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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 23341, 499]*) (*NotebookOutlinePosition[ 23982, 522]*) (* CellTagsIndexPosition[ 23938, 518]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ StyleBox[\(E/A\ In\ CR\ with\ 3\ Constants\), "Section"], "\[IndentingNewLine]"}], "\[IndentingNewLine]", \(E1const\ = \ \((\((g \ - 1)\)\ alfa\ m^2\ /\((3\ Pi\ M)\))\) \((M\ m/\((\ 4 Pi)\))\)\)}], "Input"], Cell[BoxData[ \(\(alfa\ \((\(-1\) + g)\)\ m\^3\)\/\(12\ \[Pi]\^2\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(E1overA\ = \ E1const\ \((\ C01\ x^3\ + \ \((\ 3/10)\) m^2\ \((C21\ - \ C01/Lc^2)\)\ x^5\ + \ \((9/140)\) m^4\ \((\ \(-2\)\ C21/Lc^2\ + \ 2\ C41\ + \ C01/Lc^4)\)\ x^7)\)\)], "Input"], Cell[BoxData[ \(\(alfa\ \((\(-1\) + g)\)\ m\^3\ \((C01\ x\^3 + 3\/10\ \((C21 - \ C01\/Lc\^2)\)\ m\^2\ x\^5 + 9\/140\ \((2\ C41 + C01\/Lc\^4 - \(2\ \ C21\)\/Lc\^2)\)\ m\^4\ x\^7)\)\)\/\(12\ \[Pi]\^2\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(E2const\ = \ \(-\((\((g - 1)\)\ alfa^2\ m^2\ /\((\ 6\ Pi\ M)\))\)\)\)], "Input"], Cell[BoxData[ \(\(-\(\(alfa\^2\ \((\(-1\) + g)\)\ m\^2\)\/\(6\ M\ \[Pi]\)\)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(x3coeff = \ \(\(\((M\ m/\((\ 4 Pi)\))\)^2\) \((\((eta/ Sqrt[Pi])\) \((2 C01\ ^2\ \ + C01\ C21\ Lc^2\ + \ \((3/8)\) Lc^4\ \((C21^2\ + \ 2\ C01\ C41)\)\ + \ \((15/16)\) Lc^6 \((C21\ C41\ + \((7/8)\)\ C41^2\ Lc^2)\))\)\ - \ 8\ Pi\ C02/\((M\ m)\))\)\(\[IndentingNewLine]\)\)\)], "Input"], Cell[BoxData[ \(\(m\^2\ M\^2\ \((\(eta\ \((2\ C01\^2 + C01\ C21\ Lc\^2 + 3\/8\ \ \((C21\^2 + 2\ C01\ C41)\)\ Lc\^4 + 15\/16\ Lc\^6\ \((C21\ C41 + \(7\ C41\^2\ \ Lc\^2\)\/8)\))\)\)\/\@\[Pi] - \(8\ C02\ \[Pi]\)\/\(m\ M\))\)\)\/\(16\ \ \[Pi]\^2\)\)], "Output"] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ \(x5coeff\ = \ \ \ \((M\ m/\((4 Pi)\))\)^2 \((9/ 10)\) \((\((1/\((eta\ Sqrt[Pi])\))\) \((\(-2\) C01^2\ \ + \ C01\ C21\ Lc^2\ + \ \((1/8)\) Lc^4 \((C21^2\ + \ 2\ C01\ C41)\)\ + \ \((3/16)\) Lc^6 \((C21\ C41\ + \ \((5/8)\) C41^2 Lc^2)\)\ )\)\ - \ \((\ 8\ Pi\ m/\((3 M)\))\)\ \((C22\ - \ C02/Lc^2)\))\)\)], "Input"], Cell[BoxData[ \(\(\(1\/\(160\ \[Pi]\^2\)\)\((9\ m\^2\ M\^2\ \((\(\(-2\)\ C01\^2 + C01\ \ C21\ Lc\^2 + 1\/8\ \((C21\^2 + 2\ C01\ C41)\)\ Lc\^4 + 3\/16\ Lc\^6\ \((C21\ \ C41 + \(5\ C41\^2\ Lc\^2\)\/8)\)\)\/\(eta\ \@\[Pi]\) - \(\(1\/\(3\ M\)\)\((8\ \ m\ \[Pi]\ \((\(-\(\(1\/\(Lc\^2\ m\ M\)\)\((4\ \((\(-\(1\/2\)\) + \(\(1\/\(256\ \ \@\[Pi]\)\)\((eta\ \((256 + 32\ \((4\ \((1 - 2\ eta\^2)\) + 3\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\))\) + 3\ \((16\ \((1 - 2\ eta\^2)\)\^2 + 40\ \((1 - 2\ eta\^2)\)\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\) + 