[Wien] the integration of product of 3 spherical harmonics (Gaunt coefficients)

[Maurits W. Haverkort]

Dear Fatemeh

The integral <Y_{l,m} | C_{k,q} | Y_{lp,mp}> = (-1)^{-m} [l,lp]^{1/2}
3J(l,k,lp,0,0,0) 3J(l,k,lp,-m,q,mp)

Where 3J are the 3J symbols (
http://mathworld.wolfram.com/Wigner3j-Symbol.html )
and C_{l,m}=(4 \pi)/[l])^{1/2} Y_{l,m}
and [l]=2l+1
        [l,lp]=(2l+1)(2lp+1)

i.e. these integrals are closed analytical expressions See Cowan (the
theory of atomic structure and spectra) for example or Google a bit on
3J symbols.

Maurits

PS both Mathematica and Mapel can do these things analytically

PS2 see http://en.wikipedia.org/wiki/3-jm_symbol


fatemeh.mirjani wrote:
> Dear Users;
>
> Would you mind please guiding me to calculate the integration of product of 3 spherical harmonics (Gaunt coefficients)?
> I found in SRC_lapw1/atpar.F gaunt coefficients but no subroutine. but I need the subroutine of calculation of this integral.Is there anyone that has this subroutine?
>
> Any help is appreciated.
>
>