mod_rhoin Module

Calculates the charge density inside r(irmin) in case of a non spherical input potential. Fills the array cden for the complex density of states the non spher. wavefunctions are approximated in that region in the following way:

• The regular one (ir < irmin = irws-irns) : $$\begin{equation} pns(ir,lm1,lm2) = pz(ir,l1) ar(lm1,lm2) \end{equation}$$ where $pz$ is the regular wavefct of the spherically symmetric part of the potential and ar the alpha matrix (see subroutine regns)
• The irregular one (ir < irmin) : $$\begin{equation} qns(ir,lm1,lm2) = pz(ir,l1) cr(lm1,lm2)+ qz(ir,l1) dr(lm1,lm2) \end{equation}$$ where $pz$ is the regular and $qz$ is the irregular wavefct of the spherically symmetric part of the potential and $cr$ , $dr$ the matrices calculated at the point irmin (see subroutine irwns()). The structured part of the greens-function (gmat) is symmetric in its lm-indices, therefore only one half of the matrix is calculated in the subroutine for the back-symmetrisation . Rhe gaunt coeffients are symmetric too (since the are calculated using the real spherical harmonics). Rhat is why the lm2- and the lm02- loops are only only going up to lm1 or lm01 and the summands are multiplied by a factor of 2 in the case of lm1 .ne. lm2 or lm01 .ne. lm02. (see notes by B. Drittler)