Two-body density matrix for closed s-d shell nuclei

The two-body density matrix for ⁴He,¹⁶O and ⁴⁰Ca within the Low-order approximation of the Jastrow correlation method is considered. Closed analytical expressions for the two-body density matrix, the center of mass and relative local densities and momentum distributions are presented. The effects of the short-range correlations on the two-body nuclear characteristics are investigated. Received: 11 September 1999 / Revised version: 20 December 1999     

Some considerations on the restoration of Galilei invariance in the nuclear many-body problem

The mathematical tools to restore Galilei invariance in the nuclear many-body problem with the help of projection techniques are presented. For simple oscillator configurations recursion relations for the various elementary contractions are derived. The method is then applied to simple configurations for the ground states of ⁴He, ¹⁶O and ⁴⁰Ca as well as to the corresponding one-hole and one-particle states. As a first application the spectral functions and spectroscopic factors for the above-mentioned doubly even nuclei are investigated. It turns out that the conventional picture of an uncorrelated system underestimates the single-particle strengths of the hole states from the last occupied shell while that of the higher excited hole states is overestimated considerably. These results are in complete agreement with those derived by Dieperink and de Forest using different methods. Similar effects are seen for the particle states which have not been studied before. All the calculations presented here are performed analytically and thus can be checked explicitly by the interested reader. Received: 20 February 2001 / Accepted: 11 September 2001     

Some considerations on the restoration of Galilei invariance in the nuclear many-body problem

The effects of the restoration of Galilei invariance in the nuclear many-body problem on the electromagnetic properties of simple bound states are investigated. For this purpose the form factors for elastic electron scattering from the oscillator ground states of ⁴He, ¹⁶O and ⁴⁰Ca as well as those for elastic and inelastic electron scattering between various one-hole states with respect to these reference configurations are computed with and without projection into the center-of-momentum rest frame. It is demonstrated that, in some cases, the full restoration of Galilei invariance produces results which are considerably different from those obtained with the usual approximate way to treat the center-of-mass motion. The same holds for the mathematical Coulomb sum rules and their first and second moments obtained for the above-mentioned nuclei. Received: 21 February 2001 / Accepted: 20 December 2001     

Some considerations on the restoration of Galilei invariance in the nuclear many-body problem

The effects of the restoration of Galilei invariance in the nuclear many-body problem on the energies of simple bound states are investigated. As examples we consider the oscillator ground states of ⁴He, ¹⁶O and ⁴⁰Ca as well as the various hole states with respect to these reference configurations. Density-independent as well as density-dependent interactions are studied. It turns out that the full restoration of Galilei-invariance yields considerable contributions on top of the trivial 1/A effect resulting from removing the center-of-momentum part of the Hamiltonian. Received: 20 February 2001 / Accepted: 10 May 2002     

E2 transitions in the SU(3) formalism for N = Z nuclei of the sd and pf shells

We show that the SU(3) coupling scheme reproduces the data for E2 transitions in N = Z even-even nuclei both of the sd and the pf shells. The SU(3) results are compared with large-scale shell model calculations. Along the ground-state band-like structures, the increase of the B(E2) values with spin toward a maximum value and the subsequent fall with further increasing spin are reproduced rather well. The role of the quadrupole-quadrupole term of the nuclear residual interaction is stressed.     

Configuration-mixed effective SU(3) symmetries

The procedure of Jarrio et al. (Nucl. Phys. A 528, 409 (1991)) for the determination of the effective SU(3) symmetry of nuclear states is extended to small deformations and to oblate nuclei. Self-consistency checks are carried out both for light and for heavy nuclei. Received: 23 April 2002 / Accepted: 25 July 2002 / Published online: 10 December 2002 RID="a" ID="a"e-mail: hess@nuclear.unam.mx Communicated by A. Molinari     

Flow equations for band-matrices

Continuous unitary transformations can be used to diagonalize or approximately diagonalize a given Hamiltonian. In the last four years, this method has been applied to a variety of models of condensed matter physics and field theory. With a new generator for the continuous unitary transformation proposed in this paper one can avoid some of the problems of former applications. General properties of the new generator are derived. It turns out that the new generator is especially useful for Hamiltonians with a banded structure. Two examples, the Lipkin model, and the spin-boson model are discussed in detail. Received: 2 February 1998 / Accepted: 17 March 1998     

Application of the Dyson boson expansion method to the treatment of the pairing force

The treatment of the separable pairing interaction in the context of the BRST formalism and in the Dyson boson expansion method is discussed. The approach is based on the use of the vacuum expectation value of the boson number operator to define a suitable mean field. Received: 10 April 2000 / Accepted: 6 July 2001     