35\ \((1\/2 - 2\ eta\^2 + 3\ \ eta\^4)\)\^2)\))\))\)\))\)\ \[Pi])\)\)\) + \(\(1\/\(Lc\^2\ m\ M\)\)\((4\ \ \((\(-\(1\/2\)\) + \(5\ eta\^2\)\/2 + \(\(1\/\(256\ \@\[Pi]\)\)\((eta\ \((256 \ + 32\ \((4\ \((1 - 2\ eta\^2)\) + 3\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\))\) + 3\ \((16\ \((1 - 2\ eta\^2)\)\^2 + 40\ \((1 - 2\ eta\^2)\)\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\) + 35\ \((1\/2 - 2\ eta\^2 + 3\ \ eta\^4)\)\^2)\) + 3\ \((\(-256\) + 16\ \((1 - 2\ eta\^2)\)\^2 + 24\ \((1 - 2\ eta\^2)\)\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\) + 15\ \((1\/2 - 2\ eta\^2 + 3\ \ eta\^4)\)\^2 + 32\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4 + 4\ \((1 - 2\ eta\^2)\))\))\))\))\)\))\)\ \[Pi])\ \)\))\))\)\))\))\)\)\)], "Output"] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ \(x7coeff\ = \ \((M\ m/\((4\ Pi)\))\)^2 \((69/ 140)\) \((\((1/\((eta^3\ Sqrt[Pi])\))\) \((2\ C01^2\ - \ 3\ C01\ C21\ Lc^2\ + \ \((3/8)\) Lc^4\ \((C21^2\ + \ 2 C01\ C41)\)\ + \((3/16)\) Lc^6 \((C21\ C41\ + \ \((3/8)\) C41^2\ Lc^2)\))\)\ - \((24/ 23)\) \((Pi\ m^3/M)\) \((\(-2\)\ C22/Lc^2\ + \ 2\ C42\ + \ C02/Lc^4)\))\)\)], "Input"], Cell[BoxData[ \(\(\(1\/\(2240\ \[Pi]\^2\)\)\((69\ m\^2\ M\^2\ \((\(2\ C01\^2 - 3\ C01\ \ C21\ Lc\^2 + 3\/8\ \((C21\^2 + 2\ C01\ C41)\)\ Lc\^4 + 3\/16\ Lc\^6\ \((C21\ \ C41 + \(3\ C41\^2\ Lc\^2\)\/8)\)\)\/\(eta\^3\ \@\[Pi]\) - \(\(1\/\(23\ \ M\)\)\((24\ m\^3\ \[Pi]\ \((\(\(1\/\(Lc\^4\ m\ M\)\)\((4\ \((\(-\(1\/2\)\) + \ \(\(1\/\(256\ \@\[Pi]\)\)\((eta\ \((256 + 32\ \((4\ \((1 - 2\ eta\^2)\) + 3\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\))\) + 3\ \((16\ \((1 - 2\ eta\^2)\)\^2 + 40\ \((1 - 2\ eta\^2)\)\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\) + 35\ \((1\/2 - 2\ eta\^2 + 3\ \ eta\^4)\)\^2)\))\))\)\))\)\ \[Pi])\)\) - \(\(1\/\(Lc\^4\ m\ M\)\)\((8\ \((\(-\ \(1\/2\)\) + \(5\ eta\^2\)\/2 + \(\(1\/\(256\ \@\[Pi]\)\)\((eta\ \((256 + 32\ \((4\ \((1 - 2\ eta\^2)\) + 3\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\))\) + 3\ \((16\ \((1 - 2\ eta\^2)\)\^2 + 40\ \((1 - 2\ eta\^2)\)\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\) + 35\ \((1\/2 - 2\ eta\^2 + 3\ \ eta\^4)\)\^2)\) + 3\ \((\(-256\) + 16\ \((1 - 2\ eta\^2)\)\^2 + 24\ \((1 - 2\ eta\^2)\)\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\) + 15\ \((1\/2 - 2\ eta\^2 + 3\ \ eta\^4)\)\^2 + 32\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4 + 4\ \((1 - 2\ eta\^2)\))\))\))\))\)\))\)\ \[Pi])\ \)\) + \(\(1\/\(Lc\^4\ m\ M\)\)\((8\ \((\(-\(1\/4\)\) + \(5\ eta\^2\)\/2 - 7\ eta\^4 + \(\(1\/\(256\ \@\[Pi]\)\)\((eta\ \((3\ \ \((\(-256\) + 16\ \((1 - 2\ eta\^2)\)\^2 + 24\ \((1 - 2\ eta\^2)\)\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\) + 