "\[IndentingNewLine]", 
  RowBox[{"(*", 
   RowBox[{
    RowBox[{" ", 
     RowBox[{"Figure", " ", "2", " ", "a"}], ")"}], " ", "blue", " ", "dot", 
    " ", 
    RowBox[{"\[ScriptCapitalE]_e", "^", "c"}]}], " ", 
   "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[ScriptCapitalE]c", "/", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{"10", "^", "9"}], " ", "e"}], ")"}]}], "\[IndentingNewLine]", 
  RowBox[{"(*", 
   RowBox[{
    RowBox[{" ", 
     RowBox[{"Figure", " ", "2", " ", "a"}], ")"}], " ", "purple", " ", "dot",
     " ", 
    RowBox[{"\[ScriptCapitalE]_e", "^", "f"}]}], " ", 
   "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[ScriptCapitalE]f", "/", 
   RowBox[{"(", 
    RowBox[{
     RowBox[{"10", "^", "9"}], " ", "e"}], ")"}]}], "\[IndentingNewLine]", 
  RowBox[{"(*", 
   RowBox[{
    RowBox[{" ", 
     RowBox[{"Figure", " ", "2", " ", "b"}], ")"}], " ", "blue", " ", "dot", 
    " ", 
    RowBox[{"\[Chi]_e", "^", "c"}], " ", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"\[Chi]_e", "^", "f"}], "=", 
      RowBox[{"0", " ", "always"}]}], ")"}]}], " ", 
   "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{"\[Chi]ec", "=", 
  RowBox[{"2", "\[Gamma]ec", " ", 
   RowBox[{"E0", "/", "ES"}]}]}]}], "Input",
 CellChangeTimes->{{3.852201445048253*^9, 3.85220160364121*^9}, {
   3.852201639233583*^9, 3.852201733145811*^9}, {3.852201916762659*^9, 
   3.852201966434247*^9}, {3.852202007358787*^9, 3.85220211749953*^9}, {
   3.852219071077714*^9, 3.85221928634422*^9}, {3.852219320577791*^9, 
   3.8522193752394667`*^9}, {3.8522194106553497`*^9, 3.852219796484385*^9}, {
   3.852219834180423*^9, 3.8522198379613543`*^9}, {3.852219873338623*^9, 
   3.852220058704288*^9}, 3.8522201108013897`*^9, {3.852220231659902*^9, 
   3.85222031342881*^9}, {3.852220602018907*^9, 3.852220719173004*^9}, {
   3.8522210378902483`*^9, 3.852221193296123*^9}, {3.852221266384322*^9, 
   3.8522213541334457`*^9}, 3.852221400833387*^9, {3.85222150782233*^9, 
   3.852221516840762*^9}, {3.860650231124693*^9, 3.860650295675606*^9}},
 CellLabel->"In[18]:=",ExpressionUUID->"88ef0115-a65a-4b74-82fd-6cfab32520af"],

Cell[BoxData["13.769466407343563`"], "Output",
 CellChangeTimes->{{3.852202081681612*^9, 3.8522021183132*^9}, {
   3.852219112547639*^9, 3.852219117050993*^9}, {3.852219151272949*^9, 
   3.852219153689378*^9}, 3.852219183784604*^9, {3.852219255202034*^9, 
   3.8522192867049637`*^9}, 3.852219336380186*^9, 3.852219375670068*^9, {
   3.852219421277276*^9, 3.852219464462943*^9}, {3.852219540453817*^9, 
   3.852219589527915*^9}, 3.852219650224058*^9, 3.8522196916367702`*^9, {
   3.852219728372415*^9, 3.852219796807857*^9}, 3.852219838314179*^9, 
   3.852219877945146*^9, {3.852219997173564*^9, 3.852220059165745*^9}, 
   3.852220111171113*^9, {3.852220232073709*^9, 3.852220235321628*^9}, {
   3.852220265936089*^9, 3.85222031384394*^9}, {3.852220667565275*^9, 
   3.852220719515216*^9}, 3.8522210592432756`*^9, {3.852221151911479*^9, 
   3.85222119365793*^9}, {3.85222131667103*^9, 3.852221354468031*^9}, 
   3.852221402164267*^9, 3.852221508422687*^9, 3.852221581571259*^9, 
   3.860650200584558*^9, 3.86066180505551*^9},
 CellLabel->"Out[42]=",ExpressionUUID->"6507a091-7ce1-4fc0-80ce-f872653044da"],

Cell[BoxData["3.7919641028592554`"], "Output",
 CellChangeTimes->{{3.852202081681612*^9, 3.8522021183132*^9}, {
   3.852219112547639*^9, 3.852219117050993*^9}, {3.852219151272949*^9, 
   3.852219153689378*^9}, 3.852219183784604*^9, {3.852219255202034*^9, 
   3.8522192867049637`*^9}, 3.852219336380186*^9, 3.852219375670068*^9, {
   3.852219421277276*^9, 3.852219464462943*^9}, {3.852219540453817*^9, 
   3.852219589527915*^9}, 3.852219650224058*^9, 3.8522196916367702`*^9, {
   3.852219728372415*^9, 3.852219796807857*^9}, 3.852219838314179*^9, 
   3.852219877945146*^9, {3.852219997173564*^9, 3.852220059165745*^9}, 
   3.852220111171113*^9, {3.852220232073709*^9, 3.852220235321628*^9}, {
   3.852220265936089*^9, 3.85222031384394*^9}, {3.852220667565275*^9, 
   3.852220719515216*^9}, 3.8522210592432756`*^9, {3.852221151911479*^9, 
   3.85222119365793*^9}, {3.85222131667103*^9, 3.852221354468031*^9}, 
   3.852221402164267*^9, 3.852221508422687*^9, 3.852221581571259*^9, 
   3.860650200584558*^9, 3.860661805057803*^9},
 CellLabel->"Out[43]=",ExpressionUUID->"a455a321-c6ce-4ac3-ac8b-6f687142595d"],

Cell[BoxData["111.78429223695751`"], "Output",
 CellChangeTimes->{{3.852202081681612*^9, 3.8522021183132*^9}, {
   3.852219112547639*^9, 3.852219117050993*^9}, {3.852219151272949*^9, 
   3.852219153689378*^9}, 3.852219183784604*^9, {3.852219255202034*^9, 
   3.8522192867049637`*^9}, 3.852219336380186*^9, 3.852219375670068*^9, {
   3.852219421277276*^9, 3.852219464462943*^9}, {3.852219540453817*^9, 
   3.852219589527915*^9}, 3.852219650224058*^9, 3.8522196916367702`*^9, {
   3.852219728372415*^9, 3.852219796807857*^9}, 3.852219838314179*^9, 
   3.852219877945146*^9, {3.852219997173564*^9, 3.852220059165745*^9}, 
   3.852220111171113*^9, {3.852220232073709*^9, 3.852220235321628*^9}, {
   3.852220265936089*^9, 3.85222031384394*^9}, {3.852220667565275*^9, 
   3.852220719515216*^9}, 3.8522210592432756`*^9, {3.852221151911479*^9, 
   3.85222119365793*^9}, {3.85222131667103*^9, 3.852221354468031*^9}, 
   3.852221402164267*^9, 3.852221508422687*^9, 3.852221581571259*^9, 
   3.860650200584558*^9, 3.8606618050599203`*^9},
 CellLabel->"Out[44]=",ExpressionUUID->"49349326-baee-42d2-9429-d33b35f3419c"]
}, Open  ]],

