Analytical evaluation of the lattice Green function for the face centered cubic lattice

TL;DR

This paper introduces an efficient analytical method for calculating the FCC lattice Green function using binomial expansion and acceleration techniques, achieving better convergence and agreement with numerical results.

Contribution

The paper presents a novel analytical approach for FCC lattice Green functions that improves convergence and computational efficiency over existing methods.

Findings

Series converge faster with the proposed method

Results agree well with numerical calculations

Acceleration techniques enhance efficiency

Abstract

An efficient calculation method is proposed for the face centered cubic (FCC) lattice Green function. The method is based on binomial expansion theorems, which is provide us establish analytical formulae through simple basic integrals. The resulting series present better convergence rates. Several acceleration techniques are combined to further improve the efficiency. The obtained results for the lattice Green function are in good agreement with the known numerical calculation results.