Coupling Coefficients
The Wigner 3-j, 6-j and 9-j symbols give the coupling coefficients
for combined angular momentum vectors. Since the arguments of the
standard coupling coefficient functions are integer or half-integer,
the arguments of the following functions are, by convention,
integers equal to twice the actual spin value. For information on
the 3-j coefficients see Abramowitz & Stegun, Section 27.9.
-
gsl_sf_coupling_3j(two_ja, two_jb, two_jc, two_ma, two_mb, two_mc)
These routines compute the Wigner 3-j coefficient,
\[\begin{split}\left( \begin{array}{ccc}
ja & jb & jc \\
ma & mb & mc
\end{array} \right)\end{split}\]
where the arguments are given in half-integer units, ja = two_ja / 2,
ma = two_ma / 2, etc.
-
gsl_sf_coupling_6j(two_ja, two_jb, two_jc, two_jd, two_je, two_jf)
These routines compute the Wigner 6-j coefficient,
\[\begin{split}\left( \begin{array}{ccc}
ja & jb & jc \\
jd & je & jf
\end{array} \right)\end{split}\]
where the arguments are given in half-integer units, ja = two_ja / 2,
jb = two_jb / 2, etc.
-
gsl_sf_coupling_9j(two_ja, two_jb, two_jc, two_jd, two_je, two_jf, two_jg, two_jh, two_ji)
These routines compute the Wigner 9-j coefficient,
\[\begin{split}\left( \begin{array}{ccc}
ja & jb & jc \\
jd & je & jf \\
jg & jh & ji
\end{array} \right)\end{split}\]
where the arguments are given in half-integer units, ja = two_ja / 2,
jb = two_jb / 2, etc.