Translationally Invariant Calculations of Form Factors, Densities and Momentum Distributions for Finite Nuclei with Short–Range Correlations Included: A Fresh Look

Abstract

The approach proposed in the 70s (Dementiji et al. in Sov J Nucl Phys 22:6–9, 1976), when describing the elastic and inelastic electron scattering off ⁴ He, and elaborated in (Shebeko et al.in Eur Phys J A27:143–155, 2006) for calculations of the one-body, two-body and more complex density matrices of finite bound systems has been applied (Shebeko and Grigorov in Ukr J Phys 52:830–842, 2007; Shebeko et al. in Eur. Phys. J. A48:153–172, 2012) in studying a combined effect of the center-of-mass motion and nucleon–nucleon short-range correlations on the nucleon density and momentum distributions in light nuclei beyond the independent particle model. Unlike a common practice, suitable for infinite bound systems, these distributions are determined as expectation values of appropriate intrinsic operators that depend upon the relative coordinates and momenta (Jacobi variables) and act on the intrinsic ground–state wave functions (WFs). The latter are constructed in the so-called fixed center-of-mass approximation, starting with a mean–field Slater determinant modified by some correlator (e.g., after Jastrow or Villars). Our numerical calculations of the charge form factors (F _CH (q)), densities and momentum distributions have been carried out for nuclei ⁴ He and ¹⁶ O choosing, respectively, the 1s and 1s−1p Slater determinants of the harmonic oscillator model as trial, nontranslationally invariant WFs.