J M Irvine

A variational approach to nuclear matter with realistic potentials

Abstract A lowest order constrained variational method for calculating the binding energy of nuclear matter, previously proposed by the present authors, is extended to treat the strong tensor force components of realistic NN potentials. Numerical results are given for three early potentials of Gammel, Christian and Thaler, and reasonable agreement is found with a previous calculation of Ristig, Ter Louw and Clark which included three-body cluster contributions to the energy. A range of five potentials giving good fits to the experimental two-body NN data is also studied, and binding energies of typically 22 MeV per nucleon at saturation densities corresponding to k F ≈ 1.6–1.7 fm −1 , are found. For three of the potentials considered, comparison is made with the recent results of Pandharipande and Wiringa, which include the contributions to the energy from all of the most significant many-body clusters, and excellent agreement is found. It is suggested that explicit inclusion of some of the neglected internal degrees of freedom of the nucleons, such as the possibility of excitation to Δ (1236) states, might bring the equilibrium nuclear matter results closer to the empirical values.

Constrained variation in Jastrow method at high density

A method is derived for constraining the correlation function in a Jastrow variational calculation which permits the truncation of the cluster expansion after two-body terms, and which permits exact minimization of the two-body cluster by functional variation. This method is compared with one previously proposed by Pandharipande and is found to be superior both theoretically and practically. The method is tested both on liquid 3He using the Lennard-Jones potential and on the model system of neutrons treated as Boltzmann particles (“homework” problem). Good agreement is found both with experiment and with other calculations involving the explicit evaluation of higher-order terms in the cluster expansion. The method is then applied to a more realistic model of a neutron gas up to a density of 4 neutrons per F3, and is found to give ground-state energies considerably lower than those of Pandharipande.

Model nuclear matter calculations with a new fermion lowest order constrained variational method

Abstract We extend to deal with fennions a method of lowest order constrained variation for calculating the ground-state energy of dense systems, advanced previously by the present authors and shown to give excellent agreement for the Bethe homework problem. Using one state-independent correlation function in the new formalism, results with four different potentials that model various aspects of the real NN force are shown to be in excellent agreement with the other results available from various higher-order approximations, for densities up to and beyond nuclear matter density. The agreement is clearly superior to that obtained with any other lowest order approximation. When state dependence is introduced into the two-body correlation function in the new method, we find a considerable lowering of the energy in each case. It is suggested that this is a real effect which would be replicated in the other higher-order approximations, were they also extended to deal with state-dependent correlations.

Constrained Jastrow calculations

Abstract We present an alternative to Pandharipandes lowest order constrained variational prescription for dense Fermi fluids, which is justified on both physical and strict variational grounds. Excellent results are obtained when applied to the “homework problem” of Bethe, in sharp contrast to those obtained from the Pandharipande prescription.

Neutrino masses and the cosmic-neutrino background

The distortion of the cosmic-neutrino background, should neutrinos have a finite rest mass, is discussed. The possibility of detecting such a background experimentally is investigated and the consequences for the interpretation of the analysis of the end point of the tritium beta-decay spectrum is raised.

Nuclear shell-model calculations and strong two-body correlations

Abstract Two-body Hamiltonians, like the Reid interaction, are derived by fitting the two-nucleon data. It is an assumption that the many-body eigenstates of this Hamiltonian form a representation of the observed nuclear states. At best this has been demonstrated for the ground states of a few nuclei, e.g., the triton, and there the binding energy is off by 15–20%, this being attributed to uncertainties in the off-shell behavior of the interaction and to many-body forces. Since 15% of the total nuclear binding energy is much greater than the typical energy spacings observed in nuclear spectra, it is not at all clear that the calculable approximations to the many-body eigenstates of the N - N interaction can give useful information for nuclear spectroscopy. Using the method of correlated basis states coupled with an extremely large “no core” shell model basis as a set of trial variational functions, it is demonstrated that almost 100 levels in light nuclei can be identified with eigenstates of the Reid interaction. In so doing, a prescription is presented for defining effective operators in large shell-model calculations and the question of nuclear center of mass motion is reexamined.

A variational calculation of nuclear matter binding with the Reid potential

Abstract A constrained variational calculation for the binding energy of nuclear matter using the Reid soft core interaction and with tensor correlations treated exactly, is presented. Saturation is achieved at a density given by k F ≈ 1.75 fm −1 with a binding energy of 22 MeV per nucleon. This represents considerably more binding than is obtained in low order Brueckner perturbation calculations or in Pandharipandes lowest order constrained variational approach.

Shell-model data from a realistic N-N interaction

Abstract Using a local density-dependent reaction matrix calculated by Siemens and Negele from the Reid potential Hartree-Fock calculations are carried out on the closed-shell nuclei 5 He, 16 O and 40 Ca and on the closed-shell plus one-nucleon nuclei 5 He, 17 O and 41 Ca. These calculations yield a set of single-particle wave functions which may be used in shell-model calculations. Tables of interaction matrix elements for such calculations up to, and including, the Of-lp shell are presented.

Shell-model data from a realistic N-N interaction: (II). Negative parity states in 16O and 40Ca

Abstract Using interaction matrix elements and a single-particle representation obtained from a Brueckner-Hartree-Fock (BHF) calculation described in an earlier work1) (to be referred to as I), the negative-parity states of 16O and 40Ca are calculated in the particle-hole random phase approximation (RPA). In addition to the energies of the negative-parity states, the results of calculations of the ground state electric multipole transitions are also reported.

Effective interactions for sd-shell-model calculations

A simple, effective nucleon-nucleon interaction for shell-model calculations in the sd shell is derived from the Reid soft-core potential folded with two-body correlation functions which take account of the strong short-range repulsion and large tensor component in the Reid force. The interaction is in astonishing agreement with the fitted potentials of Preedom-Wildenthal (1972) and Chung-Wildenthal (1979) in the lower half of the sd shell and with Chung-Wildenthal in the upper half of the sd shell. The mass dependence of the interaction is compared with that postulated by Wildenthal (1984). The authors conclude that most of the mass dependence resides in the diagonal matrix elements.