GWI_DP Function

private function GWI_DP(J1, M1, J2, M2, L, M) result(GWI)

Geppert-Wiebicke axisymmetric coupling coefficient $I_{j_1 m_1 j_2 m_2}^{\ell m}$ (Geppert & Wiebicke, 1991), a compact shorthand for the generation/amplification amplitude of a two-mode interaction in the Hall-MHD induction equation: $$I_{j_1 m_1 j_2 m_2}^{\ell m} = \sqrt{\frac{(2j_1+1)(2j_2+1)} {4\pi(2\ell+1)}}\,\langle j_1 0\,j_2 0|\ell 0\rangle\, \langle j_1 m_1\,j_2 m_2|\ell m\rangle.$$ This is algebraically the standard Gaunt coefficient -- the closed form for $\int Y_{j_1}^{m_1}Y_{j_2}^{m_2}(Y_\ell^m)^{*}\,d\Omega$ -- written in terms of two CGCOEFF evaluations. Built entirely from CGCOEFF, which guards all selection rules, so GWI is safe to call with any integer sextuple and returns 0 for invalid combinations (unlike GWJ, see its own selection-rule note).

Returns: $I_{j_1 m_1 j_2 m_2}^{\ell m}$, complex (real-valued in practice, but returned as COMPLEX for a uniform interface with GWJ).

Arguments

Return Value complex(kind=dp)

  FUNCTION GWI_DP(J1,M1,J2,M2,L,M) RESULT(GWI)
  IMPLICIT NONE
  INTEGER(KIND=i4), INTENT(IN) :: J1
  INTEGER(KIND=i4), INTENT(IN) :: M1
  INTEGER(KIND=i4), INTENT(IN) :: J2
  INTEGER(KIND=i4), INTENT(IN) :: M2
  INTEGER(KIND=i4), INTENT(IN) :: L
  INTEGER(KIND=i4), INTENT(IN) :: M
  COMPLEX(KIND=dp) :: GWI
  GWI=DSQRT((2.d0*J1+1.d0)*(2.d0*J2+1.d0)/(2.d0*L+1.d0)/4.d0/pi)* &
    CGCOEFF(J1,0,J2,0,L,0)*CGCOEFF(J1,M1,J2,M2,L,M)
  RETURN
  END FUNCTION GWI_DP