15\ \((1\/2 - 2\ eta\^2 + 3\ \ eta\^4)\)\^2 + 32\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4 + 4\ \((1 - 2\ eta\^2)\))\))\) + 23\/6\ \((256 + 96\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4 - 4\ \((1 - 2\ eta\^2)\))\) + 3\ \((16\ \((1 - 2\ eta\^2)\)\^2 + 8\ \((1 - 2\ eta\^2)\)\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\) + 3\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\)\ \^2)\))\) + 1\/2\ \((256 + 32\ \((4\ \((1 - 2\ eta\^2)\) + 3\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\))\) + 3\ \((16\ \((1 - 2\ eta\^2)\)\^2 + 40\ \((1 - 2\ eta\^2)\)\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\) + 35\ \((1\/2 - 2\ eta\^2 + 3\ \ eta\^4)\)\^2)\))\))\))\)\))\)\ \[Pi])\)\))\))\)\))\))\)\)\)], "Output"] }, Closed]], Cell[BoxData[ \(\(x4coeff\ = \ \(-\((M\ m/\((4 Pi)\))\)^2\) C01^2\ \((12/\((35\ Pi)\))\) \((11\ - \ 2\ Log[2])\);\)\)], "Input"], Cell[BoxData[ \(\(x6coeff\ = \ \(-\ \((M\ m\ /\((4 Pi)\))\)^2\) m^2\ \((C01\ C21\ - \ C01^2/Lc^2)\)\ \((8/\((105\ Pi)\))\) \((167/3\ \ - \ 8\ Log[2])\);\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(E2overA = E2const \((\ x3coeff\ x^3 + x4coeff\ x^4 + x5coeff\ x^5 + x6coeff\ x^6 + x7coeff\ x^7)\)\)], "Input"], Cell[BoxData[ \(\(-\(\(1\/\(6\ M\ \[Pi]\)\)\((alfa\^2\ \((\(-1\) + g)\)\ m\^2\ \((\(\(1\/\(16\ \[Pi]\^2\)\)\((m\^2\ M\^2\ \((\(eta\ \ \((2\ C01\^2 + C01\ C21\ Lc\^2 + 3\/8\ \((C21\^2 + 2\ C01\ C41)\)\ Lc\^4 + \ 15\/16\ Lc\^6\ \((C21\ C41 + \(7\ C41\^2\ Lc\^2\)\/8)\))\)\)\/\@\[Pi] - \(\(1\ \/\(m\^2\ M\^2\)\)\((32\ \((\(-\(1\/2\)\) + \(\(1\/\(256\ \@\[Pi]\)\)\((eta\ \ \((256 + 32\ \((4\ \((1 - 2\ eta\^2)\) + 3\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\))\) + 3\ \((16\ \((1 - 2\ eta\^2)\)\^2 + 40\ \((1 - 2\ eta\^2)\)\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\) + 35\ \((1\/2 - 2\ eta\^2 + 3\ \ eta\^4)\)\^2)\))\))\)\))\)\ \[Pi]\^2)\)\))\)\ x\^3)\)\) + \(\(1\/\(160\ \[Pi]\ \^2\)\)\((9\ m\^2\ M\^2\ \((\(\(-2\)\ C01\^2 + C01\ C21\ Lc\^2 + 1\/8\ \((C21\ \^2 + 2\ C01\ C41)\)\ Lc\^4 + 3\/16\ Lc\^6\ \((C21\ C41 + \(5\ C41\^2\ \ Lc\^2\)\/8)\)\)\/\(eta\ \@\[Pi]\) - \(\(1\/\(3\ M\)\)\((8\ m\ \[Pi]\ \((\(-\(\ \(1\/\(Lc\^2\ m\ M\)\)\((4\ \((\(-\(1\/2\)\) + \(\(1\/\(256\ \ \@\[Pi]\)\)\((eta\ \((256 + 32\ \((4\ \((1 - 2\ eta\^2)\) + 3\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\))\) + 3\ \((16\ \((1 - 2\ eta\^2)\)\^2 + 40\ \((1 - 2\ eta\^2)\)\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\) + 35\ \((1\/2 - 2\ eta\^2 + 3\ \ eta\^4)\)\^2)\))\))\)\))\)\ \[Pi])\)\)\) + \(\(1\/\(Lc\^2\ m\ M\)\)\((4\ \ \((\(-\(1\/2\)\) + \(5\ eta\^2\)\/2 + \(\(1\/\(256\ \@\[Pi]\)\)\((eta\ \((256 \ + 32\ \((4\ \((1 - 2\ eta\^2)\) + 