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

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.

Automated summary

This study presents a method to correct the center of mass effects by confining the system in a harmonic oscillator. The longitudinal response function in electron scattering is specifically investigated and expressions for center of mass correction are provided. A proof of principle study on the electric dipole sum rules in a two-body problem is conducted with numerical implementation, paving the way for future application on heavier nuclei.