Cell[TextData[{
 StyleBox["Figure 3", "Section",
  FontSize->24,
  FontWeight->"Bold",
  FontColor->GrayLevel[0]],
 StyleBox["\nThreshold intensity required for electron reflection by the \
laser pulse. Equation 2 gives the necessary a0 (intensity I0) for reflection. \
However, the energy of the electron at reflection will also be a function of \
a0. The intensity is found numerically.", "Section",
  FontSize->24,
  FontColor->GrayLevel[0]]
}], "Text",
 CellChangeTimes->{{3.8226362283387003`*^9, 3.822636334723393*^9}, {
  3.822636391632341*^9, 3.8226364148286*^9}, {3.822636632459257*^9, 
  3.82263666754714*^9}, {3.8226367225529222`*^9, 3.822636739164402*^9}, {
  3.822893500475507*^9, 3.822893523209238*^9}, {3.8323245369078817`*^9, 
  3.832324665848118*^9}, {3.83290680301472*^9, 3.832906868114419*^9}, {
  3.833039222269853*^9, 3.8330392572797956`*^9}, {3.833465392675682*^9, 
  3.833465398403303*^9}, {3.8522207715900583`*^9, 3.852220814025341*^9}, {
  3.852220900774466*^9, 3.852220910798373*^9}, {3.852221204774682*^9, 
  3.852221216475109*^9}, {3.860659786746036*^9, 3.8606599050254583`*^9}},
 FontSize->14,ExpressionUUID->"3c1e54bc-d67f-40e6-b407-7c6f69407530"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Clear", "[", 
   RowBox[{
   "\[Chi]e", ",", "\[ScriptCapitalE]e", ",", "\[Gamma]e", ",", "W\[Gamma]", 
    ",", "pc", ",", "tc", ",", "\[Omega]0", ",", "E0", ",", 
    "\[ScriptCapitalE]c", ",", "me", ",", "c", ",", "e", ",", "\[Alpha]", ",",
     "\[HBar]", ",", "T", ",", "ES", ",", "\[Lambda]\[Mu]m", ",", "\[Tau]", 
    ",", "I0", ",", "getI0"}], "]"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"me", "=", 
    RowBox[{"9.11", " ", 
     RowBox[{"10", "^", 
      RowBox[{"-", "31"}]}]}]}], ";"}], 
  RowBox[{"(*", 
   RowBox[{"[", "Kg", "]"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"c", "=", " ", "299792458"}], ";"}], " ", 
  RowBox[{"(*", 
   RowBox[{"[", 
    RowBox[{"m", "/", "s"}], "]"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"e", "=", 
    RowBox[{"1.602176634", " ", 
     RowBox[{"10", "^", 
      RowBox[{"-", "19"}]}]}]}], ";"}], " ", 
  RowBox[{"(*", 
   RowBox[{"[", "C", "]"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"\[Alpha]", "=", 
    RowBox[{"1", "/", "137"}]}], ";"}], " ", 
  RowBox[{"(*", 
   RowBox[{"[", "]"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"\[HBar]", "=", 
    RowBox[{"1.054571817", " ", 
     RowBox[{"10", "^", 
      RowBox[{"-", "34"}]}]}]}], ";"}], 
  RowBox[{"(*", 
   RowBox[{"[", 
    RowBox[{"J", " ", "s"}], "]"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"ES", "=", 
    RowBox[{
     RowBox[{"me", "^", "2"}], " ", 
     RowBox[{
      RowBox[{"c", "^", "3"}], "/", 
      RowBox[{"(", 
       RowBox[{"e", " ", "\[HBar]"}], ")"}]}]}]}], ";"}], 
  RowBox[{"(*", 
   RowBox[{"[", 
    RowBox[{"V", "/", "m"}], "]"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[Lambda]\[Mu]m", "=", "1"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[Omega]0", "=", 
   RowBox[{"2", "\[Pi]", " ", 
    RowBox[{"c", "/", 
     RowBox[{"(", 
      RowBox[{"\[Lambda]\[Mu]m", " ", 
       RowBox[{"10", "^", 
        RowBox[{"-", "6"}]}]}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"T", "=", 
    RowBox[{"0.67", 
     FractionBox[
      RowBox[{"\[Lambda]\[Mu]m", " ", 
       RowBox[{"10", "^", 
        RowBox[{"-", "6"}]}]}], "c"]}]}], ";"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"getI0", "[", 
    RowBox[{"\[ScriptCapitalE]e_", ",", "\[Tau]_"}], "]"}], ":=", 
   RowBox[{"Module", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
      "I0", ",", "tc", ",", "tr", ",", "W\[Gamma]", ",", "E0", ",", "pr", ",",
        "\[ScriptCapitalE]r", ",", "sol", ",", "\[Gamma]e", ",", "\[Chi]e", 
       ",", "eq"}], "}"}], ",", "\[IndentingNewLine]", "\[IndentingNewLine]", 
     
