Occupation probabilities of shell-model orbitals

Abstract

A number of observations including absolute spectral functions from (e,e′p) reactions indicate occupancies of shell-model orbitals substantially below unity, e.g. about 50% in ²⁰⁸Pb where many-body theories predict values ranging from 60 to 90%. We present the CERES method ($\text{c}\text{ombined}$$\text{e}\text{valuation}$ of $\text{r}\text{elative}$ spectroscopic factors and $\text{e}\text{lectron}$$\text{s}\text{cattering}$) for the determination of occupancies which avoids the questionable use of absolute spectroscopic factors and accounts for experimental cut-offs in the spectroscopic sums. The method is applied to the Pb-region where a network of interrelated relative spectroscopic factors from (d,³He), (e,e′p) and (³He,d) reactions has been established and combined with electron scattering results. For the 3s-proton shell in ²⁰⁸Pb an occupancy of about 85% is obtained. It is pointed out that this does not contradict the 50% value derived from truncated sums, provided short-range correlations produce long tails in the spectral functions.