CGCOEFF – FORTVSH

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private function CGCOEFF_DP(J1, M1, J2, M2, J3, M3) result(CGCOEFF)

Clebsch-Gordan coefficient $\langle j_1 m_1 j_2 m_2 | j_3 m_3\rangle$ for coupling two angular momenta $j_1,j_2$ to a total $j_3$ , via the closed-form Racah sum (evaluated in log-factorial form for numerical stability at large arguments -- see LOG_FACT): $\langle j_1 m_1 j_2 m_2|j_3 m_3\rangle = \delta_{m_3,m_1+m_2} \sqrt{2j_3+1}\,\Delta(j_1j_2j_3)\times$ $\sqrt{(j_1{+}m_1)!(j_1{-}m_1)!(j_2{+}m_2)!(j_2{-}m_2)!(j_3{+}m_3)!(j_3{-}m_3)!} \sum_k \frac{(-1)^k}{k!\,(j_1{+}j_2{-}j_3{-}k)!(j_3{-}j_1{-}m_2{+}k)! (j_3{-}j_2{+}m_1{+}k)!(j_1{-}m_1{-}k)!(j_2{+}m_2{-}k)!},$ where $\Delta(j_1j_2j_3) = \sqrt{\frac{(j_1+j_2-j_3)!(j_2+j_3-j_1)! (j_3+j_1-j_2)!}{(j_1+j_2+j_3+1)!}}$ . Adapted from David Simpson (NASA GSFC). Automatically returns 0 for any invalid combination -- violated triangle inequality $|j_1-j_2|\le j_3\le j_1+j_2$ , $|m_i|>j_i$ , or $m_1+m_2\ne m_3$ -- so it is always safe to call with an arbitrary sextuple of integers, e.g. when sweeping a parameter range.

Arguments

Type	Intent		Name
integer(kind=i4),	intent(in)	::	J1	First angular momentum, $j_1\ge0$ .
integer(kind=i4),	intent(in)	::	M1	First projection, $-j_1\le m_1\le j_1$ .
integer(kind=i4),	intent(in)	::	J2	Second angular momentum, $j_2\ge0$ .
integer(kind=i4),	intent(in)	::	M2	Second projection, $-j_2\le m_2\le j_2$ .
integer(kind=i4),	intent(in)	::	J3	Coupled angular momentum, $j_3\ge0$ .
integer(kind=i4),	intent(in)	::	M3	Coupled projection, $-j_3\le m_3\le j_3$ .

CGCOEFF Interface

Contents

Module Procedures

public interface CGCOEFF

Calls

Called by

Module Procedures

private function CGCOEFF_DP(J1, M1, J2, M2, J3, M3) result(CGCOEFF)

Arguments

Return Value real(kind=dp)