     RowBox[{
      RowBox[{"\[Chi]e", "=", 
       RowBox[{"2", "\[Gamma]e", " ", 
        RowBox[{"E0", "/", "ES"}]}]}], ";", "\[IndentingNewLine]", 
      RowBox[{"\[Gamma]e", "=", 
       RowBox[{"\[ScriptCapitalE]e", "/", 
        RowBox[{"(", 
         RowBox[{"me", " ", 
          RowBox[{"c", "^", "2"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", 
      RowBox[{"W\[Gamma]", "=", 
       RowBox[{
        RowBox[{"3", "^", 
         RowBox[{"(", 
          RowBox[{"2", "/", "3"}], ")"}]}], " ", "28", " ", 
        RowBox[{"Gamma", "[", 
         RowBox[{"2", "/", "3"}], "]"}], " ", "\[Alpha]", " ", 
        RowBox[{"me", "^", "2"}], " ", 
        RowBox[{"c", "^", "4"}], 
        RowBox[{
         RowBox[{"\[Chi]e", "^", 
          RowBox[{"(", 
           RowBox[{"2", "/", "3"}], ")"}]}], "  ", "/", 
         RowBox[{"(", 
          RowBox[{"54", " ", "\[HBar]", " ", "\[ScriptCapitalE]e"}], 
          ")"}]}]}]}], " ", ";", "\[IndentingNewLine]", 
      RowBox[{"pr", " ", "=", " ", 
       RowBox[{"W\[Gamma]", " ", "tr"}]}], ";", "\[IndentingNewLine]", 
      RowBox[{"tc", "=", 
       RowBox[{"\[Tau]", "/", 
        RowBox[{"(", 
         RowBox[{"2", 
          RowBox[{"Sqrt", "[", 
           RowBox[{"2", 
            RowBox[{"Log", "[", "2", "]"}]}], "]"}]}], ")"}]}]}], ";", 
      "\[IndentingNewLine]", 
      RowBox[{"E0", "=", 
       RowBox[{"0.855", " ", "\[Lambda]\[Mu]m", "  ", 
        RowBox[{"Sqrt", "[", 
         RowBox[{"I0", " ", 
          RowBox[{"10", "^", 
           RowBox[{"-", "18"}]}]}], "]"}], " ", "me", " ", "\[Omega]0", " ", 
        RowBox[{"c", "/", "e"}]}]}], ";", "\[IndentingNewLine]", 
      "\[IndentingNewLine]", 
      RowBox[{"(*", 
       RowBox[{
       "tr", " ", "definition", " ", "a", " ", "bit", " ", "ambiguous", " ", 
        "in", " ", "the", " ", "text"}], "*)"}], "\[IndentingNewLine]", 
      RowBox[{"tr", "=", 
       RowBox[{
        RowBox[{"tc", "/", 
         RowBox[{"Sqrt", "[", "2", "]"}]}], "  ", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{"Sqrt", "[", 
           RowBox[{"2", 
            RowBox[{"Log", "[", "2", "]"}]}], "]"}], ")"}], "^", 
         RowBox[{"(", 
          RowBox[{
           RowBox[{"\[Tau]", "/", "T"}], "-", "1"}], ")"}]}]}]}], ";", 
      "\[IndentingNewLine]", "\[IndentingNewLine]", 
      RowBox[{"\[ScriptCapitalE]r", "=", 
       RowBox[{
        RowBox[{
         RowBox[{
          RowBox[{
           RowBox[{"(", 
            RowBox[{"1", "-", 
             RowBox[{"16", "/", "63"}]}], ")"}], "^", "pr"}], "  ", 
          "\[ScriptCapitalE]e"}], "  ", "//", "N"}], "//", "Simplify"}]}], 
      ";", "\[IndentingNewLine]", "\[IndentingNewLine]", 
      RowBox[{"(*", 
       RowBox[{
       "\[ScriptCapitalE]r", " ", "will", " ", "be", " ", "a", " ", 
        "function", " ", "of", " ", "I0"}], " ", "*)"}], 
      "\[IndentingNewLine]", 
      RowBox[{"eq", "=", 
       RowBox[{
        RowBox[{"I0", " ", 
         RowBox[{"10", "^", 
          RowBox[{"-", "18"}]}]}], "==", " ", 
        RowBox[{"2", 
         RowBox[{
          RowBox[{"(", 
           RowBox[{
            RowBox[{
             RowBox[{"(", 
              RowBox[{"\[ScriptCapitalE]r", "/", 
               RowBox[{"(", 
                RowBox[{"me", " ", 
                 RowBox[{"c", "^", "2"}]}], ")"}]}], ")"}], "^", "2"}], "-", 
            "1"}], ")"}], "/", 
          RowBox[{"0.855", "^", "2"}]}]}]}]}], ";", "\[IndentingNewLine]", 
      "\[IndentingNewLine]", 
      RowBox[{"(*", " ", 
       RowBox[{"solve", " ", "numerically"}], " ", "*)"}], 
      "\[IndentingNewLine]", 
      RowBox[{"sol", "=", 
       RowBox[{"NSolve", "[", 
        RowBox[{"eq", ",", "I0", ",", "Reals"}], "]"}]}], ";", 
      "\[IndentingNewLine]", 
      RowBox[{"Return", "[", 
       RowBox[{"sol", "[", 
        RowBox[{"[", 
         RowBox[{"1", ",", "1", ",", "2"}], "]"}], "]"}], "]"}]}]}], 
    "\[IndentingNewLine]", "]"}]}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{"Show", "[", 
  RowBox[{"{", 
   RowBox[{
    RowBox[{"LogLogPlot", "[", 
     RowBox[{"I0", ",", 
      RowBox[{"{", 
       RowBox[{"I0", ",", 
        RowBox[{"10", "^", "23"}], ",", 
        RowBox[{"10", "^", "25"}]}], "}"}], ",", 
      RowBox[{"AspectRatio", "->", "1"}], ",", 
      RowBox[{"AxesLabel", "\[Rule]", 
       RowBox[{"{", 
        RowBox[{
        "\"\<\!\(\*SubsuperscriptBox[\(I\), \(0\), \
\(theory\)]\)(W/\!\(\*SuperscriptBox[\(cm\), \(2\)]\))\>\"", ",", 
         "\"\<\!\(\*SubsuperscriptBox[\(I\), \(0\), \
\(PIC\)]\)(W/\!\(\*SuperscriptBox[\(cm\), \(2\)]\))\>\""}], "}"}]}], ",", 
      RowBox[{"ImageSize", "\[Rule]", "400"}]}], "]"}], ",", 
    RowBox[{"ListLogLogPlot", "[", 
     RowBox[{
      RowBox[{
       RowBox[{"getI0", "[", 
        RowBox[{
         RowBox[{"6", " ", 
          RowBox[{"10", "^", "9"}], " ", "e"}], ",", "T"}], "]"}], " ", 
       RowBox[{"Transpose", "[", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"{", "1", "}"}], ",", 
          RowBox[{"{", "1", "}"}]}], "}"}], "]"}]}], ",", 
      RowBox[{"PlotStyle", "\[Rule]", 
       RowBox[{"Directive", "[", 
        RowBox[{"Blue", ",", 
         RowBox[{"PointSize", "->", 
          RowBox[{"0.1", "/", "3"}]}]}], "]"}]}]}], "]"}], ",", 
    RowBox[{"ListLogLogPlot", "[", 
     RowBox[{
      RowBox[{
       RowBox[{"getI0", "[", 
        RowBox[{
         RowBox[{"10", " ", 
          RowBox[{"10", "^", "9"}], " ", "e"}], ",", "T"}], "]"}], " ", 
       RowBox[{"Transpose", "[", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"{", "1", "}"}], ",", 
          RowBox[{"{", "1", "}"}]}], "}"}], "]"}]}], ",", 
      RowBox[{"PlotStyle", "\[Rule]", 
       RowBox[{"Directive", "[", 
        RowBox[{"Orange", ",", 
         RowBox[{"PointSize", "->", 
          RowBox[{"0.1", "/", "3"}]}]}], "]"}]}]}], "]"}], ",", 
    RowBox[{"ListLogLogPlot", "[", 
     RowBox[{
      RowBox[{
       RowBox[{"getI0", "[", 
        RowBox[{
         RowBox[{"30", " ", 
          RowBox[{"10", "^", "9"}], " ", "e"}], ",", 
         RowBox[{"3", "T"}]}], "]"}], " ", 
       RowBox[{"Transpose", "[", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"{", "1", "}"}], ",", 
          RowBox[{"{", "1", "}"}]}], "}"}], "]"}]}], ",", 
      RowBox[{"PlotStyle", "\[Rule]", 
       RowBox[{"Directive", "[", 
        RowBox[{"Green", ",", 
         RowBox[{"PointSize", "->", 
          RowBox[{"0.1", "/", "3"}]}]}], "]"}]}]}], "]"}], ",", 
    RowBox[{"ListLogLogPlot", "[", 
     RowBox[{
      RowBox[{
       RowBox[{"getI0", "[", 
        RowBox[{
         RowBox[{"50", " ", 
          RowBox[{"10", "^", "9"}], " ", "e"}], ",", 
         RowBox[{"5", "T"}]}], "]"}], " ", 
       RowBox[{"Transpose", "[", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"{", "1", "}"}], ",", 
          RowBox[{"{", "1", "}"}]}], "}"}], "]"}]}], ",", 
      RowBox[{"PlotStyle", "\[Rule]", 
       RowBox[{"Directive", "[", 
        RowBox[{"Red", ",", 
         RowBox[{"PointSize", "->", 
          RowBox[{"0.1", "/", "3"}]}]}], "]"}]}]}], "]"}], ",", 
    RowBox[{"ListLogLogPlot", "[", 
     RowBox[{
      RowBox[{
       RowBox[{"getI0", "[", 
        RowBox[{
         RowBox[{"100", " ", 
          RowBox[{"10", "^", "9"}], " ", "e"}], ",", 
         RowBox[{"5", "T"}]}], "]"}], " ", 
       RowBox[{"Transpose", "[", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"{", "1", "}"}], ",", 
          RowBox[{"{", "1", "}"}]}], "}"}], "]"}]}], ",", 
      RowBox[{"PlotStyle", "\[Rule]", 
       RowBox[{"Directive", "[", 
        RowBox[{"Purple", ",", 
         RowBox[{"PointSize", "->", 
          RowBox[{"0.1", "/", "3"}]}]}], "]"}]}]}], "]"}], ",", 
    RowBox[{"ListLogLogPlot", "[", 
     RowBox[{
      RowBox[{
       RowBox[{"getI0", "[", 
        RowBox[{
         RowBox[{"100", " ", 
          RowBox[{"10", "^", "9"}], " ", "e"}], ",", 
         RowBox[{"7", "T"}]}], "]"}], " ", 
       RowBox[{"Transpose", "[", 
        RowBox[{"{", 
         RowBox[{
          RowBox[{"{", "1", "}"}], ",", 
          RowBox[{"{", "1", "}"}]}], "}"}], "]"}]}], ",", 
      RowBox[{"PlotStyle", "\[Rule]", 
       RowBox[{"Directive", "[", 
        RowBox[{"Brown", ",", 
         RowBox[{"PointSize", "->", 
          RowBox[{"0.1", "/", "3"}]}]}], "]"}]}]}], "]"}]}], "}"}], 
  "]"}]}], "Input",
 CellChangeTimes->{{3.86065802998486*^9, 3.860658116897036*^9}, {
   3.8606581586303062`*^9, 3.860658381499524*^9}, {3.860658421283618*^9, 
   3.8606584519300537`*^9}, {3.8606584858761873`*^9, 3.860658549132327*^9}, {
   3.8606585798477383`*^9, 3.860658969775053*^9}, {3.8606590276649637`*^9, 
   3.860659027851391*^9}, {3.8606590633214693`*^9, 3.86065910100036*^9}, {
   3.8606591675123663`*^9, 3.860659207467963*^9}, {3.860659265063884*^9, 
   3.8606592740603228`*^9}, 3.860659305811942*^9, {3.86065942812689*^9, 
   3.860659478899055*^9}, {3.860659574032338*^9, 3.860659763533781*^9}},
 CellLabel->"In[45]:=",ExpressionUUID->"af703dc1-13cc-46bf-bbe7-85b422f712ad"],

Cell[BoxData[
 GraphicsBox[{{{{}, {}, 
     TagBox[
      {RGBColor[0.368417, 0.506779, 0.709798], AbsoluteThickness[1.6], 
       Opacity[1.], LineBox[CompressedData["
1:eJxNxXssFHAAB/DLmsulW3mtlGePHanGHddy4xQl0i16YbuwzJBk8uo4ZK5s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        "]]},
      Annotation[#, "Charting`Private`Tag$8020#1"]& ]}, {}}, {{}, 
    {RGBColor[0, 0, 1], PointSize[0.03333333333333333], AbsoluteThickness[
     1.6], PointBox[{{56.177638854988935`, 56.177638854988935`}, {
      56.177638854988935`, 56.177638854988935`}}]}, {{}, {}}}, {{}, 
    {RGBColor[1, 0.5, 0], PointSize[0.03333333333333333], AbsoluteThickness[
     1.6], PointBox[{{56.875876868543635`, 56.875876868543635`}, {
      56.875876868543635`, 56.875876868543635`}}]}, {{}, {}}}, {{}, 
    {RGBColor[0, 1, 0], PointSize[0.03333333333333333], AbsoluteThickness[
     1.6], PointBox[{{55.301588274214296`, 55.301588274214296`}, {
      55.301588274214296`, 55.301588274214296`}}]}, {{}, {}}}, {{}, 
    {RGBColor[1, 0, 0], PointSize[0.03333333333333333], AbsoluteThickness[
     1.6], PointBox[{{53.985231056828276`, 53.985231056828276`}, {
      53.985231056828276`, 53.985231056828276`}}]}, {{}, {}}}, {{}, 
    {RGBColor[0.5, 0, 0.5], PointSize[0.03333333333333333], AbsoluteThickness[
     1.6], PointBox[{{54.81960991589521, 54.81960991589521}, {
      54.81960991589521, 54.81960991589521}}]}, {{}, {}}}, {{}, 
    {RGBColor[0.6, 0.4, 0.2], PointSize[0.03333333333333333], 
     AbsoluteThickness[1.6], 
     PointBox[{{53.20823014441284, 53.20823014441284}, {53.20823014441284, 
      53.20823014441284}}]}, {{}, {}}}},
  AspectRatio->1,
  Axes->{True, True},
  AxesLabel->{
    FormBox[
    "\"\\!\\(\\*SubsuperscriptBox[\\(I\\), \\(0\\), \\(theory\\)]\\)(W/\\!\\(\
\\*SuperscriptBox[\\(cm\\), \\(2\\)]\\))\"", TraditionalForm], 
    FormBox[
    "\"\\!\\(\\*SubsuperscriptBox[\\(I\\), \\(0\\), \
\\(PIC\\)]\\)(W/\\!\\(\\*SuperscriptBox[\\(cm\\), \\(2\\)]\\))\"", 
     TraditionalForm]},
  AxesOrigin->{52.95945713886305, 52.95945723284612},
  CoordinatesToolOptions:>{"DisplayFunction" -> ({
      Exp[
       Part[#, 1]], 
      Exp[
       Part[#, 2]]}& ), "CopiedValueFunction" -> ({
      Exp[
       Part[#, 1]], 
      Exp[
       Part[#, 2]]}& )},
  DisplayFunction->Identity,
  Frame->{{False, False}, {False, False}},
  FrameLabel->{{None, None}, {None, None}},
  FrameTicks->{{Quiet[
      Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& , 
     Charting`ScaledFrameTicks[{Log, Exp}]}, {Quiet[
      Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& , 
     Charting`ScaledFrameTicks[{Log, Exp}]}},
  GridLines->{None, None},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  ImageSize->400,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, 
    "DefaultGraphicsInteraction" -> {
     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
      "Effects" -> {
       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
        "Droplines" -> {
         "freeformCursorMode" -> True, 
          "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None},
  PlotRange->NCache[{{
      Log[100000000000000000000000], 
      Log[10000000000000000000000000]}, {52.95945723284612, 
     57.564627230868076`}}, {{52.95945713886305, 57.564627324851145`}, {
    52.95945723284612, 57.564627230868076`}}],
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {
     Scaled[0.05], 
     Scaled[0.05]}},
  Ticks->FrontEndValueCache[{Quiet[
      Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& , Quiet[
      Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& }, {{{
      52.95945713886305, 
       FormBox[
        TemplateBox[{"\[Times]", "\"\[Times]\"", "1", 
          
