Showing papers on "Nuclear matter published in 1970"

Variation in Nuclear-Matter Binding Energies with Phase-Shift-Equivalent Two-Body Potentials

Abstract: For any given two-body Hamiltonian, there exists a large class of unitarily equivalent Hamiltonians that lead to the same scattering phase shifts at all energies. The purpose of this paper is to exhibit typical saturation curves for reasonable equivalent potentials. The binding energy per particle changes by several MeV in either direction, and the saturation minimum shifts to higher or lower density as the binding increases or decreases. Softening the potential increases the binding. The separation approximation for the reaction matrix provides qualitative insight into these effects. Our exact calculations start with simple local $s$-wave potentials with either a hard core or a Yukawa core. The binding energy per particle is calculated in the Brueckner approximation with self-consistent single-particle energies below the Fermi level. For our examples we use unitary transformations that differ from the identity by a short-range operator of rank 2 and transformations induced by distortions of the radial scale. The latter class of transformations alters the core radius and produces potential terms that are linear in the square of the momentum.

Nuclear surface properties with a simple effective interaction.

Abstract: A simple three-part density-dependent effective interaction is used to calculate several general properties of the semiinfinite nuclear surface. This interaction, which is referred to here as the modified $\ensuremath{\delta}$ interaction (MDI), is quite similar to one introduced by Skyrme. The three parameters of the MDI are fixed by fitting the binding energy and density of infinite nuclear matter with $N=Z$ and also the ground-state energy of $^{16}\mathrm{O}$, all in first-order perturbation theory.The nuclear surface properties are calculated in several different ways. First, they are extracted directly from the single-particle wave functions of a one-dimensional static Woods-Saxon potential. The diffuseness and depth of the potential are obtained by minimizing the surface energy. This procedure is called the independent particle model (IPM). The resulting surface thickness of 2.2 fm and surface energy of 19.3 MeV and the approximately Fermi shape of the density distribution are in good agreement with empirical results.The calculations were then repeated using the Thomas-Fermi approximation to obtain the density. The resultant surface thickness and surface energy, 2.0 fm and 16.0 MeV, are considerably smaller than the IPM results. Furthermore, the calculated density distribution has a longer "shoulder" inside the nucleus and a shorter "tail" outside than the IPM distribution.

The hyperspherical-expansion approach to nuclear bound states

Abstract: The first approximation of the hyperspherical-expansion approach to nuclear bound states is discussed in the limit of largeA. For velocity-independent potentials, the results given in a previous paper are rederived in a more explicit and straightforward fashion, and a more complete discussion of the next-to-leading terms in the asymptotic formula for the binding energy is given. For velocity-dependent potentials similar results are obtained. The density distribution that obtains in this treatment is exhibited and discussed. A comparison with the analogous formula for the binding energy per nucleon that obtains in the Fermi-gas treatment of nuclear matter is made, including the presentation of numerical results for the potential of Nestor, Davies, Krieger and Baranger.

Models for neutron-core stars based on realistic nuclear-matter calculations

Abstract: Neutron core star models based on realistic nuclear matter calculations and hyperons equation of state

Lambda n tensor forces for scattering and for the lambda particle binding in nuclear matter

