J. da Providência

Some aspects of short-range correlations in nuclei

Abstract Short-range correlations are introduced into the nuclear wave function using a unitary operator whose form was originally suggested by Villars. The modification of electric-dipole transition rates as calculated in the shell model is discussed and is found to be small for the correlation we have assumed. Further, the effective interaction to be used for shell-model calculations is considered in the context of this theory and specific suggestions as to the nature of this interaction are put forth. Finally, it is shown how a modified Hartree-Fock procedure can be constructed for a finite system having short-range correlations.

VARIATIONAL APPROACH TO THE MANY BODY PROBLEM

Abstract The properties of a system of many fermions are studied with the help of the variational principle of quantum mechanics. A trial wave function is assumed which takes into account two-body correlations but neglects higher-order effects. From this assumption it follows in a natural manner that the ground-state energy of the system is essentially given by a simplified version of the Brueckner theory, but the excitation energies are given by the second random phase approximation. The existence of a variational basis for the equations derived may be useful for obtaining approximate solutions in practical cases.

First sound versus zero sound in finite Fermi systems

Abstract Based on a simple energy density functional results are presented for first and zero sound modes in small finite droplets of Fermi liquid with smooth, self-consistently determined equilibrium density ϱ 0 ( r ). The first sound results confirm the conclusions of the standard liquid drop model. They are contrasted to results of the fluid-dynamical scheme which was derived earlier from the generalized scaling approximation, which takes low-multipolarity distortions of the local Fermi surface into account. Energies, transition densities, currents and B (E l ) values are given for isoscalar electric modes for A = 208 and A = 1000. The comparison supports the view to consider giant resonances as zero sound modes of finite Fermi systems.

An extension of the random phase approximation

Abstract A theoretical scheme appropriate for generalizing the Hartree-Fock and RPA theories to include ground state correlations is developed. The Beliaev-Zelevinsky expansion is used for expanding the Hamiltonian in boson operators. The ground state wave function is defined as the independent boson wave function which minimizes the expectation value of the Hamiltonian. It follows that the ground state cannot mix with one- or two-boson wave functions, and this condition yields immediately equations generalizing the Hartree-Fock and the RPA equations. By considering the oscillations of slightly modified independent-boson wave functions around the equilibrium position, the boson-boson correlations due to anharmonic effects are introduced. Finally, it is shown that the present approach possesses formal properties similar to those of the RPA theory.

On Generalized Numerical Ranges of Operators on an Indefinite Inner Product Space

In this article, numerical ranges associated with operators on an indefinite inner product space are investigated. Boundary generating curves, corners, shapes and computer generations of these sets are studied. In particular, the Murnaghan–Kippenhahn theorem for the classical numerical range is generalized.

Effects of eight-quark interactions on the hadronic vacuum and mass spectra of light mesons

Abstract The combined effective low energy QCD Lagrangians of Nambu–Jona-Lasinio (NJL) and ’t Hooft are supplemented with eight-quark interactions. This work is a follow-up of recent findings, namely (i) the six quark flavour determinant ’t Hooft term destabilizes the NJL vacuum, (ii) the addition of a chiral invariant eight-fermion contact term renders the ground state of the theory globally stable; (iii) stability constrains the values of coupling constants of the model, meaning that even in the presence of eight-quark forces the system can be unstable in a certain parameter region. In the present work we study a phenomenological output of eight-quark interactions considering the mass spectra of pseudoscalar and scalar mesons. Mixing angles are obtained and their equivalence to the two angle approach is derived. We show that the masses of pseudoscalars are almost neutral to the eight-quark forces. The only marked effect of the second order in the SU(3) breaking is found in the η – η ′ system. The scalars are more sensitive to the eight-quark interactions. A strong repulsion between the singlet and octet members is the reason for the obtained low mass of the σ state within the model considered.

Mean-field theories with mixed states and associated boson expansions

Abstract A variational derivation of the Liouville-von Neumann equation of quantum-statistical mechanics is presented, in order to formulate mean-field approximations appropriate to mixed states. The Hartree-Fock and the RPA at finite temperatures are particular cases of the general formalism. A thermal boson expansion is defined, which allows us to describe anharmonic motion around a thermal excited state. In a numerical application on the basis of the Lipkin model, temperature-dependent phase transitions are observed.

Determination of the correlation structure of nuclei via inelastic electron scattering

Abstract It is suggested that the correlation structure of nuclei may be studied through the investigation of inelastic electron scattering form factors at large momentum transfer. A specific example, the excitation of the 3.56 MeV state in Li6, is considered in the Born approximation. The correlation correction is carried out using a cluster development for the transition operators, and quite large modifications of the shell-model amplitudes due to short-range correlations are found for q ≈ 3 fm−1.

Cluster expansion of operator averages for systems of many particles

Abstract A systematic method enabling us to expand operator averages of many-body systems in terms of cluster integrals has been developed. The cluster integrals may be conveniently defined with the help of a diagram technique anologous to the one used in perturbation theory and the method proposed is suitable for applying both the time independent and the time dependent variational principles to many-particle systems involving singular interactions. The Pauli principle is naturally incorporated into the definition of the cluster integrals and this may lead to a rapid convergence of the expansions. The expressions obtained are, as in the Hartree-Fock case, invariant under unitary transformations in the subspaces of the occupied and of the unoccupied single particle states.

Variational approach to nuclear fluid dynamics

Abstract A variational derivation of a fluid-dynamical formalism for finite Fermi systems is presented which is based on a single determinant as variational function and does not exclude the possibility of transverse flow. Therefore the explicit specification of the time-odd part has to go beyond the local χ-approximation, while the time-even part is taken in the generalized scaling form. The necessary boundary conditions are derived from the variation of the lagrangian. The results confirm previous simplified approaches to a remarkable degree for quadrupole modes; for other multipolarities the deviations are much less than might be expected according to a sizeable change in the transverse sound speed.