Removing center of mass effects in response function and sum rule calculations based on the harmonic oscillator basis

TL;DR

This paper develops analytical formulas to remove center of mass effects from response function calculations in nuclear physics, improving the accuracy of theoretical-experimental comparisons especially for heavier nuclei.

Contribution

It introduces a new formalism based on harmonic oscillator confinement to analytically subtract center of mass contaminations in response functions and sum rules.

Findings

Derived explicit formulas for center of mass correction functions.

Validated the method with a two-body electric dipole sum rule example.

Paves the way for applying the approach to heavier nuclei.

Abstract

Response functions are at the heart of any comparison of theory with experiment in studies of the nuclear dynamics with electroweak probes. Calculations performed in the laboratory frame often suffer from center of mass contaminations that need to be removed. By confining the system in a harmonic oscillator, we derive a set of analytical formulas to subtract the center of mass effects from calculations of response functions and associated sum rules. After a general analytical derivation, we first deal specifically with the longitudinal response function appearing in electron scattering and provide expressions for the center of mass correcting functions. Next, we present a proof of principle study for the case of the electric dipole sum rules in a two-body problem with a numerical implementation of our formalism. These steps pave the way to applying the proposed method to heavier nuclei in the future.