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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[ 109436, 3015]*) (*NotebookOutlinePosition[ 110975, 3062]*) (* CellTagsIndexPosition[ 110709, 3052]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Nuclear convolution", "Title", Background->RGBColor[0.501961, 0.74902, 0.74902]], Cell[BoxData[{ \(Clear["\"]\), "\n", \(\(\(<< Graphics`\)\(\[IndentingNewLine]\) \) (*\ << Graphics`Arrow`\ *) \), "\n", \(<< Graphics`MultipleListPlot`\), "\n", \(<< Graphics`Legend`\), "\[IndentingNewLine]", \( (*\ << Statistics`DataManipulation`\ *) \)}], "Input"], Cell[BoxData[{ 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\[IndentingNewLine]x^2* f0LT[xi, q2, p2]/\((xi^2\ tau^1.5)\)\ + \ 6*p2*x^3/\((q2*tau^2)\)*\ tmcint[f1LT, xi, q2, p2]\[IndentingNewLine])\);\)\), "\[IndentingNewLine]", \(\(TMC1[xf1LT_, f2LT_, x_?NumberQ, q2_?NumberQ, p2_?NumberQ]\ := \ \((tau = 1 + 4\ p2\ x^2/q2; \ xi = 2\ x/\((1 + Sqrt[tau])\); \[IndentingNewLine]x^2* xf1LT[xi, q2, p2]/\((xi^2*\ tau^0.5)\)\ + \ \ p2* x^3/\((q2*tau)\)* tmcint[f2LT, xi, q2, p2]\ \[IndentingNewLine])\);\)\), "\[IndentingNewLine]", \(\(TMC3[xf3LT_, f2LT_, x_?NumberQ, q2_?NumberQ, p2_?NumberQ]\ := \ \((tau = 1 + 4\ p2\ x^2/q2; \ xi = 2\ x/\((1 + Sqrt[tau])\); \[IndentingNewLine]x^2* xf3LT[xi, q2, p2]/\((xi^2*\ tau)\)\ + \ 2*p2*x^3/\((q2*tau^1.5)\)*\ tmcint[f2LT, xi, q2, p2]\[IndentingNewLine])\);\)\ \)}], "Input"], Cell[TextData[{ "Expansion of GP TMC expressions in powers of ", Cell[BoxData[ \(TraditionalForm\`1/Q\^2\)]], ".\nWe keep only ", Cell[BoxData[ \(TraditionalForm\`1/Q\^2\)]], " term" }], "Text", Background->GrayLevel[0.900008]], Cell[BoxData[{ 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For more information type ?setdeuteron, psi, ed."\)], \ "Print"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(?\ setdeuteron\ psi\ ed\)\)], "Input"], Cell[BoxData[ \("setdeuteron[type] defines the definitions for the Paris (type=1) and \ the Bonn (type=2) deuteron wave function"\)], "Print", CellTags->"Info3384088821-2440563"], Cell[BoxData[ \("psi[space,l,r] is the s-wave (l=0) or d-wave (l=2) deuteron wave \ function in configuration space (space=1, in this case r is relative nucleon \ separation in Fm) or momentum space (space=0, in this case r is momentum in \ 1/Fm)."\)], "Print", CellTags->"Info3384088821-1378630"], Cell[BoxData[ \("Deuteron binding energy in 1/Fm."\)], "Print", CellTags->"Info3384088821-7327584"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(setdeuteron[1];\)\)], "Input"], Cell[BoxData[ \("Setting up the Paris wave function..."\)], "Print"], Cell[BoxData[ \("Done."\)], "Print"] }, Open ]], Cell[TextData[{ "Deuteron binding energy eD (in ", Cell[BoxData[ \(TraditionalForm\`fm\^\(-1\)\)]], ") and momentum distribution ", Cell[BoxData[ FormBox[ RowBox[{\(\(n\_d\)(k, \ cos\[Theta])\), "=", RowBox[{"|", RowBox[{\(\[CapitalPsi]\_d\), "(", StyleBox["k", FontWeight->"Bold"], ")"}], \( | \^2\)}]}], TraditionalForm]]], " " }], "Text", Background->GrayLevel[0.900008]], Cell[BoxData[ \(\(eD = ed\ ;\)\)], "Input"], Cell[BoxData[{ \(\(psi0[k_] := psi[0, 0, k];\)\), "\[IndentingNewLine]", \(\(psi2[k_] := psi[0, 2, k];\)\)}], "Input"], Cell[BoxData[ \(\(ndParis[k_, y_]\ := psi0[k]^2 + psi2[k]^2\ ;\)\)], "Input"], Cell["Mean momentum squared and separation energy in the deuteron:", "Text", Background->GrayLevel[0.900008]], Cell[BoxData[{ \(\(ksqD = NIntegrate[\ k^4*ndParis[k, y], {k, 0, 7. }, {PrecisionGoal\ -> \ 5}];\)\), "\[IndentingNewLine]", \(\(ekinD = ksqD/\((2 mN)\);\)\), "\[IndentingNewLine]", \(\(epsD = eD - ekinD;\)\), "\[IndentingNewLine]", \(\(virD = 2*\((epsD - ekinD)\)/mN;\)\)}], "Input"], Cell["Deuteron elastic form-factor SD", "Text", Background->GrayLevel[0.900008]], Cell[BoxData[ RowBox[{"(*", "\[IndentingNewLine]", RowBox[{\(zmn = 0\), ";", "\n", \(zmx = 1\), ";", "\n", RowBox[{\(SD[k_?NumericQ, wf2_]\), ":=", RowBox[{"Block", "[", RowBox[{\({r = Log[1/z]}\), ",", "\[IndentingNewLine]", RowBox[{ "NIntegrate", "[", \(wf2[r]*Sin[k*r]/\((k*r*z)\), \ {z, zmn, zmx}, MaxRecursion \[Rule] 30, PrecisionGoal \[Rule] 4\), StyleBox[" ", "MR"], "]"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", "*)"}]], "Input"], Cell["Mean nucleon light-cone momentum in the deuteron:", "Text", Background->GrayLevel[0.900008]], Cell[CellGroupData[{ Cell[BoxData[ \(1 + \((epsD + 2/3*ekinD)\)/mN\)], "Input"], Cell[BoxData[ \(0.9942862203934701`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(virD\)], "Input"], Cell[BoxData[ \(\(-0.04487214988918641`\)\)], "Output"] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell["Off-shell corrections", "Section", Background->RGBColor[0.533333, 0.768627, 1]], Cell["\<\ Generic off-shell correction. 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