Showing papers on "Nuclear matter published in 1968"
TL;DR: In this paper, a reformulation of the optical model is developed in which the real parts of the potential are obtained from nuclear-matter distributions and the nucleon-nucleon force.
Abstract: A reformulation of the optical model is developed in which the real parts of the potential are obtained from nuclear-matter distributions and the nucleon-nucleon force. The model is applied to proton elastic scattering data at 14.5, 30.3, and 40.0 MeV and succeeds in fitting the data as well as, or better than, the standard optical model despite the fact that two fewer parameters are needed in the new model. Values, accurate to a few percent, are obtained for the nuclear rms matter radii which are independent of the incident proton energy. These values are greater than the corresponding rms proton radii obtained from electron scattering and muonic x-ray work, and indicate that nuclear neutron rms radii are greater than nuclear proton rms radii by about 0.6 F. Information is also obtained concerning the spin-isospin-independent part of the nucleon-nucleon force, indicating a mean-square radius of 2.25\ifmmode\pm\else\textpm\fi{}0.6 ${\mathrm{F}}^{2}$ and a volume integral of 400\ifmmode\pm\else\textpm\fi{}20 MeV ${\mathrm{F}}^{3}$. The neutron and proton density distributions found from this work and muonic studies are used to calculate the imaginary potential, and this is compared with the phenomenological form found in the analyses performed with the new model. The good measure of agreement between the two potentials indicates that the model can be extended to include this term in a more logical manner, and with fewer parameters, than in the standard formulation of the optical model. The model is readily extended, in appropriate cases, for use with complex particles.
297 citations
Abstract: A Thomas-Fermi theory of large, finite nuclei is developed. Realistic nuclear forces with repulsive core are assumed, and maximum use is made of the theory of nuclear matter. Simplifications are introduced wherever permissible. The local-density approximation with a certain correction is found to be valid. Tensor forces are replaced by a density-dependent, effective central force, the repulsive core by a density-dependent $\ensuremath{\delta}$-function interaction. The Thomas-Fermi expression for kinetic energy is shown to be good whenever the density is at least 17% of nuclear-matter density; under the same conditions, the Slater approximation to the mixed density $\ensuremath{\rho}({r}_{1}, {r}_{2})$ is valid. From the total energy of the nucleus, an integral equation is derived for the density $\ensuremath{\rho}(r)$. This is approximated by a differential equation which is solved analytically. The resulting density distribution has both similarities with and differences from the conventional, Fermi-type distribution. Our density agrees as well with electron-scattering experiments as the Fermi type does. The thickness of the nuclear surface comes out about 10% too large from our theory; the surface energy is in good agreement with the semiempirical value. So far, the number of neutrons and protons has been assumed equal, and the Coulomb force has been neglected.
149 citations
87 citations
TL;DR: The nuclei of a piece of iron compressed to a density of 108 g cm3~ will arrange themselves into a body centred cubic lattice with a melting temperature near 2 × 108 °K, corresponding to a thermal energy about 1 per cent of the coulomb repulsion between neighbouring nuclei as mentioned in this paper.
Abstract: The nuclei of a piece of iron compressed to a density of 108 g cm3~ will arrange themselves into a body centred cubic lattice with a melting temperature near 2 × 108 °K, corresponding to a thermal energy about 1 per cent of the coulomb repulsion between neighbouring nuclei1. For matter near the end point of thermonuclear evolution compressed to still higher densities the dominant nuclear species shift towards very neutron rich nuclei, with Z between 30 and 50, which arrange themselves into crystal lattices with an even greater melting temperature. Crystallization among nuclei can occur up to densities close to that of conventional nuclear matter where those protons that remain cluster into very neutron-rich nuclei which are surrounded by and exchange neutrons with an ambient degenerate neutron sea. Because canonical neutron star interiors are estimated to cool to an average temperature below 5 × 108 °K in less than 103 years2–4, the outer regions of such stars should be solid.
63 citations
TL;DR: Using the consistency condition on strong interactions implied by a partially conserved axial vector current together with reasonable assumptions about the behavior of the pion-nucleon scattering amplitude under extrapolation in pion mass, it was shown that long-range three-body forces in nuclear matter are essentially zero as discussed by the authors.
40 citations
TL;DR: In this paper, the energy density of neutron star matter is determined from Brueckner-theory calculations of nuclear matter and the pure neutron gas, and the relative density of protons, determined by minimizing the total energy, is found to increase with increasing matter density.
