Experimental study of shell-model occupancies employing a new sum rule

Despite the obvious success of the nuclear shell model the occupation numbers of nucleons in the shell model orbitals could not be determined precisely. The interpretation of one-nucleon transfer and quasi-free knock-out experiments, the classical tools for nuclear structure studies, did not yield reliable absolute spectroscopic factors mainly because of the uncertain distortions. In contrast, relative spectroscopic factors can be extracted with high precision because many sources of systematic experimental errors vanish and the uncertain DWBA (distorted wave Born approximation) or DWIA (distorted wave impulse approximation) predictions enter as corrections only. On the other hand, elastic electron scattering represents a high precision tool to study nuclear charge density distributions which, however, offers no direct model-independent access to occupation numbers. To exploit the advantages of the different probes a Combined Evaluation of Relative spectroscopic factors and Electron Scattering, the CERES approach, has been developed to study the occupation numbers of the 3s1/2 proton orbital in 208Pb. New precise relative experiments on 204Hg, 205Tl and 206,208Pb provide the necessary input data for the CERES sum rule. The occupation number N3s (208) for the 3s1/2 proton orbital in 208Pb is found as n3s(208) = 2.46(16)*z, where z represents the absolute 3s1/2 contribution to the charge density difference of 206Pb-205Tl. Based on the most recent interpretation of z = 0.64(6) we obtain n3s(208) 1.57(10)[17]. The resulting depletion of ≅ 20% agrees well with other recent experimental findings and constraints the mean-field predictions. (Author)