Block recursion and Green matrices

TL;DR

This paper generalizes the recursion method for calculating entire Green matrices in angular momentum space, enabling more comprehensive response function and cross-section computations beyond spectral densities.

Contribution

It introduces a generalized recursion approach for Green matrices, extending previous methods that focused only on diagonal elements.

Findings

Successfully computes full Green matrices for complex systems

Enables calculation of response functions and cross-sections

Provides examples demonstrating the method's effectiveness

Abstract

We present here generalization of the recursion method of Haydock et al [1] for the calculation of Green matrices (in angular momentum space). Earlier approaches concentrated on the diagonal elements, since the focus was on spectral densities. However, calculations of configuration averaged response functions or neutron scattering cross-sections require the entire Green matrices and self-energy matrices obtained from it. This necessitated the generalization of the recursion method presented here with examples.