Abstract: The energy density of neutron star matter is determined from Brueckner-theory calculations of nuclear matter and the pure neutron gas. Three-body clusters are assumed to contribute negligibly to the nuclear energy, according to the theory of Bethe. The relative density of protons, determined by minimizing the total energy, is found to increase with increasing matter density. In addition, we find that muons would appear at about half the normal nuclear density.
37 citations
TL;DR: In this paper, an effective nucleon-nucleon potential for use in nuclear Hartree-Fock calculations has been constructed from a central potential, a velocity-dependent repulsive potential and tensor and spin-orbit potentials.
36 citations
TL;DR: In this paper, the binding energy was calculated from the energy-versus-density curve and the calculated parameters of Brueckner's theory of nuclei, and the results were not in conflict with each other, but they are only about 13 of the values bsed by Migdal and collaborators.
36 citations
TL;DR: The pionic three-body potential in nuclear matter is shown to be comparable with the two body potential in this paper, which is the pionic pionic potential in the case of nuclear matter.
Abstract: The pionic three-body potential in nuclear matter is shown to be comparable with the two-body potential.
33 citations
TL;DR: In this article, it is shown that procedures now exist which make it possible to obtain accurate information on the distribution of neutrons in nuclei, however, these procedures make considerable simplifications in their approach to the many-body problem and hence verification of their predictions through direct high energy experiments is urgently required.
TL;DR: In this article, an expansion of the ground state energy and of the single-particle excitation spectrum in powers of a small parameter p F a 0 (p F is the Fermi momentum, a 0 the radius of interaction).
TL;DR: In this paper, the surface properties of large nuclei were calculated based on the Thomas-Fermi theory of nuclear structure, where the realistic nuclear forces of Reid are assumed.
TL;DR: In this article, the authors examined pairing correlations in nuclear matter in a self-consistent model defined by a slightly generalized Bogoliubov-Valatin transformation on the entire Hamiltonian and compared with simpler models in which single-particle energies are given by Hartree-Fock and effective mass approximations.
TL;DR: In this article, collective motion in the nucleus is defined as change of the density distribution of nuclear matter in time, and the Hamiltonian of nuclear rotation is obtained with moments of inertia corresponding satisfactorily to experimental data.
Abstract: Collective motion in the nucleus is defined as change of the density distribution of nuclear matter in time On the basis of this definition the Hamiltonian of nuclear rotation is obtained with moments of inertia corresponding satisfactorily to experimental data The theory is easily applied to nuclei with non-axial equilibrium shape For the latter the parameters of non-axiality are considerably smaller than in the DAVYDOV-FILIPPOV model
TL;DR: In this article, the bulk properties of liquid 3He using the Bethe-Goldstone method and using Goldstone perturbation theory were calculated using all two and three-body Goldstone diagrams.
TL;DR: In this paper, all cluster contributions of zeroth and first-order in the cluster expansion of the expected Λ binding energy B Λ were evaluated and the resulting cluster convergence appears very satisfactory in all cases.
TL;DR: In this article, the Hartree-Fock approximation of the energy per particle function was shown to have saturation properties for certain classes of correlations using the realistic potential of Gammel, Christian and Thaler.
Abstract: The theory of nuclear matter is investigated by means of the method of unitary transformations in the special case of point transformations. The general formula for the energy per particle as a function of the density is given in Hartree-Fock approximation being neglected the induced three and more body forces for reasonable correlation functions. This function always shows saturation due to a term proportional tokF5 in the direct part of the approximation. The physical connexion of this term with the scattering amplitudes of the potential is shown. We point out the equivalence to orderkF3 of the energy per particle function of the unitary method with Jastrow and separation methods in their simplest form. The saturation properties are calculated for certain classes of correlations using the realistic potential of Gammel, Christian and Thaler.
TL;DR: In this article, the one-boson exchange potential model is studied in some detail and the parameters of a velocity-dependent potential based on such a model are fitted to reproduce two-body scattering data.
Abstract: The one-boson-exchange potential model is studied in some detail. The parameters of a velocity-dependent potential based on such a model are fitted to reproduce two-body scattering data. This potential is then used in nuclear-matter calculations. It is shown that the average binding energy of a nucleon in nuclear matter and the saturation density are in reasonable agreement with the experimental values.
