D. Van Neck

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.

The spectroscopic factors for the low-lying quasihole states observed in the ¹⁶O(e,e′p)¹⁵N reaction are reinvestigated with a variational Monte Carlo calculation for the structure of the initial and final nucleus. A computational error in a previous report is rectified. It is shown that a proper treatment of center-of-mass motion does not lead to a reduction of the spectroscopic factor for p-shell quasihole states, but rather to a 7% enhancement. This is in agreement with analytical results obtained in the harmonic oscillator model. The center-of-mass effect worsens the discrepancy between present theoretical models and the experimentally observed single-particle strength. We discuss the present status of this problem, including some other mechanisms that may be relevant in this respect.

Long-range correlations, which are partially responsible for the observed fragmentation and depletion of low-lying single-particle strength, are studied in the Green's function formalism. The self-energy is expanded up to second order in the residual interaction. We compare two methods of implementing self-consistency in the solution of the Dyson equation beyond Hartree-Fock, for the case of the 16O nucleus. It is found that the energy-bin method and the BAGEL method lead to globally equivalent results. In both methods the final single-particle strength functions are characterized by exponential tails at energies far from the Fermi level.

A recent theorem states that for quantum many-body systems with short-range interactions the following property holds: the single-particle overlap functions, spectroscopic factors and separation energies of bound eigenstates of the (A-1)(A-1)-particle system are fully determined by the one-body density matrix of the AA-particle system in its ground state. We confirm this property, by explicit construction, for the case of a schematic, exactly solvable system.

The single-particle self-energy in finite nuclei is constructed in a microscopic way by means of the Green-function formalism. We present calculations for the ²⁰⁸Pb system which are fully self-consistent up to second order in the residual interaction. This leads to an improved description of damping effects in the spectral function for deeply bound hole states. The theoretical results are compared with experimental (e, e'p) results. Global properties of the single-particle strength distributions for deep hole states, such as the centroids and widths, are well reproduced. Finally some comments are made about the meaning of occupation probabilities for shell-model orbits.