3\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\))\) + 3\ \((16\ \((1 - 2\ eta\^2)\)\^2 + 40\ \((1 - 2\ eta\^2)\)\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\) + 35\ \((1\/2 - 2\ eta\^2 + 3\ \ eta\^4)\)\^2)\) + 3\ \((\(-256\) + 16\ \((1 - 2\ eta\^2)\)\^2 + 24\ \((1 - 2\ eta\^2)\)\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\) + 15\ \((1\/2 - 2\ eta\^2 + 3\ \ eta\^4)\)\^2 + 32\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4 + 4\ \((1 - 2\ eta\^2)\))\))\))\))\)\))\)\ \[Pi])\ \)\))\))\)\))\)\ x\^5)\)\) + \(\(1\/\(2240\ \[Pi]\^2\)\)\((69\ m\^2\ M\^2\ \ \((\(2\ C01\^2 - 3\ C01\ C21\ Lc\^2 + 3\/8\ \((C21\^2 + 2\ C01\ C41)\)\ Lc\^4 \ + 3\/16\ Lc\^6\ \((C21\ C41 + \(3\ C41\^2\ Lc\^2\)\/8)\)\)\/\(eta\^3\ \@\[Pi]\ \) - \(\(1\/\(23\ M\)\)\((24\ m\^3\ \[Pi]\ \((\(\(1\/\(Lc\^4\ m\ M\)\)\((4\ \ \((\(-\(1\/2\)\) + \(\(1\/\(256\ \@\[Pi]\)\)\((eta\ \((256 + 32\ \((4\ \((1 - 2\ eta\^2)\) + 3\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\))\) + 3\ \((16\ \((1 - 2\ eta\^2)\)\^2 + 40\ \((1 - 2\ eta\^2)\)\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\) + 35\ \((1\/2 - 2\ eta\^2 + 3\ \ eta\^4)\)\^2)\))\))\)\))\)\ \[Pi])\)\) - \(\(1\/\(Lc\^4\ m\ M\)\)\((8\ \((\(-\ \(1\/2\)\) + \(5\ eta\^2\)\/2 + \(\(1\/\(256\ \@\[Pi]\)\)\((eta\ \((256 + 32\ \((4\ \((1 - 2\ eta\^2)\) + 3\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\))\) + 3\ \((16\ \((1 - 2\ eta\^2)\)\^2 + 40\ \((1 - 2\ eta\^2)\)\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\) + 35\ \((1\/2 - 2\ eta\^2 + 3\ \ eta\^4)\)\^2)\) + 3\ \((\(-256\) + 16\ \((1 - 2\ eta\^2)\)\^2 + 24\ \((1 - 2\ eta\^2)\)\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\) + 15\ \((1\/2 - 2\ eta\^2 + 3\ \ eta\^4)\)\^2 + 32\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4 + 4\ \((1 - 2\ eta\^2)\))\))\))\))\)\))\)\ \[Pi])\ \)\) + \(\(1\/\(Lc\^4\ m\ M\)\)\((8\ \((\(-\(1\/4\)\) + \(5\ eta\^2\)\/2 - 7\ eta\^4 + \(\(1\/\(256\ \ \@\[Pi]\)\)\((eta\ \((3\ \((\(-256\) + 16\ \((1 - 2\ eta\^2)\)\^2 + 24\ \((1 - 2\ eta\^2)\)\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\) + 15\ \((1\/2 - 2\ eta\^2 + 3\ \ eta\^4)\)\^2 + 32\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4 + 4\ \((1 - 2\ eta\^2)\))\))\) + 23\/6\ \((256 + 96\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4 - 4\ \((1 - 2\ eta\^2)\))\) + 3\ \((16\ \((1 - 2\ eta\^2)\)\^2 + 8\ \((1 - 2\ eta\^2)\)\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\) + 3\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\)\ \^2)\))\) + 1\/2\ \((256 + 32\ \((4\ \((1 - 2\ eta\^2)\) + 3\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\))\) + 3\ \((16\ \((1 - 2\ eta\^2)\)\^2 + 40\ \((1 - 2\ eta\^2)\)\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\) + 