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

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

(* CreatedBy='Mathematica 11.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[      3848,        135]
NotebookOptionsPosition[      3613,        122]
NotebookOutlinePosition[      3949,        137]
CellTagsIndexPosition[      3906,        134]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[{
 RowBox[{
  RowBox[{"phi", "[", 
   RowBox[{"a_", ",", "r_"}], "]"}], ":=", 
  RowBox[{
   RowBox[{
    RowBox[{"(", 
     RowBox[{"2", 
      RowBox[{"a", "/", "\[Pi]"}]}], ")"}], "^", 
    RowBox[{"(", 
     RowBox[{"3", "/", "4"}], ")"}]}], 
   RowBox[{"Exp", "[", 
    RowBox[{
     RowBox[{"-", "a"}], " ", 
     RowBox[{"r", "^", "2"}]}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"P1s", "[", 
   RowBox[{"Z_", ",", "r_"}], "]"}], ":=", 
  RowBox[{
   RowBox[{
    RowBox[{"Z", "^", 
     RowBox[{"(", 
      RowBox[{"3", "/", "2"}], ")"}]}], "/", 
    RowBox[{"Sqrt", "[", "\[Pi]", "]"}]}], 
   RowBox[{"Exp", "[", 
    RowBox[{
     RowBox[{"-", "Z"}], " ", "r"}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"P2s", "[", 
   RowBox[{"Z_", ",", "r_"}], "]"}], ":=", 
  RowBox[{
   RowBox[{
    RowBox[{"Z", "^", 
     RowBox[{"(", 
      RowBox[{"3", "/", "2"}], ")"}]}], "/", 
    RowBox[{"(", 
     RowBox[{"4", 
      RowBox[{"Sqrt", "[", 
       RowBox[{"2", "\[Pi]"}], "]"}]}], ")"}]}], 
   RowBox[{"(", 
    RowBox[{"2", "-", 
     RowBox[{"Z", " ", "r"}]}], ")"}], 
   RowBox[{"Exp", "[", 
    RowBox[{
     RowBox[{"-", "Z"}], " ", 
     RowBox[{"r", "/", "2"}]}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"sij", "[", 
   RowBox[{"a1_", ",", "a2_"}], "]"}], ":=", 
  RowBox[{
   RowBox[{"(", 
    RowBox[{"2", 
     RowBox[{
      RowBox[{"Sqrt", "[", 
       RowBox[{"a1", " ", "a2"}], "]"}], "/", 
      RowBox[{"(", 
       RowBox[{"a1", "+", "a2"}], ")"}]}]}], ")"}], "^", 
   RowBox[{"(", 
    RowBox[{"3", "/", "2"}], ")"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"hij", "[", 
   RowBox[{"a1_", ",", "a2_"}], "]"}], ":=", 
  RowBox[{
   RowBox[{"(", 
    RowBox[{
     RowBox[{"3", "a1", " ", 
      RowBox[{"a2", "/", 
       RowBox[{"(", 
        RowBox[{"a1", "+", "a2"}], ")"}]}]}], "-", 
     RowBox[{"Z", " ", 
      RowBox[{"2", "/", 
       RowBox[{"Sqrt", "[", "\[Pi]", "]"}]}], 
      RowBox[{"Sqrt", "[", 
       RowBox[{"a1", "+", "a2"}], "]"}]}]}], ")"}], 
   RowBox[{"sij", "[", 
    RowBox[{"a1", ",", "a2"}], "]"}]}]}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{"gijkl", "[", 
   RowBox[{"a1_", ",", "a2_", ",", "a3_", ",", "a4_"}], "]"}], ":=", 
  RowBox[{
   RowBox[{"16", "/", 
    RowBox[{"Sqrt", "[", "\[Pi]", "]"}]}], 
   RowBox[{
    RowBox[{
     RowBox[{"Sqrt", "[", 
      RowBox[{"a1", " ", "a2", " ", "a3", " ", "a4"}], "]"}], "^", 
     RowBox[{"(", 
      RowBox[{"3", "/", "2"}], ")"}]}], "/", 
    RowBox[{"(", 
     RowBox[{
      RowBox[{"(", 
       RowBox[{"a1", "+", "a2"}], ")"}], 
      RowBox[{"(", 
       RowBox[{"a3", "+", "a4"}], ")"}], 
      RowBox[{"Sqrt", "[", 
       RowBox[{"a1", "+", "a2", "+", "a3", "+", "a4"}], "]"}]}], 
     ")"}]}]}]}]}], "Input",
 CellChangeTimes->{{3.785683424288864*^9, 3.7856835476411333`*^9}, {
  3.785683690377933*^9, 3.785683751193809*^9}, {3.785683795834922*^9, 
  3.785683796652039*^9}, {3.78568390938768*^9, 3.7856839630681753`*^9}, {
  3.785684053484631*^9, 3.785684132733161*^9}}]
},
WindowSize->{1025, 885},
WindowMargins->{{Automatic, 204}, {Automatic, 72}},
FrontEndVersion->"11.0 for Linux x86 (64-bit) (July 28, 2016)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[558, 20, 3051, 100, 143, "Input"]
}
]
*)

(* End of internal cache information *)