Abstract: The effect of ΛN tensor forces on the Λ-particle binding in nuclear matter is studied with the use of second-order perturbation theory and the Brueckner-Bethe reaction-matrix approach in the g-matrix approximation. The g matrix is calculated self-consistently by use of the Kallio-Day version of the reference-spectrum method. The free kinetic energies are assumed for the unoccupied states. One-boson-exchange (OBE) models indicate that the ΛN tensor force is expected to be of short range and moderate strength. For short-range tensor forces the dominant momentum components are very large, and the effects of such forces are only slightly modified by the nuclear medium. On the other hand, if the ΛN tensor forces were of rather long range, they would be quite strongly suppressed in nuclear matter. These features are very clearly exhibited by consideration of the effective nonlocal central potentials that represent the (s-state) effect of tensor forces for nuclear matter and for scattering. The ratio of the (nuclear-matter) expectation values of these two effective potentials is a good measure of the suppression. The expectation value of the effective potential for nuclear matter is just the second-order perturbation-theory energy. Reaction-matrix calculations show that higher-order effects may become quite important for shorter ranges. Such calculations have, in particular, been made for various mixtures of central and tensor forces chosen to give a constant s-wave scattering length. Yukawa shapes corresponding to the kaon and one- and two-pion masses were used, as well as "realistic" OBE potentials with a hard core and a tensor component due to kaon exchange (and also approximately due to η exchange). For a particular mixture, the suppression is measured by the reduction in the well depth relative to the depth for a purely central potential which has the same hard core and the same scattering length and effective range as the mixture. For the short-range tensor forces there is rather little suppression even for very strong tensor forces which account for all the triplet scattering. Different assumptions about the d-state interaction have an almost negligible effect on the s-state well depth if the same assumption is made for both scattering and nuclear matter. Similar considerations are made for the effect of tensor forces in the p wave, for which we find very little suppression (≲1 MeV). We conclude that if central and short-range tensor forces are chosen to compensate each other for low-energy scattering, they will also compensate each other quite closely for nuclear matter. In particular, for the OBE potentials with strengths consistent with the phenomenological values of the ΛNK¯ coupling constants, the reduction in the well depth is at most about 4 MeV. The conclusions about the ΛN interaction obtained from a comparison of the calculated and phenomenological well depths are, therefore, effectively unchanged by the presence of a ΛN tensor force. Consequently, in order to bring the two numbers into agreement, it is necessary to invoke a substantial short-range repulsion, a rather weak p-state interaction, and suppression of the ΛN−ΣN coupling and/or repulsive ΛNN three-body forces.

Nuclear Forces and Nuclear Energetics

Abstract: Both a static and a momentum-dependent potential are derived from one-meson-exchange Born amplitudes, and are adjusted to fit (i) the deuteron binding energy and quadrupole moment, (ii) $S$, $P$, and $D$ partial waves from 25 to 310 MeV, and (iii) the binding energy and saturation property of nuclear matter. This is possible through a different form of the central and tensor potentials which has not been used previously to calculate problems (i), (ii), and (iii) above. We find the $\ensuremath{\sigma}$ meson unsuitable to describe the two-pion-exchange region in that a potential with meson parameters common to all partial waves is not achieved.

Fundamental nuclear interaction.

Abstract: GOPEB based upon known mesons have been found which realistically describe a massive accumulation of the experimental nuclear data up to 400 Mev. The N-N potential according to these models consists primarily of weak residual central terms surviving the cancellation of large repulsive and attractive vector and scalar static components; relativistic interactions arising from the exchange of pseudoscalar, vector, and scalar mesons and dipole type terms arising from the ρ meson. The major dynamic terms are direct analogs of magnetic interactions illustrated in Fig. 1. Allowance must be made for the effective dependence of the coupling constants upon spin and isospin states. The nucleons are distributed sources which give rise to nonsingular generalized Yukawa functions in N-N potentials.

The nuclear surface

Abstract: The nuclear surface cannot be sharply defined since the nuclear density is a continuous function of radius. By convention, one defines a surface thickness parameter as the width of the region in which the nuclear density falls from 90% to 10% of the central density. This parameter is known to be approximately 2?5 fm for the whole range of spherical nuclei, at least for those nuclei for which a central region of roughly constant density has meaning, that is above, say, A = 40. Experimentally it is an ill-defined parameter and appears to be independent of mass number - again this statement applies only to spherical nuclei. It is a matter of some speculation whether or not the constitution of this surface region is the same as that of the interior. Theoretically a preponderance of neutrons (i.e. a neutron/proton ratio greater than N/Z) is desirable in the surface and the experimental measurements are consistent with a `neutron skin' of perhaps 0?2 to 0?3 fm. Though the size of the nuclear charge distribution has been determined with great precision, the nuclear matter distribution is known with much less certainty and one still cannot rule out the possibility that protons and neutrons have a common distribution. One must also consider the possibility that nucleons in the nucleus are clustered into sub-units such as ?-particles. Experiments designed to test this by knocking out these clusters look specifically at the nuclear surface since the mean free path of these sub-units in the central region must be too small to allow them to escape even if struck by a deeply penetrating probe. The results of such experiments seem to indicate that the nuclear matter in the surface region is largely condensed into ?-particles. Another class of experiments involving meson-probes indicates a degree of spatial correlation of nucleons in the nuclear surface which is consistent with ?-particle clustering. Recently doubt has been thrown on the interpretation of these experiments, so clustering into ?-particles cannot be considered to be established.