From scattering to very deeply bound neutrons in 208Pb: Extended and improved moment approaches

Abstract

Two new methods are developed which improve and extend the iterative moment approach to the extrapolation of the nuclear mean field from positive towards negative energy and to the prediction of various single-particle properties. These two methods still use as sole input a set of phenomenological optical-model potentials. They are improvements of the original approach because they yield more accurate predictions. They are extensions of the original approach because they provide the imaginary part of the mean field, in addition to its real part; this enables one to evaluate scattering cross sections, spectral functions and occupation probabilities, which was not possible in the previous version. These extended approaches are used to construct the neutron- 208Pb mean field from +40 MeV down to −60 MeV. They yield practically identical results. These results are moreover extremely close to those recently obtained from a dispersive optical-model analysis of the experimental n− 208Pb scattering cross sections. It is shown that the radial shape of the real part of the full mean field depends upon energy but remains very close to a Woods-Saxon. One of the two new methods, dubbed the variational moment approach, is well suited for the evaluation of the accuracy of the calculated Woods-Saxon parameters. If the diffuseness is set equal to 0.70 fm, the potential radius at the Fermi energy ( E F = −5.65 MeV) is found equal to (1.238±0.015)A 1 3 fm , and its volume integral per nucleon at E F to −401 ±6 MeV · fm 3. The energy dependence of the calculated real part of the full mean field is characterized by an effective mass m∗(r; E). The effective mass at the nuclear centre and at the Fermi energy, m∗(0; E F ) , must always be larger than the value that it takes in the Hartree-Fock approximation; this property was violated in the original iterative moment approach, but is fulfilled in both of the new methods developed here. One obtains m∗(0; E F )/m = 0.82 , in close agreement with the value found in a recent dispersive optical model analysis; in the latter, however, the quantity m∗(0; E) was infinite at several energies, while here m∗(0; E) is a smooth function of energy. The complex mean field constructed from the extended iterative moment approaches predicts n- 208Pb cross sections which are in quite good agreement with the experimental values in an energy domain which extends up to 40 MeV. The following properties are calculated for the very deeply, deeply, weakly bound and quasibound single-particle states: energies, spreading widths, spectral functions, spectroscopic factors, occupation probabilities and root-mean-square radii. The calculated energies of the valence subshells are in close agreement with experiment. Right below the Fermi energy, the calculated occupation probability is equal to 0.85, and the spectroscopic factor to 0.73. At the bottom of the Fermi sea, the calculated occupation probability is close to 0.95. The predicted energy distributions of the strengths of the 1h 11 2 , 1g 7 2 and 1 g 9 2 deeply bound states and of the 2 h 11 2 , 1 k 17 2 and 1 j 13 2 quas good agreement with experimental evidence.