          TemplateBox[{"10", "23"}, "Superscript", SyntaxForm -> 
           SuperscriptBox]}, "RowWithSeparators"], TraditionalForm], {0.01, 
       0.}}, {54.568895051297154`, 
       FormBox[
        TemplateBox[{"\[Times]", "\"\[Times]\"", "5", 
          
          TemplateBox[{"10", "23"}, "Superscript", SyntaxForm -> 
           SuperscriptBox]}, "RowWithSeparators"], TraditionalForm], {0.01, 
       0.}}, {55.262042231857095`, 
       FormBox[
        TemplateBox[{"\[Times]", "\"\[Times]\"", "1", 
          
          TemplateBox[{"10", "24"}, "Superscript", SyntaxForm -> 
           SuperscriptBox]}, "RowWithSeparators"], TraditionalForm], {0.01, 
       0.}}, {56.8714801442912, 
       FormBox[
        TemplateBox[{"\[Times]", "\"\[Times]\"", "5", 
          
          TemplateBox[{"10", "24"}, "Superscript", SyntaxForm -> 
           SuperscriptBox]}, "RowWithSeparators"], TraditionalForm], {0.01, 
       0.}}, {57.564627324851145`, 
       FormBox[
        TemplateBox[{"\[Times]", "\"\[Times]\"", "1", 
          
          TemplateBox[{"10", "25"}, "Superscript", SyntaxForm -> 
           SuperscriptBox]}, "RowWithSeparators"], TraditionalForm], {0.01, 
       0.}}, {52.266309958303104`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      52.44863151509706, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      52.602782194924316`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      52.73631358754884, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      52.85409662320522, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      53.652604319423, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      54.05806942753116, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      54.34575149998294, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      54.751216608091106`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      54.90536728791837, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      55.038898680542886`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      55.15668171619927, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      55.95518941241704, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      56.36065452052521, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      56.64833659297699, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      57.05380170108515, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      57.20795238091241, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      57.34148377353693, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      57.459266809193316`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      58.257774505411085`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      58.66323961351925, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      58.95092168597103, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      59.17406523728524, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}}, {{
      52.95945713886305, 
       FormBox[
        TemplateBox[{"\[Times]", "\"\[Times]\"", "1", 
          
          TemplateBox[{"10", "23"}, "Superscript", SyntaxForm -> 
           SuperscriptBox]}, "RowWithSeparators"], TraditionalForm], {0.01, 
       0.}}, {54.568895051297154`, 
       FormBox[
        TemplateBox[{"\[Times]", "\"\[Times]\"", "5", 
          
          TemplateBox[{"10", "23"}, "Superscript", SyntaxForm -> 
           SuperscriptBox]}, "RowWithSeparators"], TraditionalForm], {0.01, 
       0.}}, {55.262042231857095`, 
       FormBox[
        TemplateBox[{"\[Times]", "\"\[Times]\"", "1", 
          
          TemplateBox[{"10", "24"}, "Superscript", SyntaxForm -> 
           SuperscriptBox]}, "RowWithSeparators"], TraditionalForm], {0.01, 
       0.}}, {56.8714801442912, 
       FormBox[
        TemplateBox[{"\[Times]", "\"\[Times]\"", "5", 
          
          TemplateBox[{"10", "24"}, "Superscript", SyntaxForm -> 
           SuperscriptBox]}, "RowWithSeparators"], TraditionalForm], {0.01, 
       0.}}, {57.564627324851145`, 
       FormBox[
        TemplateBox[{"\[Times]", "\"\[Times]\"", "1", 
          
          TemplateBox[{"10", "25"}, "Superscript", SyntaxForm -> 
           SuperscriptBox]}, "RowWithSeparators"], TraditionalForm], {0.01, 
       0.}}, {52.266309958303104`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      52.44863151509706, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      52.602782194924316`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      52.73631358754884, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      52.85409662320522, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      53.652604319423, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      54.05806942753116, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      54.34575149998294, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      54.751216608091106`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      54.90536728791837, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      55.038898680542886`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      55.15668171619927, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      55.95518941241704, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      56.36065452052521, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      56.64833659297699, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      57.05380170108515, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      57.20795238091241, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      57.34148377353693, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      57.459266809193316`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      58.257774505411085`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      58.66323961351925, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      58.95092168597103, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      59.17406523728524, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      59.26937541708957, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      59.3563867940792, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
      59.436429501752734`, 
       FormBox[
        TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 
       0.}}}}]]], "Output",
 CellChangeTimes->{{3.860658518559988*^9, 3.860658549629025*^9}, {
   3.86065858119366*^9, 3.860658600521822*^9}, {3.860658658181438*^9, 
   3.8606586654308453`*^9}, {3.8606587062565737`*^9, 3.8606589186563807`*^9}, 
   3.860658970820611*^9, 3.860659028683248*^9, {3.860659069431287*^9, 
   3.860659101889538*^9}, {3.8606591687407827`*^9, 3.860659179104169*^9}, 
   3.8606592094593573`*^9, {3.860659296120943*^9, 3.860659306644311*^9}, {
   3.860659461461237*^9, 3.860659480008595*^9}, 3.860659585749977*^9, 
   3.860659659438633*^9, {3.860659731812504*^9, 3.86065976436753*^9}, 
   3.860661805919923*^9},
 CellLabel->"Out[56]=",ExpressionUUID->"045b9cab-0213-49c9-a0fb-3ff3fa37941d"]
}, Open  ]],

Cell[TextData[{
 StyleBox["Figure 2", "Section",
  FontSize->24,
  FontWeight->"Bold",
  FontColor->GrayLevel[0]],
 StyleBox["\n\[Gamma]min=1/Sqrt[2 \[CapitalDelta]n]\nIn the limit \[Chi]\
\[Gamma]<<1 \[CapitalDelta]n=8\[Alpha] E0^2/(45 \[Pi] ES^2)", "Section",
  FontSize->24,
  FontColor->GrayLevel[0]]
}], "Text",
 CellChangeTimes->{{3.8226362283387003`*^9, 3.822636334723393*^9}, {
   3.822636391632341*^9, 3.8226364148286*^9}, {3.822636632459257*^9, 
   3.82263666754714*^9}, {3.8226367225529222`*^9, 3.822636739164402*^9}, {
   3.822893500475507*^9, 3.822893523209238*^9}, {3.8323245369078817`*^9, 
   3.832324665848118*^9}, {3.83290680301472*^9, 3.832906868114419*^9}, {
   3.833039222269853*^9, 3.8330392572797956`*^9}, {3.833465392675682*^9, 
   3.833465398403303*^9}, {3.8522207715900583`*^9, 3.852220814025341*^9}, {
   3.852220900774466*^9, 3.852220910798373*^9}, {3.852221204774682*^9, 
   3.852221216475109*^9}, {3.860660068027053*^9, 3.860660105310502*^9}, 
   3.860660483495945*^9, 3.860660852106051*^9},
 FontSize->14,ExpressionUUID->"6b9913d9-0165-44e2-b8a4-397dafaaf2e0"],

