F. Catara

Ground-state correlations beyond RPA

Abstract An approach is proposed which includes ground-state correlations beyond RPA. This is achieved by using a renormalized quasiboson approximation with reference to the correlated ground-state of the system, rather than to the uncorrelated Hartree-Fock one, and by expressing the particle-particle and hole-hole pair operators in terms of the particle-hole ones. The set of the so-obtained nonlinear equations for the one-phonon energy and amplitudes are first solved within the Lipkin-Meshkov-Glick model and the results are compared with those of previous approaches as well as with the exact ones. Applications to realistic nuclei, starting from fully self-consistent HF + RPA calculations with a Skyrme force are also presented.

Role of anharmonicities and nonlinearities in heavy ion collisions A microscopic approach

Abstract Using a microscopic approach beyond RPA to treat anharmonicities, we mix two-phonon states among themselves and with one-phonon states. We also introduce nonlinear terms in the external field. These nonlinear terms and the anharmonicities are not taken into account in the “standard” multiphonon picture. Within this framework we calculate Coulomb excitation of 208Pb and 40Ca by a 208Pb nucleus at 641 and 1000 MeV/A. We show with different examples the importance of the nonlinearities and anharmonicities for the excitation cross section. We find an increase of 10% for 208Pb and 20% for 40Ca of the excitation cross section corresponding to the energy region of the double giant dipole resonance with respect to the “standard” calculation. We also find important effects in the low-energy region. The predicted cross section in the DGDR region is found to be rather close to the experimental observation.

Low-lying component in strength distributions of weakly bound neutron-rich nuclei

Abstract We study the multipole response of nuclei for situations in which the neutron content becomes progressively rich. It is observed that the occurrence of weakly bound states towards the neutron drip line gives rise to low-lying concentrations of strength in the continuum which are not of a resonant character. These do not result from a redistribution of the expected high-lying response, but rather amount to a significant source of additional strength. The effect can be accounted for in terms of sum rules that grow — beyond a straightforward increase in the number of particles involved — because of the large spatial extent of the weakly bound orbitals.

Microscopic structure of monopole and quadrupole bosons

Abstract Within the pairing-plus-quadrupole model the wave function of the intrinsic state will be described as a product of basic fermion pairs, which are a linear combination of correlated monopole and quadrupole pairs only. The microscopic structure of these S- and D-pairs, as well as the mixture coefficient between them, are determined by minimizing the total energy within the field approximation. While the mixture between monopole and quadrupole pairs changes drastically to account for the transition from sphericity to static deformation, their internal structure remains fairly constant when varying the number of particles.

PARTICLE-HOLE EXCITATIONS WITH A COMPLETE SINGLE-PARTICLE BASIS. I. THE POINT SPECTRUM.

Abstract The truncated set of single particle wave functions commonly used in nuclear spectroscopic TD calculations has been completed so as to allow the construction of a complete set of particle-hole states. In the space spanned by such states the method of the equivalent problem in a subspace has been applied to get the discrete spectrum of 0 − , 1 − , and 3 − particle-hole excitations in C 12 and O 16 , by using explicitly given projection operators and a suitably simplified extension of the standard TD hamiltonian with zero range two-body interactions. The here defined extended TD approximation gives, as expected on general grounds, eigenvalues lower than the corresponding ones obtained in the usual TD approximation: but the shift never exceeds 1 MeV in the considered cases. The main effect of the extension has therefore to be read in the wave function dependent properties of the states, whose investigation is deferred to a second paper.

A rigorous method for solving nonlinear equations: Hartree-Fock and related problems

