A simultaneous center-of-mass correction of nucleon density and momentum distributions in nuclei

TL;DR

This paper presents a method to correct nucleon density and momentum distributions in nuclei for center-of-mass motion effects, incorporating short-range correlations, with numerical application to helium-4.

Contribution

It introduces a simplified analytic approach using Tassie-Barker factors for simultaneous center-of-mass correction in density and momentum distributions.

Findings

Corrected distributions show a shrinking effect compared to uncorrected ones.

The method effectively accounts for short-range correlations in translationally invariant wavefunctions.

Numerical results for helium-4 demonstrate the impact of center-of-mass correction.

Abstract

The approach exposed in the recent paper (A. Shebeko, P. Papakonstantinou, E. Mavrommatis, Eur. Phys. J. A 27, 143 (2006)) has been applied in studying center-of-mass motion effects on the nucleon density and momentum distributions in nuclei. We are focused upon effects due to the center-of-mass and short-range nucleon correlations embedded in translationally invariant ground-state wavefunctions. The latter are constructed in the so-called fixed center-of-mass approximation, starting with a Slater determinant wave function modified by some correlator (e.g., after Jastrow or Villars). It is shown how one can simplify evaluation of the corresponding expectation values that determine the distributions. The analytic expressions derived here involve the own "Tassie-Barker" factors for each distribution. As an illustration, numerical calculations have been carried out for the nucleus ^{4}He with the Slater determinant to describe the nucleon (1s)^4 configuration composed of single-particle orbitals which differ from harmonic oscillator ones at small distances. Such orbitals simulate somewhat short-range repulsion between nucleons. Special attention is paid to a simultaneous shrinking of the center--of--mass corrected density and momentum distributions compared to the purely (1s)^4 shell nontranslationally invariant ones.