Large-scale shell model calculations for exotic nuclei

Recent shell model calculations for the neutron-rich nuclei around the magic numbers N = 20, N = 28 and N = 40 are reviewed. We stress two points: i) The crucial role played by the monopole part of the effective interaction that determines the evolution of the spherical mean field. In particular, the reduction in the quasiparticle gaps at the magic numbers can erode or even erase the shell closures. ii) The rich variety of structures that can be found in these situations, with coexisting deformed and spherical states, rapid changes of behaviour with N or Z, and the massive occurrence of intruder states as ground states. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"e-mail: alfredo.poves@uam.es     

Nuclear mean fields through self-consistent semiclassical calculations

Semiclassical expansions derived in the framework of the Extended Thomas-Fermi approach for the kinetic energy density τ( r) and the spin-orbit density J( r) as functions of the local density ρ( r) are used to determine the central nuclear potentials V _n( r) and V _p( r) of the neutron and proton distribution for effective interactions of the Skyrme type. We demonstrate that the convergence of the resulting semiclassical expansions for these potentials is fast and that they reproduce quite accurately the corresponding Hartree-Fock average fields. Received: 12 February 2000 / Accepted: 14 March 2002     

Cluster structures in light nuclei

Clustering in light stable and unstable nuclei is discussed. After a brief review of the clustering in stable nuclei, we make a new prediction of the existence of the alpha cluster condensed states in ¹²C and ¹⁶O. Discussions of clustering in light unstable nuclei are made in the cases of Be and B isotopes up to the neutron dripline. Received: 1 May 2001 / Accepted: 4 December 2001     

Extension of the spectroscopic Monte Carlo method to realistic effective interactions

We propose an extension of the spectroscopic Monte Carlo method to realistic effective interactions. The scheme is applied to the recently introduced GXPF1 interaction for fp nuclei for the ground state of ⁶⁰Fe, ⁵⁶Ni, ⁶⁴Ni and ⁶⁰Zn. The method hinges on the use of Hartree-Fock-Bogoliubov wave functions (properly projected before variation) and on a reformulation of the effective interaction so that it is a sum of negative squares of Hermitian one-quasi-particle operators, so the application of the Hubbard-Stratonovich transformation to the elementary propagator exp[- ] gives a functional integral over a Hermitian propagator. Limitations and difficulties encountered in the calculation are discussed.     

Giant dipole resonance and shape transitions in warm and rapidly rotating nuclei

We discuss the shape transitions in few medium heavy-mass nuclei with emphasis on low-temperature behaviour of the giant dipole resonance (GDR) observables. We employ a macroscopic approach towards GDR in which the GDR observables are related to the nuclear shapes. Shape calculations were done using the cranked Nilsson-Strutinsky method (CNSM) extended to finite temperature. Thermal shape fluctuations are computed with free energies calculated employing Landau parameterization as well as those calculated exactly (without using parameterizations) at given spin and temperature. The results obtained are confronted with the experimental data wherever available. Our study reveals that if the fluctuations are treated properly, then, in spite of thermal fluctuations, GDR observables could very well reflect the shape transitions at low temperature.     

Probing the pairing-phase transition with pair-transfer reactions in unstable nuclei

The critical point solution of the pairing phase transition from vibrational to rotational regimes and an application to lead isotopes are described. Suggestions on how to confirm the validity of the E(2) model with transfer reactions using weakly-bound beams are discussed.     

Quadrupole collectivity of neutron-rich neon isotopes

The Angular Momentum Projected Generator Coordinate Method, with the quadrupole moment as collective coordinate and the Gogny force (D1S) as the effective interaction, is used to describe the properties of the ground state and low-lying excited states of the even-even neon isotopes ^20-34Ne, that is, from the stability valley up to the drip line. It is found that the ground state of the N = 20 nucleus ³⁰Ne is deformed but to a lesser extent than the N = 20 isotope of the magnesium. In the calculations, the isotope ³²Ne is at the drip line in good agreement with other theoretical predictions. On the other hand, rather good agreement with experimental data for many observables is obtained. Received: 19 Novemeber 2002 / Accepted: 24 January 2003 / Published online: 8 April 2003     

Semi-inclusive deep inelastic lepton scattering off complex nuclei

It is shown that in semi-inclusive deep inelastic scattering (DIS) of electrons off complex nuclei, the detection, in coincidence with the scattered electron, of a nucleus (A−1) in the ground state, as well as of a nucleon and a nucleus (A−2), also in the ground state, may provide unique information on several long standing problems, such as: i) the nature and the relevance of the final state interaction in DIS; ii) the validity of the spectator mechanism in DIS; iii) the medium induced modifications of the nucleon structure function; iv) the origin of the EMC effect. Received: 4 March 1999