We make use of a subtraction procedure, introduced to overcome double--counting problems in beyond--mean--field theories, in the second random--phase--approximation (SRPA) for the first time. This procedure guarantees the stability of SRPA (so that a
ll excitation energies are real). We show that the method fits perfectly into nuclear density--functional theory. We illustrate applications to the monopole and quadrupole response and to low--lying $0^+$ and $2^+$ states in the nucleus $^{16}$O. We show that the subtraction procedure leads to: (i) results that are weakly cutoff dependent; (ii) a considerable reduction of the SRPA downwards shift with respect to the random--phase approximation (RPA) spectra (systematically found in all previous applications). This implementation of the SRPA model will allow a reliable analysis of the effects of 2 particle--2 hole configurations ($2p2h$) on the excitation spectra of medium--mass and heavy nuclei.
Phenomenological effective interactions like Skyrme forces are currently used in mean--field calculations in nuclear physics. Mean--field models have strong analogies with the first order of the perturbative many--body problem and the currently used
effective interactions are adjusted at the mean--field level. In this work, we analyze the renormalizability of the nuclear many--body problem in the case where the effective Skyrme interaction is employed in its standard form and the perturbative problem is solved up to second order. We focus on symmetric nuclear matter and its equation of state, which can be calculated analytically at this order. It is shown that only by applying specific density dependence and constraints to the interaction parameters could renormalizability be guaranteed in principle. This indicates that the standard Skyrme interaction does not in general lead to a renormalizable theory. For achieving renormalizability, other terms should be added to the interaction and employed perturbatively only at first order.
Bubble nuclei are characterized by a depletion of their central density. Their existence is examined within three different theoretical frameworks: the shell model as well as non-relativistic and relativistic microscopic mean-field approaches. We pro
pose $^{34}$Si and $^{22}$O as possible candidates for proton and neutron bubble nuclei, respectively. In the case of $^{22}$O, we observe a significant model dependence, thereby calling into question the bubble structure of $^{22}$O. In contrast, an overall agreement among the models is obtained for $^{34}$Si. Indeed, all models predict a central proton density depletion of about 40%. This result provides strong evidence in favor of a proton bubble in $^{34}$Si.