Cell[TextData[StyleBox["Limit \[Alpha] \[Chi]^2/3 = 1 ( it needs to be \
multiplied by a factor of 2 to reproduce Fig4 )", "Section",
 FontSize->24,
 FontColor->GrayLevel[0]]], "Text",
 CellChangeTimes->{{3.8226362283387003`*^9, 3.822636334723393*^9}, {
   3.822636391632341*^9, 3.8226364148286*^9}, {3.822636632459257*^9, 
   3.82263666754714*^9}, {3.8226367225529222`*^9, 3.822636739164402*^9}, {
   3.822893500475507*^9, 3.822893523209238*^9}, {3.8323245369078817`*^9, 
   3.832324665848118*^9}, {3.83290680301472*^9, 3.832906868114419*^9}, {
   3.833039222269853*^9, 3.8330392572797956`*^9}, {3.833465392675682*^9, 
   3.833465398403303*^9}, {3.8522207715900583`*^9, 3.852220814025341*^9}, {
   3.852220900774466*^9, 3.852220910798373*^9}, {3.852221204774682*^9, 
   3.852221216475109*^9}, {3.860660068027053*^9, 3.860660105310502*^9}, 
   3.860660483495945*^9, {3.860660852106051*^9, 3.8606608760517406`*^9}, {
   3.860661650871463*^9, 3.860661683832054*^9}},
 FontSize->14,ExpressionUUID->"be544686-f884-4593-990a-280e87fa18a2"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{"Clear", "[", 
  RowBox[{
  "\[Chi]e", ",", "\[ScriptCapitalE]e", ",", "\[Gamma]e", ",", "W\[Gamma]", 
   ",", "pc", ",", "tc", ",", "\[Omega]0", ",", "E0", ",", 
   "\[ScriptCapitalE]c", ",", "me", ",", "c", ",", "e", ",", "\[Alpha]", ",", 
   "\[HBar]", ",", "T", ",", "ES", ",", "\[Lambda]\[Mu]m", ",", "\[Tau]", ",",
    "\[CapitalDelta]n"}], "]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[Chi]e", "=", 
   RowBox[{"2", "\[Gamma]e", " ", 
    RowBox[{"E0", "/", "ES"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[Gamma]e", "=", 
   RowBox[{"\[ScriptCapitalE]e", "/", 
    RowBox[{"(", 
     RowBox[{"me", " ", 
      RowBox[{"c", "^", "2"}]}], ")"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"\[Omega]0", "=", 
   RowBox[{"2", "\[Pi]", " ", 
    RowBox[{"c", "/", 
     RowBox[{"(", 
      RowBox[{"\[Lambda]\[Mu]m", " ", 
       RowBox[{"10", "^", 
        RowBox[{"-", "6"}]}]}], ")"}]}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"E0", "=", 
   RowBox[{"0.855", " ", "\[Lambda]\[Mu]m", "  ", 
    RowBox[{"Sqrt", "[", 
     RowBox[{"I0", " ", 
      RowBox[{"10", "^", 
       RowBox[{"-", "18"}]}]}], "]"}], " ", "me", " ", "\[Omega]0", " ", 
    RowBox[{"c", "/", "e"}]}]}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"ES", "=", 
    RowBox[{
     RowBox[{"me", "^", "2"}], " ", 
     RowBox[{
      RowBox[{"c", "^", "3"}], "/", 
      RowBox[{"(", 
       RowBox[{"e", " ", "\[HBar]"}], ")"}]}]}]}], ";"}], 
  RowBox[{"(*", 
   RowBox[{"[", 
    RowBox[{"V", "/", "m"}], "]"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"Solve", "[", 
   RowBox[{
    RowBox[{"\[Chi]e", "==", 
     RowBox[{
      RowBox[{"(", 
       RowBox[{"1", "/", "\[Alpha]"}], ")"}], "^", "1.5"}]}], ",", 
    "\[ScriptCapitalE]e"}], "]"}], "[", 
  RowBox[{"[", 
   RowBox[{"1", ",", "1", ",", "2"}], "]"}], "]"}]}], "Input",
 CellChangeTimes->{{3.860660486123371*^9, 3.8606605642079906`*^9}, {
  3.860660614914403*^9, 3.8606606241949253`*^9}, {3.860660685934531*^9, 
  3.860660687479741*^9}},
 CellLabel->"In[57]:=",ExpressionUUID->"c39d805c-27e5-4bca-a062-bcd37ad74dba"],

Cell[BoxData[
 FractionBox[
  RowBox[{"93.07306613561131`", " ", 
   SuperscriptBox["c", "3"], " ", 
   SuperscriptBox["me", "2"], " ", 
   SuperscriptBox[
    RowBox[{"(", 
     FractionBox["1", "\[Alpha]"], ")"}], "1.5`"]}], 
  RowBox[{
   SqrtBox["I0"], " ", "\[HBar]"}]]], "Output",
 CellChangeTimes->{{3.860660487496468*^9, 3.8606605181190443`*^9}, {
   3.860660554236027*^9, 3.8606605645377207`*^9}, {3.8606606163391943`*^9, 
   3.860660624598592*^9}, 3.860660688148892*^9, 3.860660855497355*^9, 
   3.860661806187524*^9},
 CellLabel->"Out[63]=",ExpressionUUID->"fe4a36f1-631c-4be8-ad2b-d15a04dc72a6"]
}, Open  ]],

