Restoration of overlap functions and spectroscopic factors in nuclei

Abstract

An asymptotic restoration procedure is applied for analyzing bound-state overlap functions, separation energies and single-nucleon spectroscopic factors by means of a model onebody density matrix emerging from the Jastrow correlation method in its lowest order approximation for 16 -15]. The growing interest is motivated in principle by the possibility to clarify the limitation of the nuclear mean-field picture. For instance, the relatively low values of the spectroscopic factors deduced from these experiments show clearly the importance of the short-range correlation effects in nuclei and the necessity of detailed investigations of the high-momentum components of the nucleon wave function which cannot be included within the mean-field approximation [16][17][18][19][20].The underlying relationship between the differential cross-section and the structure of the nuclear wave function is often empirically analyzed using the plane-wave impulse approximation (PWIA). For instance, in this approximation the (e, e′p)-reaction cross-section for a transition to a specific state with quantum numbers α in the residual nucleus has the following form (see e.g. [12,22])The first term K is kinematical factor , σ ep is the offshell electron-proton scattering cross-section [23] and the nuclear structure component | φ α (k) | 2 is the squared Fourier transform of the overlap function between the ground state of the target nucleus Ψ (A) and the final state of the residual nucleus Ψ (A−1) [24,25,16]:a(r) being an annihilation operator for a nucleon with spatial coordinate r (spin and isospin coordinates are not put in evidence). The overlap functions (2) are not orthonormalized. Their norm defines the spectroscopic factor of the level αand the normalized overlap functioñUsually,φ α (r) is calculated from an empirical SaxonWoods potential with a distinct potential radius for each separate transition α. Quantitative estimates are then deduced by fitting both the potential radius and the spectroscopic factor S α in order to obtain a good agreement between the experimentally measured cross sections (dσ/dΩ) exp and those predicted from appropriate calculations for the reaction process.The full theoretical description of the experiments mentioned above has many components. We should like to mention among them the proper account of the reaction mechanism, of the distortion effects (including the distortion due to the final state interaction), of the meson exchange currents contributions, the study of the A-dependence and others (see e.g. [22,12]). Obviously, however, the theoretical estimates of the overlap functions (2) and the spectroscopic factors (3) are of crucial importance for the adequate evaluation of recent (e, e′p), (d, 3 He) and (γ, p) experiments. The problem is that the normalized overlap functions (4) cannot be identified with a phenomenological shell-model single-particle wave function especially for energies farther from the Fermi energy, sometimes even within the valence shell [16]. It is known that generally, the indepe...

Overlap functions in correlation methods and quasifree nucleon knockout from16O

“…Only the overlap function from the OBDM of ref. [18] gives a fair agreement with the size and the shape of the (γ, p) data in Fig. 5.…”

“…An example for the transition to the 3/2 − state at 6.3 MeV is presented in [18]. In contrast, the shape is much better reproduced by the more complete calculations including also the seagull current.…”

“…Also at E γ = 72 MeV the HF wave function and the overlap function from the OBDM of ref. [18] can reproduce the size of the experimental cross section only at low values of the scattering angle and are unable to give a proper description of the shape of the angular distribution. The cross section calculated with the overlap function from ref.…”

“…A simple but effective approach accounting for the SRC within the Jastrow correlation method in its low-order approximation has been used to obtain the OBDM [23] and to calculate the s.p. overlap functions [18]. Another type of overlap functions has been obtained [19] within the framework of the CBF theory using the cluster expansion and correlation functions from Variational Monte Carlo calculations with the Argonne potential.…”

Effects of short-range correlations in(e,e′p)reactions and nuclear overlap functions

“…[19]. In the following we compare the results provided by these methods for different choices of the asymptotic interval [a l , a u ] where the fit is performed.…”