35\ \((1\/2 - 2\ eta\^2 + 3\ \ eta\^4)\)\^2)\))\))\))\)\))\)\ \[Pi])\)\))\))\)\))\)\ x\^7)\)\) - \(\((C01\ \ C21 - C01\^2\/Lc\^2)\)\ m\^4\ M\^2\ x\^6\ \((167\/3 - 8\ Log[2])\)\)\/\(210\ \ \[Pi]\^3\) - \(3\ C01\^2\ m\^2\ M\^2\ x\^4\ \((11 - 2\ Log[2])\)\)\/\(140\ \ \[Pi]\^3\))\))\)\)\)\)], "Output"] }, Closed]], Cell[BoxData[ RowBox[{"\[IndentingNewLine]", StyleBox[\(checking\ the\ coefficients\), "Subsection"]}]], "Input"], Cell[BoxData[ \(\(c2t\ = \ 1 - \ 2\ eta^2;\)\)], "Input"], Cell[BoxData[ \(\(c4t\ = \ 3\ eta^4\ - \ 2 eta^2\ + \ 1/2;\)\)], "Input"], Cell[BoxData[ \(\(B\ = \ eta/\((256\ Sqrt[Pi])\);\)\)], "Input"], Cell[BoxData[ \(\(\(h0\ = \ 256\ + \ 32\ \((\ 4 c2t\ + \ 3 c4t)\)\ + \ 3\ \((16 c2t^2\ + \ 40\ c2t\ c4t\ + \ 35\ c4t^2)\);\)\(\[IndentingNewLine]\)\)\)], "Input"], Cell[BoxData[ \(\(\(h2\ = \ 3\ \((\ \(-256\)\ + \ 32\ \((4 c2t\ + \ c4t\ )\)\ + \ \ 16\ c2t^2\ + \ 24\ c2t\ c4t\ + \ 15\ c4t^2)\);\)\(\[IndentingNewLine]\)\(\[IndentingNewLine]\)\)\ \)], "Input"], Cell[BoxData[ \(\(h4\ = \ \((23/6)\) \((\ 256\ + \ 96\ \((\ \(-4\) c2t\ + \ c4t)\)\ + \ 3 \((16 c2t^2\ + \ 8\ c2t\ c4t\ + \ 3\ c4t^2)\))\);\)\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(C02\ = \ \((4 Pi/\((M\ m)\))\) \((\ \(-1\)/2\ + \ h0\ B)\)\)], "Input"], Cell[BoxData[ \(\(\(1\/\(m\ M\)\)\((4\ \((\(-\(1\/2\)\) + \(\(1\/\(256\ \ \@\[Pi]\)\)\((eta\ \((256 + 32\ \((4\ \((1 - 2\ eta\^2)\) + 3\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\))\) + 3\ \((16\ \((1 - 2\ eta\^2)\)\^2 + 40\ \((1 - 2\ eta\^2)\)\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\) + 35\ \((1\/2 - 2\ eta\^2 + 3\ \ eta\^4)\)\^2)\))\))\)\))\)\ \[Pi])\)\)\)], "Output"] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(C22\ = \ \((4\ Pi/\((M\ m)\))\) \((\ \(-1\)/ 2\ + \ 5\ eta^2\ /2\ + \ B \((\ h0\ + \ h2)\))\)/ Lc^2\)\)\)], "Input"], Cell[BoxData[ \(\(\(1\/\(Lc\^2\ m\ M\)\)\((4\ \((\(-\(1\/2\)\) + \(5\ eta\^2\)\/2 + \ \(\(1\/\(256\ \@\[Pi]\)\)\((eta\ \((256 + 32\ \((4\ \((1 - 2\ eta\^2)\) + 3\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\))\) + 3\ \((16\ \((1 - 2\ eta\^2)\)\^2 + 40\ \((1 - 2\ eta\^2)\)\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\) + 35\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\)\^2)\) + 3\ \((\(-256\) + 16\ \((1 - 2\ eta\^2)\)\^2 + 24\ \((1 - 2\ eta\^2)\)\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\) + 15\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4)\)\^2 + 32\ \((1\/2 - 2\ eta\^2 + 3\ eta\^4 + 4\ \((1 - 2\ eta\^2)\))\))\))\))\)\))\)\ \[Pi])\)\ \)\)], "Output"] }, Closed]], Cell[CellGroupData[{ Cell[BoxData[ \(C42\ = \ \((4 Pi/\((M\ m)\))\) \((\(-1\)/4\ + \ 5\ eta^2/2\ - 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