Spectral function for $^4$He using the Chebyshev expansion in coupled-cluster theory

TL;DR

This paper introduces a stable, memory-efficient method combining coupled-cluster theory and Chebyshev polynomial expansion to compute the spectral function of helium-4, with implications for modeling lepton-nucleus interactions at high energies.

Contribution

The authors develop a novel approach integrating Chebyshev expansion with coupled-cluster theory for spectral function calculation, improving stability and reducing memory compared to traditional methods.

Findings

Accurate spectral function for helium-4 computed.

Method shows lower memory usage and numerical stability.

Results align with existing data and predictions.

Abstract

We compute spectral function for $^4$He by combining coupled-cluster theory with an expansion of integral transforms into Chebyshev polynomials. Our method allows to estimate the uncertainty of spectral reconstruction. The properties of the Chebyshev polynomials make the procedure numerically stable and considerably lower in memory usage than the typically employed Lanczos algorithm. We benchmark our predictions with other calculations in the literature and with electron scattering data in the quasi-elastic peak. The spectral function formalism allows one to extend ab-initio lepton-nucleus cross sections into the relativistic regime. This makes it a promising tool for modeling this process at higher energy transfers. The results we present open the door for studies of heavier nuclei, important for the neutrino oscillation programs.