rllsll Subroutine

public subroutine rllsll(rpanbound, rmesh, vll, rll, sll, tllp, ncheb, npan, lmsize, lmsize2, lbessel, nrmax, nvec, jlk_index, hlk, jlk, hlk2, jlk2, gmatprefactor, cmoderll, cmodesll, cmodetest, use_sratrick1, alphaget)

Calculation o radial wave functions by the integral equation method of Gonzalez et al, Journal of Computational Physics 134, 134-149 (1997) which has been extended for KKR using non-sperical potentials. Further information can be found in David Bauer, Development of a relativistic full-potential first-principles multiple scattering Green function method applied to complex magnetic textures of nano structures at surfaces, PhD Thesis, 2014

This routine solves the following two equations: $$\begin{equation} ULL(r) = J(r) - PRE J(r) \int_0^r\left( dr' r'^2 H2(r') op(V(r')) ULL(r') \right) +PRE H(r) \int_0^r\left( dr' r'^2 J2(r') op(V(r')) ULL(r') \right) \end{equation}$$ $$\begin{equation} SLL(r) = H(r) - PRE H(r) \int_0^r\left( dr' r'^2 H2(r') * op(V(r')) * RLL(r') \right)+ PRE J(r) \int_0^r\left( dr' r'^2 H2(r') op(V(r')) SLL(r') \right) \end{equation}$$ where the integral $\int_0^r()$ runs from 0 to $r$ * Green function prefacor $PRE=GMATPREFACTOR$ (scalar value) tipically $\kappa$ for non-relativistic and $M_0$ $\kappa$ for SRA

The discretization of the Lippmann-Schwinger equation results in a matrix equation which is solved in this routine. Further information is given in section 5.2.3, page 90 of Bauer, PhD Source terms : right solution: $J$, $H$ (nvec*lmsize,lmsize) or (lmsize,nvec*lmsize) left solution: $J2$, $H2$ (lmsize,nvec*lmsize) or (nvec*lmsize,lmsize) Example: The source term $J$ is for LMSIZE=3 and NVEC=2 given by: $$\begin{equation} J= \begin{bmatrix} jlk(jlk_index(1)) & 0 & 0 \\ 0 & jlk(jlk_index(2)) & 0 \\0 & 0 & jlk(jlk_index(3)) \\ jlk(jlk_index(4)) & 0 & 0 \\0 & jlk(jlk_index(5)) & 0 \\0 & 0 & jlk(jlk_index(6)) \end{bmatrix} \end{equation}$$ first 3 rows are for the large and the last 3 rows for the small component

Operator $op()$ can be chosen to be a unity or a transpose operation The unity operation is used to calculate the right solution The transpose operation is used to calculate the left solutionf the regular and irregular solutions

Arguments

Type	Intent	Optional	Attributes		Name
real(kind=dp)				::	rpanbound(0:npan)
real(kind=dp)				::	rmesh(nrmax)	Integration matrix from left ( CS_LC^-1 in eq. 5.53) Same from right ( CS_RC^-1 in eq. 5.54) Radial mesh point
complex(kind=dp)				::	vll(lmsize*nvec,lmsize*nvec,nrmax)	irr. volterra sol. reg. fredholm sol. t-matrix potential term in 5.7 Bauer, PhD
complex(kind=dp)				::	rll(lmsize2,lmsize,nrmax)	irr. volterra sol. reg. fredholm sol. t-matrix potential term in 5.7 Bauer, PhD
complex(kind=dp)				::	sll(lmsize2,lmsize,nrmax)	irr. volterra sol. reg. fredholm sol. t-matrix potential term in 5.7 Bauer, PhD
complex(kind=dp)				::	tllp(lmsize,lmsize)	irr. volterra sol. reg. fredholm sol. t-matrix potential term in 5.7 Bauer, PhD
integer				::	ncheb	number of chebyshev nodes
integer				::	npan	number of panels
integer				::	lmsize	lm-components * nspin
integer				::	lmsize2	lmsize * nvec
integer				::	lbessel
integer				::	nrmax	total number of rad. mesh points
integer				::	nvec	spinor integer: nvec=1 non-rel, nvec=2 for sra and dirac
integer				::	jlk_index(nvec*lmsize)
complex(kind=dp)				::	hlk(lbessel,nrmax)
complex(kind=dp)				::	jlk(lbessel,nrmax)
complex(kind=dp)				::	hlk2(lbessel,nrmax)
complex(kind=dp)				::	jlk2(lbessel,nrmax)
complex(kind=dp)				::	gmatprefactor	prefactor of green function (non-rel: = kappa = sqrt e, rel: including mass correction)
character(len=1)				::	cmoderll	These define the op(V(r)) in the eqs. above (comment in the beginning of this subroutine) cmoderll ="1" : op( )=identity for reg. solution cmoderll ="T" : op( )=transpose in L for reg. solution cmodesll: same for irregular
character(len=1)				::	cmodesll	These define the op(V(r)) in the eqs. above (comment in the beginning of this subroutine) cmoderll ="1" : op( )=identity for reg. solution cmoderll ="T" : op( )=transpose in L for reg. solution cmodesll: same for irregular
character(len=1)				::	cmodetest	These define the op(V(r)) in the eqs. above (comment in the beginning of this subroutine) cmoderll ="1" : op( )=identity for reg. solution cmoderll ="T" : op( )=transpose in L for reg. solution cmodesll: same for irregular
integer				::	use_sratrick1
complex(kind=dp)				::	alphaget(lmsize,lmsize)