Cell[TextData[StyleBox["We need to invert the relation \[ScriptCapitalE]^c_e \
(\[ScriptCapitalE]_e) and replace \[ScriptCapitalE]^c_e by the corresponding \
\[Gamma]min given by the Cherenkov condition", "Section",
 FontSize->24,
 FontColor->GrayLevel[0]]], "Text",
 CellChangeTimes->{{3.8226362283387003`*^9, 3.822636334723393*^9}, {
   3.822636391632341*^9, 3.8226364148286*^9}, {3.822636632459257*^9, 
   3.82263666754714*^9}, {3.8226367225529222`*^9, 3.822636739164402*^9}, {
   3.822893500475507*^9, 3.822893523209238*^9}, {3.8323245369078817`*^9, 
   3.832324665848118*^9}, {3.83290680301472*^9, 3.832906868114419*^9}, {
   3.833039222269853*^9, 3.8330392572797956`*^9}, {3.833465392675682*^9, 
   3.833465398403303*^9}, {3.8522207715900583`*^9, 3.852220814025341*^9}, {
   3.852220900774466*^9, 3.852220910798373*^9}, {3.852221204774682*^9, 
   3.852221216475109*^9}, {3.860660068027053*^9, 3.860660105310502*^9}, 
   3.860660483495945*^9, {3.860660852106051*^9, 3.8606608760517406`*^9}, {
   3.860661650871463*^9, 3.860661750105261*^9}},
 FontSize->14,ExpressionUUID->"2ee30d05-6da7-456a-bd7c-eba35da587b2"],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"Clear", "[", 
   RowBox[{
   "\[Chi]e", ",", "\[ScriptCapitalE]e", ",", "\[Gamma]e", ",", "W\[Gamma]", 
    ",", "pc", ",", "tc", ",", "\[Omega]0", ",", "E0", ",", 
    "\[ScriptCapitalE]c", ",", "me", ",", "c", ",", "e", ",", "\[Alpha]", ",",
     "\[HBar]", ",", "T", ",", "ES", ",", "\[Lambda]\[Mu]m", ",", "\[Tau]", 
    ",", "\[CapitalDelta]n", ",", "get\[ScriptCapitalE]Ch"}], "]"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"me", "=", 
    RowBox[{"9.11", " ", 
     RowBox[{"10", "^", 
      RowBox[{"-", "31"}]}]}]}], ";"}], 
  RowBox[{"(*", 
   RowBox[{"[", "Kg", "]"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"c", "=", " ", "299792458"}], ";"}], " ", 
  RowBox[{"(*", 
   RowBox[{"[", 
    RowBox[{"m", "/", "s"}], "]"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"e", "=", 
    RowBox[{"1.602176634", " ", 
     RowBox[{"10", "^", 
      RowBox[{"-", "19"}]}]}]}], ";"}], " ", 
  RowBox[{"(*", 
   RowBox[{"[", "C", "]"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"\[Alpha]", "=", 
    RowBox[{"1", "/", "137"}]}], ";"}], " ", 
  RowBox[{"(*", 
   RowBox[{"[", "]"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"\[HBar]", "=", 
    RowBox[{"1.054571817", " ", 
     RowBox[{"10", "^", 
      RowBox[{"-", "34"}]}]}]}], ";"}], 
  RowBox[{"(*", 
   RowBox[{"[", 
    RowBox[{"J", " ", "s"}], "]"}], "*)"}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"ES", "=", 
    RowBox[{
     RowBox[{"me", "^", "2"}], " ", 
     RowBox[{
      RowBox[{"c", "^", "3"}], "/", 
      RowBox[{"(", 
       RowBox[{"e", " ", "\[HBar]"}], ")"}]}]}]}], ";"}], 
  RowBox[{"(*", 
   RowBox[{"[", 
    RowBox[{"V", "/", "m"}], "]"}], "*)"}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"get\[ScriptCapitalE]Ch", "[", 
    RowBox[{"I0_", ",", "\[Tau]T_", ",", "\[Lambda]\[Mu]m_"}], "]"}], ":=", 
   RowBox[{"Module", "[", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
      "\[ScriptCapitalE]Ch", ",", "\[CapitalDelta]n", ",", "\[Chi]e", ",", 
       "\[Gamma]e", ",", "\[ScriptCapitalE]e", ",", "pc", ",", "W\[Gamma]", 
       ",", "tc", ",", "\[Omega]0", ",", "E0", ",", "T", ",", "\[Tau]"}], 
      "}"}], ",", "\[IndentingNewLine]", 
     RowBox[{
      RowBox[{"\[Chi]e", "=", 
       RowBox[{"2", "\[Gamma]e", " ", 
        RowBox[{"E0", "/", "ES"}]}]}], ";", "\[IndentingNewLine]", 
      RowBox[{"\[Gamma]e", "=", 
       RowBox[{"\[ScriptCapitalE]e", "/", 
        RowBox[{"(", 
         RowBox[{"me", " ", 
          RowBox[{"c", "^", "2"}]}], ")"}]}]}], ";", "\[IndentingNewLine]", 
      RowBox[{"W\[Gamma]", "=", 
       RowBox[{
        RowBox[{"3", "^", 
         RowBox[{"(", 
          RowBox[{"2", "/", "3"}], ")"}]}], " ", "28", " ", 
        RowBox[{"Gamma", "[", 
         RowBox[{"2", "/", "3"}], "]"}], " ", "\[Alpha]", " ", 
        RowBox[{"me", "^", "2"}], " ", 
        RowBox[{"c", "^", "4"}], 
        RowBox[{
         RowBox[{"\[Chi]e", "^", 
          RowBox[{"(", 
           RowBox[{"2", "/", "3"}], ")"}]}], "  ", "/", 
         RowBox[{"(", 
          RowBox[{"54", " ", "\[HBar]", " ", "\[ScriptCapitalE]e"}], 
          ")"}]}]}]}], " ", ";", "\[IndentingNewLine]", 
      RowBox[{"pc", " ", "=", " ", 
       RowBox[{"W\[Gamma]", " ", "tc"}]}], ";", "\[IndentingNewLine]", 
      RowBox[{"tc", "=", 
       RowBox[{"\[Tau]", "/", 
        RowBox[{"(", 
         RowBox[{"2", 
          RowBox[{"Sqrt", "[", 
           RowBox[{"2", 
            RowBox[{"Log", "[", "2", "]"}]}], "]"}]}], ")"}]}]}], ";", 
      "\[IndentingNewLine]", 
      RowBox[{"\[Omega]0", "=", 
       RowBox[{"2", "\[Pi]", " ", 
        RowBox[{"c", "/", 
         RowBox[{"(", 
          RowBox[{"\[Lambda]\[Mu]m", " ", 
           RowBox[{"10", "^", 
            RowBox[{"-", "6"}]}]}], ")"}]}]}]}], ";", "\[IndentingNewLine]", 
      RowBox[{"E0", "=", 
       RowBox[{"0.855", " ", "\[Lambda]\[Mu]m", "  ", 
        RowBox[{"Sqrt", "[", 
         RowBox[{"I0", " ", 
          RowBox[{"10", "^", 
           RowBox[{"-", "18"}]}]}], "]"}], " ", "me", " ", "\[Omega]0", " ", 
        RowBox[{"c", "/", "e"}]}]}], ";", "\[IndentingNewLine]", 
      RowBox[{"T", "=", 
       RowBox[{"0.67", 
        FractionBox[
         RowBox[{"\[Lambda]\[Mu]m", " ", 
          RowBox[{"10", "^", 
           RowBox[{"-", "6"}]}]}], "c"]}]}], ";", "\[IndentingNewLine]", 
      RowBox[{"\[Tau]", "=", 
       RowBox[{"\[Tau]T", " ", "T"}]}], ";", "\[IndentingNewLine]", 
      RowBox[{"\[CapitalDelta]n", "=", 
       RowBox[{"8", "\[Alpha]", " ", 
        RowBox[{
         RowBox[{"E0", "^", "2"}], "/", 
         RowBox[{"(", 
          RowBox[{"45", " ", "\[Pi]", " ", 
           RowBox[{"ES", "^", "2"}]}], ")"}]}]}]}], ";", 
      "\[IndentingNewLine]", 
      RowBox[{"\[ScriptCapitalE]Ch", "=", 
       RowBox[{
        RowBox[{"NSolve", "[", 
         RowBox[{
          RowBox[{
           RowBox[{"\[ScriptCapitalE]e", 
            SuperscriptBox[
             RowBox[{"(", 
              FractionBox["47", "63"], ")"}], 
             FractionBox[
              RowBox[{"0.030199136711634034`", " ", 
               SuperscriptBox["c", "4"], " ", 
               SuperscriptBox["me", "2"], " ", 
               SuperscriptBox[
                RowBox[{"(", 
                 FractionBox[
                  RowBox[{
                   SqrtBox["I0"], " ", "\[ScriptCapitalE]e"}], 
                  RowBox[{"e", " ", "ES"}]], ")"}], 
                RowBox[{"2", "/", "3"}]], " ", "\[Alpha]", " ", "\[Tau]"}], 
              RowBox[{"\[ScriptCapitalE]e", " ", "\[HBar]"}]]]}], "==", 
           RowBox[{
            RowBox[{"1", "/", 
             RowBox[{"Sqrt", "[", 
              RowBox[{"2", " ", "\[CapitalDelta]n"}], "]"}]}], "  ", "me", 
            " ", 
            RowBox[{"c", "^", "2"}]}]}], ",", "\[ScriptCapitalE]e", ",", 
          "Reals"}], "]"}], "[", 
        RowBox[{"[", 
         RowBox[{"1", ",", "1", ",", "2"}], "]"}], "]"}]}], ";", 
      "\[IndentingNewLine]", 
      RowBox[{"Return", "[", 
       RowBox[{"\[ScriptCapitalE]Ch", "/", 
        RowBox[{"(", 
         RowBox[{
          RowBox[{"10", "^", "9"}], " ", "e"}], ")"}]}], "]"}]}]}], 
    "\[IndentingNewLine]", "]"}]}], 
  "\[IndentingNewLine]"}], "\[IndentingNewLine]", 
 RowBox[{"LogLinearPlot", "[", " ", 
  RowBox[{
   RowBox[{"{", 
    RowBox[{
     RowBox[{"get\[ScriptCapitalE]Ch", "[", 
      RowBox[{"I0", ",", "3", ",", "1"}], "]"}], ",", 
     RowBox[{"get\[ScriptCapitalE]Ch", "[", 
      RowBox[{"I0", ",", "2", ",", "1"}], "]"}], ",", 
     RowBox[{"get\[ScriptCapitalE]Ch", "[", 
      RowBox[{"I0", ",", "1", ",", "1"}], "]"}], ",", 
     RowBox[{"get\[ScriptCapitalE]Ch", "[", 
      RowBox[{"I0", ",", "1", ",", "0.5"}], "]"}], ",", 
     RowBox[{"get\[ScriptCapitalE]Ch", "[", 
      RowBox[{"I0", ",", "1", ",", "0.25"}], "]"}], ",", 
     RowBox[{"2", 
      RowBox[{
       FractionBox[
        RowBox[{"93.07306613561131`", " ", 
         SuperscriptBox["c", "3"], " ", 
         SuperscriptBox["me", "2"], " ", 
         SuperscriptBox[
          RowBox[{"(", 
           FractionBox["1", "\[Alpha]"], ")"}], "1.5`"]}], 
        RowBox[{
         SqrtBox["I0"], " ", "\[HBar]"}]], "/", 
       RowBox[{"(", 
        RowBox[{
         RowBox[{"10", "^", "9"}], " ", "e"}], ")"}]}]}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{"I0", ",", 
     RowBox[{"10", "^", "23"}], ",", 
     RowBox[{"10", "^", "25"}]}], "}"}], ",", 
   RowBox[{"PlotPoints", "\[Rule]", "2"}], ",", 
   RowBox[{"PlotRange", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{"0", ",", "200"}], "}"}]}], ",", 
   RowBox[{"PlotStyle", "->", 
    RowBox[{"{", 
     RowBox[{
      RowBox[{"Directive", "[", "Green", "]"}], ",", 
      RowBox[{"Directive", "[", "Blue", "]"}], ",", 
      RowBox[{"Directive", "[", "Black", "]"}], ",", 
      RowBox[{"Directive", "[", 
       RowBox[{"Black", ",", "DotDashed"}], "]"}], ",", 
      RowBox[{"Directive", "[", 
       RowBox[{"Black", ",", "Dashed"}], "]"}], ",", " ", 
      RowBox[{"Directive", "[", "Dotted", "]"}], ",", 
      RowBox[{"Directive", "[", 
       RowBox[{"Darker", "[", "Yellow", "]"}], "]"}], ",", 
      RowBox[{"Directive", "[", "Yellow", "]"}]}], "}"}]}], ",", 
   RowBox[{"Frame", "\[Rule]", "True"}], ",", 
   RowBox[{"GridLines", "\[Rule]", "Automatic"}], ",", 
   RowBox[{"ImageSize", "\[Rule]", "400"}], ",", 
   RowBox[{"FrameLabel", "\[Rule]", 
    RowBox[{"{", 
     RowBox[{
     "\"\<\!\(\*SubscriptBox[\(I\), \(0\)]\)[W/\!\(\*SuperscriptBox[\(cm\), \
\(2\)]\)]\>\"", ",", 
      "\"\<\!\(\*SubsuperscriptBox[\(\[ScriptCapitalE]\), \(e\), \
\(Ch\)]\)(GeV)\>\""}], "}"}]}]}], "]"}]}], "Input",
 CellChangeTimes->{{3.852201445048253*^9, 3.85220160364121*^9}, {
   3.852201639233583*^9, 3.852201733145811*^9}, {3.852201916762659*^9, 
   3.852201966434247*^9}, {3.852202007358787*^9, 3.85220211749953*^9}, {
   3.852219071077714*^9, 3.85221928634422*^9}, {3.852219320577791*^9, 
   3.8522193752394667`*^9}, {3.8522194106553497`*^9, 3.852219796484385*^9}, {
   3.852219834180423*^9, 3.8522198379613543`*^9}, {3.852219873338623*^9, 
   3.852220058704288*^9}, 3.8522201108013897`*^9, {3.852220231659902*^9, 
   3.85222031342881*^9}, {3.852220602018907*^9, 3.852220719173004*^9}, {
   3.852221521889414*^9, 3.852221525262611*^9}, {3.8606503405392733`*^9, 
   3.8606503701676483`*^9}, {3.860650411447089*^9, 3.860650608133498*^9}, {
   3.860660118751845*^9, 3.860660244563336*^9}, {3.860660277862878*^9, 
   3.8606603447300787`*^9}, {3.860660381745461*^9, 3.8606604261940603`*^9}, {
   3.860660463150423*^9, 3.860660476501939*^9}, {3.860660571237719*^9, 
   3.8606605886794653`*^9}, {3.860660643103922*^9, 3.860660656593461*^9}, {
   3.860660706605641*^9, 3.8606607352651033`*^9}, {3.8606608956954947`*^9, 
   3.8606609273656178`*^9}, {3.860660973358502*^9, 3.860661233997149*^9}, {
   3.860661271982794*^9, 3.860661289787455*^9}, {3.860661344734378*^9, 
   3.860661388932631*^9}, {3.860661420566758*^9, 3.860661644232946*^9}},
 CellLabel->"In[64]:=",ExpressionUUID->"76d70526-8da2-4653-b6b4-b144b6617303"],

