22.2 Evaluation
257
j1
j2
j12
j3
J
j23
jj6j
__
___
___
__
___
___
_______
1
0.5
0.5
2
2.5
1.5
-0.2582
1
0.5
0.5
2
2.5
2.5
0.1972
1
0.5
1.5
2
2.5
1.5
0.17078
1
0.5
1.5
2
2.5
2.5
0.14907
Please note that the total angular momentum J is on table position “5” and
the third angular momentum j 3 we want to couple is on position “4”. The
output arguments are the object “obj” with properties “JJ6j”, a table of the
corresponding values and property “info” with some general information, and
“er” an array of the corresponding values.
22.2.3 Wigner 9j-Symbols
Wigner 9j-symbols can be evaluated with the SPECFUNPHYS class jj9j with
syntax [obj, er] = jj9j(j1,j2,j3,j4) to evaluate all possible 9jsymbols based on the coupling angular momenta (j 1 , j 2 , j 3 , j 4 ) and
[obj, er] = jj9j(j1,j2,j3,j4, J) restricted to the total angular
momentum J ; with
[obj, er] = jj9j(j11,j12,j13, j21,j22,j23, j31,j32,j33)
the corresponding single value will be computed. The output arguments are the
object “obj” with property “JJ9j”, a table of the corresponding values of the Wigner
9j-symbol and property “info” with some general information, and array “er”, an
array with the values of the 9j-symbol. The computation is based on Eq. (22.16).
Please note that the angular momenta (j 1 , j 2 , j 3 , j 4 ) are on position “j11”, “j12”,
“j21”, “j22” and the total angular momenta “J” is on table position “j33”.
Example
>> obj=jj9j(1,2,0.5,1.5,0)
% j1=j11=1,j2=j12=2,j21=j3=0.5,j22=j4=1.5,j33=J=0
>> obj.JJ9j
ans =
4x10 table
j11 j12 j13 j21 j22 j23 j31 j32 j33
jj9j
___ ___ ___ ___ ___ ___ ___ ___ ___ _________
1
2
1
0.5 1.5
1
0.5 0.5
0
0.11785
1
2
1
0.5 1.5
1
1.5 1.5
0
0.058926
1
2
2
0.5 1.5
2
0.5 0.5
0
0.070711
1
2
2
0.5 1.5
2
1.5 1.5
0 -0.035355