TL;DR: In this paper, a local, central, density-dependent potential is derived from a given two-nucleon tensor force in nuclear matter, which can be used in finite nuclei calculations in order to determine the gross properties of nuclei.
Abstract: A local, central, density-dependent potential is derived from a given two-nucleon tensor force in nuclear matter. Such an effective force can be used in finite-nuclei calculations in place of the tensor force to determine the gross properties of nuclei.
TL;DR: In this article, a comparison of various methods used to calculate the second-order energy in nuclear matter is made and a general expression is derived for integrands depending only on k2,k′2 and k·k′, wherekandk′ are relative momenta.
TL;DR: In this paper, the ground state properties of nuclear matter were calculated in the Λ 11 -approximation proposed by Puff et al. Using a simple nucleon-nucleon interaction of the Yamaguchi type, the high momentum tail of the momentum distribution function was estimated.
TL;DR: In this paper, a functional variation, under a suitable integral constraint, of the first-order (−ϱ = 0.172 nucleon/fm3) trial expression derived by Downs and Grypeos [1] for the ground state energy of a Λ-particle in nuclear matter, is performed.
TL;DR: In this paper, the ground state properties of nuclear matter are calculated in the Λ11-approximation and a nucleon-nucleon interaction of the Yamaguchi-type and the s-wave part of Tabakin's potential have been considered.
Abstract: The ground state properties of nuclear matter are calculated in theΛ11-approximation1. A nucleon-nucleon interaction of the Yamaguchi-type and thes-wave part ofTabakin's potential have been considered. In both cases too large values for the density of nuclear matter and the binding energy per nucleon are found. The momentum distribution turns out to be very small for momenta larger than the Fermi momentum.
TL;DR: In this article, the role of real nuclear and Coulomb phase shifts in elastic scattering of strongly absorbed projectiles is investigated, and it is shown that the introduction of the Coulomb phases equally raises the minima, while the real nuclear phases raises some minima and reduces others.
TL;DR: In this article, the binding energy of nuclear matter has been analyzed in terms of the two-body and three-body contributions to the bounding energy of the nuclear force, and the results for the soft core and B-J potentials have been obtained.
Abstract: The theory of nuclear matter is modified in such a way that the concept of the one-body potential is given up for the off-energy shell and kept only for the on-energy shell. In this method no longer occur such complications as many-particle excitations which couple one by one through the off-en~rgy shell potential and we treat all higher order terms with a giv~n number of hole lines as a whole. Following this method the two-body and three-body con tributions to the binding energy are calculated for the hard core and soft core potentials. The two-body contributions are about 10 MeV for the soft core and 5 to 7 MeV for the hard core potentials. The three-body contribution is found to be sensitive to the behavior of the two-body correlation function in the outer healing region. The three-body contributions are repulsive and about 0.5 MeV at ro=1.1 fm for the soft core and 0.8 MeV at ro=1.6 fm for the B-J potential. In the· recent calculations of the binding energy of nuclear matter several methods have been developed and many results of the calculations based on these methods have been accumulated. Also the differences among the results from various types of nuclear force, especially the hard core and soft core potentials, have been investigated. In these numerical results, however, there are some ambiguities related to the treatment of the ofE-energy-shell one-body. potential and the higher cluster terms, especially the three-body correlations. In the calculation by Brueckner and GammeP) they obtained about 15 Me V for the binding energy per particle, which is quite close to the experimental value. They treated, however, the off-energy-shell effect inadequately, though the effect is included in the formalism itself. Bethe, Brandow and PetscheP) pointed out the importance of dealing with the off-energy-shell, effect correctly. Careful calculations have been performed by many authors.3) It has been shown that in the case of the hard core potentials the off-energy-shell effect brings about a large repulsive contribution and consequently much less binding energy.Sa,b,c) 'Harada et al. 3d ) made calculations for the soft core potentials and showed that in this case the off-energy-shell effect is not so remarkable and the binding energy is *) The preliminary work of this paper was contributed to International Conference on Nuclear Structure in Tokyo, 1967.
TL;DR: In this paper, the perturbation theory calculation of the core-polarization contribution to effective interactions in mass 18 nuclei is carried to higher order, and it is shown that the perturbing series appears to diverge.
TL;DR: In this paper, a variational calculation of the nuclear density distribution reveals that the neutron and proton distributions have the same half-density radius, the neutron surface thickness increases with neutron excess and the nuclear compressibility is reduced considerably from that of nuclear matter by the surface.