(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.0' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. 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[ 76503, 2246]*) (*NotebookOutlinePosition[ 77907, 2289]*) (* CellTagsIndexPosition[ 77732, 2281]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Deuteron wave function. ", "Title", Background->RGBColor[0, 1, 0]], Cell[TextData[{ "The deuteron wave function is parameterized in a standard way as follows: \ \n ", Cell[BoxData[ FormBox[ RowBox[{\(\(\[CapitalPsi]\_m\)(r)\), " ", "=", " ", RowBox[{\(1\/\@\(4 \[Pi]\)\), RowBox[{"(", RowBox[{\(\(u(r)\)\/r\), " ", "+", " ", RowBox[{\(\(w(r)\)\/r\), FractionBox[ RowBox[{\(S\_12\), "(", OverscriptBox[ StyleBox["r", FontWeight->"Bold"], "^"], ")"}], \(\@8\)]}]}], ")"}], \(\[Chi]\_\(1 m\)\)}]}], TraditionalForm]]], ", \nwhere ", Cell[BoxData[ \(TraditionalForm\`u(r)\)]], " and ", Cell[BoxData[ \(TraditionalForm\`w(r)\)]], " are the S- and D-wave radial w.f. respectively, ", Cell[BoxData[ \(TraditionalForm\`\[Chi]\_\(1 m\)\)]], " is the spin 1 w.f. with ", Cell[BoxData[ \(TraditionalForm\`S\_z = m\)]], ", ", Cell[BoxData[ FormBox[ RowBox[{\(\(S\_12\)(r\&^)\), " ", "=", " ", RowBox[{ RowBox[{"3", RowBox[{ SubscriptBox[ StyleBox["\[Sigma]", FontWeight->"Bold"], "1"], "\[CenterDot]", \(r\&^\)}], RowBox[{ SubscriptBox[ StyleBox["\[Sigma]", FontWeight->"Bold"], "2"], "\[CenterDot]", \(r\&^\)}]}], "-", RowBox[{ SubscriptBox[ StyleBox["\[Sigma]", FontWeight->"Bold"], "1"], "\[CenterDot]", SubscriptBox[ StyleBox["\[Sigma]", FontWeight->"Bold"], "2"]}]}]}], TraditionalForm]]], " with ", Cell[BoxData[ FormBox[ RowBox[{ OverscriptBox[ StyleBox["r", FontWeight->"Bold"], "^"], "=", RowBox[{ OverscriptBox[ StyleBox["r", FontWeight->"Bold"], "\[RightArrow]"], "/", "r"}]}], TraditionalForm]]], " is the tensor operator constructed from the Pauli matrices and which \ acts as a projector onto the ", Cell[BoxData[ \(TraditionalForm\`l = 2\)]], " state. 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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->"Info3384078514-2916684"], 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->"Info3384078514-3806456"], Cell[BoxData[ \("Deuteron binding energy in 1/Fm."\)], "Print", CellTags->"Info3384078514-3739581"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(setdeuteron[1];\)\)], "Input"], Cell[BoxData[ \("Setting up the Paris wave function..."\)], "Print"], Cell[BoxData[ \("Done."\)], "Print"] }, Open ]], Cell[BoxData[{ \(\(u[r_] = psi[1, 0, r];\)\), 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SequenceForm[ "\[LeftAngleBracket]T\[RightAngleBracket] = ", 9.4534684881895803, " MeV"], Editable->False]], "Print"], Cell[BoxData[ \("Bonn:"\)], "Print"], Cell[BoxData[ InterpretationBox[\("\[LeftAngleBracket]\!\(q\^2\)\!\(\(\ \[RightAngleBracket]\_S\)\) = "\[InvisibleSpace]0.25573405964169255`\ \[InvisibleSpace]" \!\(fm\^\(-2\)\) "\), SequenceForm[ "\[LeftAngleBracket]\!\(q\^2\)\!\(\(\[RightAngleBracket]\_S\)\) = ", \ .25573405964169255, " \!\(fm\^\(-2\)\) "], Editable->False]], "Print"], Cell[BoxData[ InterpretationBox[\("\[LeftAngleBracket]\!\(q\^2\)\!\(\(\ \[RightAngleBracket]\_D\)\) = "\[InvisibleSpace]0.10581321309988684`\ \[InvisibleSpace]" \!\(fm\^\(-2\)\) "\), SequenceForm[ "\[LeftAngleBracket]\!\(q\^2\)\!\(\(\[RightAngleBracket]\_D\)\) = ", \ .10581321309988684, " \!\(fm\^\(-2\)\) "], Editable->False]], "Print"], Cell[BoxData[ InterpretationBox[\("\[LeftAngleBracket]\!\(q\^2\)/2\!\(m\_N\)\!\(\(\ \[RightAngleBracket]\_S\)\) = "\[InvisibleSpace]5.302781389059288`\ \[InvisibleSpace]" MeV"\), SequenceForm[ "\[LeftAngleBracket]\!\(q\^2\)/2\!\(m\_N\)\!\(\(\[RightAngleBracket]\_S\ \)\) = ", 5.3027813890592883, " MeV"], Editable->False]], "Print"], Cell[BoxData[ InterpretationBox[\("\[LeftAngleBracket]\!\(q\^2\)/2\!\(m\_N\)\!\(\(\ \[RightAngleBracket]\_D\)\) = "\[InvisibleSpace]2.1940931056614215`\ \[InvisibleSpace]" MeV"\), SequenceForm[ "\[LeftAngleBracket]\!\(q\^2\)/2\!\(m\_N\)\!\(\(\[RightAngleBracket]\_D\ \)\) = ", 2.1940931056614215, " MeV"], Editable->False]], "Print"], Cell[BoxData[ InterpretationBox[\("\[LeftAngleBracket]T\[RightAngleBracket] = "\ \[InvisibleSpace]7.496874494720711`\[InvisibleSpace]" MeV"\), SequenceForm[ "\[LeftAngleBracket]T\[RightAngleBracket] = ", 7.4968744947207107, " MeV"], Editable->False]], "Print"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Plots", "Subsection", Background->RGBColor[1, 1, 0]], Cell[CellGroupData[{ Cell[BoxData[ \(\(Plot[{u[r], w[r]}, {r, 0.001, 3. }\[IndentingNewLine] (*\(,\)\(Frame\ -> 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