C. M. Shakin

RELATIVISTIC NUCLEAR STRUCTURE PHYSICS

Abstract We review a recently developed relativistic model of nuclear structure, and discuss the binding energy and saturation properties of nuclear matter, the density and momentum-transfer dependence of the effective force in nuclei and the parameters of a relativistic optical model. The model we describe is free of parameters other than those introduced in fitting free-space nucleon-nucleon scattering data. In contrast to standard models, the relativistic formulation is able to give a satisfactory description of the saturation properties of nuclear matter. The mechanism responsible for saturation in the relativistic model also accounts for the strong density dependence of the scalar-isoscalar part of the effective nuclear interaction found in phenomenological studies. The calculated values of the self-energy of a continuum nucleon in nuclear matter may also be used to estimate the parameters of the optical potentials used to fit nucleon-nucleus scattering data. Estimates based upon the local-density approximation are successful in reproducing both the energy and density dependence of the phenomenological optical potential.

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.

Vibrations of spherical nuclei

A second-order perturbation calculation of the low and intermediate energy levels of spherical nuclei is presented. The Hamiltonian for the nucleus is expanded in powers of terms that are, in a sense, proportional to the quadrupole tensor, and of terms that are proportional to the first time derivatlves of these quadrupole-tensor terms. The results are compared with the observed levels of Ni/sup 62/ between 1.17 and 2.89 Mev. (T.F.H.)

Single-particle resonances in the unified theory of nuclear reactions

Abstract A method for the treatment of single-particle resonances in the theory of nucleon-nucleus scattering is introduced which finds application in the projection operator theory of Feshbach. The example of the d 3 2 neutron resonance in the scattering from 16O is discussed.

Relativistic nuclear physics : theories of structure and scattering

The last decade has seen a revolution in how we think about nuclear structure. It has become clear that the nucleus is a relativistic system and that the motion of nucleons is best described by the Dirac equation. The book describes some of the successes achieved in the relativistic approach with an emphasis on parameter-free models.

ON MODEL CALCULATIONS OF NEUTRON WIDTHS AND STRENGTH FUNCTIONS

Abstract A procedure for calculating the neutron strength function as advanced by B. Block and H. Feshbach is considered. Methods are developed which relate the calculation of the strength function to the usual concepts of the shell model and nuclear optical model. Specific consideration is given to the isotopes of lead and tin and the agreement with experiment is good. Further, it is also shown that the neutron widths calculated for very simple excitations can be quite small for heavy nuclei due to cancellations which appear in a certain overlap integral. This result implies that the observation of a resonance of very small width does not necessarily imply the formation of a compound state of great complexity. The simple excitations were consider are a reasonable approximation to the virtual states of a compound nucleus such as Pb 209 , and in this case, the calculated widths agree in order of magnitude with the widths found experimentally.

Direct and compound nucleus effects in nuclear photodisintegration

Abstract A modified form of H. Feshbachs unified theory of nuclear reactions is used to construct the correct final state for the calculations of photodisintegration. The reaction theory used satisfies the requirements of the Pauli Principle. Further, a correlation is made between resonance phenomena and shell model states whose energies are determined to lie in the continuum of the complete nuclear Hamiltonian. Our calculated cross-sections include, in addition to the usual Breit-Wigner expression, another contribution which may be termed “direct.” It is important to note that the direct contribution to the cross section exhibits resonant behavior simultaneously with the Breit-Wigner expression.

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.

Description of gluon propagation in the presence of an A**2 condensate

There is a good deal of current interest in the condensate which has been seen to play an important role in calculations which make use of the operator product expansion. That development has led to the publication of a large number of papers which discuss how that condensate could play a role in a gauge-invariant formulation. In the present work we consider gluon propagation in the presence of such a condensate which we assume to be present in the vacuum. We show that the gluon propagator has no on-mass-shell pole and, therefore, a gluon cannot propagate over extended distances. That is, the gluon is a nonpropagating mode in the gluon condensate. In the present work we discuss the properties of both the Euclidean-space and Minkowski-space gluon propagator. In the case of the Euclidean-space propagator we can make contact with the results of QCD lattice calculations of the propagator in the Landau gauge. With an appropriate choice of normalization constants, we present a unified representation of the gluon propagator that describes both the Minkowski-space and Euclidean-space dynamics in which the condensate plays an important role.

Off-shell effects, form factors and electromagnetic operators in nuclei

Abstract We suggest that the nucleon is larger in nuclei than in vacuum. For the larger nucleons we have calculated modified electromagnetic form factors. Evidence for these modifications of nucleon properties may be obtained from the study of the EMC effect, the quenching of the longitudinal response, and the distribution of charge and matter in nuclei.