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Physical Review C

Single-particle properties in self-bound systems

Dimitri Van Neck, Michel Waroquier

Published Dec 1, 1998• 8 citations
Publisher

Abstract

We construct a consistent framework for treating single-particle properties in finite translationally invariant (self-bound) many-body systems. The differences with the standard case of fixed-center systems are discussed. For some properties which result from the Pauli principle in many-fermion systems, these differences are shown to persist even in the limit of a large number of particles.

DOI
10.1103/physrevc.58.3359

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We construct a consistent framework for treating single-particle properties in finite translationally invariant (self-bound) many-body systems. The differences with the standard case of fixed-center systems are discussed. For some properties which result from the Pauli principle in many-fermion systems, these differences are shown to persist even in the limit of a large number of particles.
A method is presented for the calculation of the one-body and two-body density matrices and their Fourier transforms in momentum space, that is consistent with the requirement for translational invariance, in the case of a nucleus (a finite self-bound system). We restore translational invariance by using the so-called fixed center-of-mass approximation for constructing an intrinsic nuclear ground state wavefunction by starting from a non-translationally invariant wavefunction and applying a projection prescription. We discuss results for the one-body and two-body momentum distributions of the 4He nucleus calculated with the Slater determinant of the harmonic oscillator orbitals, as the initial non-translationally invariant wavefunction. Effects of such an inclusion of CM correlations are found to be quite important in the momentum distributions.
A method is presented for the calculation of the one‐body (1DM) and two‐body (2DM) density matrices and their Fourier transforms in momentum space, that is consistent with the requirement for translational invariance (TI), in the case of a nucleus (a finite self‐bound system). We restore TI by using the so‐called fixed center‐of‐mass (CM) approximation for constructing an intrinsic nuclear ground state wavefunction (WF) by starting from a non‐translationally invariant (nTI) WF and applying a projection prescription. We discuss results for the one‐body (OBMD) and two‐body (TBMD) momentum distributions of the 4He nucleus calculated with the Slater determinant of the harmonic oscillator (HO) orbitals, as the initial nTI WF. Effects of such an inclusion of CM correlations are found to be quite important in the momentum distributions.