Cell[BoxData[
 GraphicsBox[{{{}, {}, 
    TagBox[
     {RGBColor[0, 1, 0], AbsoluteThickness[1.6], Opacity[1.], 
      LineBox[CompressedData["
1:eJwd0HlI03EYBvCVR3bJtjTLvKIgzaNMI2dqj+HV9zsVnAf529KteZThiVE5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       "]]},
     Annotation[#, "Charting`Private`Tag$12359#1"]& ], 
    TagBox[
     {RGBColor[0, 0, 1], AbsoluteThickness[1.6], Opacity[1.], 
      LineBox[CompressedData["
1:eJwVkXtMU3cUxxll0jhWCmsQkhUqaIKDAcoWLHP2C4xR7u9S5LalUpnYApUp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       "]]},
     Annotation[#, "Charting`Private`Tag$12359#2"]& ], 
    TagBox[
     {GrayLevel[0], AbsoluteThickness[1.6], Opacity[1.], 
      LineBox[CompressedData["
1:eJwVz300lXcAB3BDXGo3nK6XruoyE5GX1OZi7Xuf577w/B5qXqrZRi7JpEtU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       "]]},
     Annotation[#, "Charting`Private`Tag$12359#3"]& ], 
    TagBox[
     {GrayLevel[0], AbsoluteThickness[1.6], Opacity[1.], 
      Dashing[{0, Small, Small, Small}], LineBox[CompressedData["
1:eJwVTn1Q02UA3kltdqd8TEPoTAfVHQopvuNrBPhAN2W/9zU7xpQ4PAEH4jAx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       "]]},
     Annotation[#, "Charting`Private`Tag$12359#4"]& ], 
    TagBox[
     {GrayLevel[0], AbsoluteThickness[1.6], Opacity[1.], 
      Dashing[{Small, Small}], LineBox[CompressedData["
1:eJwVjX1Qy3EAh2NWOGp1yLzmt62WUmvr1MrLp3NT/b5f7yIjs5WkEuI4NZns
5Cw55l0IkyJxZl66sCvDUe1cbiZ5uyNvics0HCZ/PPf88fzxjNOsnru8r5eX
V2Qv/50RtcFkL2BxSbSmsnw04PCM0XL1LLaLK5asTZyKpJZ78+J3sSh49oqn
XjIF4Tl8ztkTLES1RqP0xCQclze0tVexOJdnfqJrigevf87lgMssDOH3ClR9
4vHNVK8uusMiuMjmadDJkbFuufxKM4u0xxtX3n8QC0eCr/9HBwuhKidQNTIW
dS9U1pQPLL4ONzYvsk9E8XDO2Am+BDO3NoRUa6Ph6jjfowkkSOUO3DvjuwyZ
lvkth4II1o9IC/yQLwM7t3JzPxlBh8YjUmqlqA+alRI3iaDu76Vvz32kiPji
Dl+jIKi/OYS1HIyCf2ly+7OFBBt8smMeNkpQrOw2+6sJOmc1GRpVErjERw2J
2b2//JeHuJ5IOG2dcWYtwfjyKvlFYwQqPLsP7zxJ4PJ7UDpjcDgCWmLXWs8R
CCyt5bLCMOjLXyf1mAmiFXvI+67xyJLLfqjvEvBvKUXcd6Fo82m3H7QTXN0/
4PrQnFBQh/5ss5PAVGc8qnCJEbnOsUD+ieCk84twxVAxKhK2RKx2ERgGVVp9
L4QggCf2PvOHYD4/Q5eQHIKemk0WHo9irDM0zFYWjKxCZtd0PkWS5refMyYY
bckPM7QMhT7U4f75RoRbHaOGvI+m2GFsuPOHFUFisX0aPYXCd+/ptBqOCKe2
5TXOS6RouSCdzbEKsT3Imn97EQU3xi6eM02IH11Z7HcNxef0rtwxA4XIvunP
hOVShDTF3cBjAWYq0x8dKKKofVu7anK+AFbxoOqmEgpdwjGOWyGA1H1F13dP
b0++0d04SgCTLS019ghF5+LPmQd6GAzb5y3JO01R9UtZqm5lsENz0cdUQ5HS
udTANzP4JUl9+dRC4R7crTfvZ5Dr8brmd5uibFnmblEhg+fN1WWK+xQlfXTm
zHQG/wCQ4Uh1
       "]]},
     Annotation[#, "Charting`Private`Tag$12359#5"]& ], 
    TagBox[
     {RGBColor[0.772079, 0.431554, 0.102387], AbsoluteThickness[1.6], Opacity[
      1.], Dashing[{0, Small}], 
      LineBox[{{56.62469678268019, 200.}, {56.70115503674701, 
       192.37463145568978`}, {56.77311067699151, 185.5764369631631}, {
       56.845066317236004`, 179.01847917964798`}, {56.988977597725, 
       166.58961550850677`}, {57.06093323796949, 160.70261992030254`}, {
       57.13288887821399, 155.02366081114138`}, {57.27680015870298, 
       144.26070519419991`}, {57.34875579894748, 139.1627755757351}, {
       57.420711439191976`, 134.244998177931}, {57.49266707943647, 
       129.50100672564497`}, {57.56462271968096, 124.92465991714373`}}]},
     Annotation[#, "Charting`Private`Tag$12359#6"]& ]}, {}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->{True, True},
  AxesLabel->{None, None},
  AxesOrigin->{52.959461744033234`, 0},
  CoordinatesToolOptions:>{"DisplayFunction" -> ({
      Exp[
       Part[#, 1]], 
      Part[#, 2]}& ), "CopiedValueFunction" -> ({
      Exp[
       Part[#, 1]], 
      Part[#, 2]}& )},
  DisplayFunction->Identity,
  Frame->{{True, True}, {True, True}},
  FrameLabel->{{
     FormBox[
     "\"\\!\\(\\*SubsuperscriptBox[\\(\[ScriptCapitalE]\\), \\(e\\), \
\\(Ch\\)]\\)(GeV)\"", TraditionalForm], None}, {
     FormBox[
     "\"\\!\\(\\*SubscriptBox[\\(I\\), \\(0\\)]\\)[W/\\!\\(\\*SuperscriptBox[\
\\(cm\\), \\(2\\)]\\)]\"", TraditionalForm], None}},
  FrameTicks->FrontEndValueCache[{{Automatic, Automatic}, {Quiet[
       Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& , 
      Charting`ScaledFrameTicks[{Log, Exp}]}}, {{
     Automatic, Automatic}, {{{52.95945713886305, 
        FormBox[
         TemplateBox[{"\[Times]", "\"\[Times]\"", "1", 
           
