M. Waroquier

We consider the groundstate of a system of A interacting fermions and construct relationships connecting the asymptotic behaviour of the one-body density matrix with the overlap functions of the eigenstates in the (A−1)-particle system. It is shown that the knowledge of the exact one-body density matrix is sufficient to determine the overlap functions, spectroscopic factors and separation energies of the bound (A−1)-particle eigenstates. We also derive sumrules linking the overlap functions with the natural orbitals of the system.

Calculations have been performed for the ¹⁶O(γ,pn) reaction in the photon-energy range E_γ=50–300MeV. Effects due to both one-pion exchange currents and the Δ have been included. We discriminate between different couplings of the initial proton-neutron (pn) pair involved in the reaction. At lower photon energies where the pion exchange currents dominate the cross section it is found that pn pairs in the finite nucleus do not fully behave like a quasideuteron. Therefore, we feel that the factorized form of the (γ,pn) cross section should be used with reservation.

It is reminded that a shell-model approach for occupation numbers in nuclei imposes constraints on the number of particles that can be lifted out of the Fermi sea. These constraints do not depend on the details of the calculation, such as the applied effective interaction, the size of the shell-model space or the way of tackling the shell-model equations. In some recent papers these constraints are violated. It is shown that this points to inconsistencies in the normalization of the many-body wave function calculated within perturbation theory.

We present results of self-consistent Hartree-Fock (HF) and continuum random-phase-approximation (RPA) calculations for proton emission following the electro-excitation of 58Ni in the energy range ω = 25–42 MeV. The calculations are performed for four different values of the momentum transfer ranging between 0.4 and 0.8 fm⁻¹. For the above kinematics, an extensive amount of data is available. We confront the data with the theoretical results obtained within the plane-wave impulse approximation (PWIA), HF and RPA. The role of the final-state interaction (FSI) is investigated. Furthermore, we investigate in how far the angular distributions may reflect the occurrence of giant resonances. A quasi-free knockout (QFK) reaction picture is found unable to account for details of the data. Although the RPA offers a reasonable description of the overall q and ω behaviour of the angular distributions, it does not provide a good description of the proton-decay branch of the quadrupole and octupole resonance.