Occupation Probabilities of Shell-Model Orbits in the Lead Region

Abstract

The occupation probabilities of shell-model orbits in the lead region are estimated by the addition of random-phase-approximation corrections to nuclear-matter results. The occupation probabilities of single-particle states in shells just below and above the Fermi energy are found to be ~ 0.7 and 0.1, respectively. It is shown that these estimates explain the quenching of the single-particle contribution observed in many elastic and inelastic electronscattering experiments.PACS numbers: 21.60. Cs, 27.80. + W Substantial empirical evidence indicates that the independent-particle model provides only a partially successful description of some of the simplest nuclear excitations in heavy nuclei. Mean-field theories correctly predict the shape of transition densities but they systematically underestimate the strength of these simple excitations. Various mechanisms have been proposed to explain this quenching of single-particle strength, particularly for the high-spin magnetic transitions in lead. Hamamoto, Lichtenstadt, and Bertsch 1 have studied the quenching due to first-order core polarization, but subsequent studies 2 " 4 found this effect to be small. While Krewald and Speth 2 could explain the quenching with particle-vibration coupling, selfconsistent first-and second-order random-phaseapproximation (RPA) calculations 3 could not. The effect of meson exchange currents, left out in these calculations, was estimated by Suzuki and Hyuga 4 and found to be small.In this Letter we examine the empirical evidence for the quenching of the single-particle strength in both elastic and inelastic scattering measurements. We find that the mechanisms explored so far account only for part of the effect. Reasonable agreement with the data is achieved when the effect of short-range correlations is also included.In Table I we list transitions to relatively pure shell-model states. The magnitude of the quenching is directly obtained by comparison of the observed and the single-particle form factors for electron scattering. It is central to our argument that in all these cases the observed form factor can be separated, mainly through its momentum dependence, into a quenched single-particle term and a background term: F(q) = QF sv (q)+F H (q).(1)The form factors of the differences in the charge and current densities of neighboring nuclei, measured in the elastic electron-scattering experiments listed in Table II, also have a quenched singleparticle part. The quenching Q observed in both elastic and inelastic scattering experiments is ~ 0.6. We first review the connection between Q, the quenching factor, and the occupation numbers. Consider a transition from a state |/) to the state \f). Let \i m ) and \f m ) denote the independentparticle-model approximations of |/) and \f). The single-particle states occupied in |/ m ) are denoted by h n , n = 1,A, and the unoccupied states are p n , n = 1, oo. The single-particle part of the transition corresponds to a nucleon being transferred from orbit h to p, so that \f m ) =p^h \i m ), and the...

Self-consistent Green's function method for nuclei and nuclear matter

“…4.6 for the fully self-consistent results. The latter results formed the basis of the now corroborated prediction [54,146,147] for the occupation numbers in 208 Pb [143].…”

Radial Dependence of the Nucleon Effective Mass in10B

“…We present a combined analysis of inelastic electron-scattering data and electron-induced proton knockout measurements in an effort to obtain phenomenological information on nucleon-nucleon correlations. Our results indicate that the ratio of radial wave functions extracted from precise 10 B͑e, e 0 ͒ and 10 B͑e, e 0 p͒ measurements evolve from an interior depression for small E m , characteristic of short-range correlations, to a surface-peaked enhancement for larger E m , characteristic of longrange correlations. This observation can be interpreted in terms of the nucleon effective mass.…”

“…Thus, if h e,e 0~m k ͑r͒͞m and h e,e 0 pm ‫ء‬ ͑r, E m ͒͞m, we would expect to find that the ratio of radial functions extracted from ͑e, e 0 ͒ and ͑e, e 0 p͒ experiments resembles the E mass, such that k͑r, E m ͒m E ͑r, E m ͒͞m. The 10 B͑e, e 0 p͒ data employed to investigate these ideas were taken from an experiment performed at the medium-energy electron accelerator at NIKHEF. The energy, duty factor, and average current of the beam were 407.3 6 0.2 MeV, 1%, and 1.5 mA, respectively.…”

Overview of nuclear structure with electrons

“…These measurements were brought together in a coherent picture by Pandharipande, Papanicolas and Wambach [14] who showed that the combination of nuclear matter and random-phase approximation calculations shown in Fig. 3 could explain the occupation probabilities of single particle orbitals in the Pb region.…”

“…FIGURE 3. Calculated occupation numbers for single particle and hole states near the Fermi surface in Pb [14]. The dashed curve is a nuclear matter calculation including short-range correlations (long dashed) and long-range correlations and the points (crosses for proton statea and circles for neutron states) include RPA correlations.…”