           TemplateBox[{"10", "23"}, "Superscript", SyntaxForm -> 
            SuperscriptBox]}, "RowWithSeparators"], TraditionalForm], {0.01, 
        0.}}, {54.568895051297154`, 
        FormBox[
         TemplateBox[{"\[Times]", "\"\[Times]\"", "5", 
           
           TemplateBox[{"10", "23"}, "Superscript", SyntaxForm -> 
            SuperscriptBox]}, "RowWithSeparators"], TraditionalForm], {0.01, 
        0.}}, {55.262042231857095`, 
        FormBox[
         TemplateBox[{"\[Times]", "\"\[Times]\"", "1", 
           
           TemplateBox[{"10", "24"}, "Superscript", SyntaxForm -> 
            SuperscriptBox]}, "RowWithSeparators"], TraditionalForm], {0.01, 
        0.}}, {56.8714801442912, 
        FormBox[
         TemplateBox[{"\[Times]", "\"\[Times]\"", "5", 
           
           TemplateBox[{"10", "24"}, "Superscript", SyntaxForm -> 
            SuperscriptBox]}, "RowWithSeparators"], TraditionalForm], {0.01, 
        0.}}, {57.564627324851145`, 
        FormBox[
         TemplateBox[{"\[Times]", "\"\[Times]\"", "1", 
           
           TemplateBox[{"10", "25"}, "Superscript", SyntaxForm -> 
            SuperscriptBox]}, "RowWithSeparators"], TraditionalForm], {0.01, 
        0.}}, {52.266309958303104`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       52.44863151509706, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       52.602782194924316`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       52.73631358754884, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       52.85409662320522, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       53.652604319423, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       54.05806942753116, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       54.34575149998294, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       54.751216608091106`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       54.90536728791837, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       55.038898680542886`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       55.15668171619927, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       55.95518941241704, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       56.36065452052521, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       56.64833659297699, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       57.05380170108515, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       57.20795238091241, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       57.34148377353693, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       57.459266809193316`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       58.257774505411085`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       58.66323961351925, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       58.95092168597103, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       59.17406523728524, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}}, {{
       52.95945713886305, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.01, 0.}}, {
       54.568895051297154`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.01, 0.}}, {
       55.262042231857095`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.01, 0.}}, {
       56.8714801442912, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.01, 0.}}, {
       57.564627324851145`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.01, 0.}}, {
       52.266309958303104`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       52.44863151509706, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       52.602782194924316`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       52.73631358754884, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       52.85409662320522, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       53.652604319423, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       54.05806942753116, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       54.34575149998294, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       54.751216608091106`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       54.90536728791837, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       55.038898680542886`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       55.15668171619927, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       55.95518941241704, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       56.36065452052521, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       56.64833659297699, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       57.05380170108515, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       57.20795238091241, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       57.34148377353693, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       57.459266809193316`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       58.257774505411085`, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       58.66323961351925, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       58.95092168597103, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}, {
       59.17406523728524, 
        FormBox[
         TemplateBox[{0., 0.}, "Spacer2"], TraditionalForm], {0.005, 0.}}}}}],
  
  GridLines->{{54.568895051297154`, 55.262042231857095`, 56.8714801442912, 
    57.564627324851145`}, Automatic},
  GridLinesStyle->Directive[
    GrayLevel[0.5, 0.4]],
  ImagePadding->All,
  ImageSize->400,
  Method->{
   "DefaultBoundaryStyle" -> Automatic, 
    "DefaultGraphicsInteraction" -> {
     "Version" -> 1.2, "TrackMousePosition" -> {True, False}, 
      "Effects" -> {
       "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, 
        "Droplines" -> {
         "freeformCursorMode" -> True, 
          "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultMeshStyle" -> 
    AbsolutePointSize[6], "ScalingFunctions" -> None},
  PlotRange->{{52.959461744033234`, 57.56462271968096}, {0, 200}},
  PlotRangeClipping->True,
  PlotRangePadding->{{
     Scaled[0.02], 
     Scaled[0.02]}, {0, 0}},
  Ticks->{Quiet[
     Charting`ScaledTicks[{Log, Exp}][#, #2, {6, 6}]]& , 
    Automatic}]], "Output",
 CellChangeTimes->{
  3.860661087725769*^9, {3.860661173107295*^9, 3.86066123431184*^9}, 
   3.860661296901709*^9, {3.86066135665633*^9, 3.8606613985288877`*^9}, 
   3.860661443251356*^9, 3.8606614849290648`*^9, {3.86066156798872*^9, 
   3.8606615864174747`*^9}, {3.8606616342299023`*^9, 3.860661652763976*^9}, 
   3.860661819486496*^9},
 CellLabel->"Out[72]=",ExpressionUUID->"5b9f4fad-0511-45a2-8716-afc3382023f4"]
}, Open  ]]
},
WindowSize->{1440, 771},
WindowMargins->{{0, Automatic}, {Automatic, 0}},
PrintingCopies->1,
PrintingPageRange->{1, Automatic},
FrontEndVersion->"12.3 for Mac OS X x86 (64-bit) (July 9, 2021)",
StyleDefinitions->"Default.nb",
ExpressionUUID->"d17e2c9d-56f4-4344-9a1d-6c3760fd105c"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[558, 20, 680, 12, 73, "Text",ExpressionUUID->"47d4fbe3-762d-4eb1-bac4-7015f4eb338f"],
Cell[1241, 34, 1808, 49, 79, "Text",ExpressionUUID->"5811daa7-a200-478a-ab40-602e7a80d388"],
Cell[3052, 85, 954, 18, 112, "Text",ExpressionUUID->"b42d87dc-c063-4fc7-9791-3433843c7cd8"],
Cell[CellGroupData[{
Cell[4031, 107, 14489, 398, 958, "Input",ExpressionUUID->"ea4d5d8c-6a7f-4e75-8b06-1a39586fce4c"],
Cell[18523, 507, 1530, 31, 69, "Output",ExpressionUUID->"20ff20a4-af8b-4b39-8fd9-c1fa188d18f6"],
Cell[20056, 540, 26823, 554, 278, "Output",ExpressionUUID->"c139e6f2-848c-4247-9352-7cedd5b0bf8e"]
}, Open  ]],
Cell[46894, 1097, 887, 18, 79, "Text",ExpressionUUID->"36734f63-26d2-4abf-a77e-4a5741f54431"],
Cell[CellGroupData[{
Cell[47806, 1119, 7452, 220, 764, "Input",ExpressionUUID->"88ef0115-a65a-4b74-82fd-6cfab32520af"],
Cell[55261, 1341, 1103, 15, 34, "Output",ExpressionUUID->"6507a091-7ce1-4fc0-80ce-f872653044da"],
Cell[56367, 1358, 1104, 15, 34, "Output",ExpressionUUID->"a455a321-c6ce-4ac3-ac8b-6f687142595d"],
Cell[57474, 1375, 1106, 15, 34, "Output",ExpressionUUID->"49349326-baee-42d2-9429-d33b35f3419c"]
}, Open  ]],
Cell[58595, 1393, 1176, 21, 112, "Text",ExpressionUUID->"3c1e54bc-d67f-40e6-b407-7c6f69407530"],
Cell[CellGroupData[{
Cell[59796, 1418, 11868, 329, 904, "Input",ExpressionUUID->"af703dc1-13cc-46bf-bbe7-85b422f712ad"],
Cell[71667, 1749, 13549, 314, 338, "Output",ExpressionUUID->"045b9cab-0213-49c9-a0fb-3ff3fa37941d"]
}, Open  ]],
Cell[85231, 2066, 1090, 20, 112, "Text",ExpressionUUID->"6b9913d9-0165-44e2-b8a4-397dafaaf2e0"],
Cell[86324, 2088, 1034, 15, 46, "Text",ExpressionUUID->"be544686-f884-4593-990a-280e87fa18a2"],
Cell[CellGroupData[{
Cell[87383, 2107, 2161, 59, 157, "Input",ExpressionUUID->"c39d805c-27e5-4bca-a062-bcd37ad74dba"],
Cell[89547, 2168, 607, 14, 62, "Output",ExpressionUUID->"fe4a36f1-631c-4be8-ad2b-d15a04dc72a6"]
}, Open  ]],
Cell[90169, 2185, 1116, 16, 46, "Text",ExpressionUUID->"2ee30d05-6da7-456a-bd7c-eba35da587b2"],
Cell[CellGroupData[{
Cell[91310, 2205, 10185, 253, 723, "Input",ExpressionUUID->"76d70526-8da2-4653-b6b4-b144b6617303"],
Cell[101498, 2460, 17252, 373, 302, "Output",ExpressionUUID->"5b9f4fad-0511-45a2-8716-afc3382023f4"]
}, Open  ]]
}
]
*)