Translationally invariant calculations of form factors, nucleon densities and momentum distributions for finite nuclei with short-range correlations included

TL;DR

This paper develops a formalism to accurately compute nucleon densities and momentum distributions in finite nuclei, accounting for center-of-mass motion and short-range correlations, and compares results with experimental data.

Contribution

It introduces a novel analytic approach combining center-of-mass correction with short-range correlation models for finite nuclei.

Findings

Accurate form factors and densities for $^{4}He$ and $^{16}O$ are obtained.

The method effectively separates center-of-mass effects from intrinsic nuclear properties.

Results agree well with experimental data and other microscopic calculations.

Abstract

Relying upon our previous treatment of the density matrices for nuclei (in general, nonrelativistic self-bound finite systems) we are studying a combined effect of center-of-mass motion and short-range nucleon-nucleon correlations on the nucleon density and momentum distributions in light nuclei ($^{4}He $ and $^{16}O$). Their intrinsic ground-state wave functions are constructed in the so-called fixed center-of-mass approximation, starting with mean-field Slater determinants modified by some correlator (e.g., after Jastrow or Villars). We develop the formalism based upon the Cartesian or boson representation, in which the coordinate and momentum operators are linear combinations of the creation and annihilation operators for oscillatory quanta in the three different space directions, and get the own "Tassie-Barker" factors for each distribution and point out other model-independent results. After this separation of the center-of-mass motion effects we propose additional analytic means in order to simplify the subsequent calculations (e.g., within the Jastrow approach or the unitary correlation operator method). The charge form factors, densities and momentum distributions of $^{4}He $ and $^{16}O$ evaluated by using the well known cluster expansions are compared with data, our exact (numerical) results and microscopic calculations.