SummaryA rigorous iteration method for the solution of nonlinear equations in Banach spaces, due to Isaac Newton and Kantorovič, is reported. We consider its application to three nonlinear problems of atomic and nuclear physics, in finite-dimensional spaces: the ordinary, the constrained and a generalized Hartree-Fock problem. We have proved the existence of a solution of the Hartree-Fock equations and its uniqueness in a definite small region of the functional space, for the nucleus16O. This method converges faster than the usual Hartree algorithm and displays some further advantages.RiassuntoSi descrive un rigoroso metodo iterativo per la soluzione di equazioni non lineari in spazi di Banach, dovuto ad Isaac Newton ed a Kantorovič. Ne consideriamo l’applicazione a tre problemi non lineari di fisica atomica e nucleare, in spazi a dimensione finita: il problema di Hartree-Fock ordinario, quello con vincoli ed un problema generalizzato. Per il nucleo16O abbiamo dimostrato l’esistenza di una soluzione delle equazioni di Hartree-Fock e la sua unicità in una ben definita, piccola regione dello spazio funzionale. Questo metodo converge più velocemente dell’usuale algoritmo di Hartree e presenta alcuni ulteriori vantaggi.РеэюмеПредлагается строгий итерационный метод для рещения нелинейных уравнений в пространствах Банаха, раэработанный Исааком Ньютоном и Канторовичем. Мы рассматриваем применение зтого метода к трем нелинейным проблемам атомной и ядерной фиэики в конечно-мерных пространствах: обыкновенной, ограниченной и обобшенной проблеме Хартри-Фока. Мы докаэали сушествование рещения уравнений Хартри-Фока и его единственность в определенной малой области функционального пространства, для ядра16O. Этот метод сходится быстрее, чем обычный алгоритм Хартри и обнаруживает некоторые дополнительные преимушества.

Collective nuclear excitations with Skyrme-second random-phase approximation

Abstract Second RPA calculations with a Skyrme force are performed to describe both highand low-lying excited states in O. The coupling between 1 particle-1 hole and 2 particle-2 hole as well as that between 2 particle-2 hole configurations among themselves are fully taken into account and the residual interaction is never neglected, not resorting therefore to a generally used approximate scheme where only the first kind of coupling is considered. The issue of the rearrangement terms in the matrix elements beyond standard RPA is addressed and discussed. As a general feature of second RPA results, a several-MeV shift of the strength distribution to lower energies is systematically found with respect to RPA distributions. A much more important fragmentation of the strength is also naturally provided by second RPA due to the huge number of 2 particle-2 hole configurations. A better description of the excitation energies of the low-lying 0 and 2 states is obtained with second RPA with respect to RPA.

Residual interaction in second random-phase approximation with density-dependent forces: rearrangement terms

We derive the expressions of the rearrangement terms of the residual interaction to be used in the framework of the second random-phase approximation with density-dependent forces. These expressions are deduced within a variational derivation of the second random-phase-approximation equations. It is found that the rearrangement terms appearing in the beyond-random-phase-approximation matrix elements (which couple one-particle–one-hole with two-particle–two-hole and two-particle–two-hole with two-particle–two-hole configurations) are different from the standard random-phase-approximation rearrangement terms. This result indicates that both the currently used prescriptions, namely (a) using the same type of rearrangement terms in random-phase-approximation and in beyond-random-phase-approximation matrix elements, and (b) neglecting the rearrangement terms in beyond-random-phase-approximation matrix elements, are not correct. The quality of the approximations (a) and (b) is checked by comparing the approximated and correct results in the case of the monopole and quadrupole isoscalar strength distributions for the nucleus 16O. It is found that both approximations lead to quite different strength profiles with respect to the result obtained by applying the full second random-phase-approximation method.

Two-and four-particle surface clusterization in heavy deformed nuclei

Abstract We study the problem of the influence of the pairing interaction on two- and four-particle surface correlations in deformed nuclei. Taking the overlap between the two- or four-particle wave function and a di-nucleon or alpha-particle wave function, respectively, one obtains cluster probability distributions, as functions of the center-of-mass coordinate of the considered particles. For particles moving in pure Nilsson orbits the probability is localized in the intrinsic frame in different region of the nuclear surface, according to the K -quantum numbers of the considered orbitals. The inclusion of the pairing interaction leads to a probability distributed over the entire surface but at the same time to values of the total spectroscopic factors orders of magnitude larger than those associated with pure Nilsson orbits.

Microscopic description of β-band in the collective pair approximation

Abstract The collective pair approximation, previously used in the description of the ground-state band in deformed nuclei, is extended to the description of the β-band. This is obtained by promoting to an excited state one of the basic pairs defining the ground-state condensate in the intrinsic frame. The microscopic structure of the excited pair is determined variationally by minimizing the energy associated with the pairing-plus-quadrupole hamiltonian with the constraint of orthogonality to the ground state. We found that while the collective pair defining the ground-state condensate was dominated by the monopole and quadrupole components and exhibited a microscopic structure smoothly varying with the number of particles, high multipole pairs are dominant in the β-pair and its structure is strongly dependent on the movement of the Fermi surface. This casts serious doubts on the nature of the excited bands obtained in the framework of the interacting boson model.