PT violating single particle nuclear potential

We calculate aPT-odd one-loop meson radiative correction to the scattering amplitude of a nucleon on the external field of the nucleus. The nonrelativistic limit of this amplitude, Fourier transformed to the configuration space, can be interpreted as a single particlePT-odd potential for a valence nucleon. Bound state effects on this potential are evaluated and found to be negligible.     

The two-pion-exchange three-nucleon potential and nuclear matter

We derive the complete three-nucleon potential of the two-pion-exchange type, suitable for nuclear structure calculations, by extending away from the forward direction the subthreshold off-pion-mass-shell πN scattering amplitude of Coon, Scadron and Barrett. The off-mass-shell extrapolation, subject to current algebra and PCAC constraints, yields approximately model independent amplitudes (in that they depend primarily on πN data) in the complete potential. The subtraction of the forward propagating nucleon term from the amplitudes is done in greater generality than before. The contribution of this three-nucleon potential to the binding energy of symmetric nuclear matter is estimated using the perturbative formalism of McKellar and Rajaraman. In our treatment of correlations in nuclear matter, the dominant three-nucleon potential has strong components from both s-wave and p-wave πN scattering. A three-body potential based on the p-wave Δ isobar can be considered a special case of the derived potential. Therefore, we are able to trace most of the discrepancies in previously reported binding energy contributions back to the assumed energy denominator in second order. We find the contribution of the three nucleon potential to the energy of symmetric nuclear matter to be ? 1.90 ± 0.2 MeV.     

The two-pion exchange NN potential in nuclear matter and nuclear stability

A meson exchange model of the ππ interaction which fits free ππ scattering data is used to calculate the interactions of pions in nuclear matter as a function of nuclear density. Polarization of the nuclear medium by the pions results in a marked increase in the s-wave ππ attraction at low energy. The influence of this effect on the nucleon-nucleon interaction is a corresponding increase with density of the NN central potential due to the exchange of two correlated pions, resulting in an NN interaction which fails to saturate. A possible mechanism for restoring the theoretical stability of nuclear matter is explored and found to be effective.     

Optical potential and nuclear matter

The relation of the parameters of the optical nucleon-nucleus potential to the characteristics of nuclear matter is established. The existing values of the parameters of the optical potential reflect well the binding energy per nucleon and the symmetry energy of nuclear matter. It is shown that the theorem of Hugenholtz and van Hove is not valid for the real part of the optical potential.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 97–100, January, 1978.     

Asymmetric nuclear matter and Skyrme potential

The binding energy, symmetry energy, pressure, incompressibility, and the velocity of sound are calculated for asymmetric nuclear matter using Skyrme interaction SkO’. The behavior of these physical quantities is studied for different values of the asymmetry parameter α _τ , the density ρ, and the temperature T. Good agreement is obtained in comparison with previous theoretical estimates and experimental data. The text was submitted by the authors in English.     

The energy dependent nucleus-nucleus optical potential in a nuclear matter approach

We calculated the energy dependent real and imaginary part of the nucleus-nucleus optical potential in a lab. energy domain between 50MeV and 225MeV per nucleon for the systems¹²C-¹²C and⁵⁸Ni-⁵⁸Ni. In our model we assume that the energetical behaviour of the colliding nucleons inside of the two overlapping nuclei is locally that of two colliding nuclear matter systems. Therefore the effective nucleon-nucleon interaction is calculated using a Bethe-Goldstone equation that includes the Pauli blocking caused by the two Fermi spheres and takes account of the presence of the other nucleons by their mean field. Neglecting finite range effects one can calculate the real and imaginary part by a folding procedure.     

The imaginary part of the nucleon optical potential in nuclear matter

We show that the energy dependence of the real part of the optical potential, or equivalently the effective mass of nucleons in nuclear matter, gives significant corrections to the imaginary part calculated with either impulse approximation or Brueckner's theory. These corrections greatly reduce the difference between theoretical and empirical strengths of the imaginary potential.     

The single-particle potential of nuclear matter in the LOCV framework

The density and momentum dependence of single-particle potential (SPP) and effective mass of symmetric nuclear matter are studied in the framework of lowest order constrained variational (LOCV) method. The Reid68, the Reid68-Δ and the ₁₈Av interactions are considered as the input nucleon-nucleon potentials. It is shown that the SPP of nuclear matter, at fixed density, is an increasing function of nucleon momentum, and it has different behavior for the Reid type potentials with respect to ₁₈Av interaction. We find good agreements between our LOCV SPP and those coming from others many-body techniques such as the (Dirac-)Brueckner-Hartree-Foch ((D)BHF), the fermion hypernetted chain (FHNC), mean field (MF), etc. On the other hand SPP dramatically depends on the density at low and high nucleon momentums. While the effective mass of nuclear matter increases as we increase the nucleon momentum, it decreases at the Fermi surface. Again, good agreements are observed between our calculated effective mass and those coming from the methods mentioned above.     

Density dependence of the single-particle potential in nuclear matter

The single-particle potential in infinite nuclear matter is computed as a function of density and energy in a variety of relativistic mean-field models of nuclear matter. A comparison of this potential is made with that computed by Friedman and Pandharipande using the variational method. We also show that the self-consistent mean-field Hartree approximation satisfies the Hugenholtz-van Hove theorem. High-density behavior of the single-particle potential is considered.     

Nuclear matter equation of state with single particle correlations

Symmetrical nuclear matter at finite temperature is studied in the framework of the Brueckner-Hartree-Fock approximation extended to include single-particle correlations. A liquid-vapor phase transition is observed, wtih a critical temperature of about 20 MeV, in close similarity with Skyrme force calculations. The inclusion of single-particle correlations introduces a significant temperature dependence in the single-particle potential as well as in the nucleon effective mass. In this scheme the Hughenholtz-Van Hove theorem is well satisfied throughout the range of density and temperature considered.     

Single particle potentials of asymmetric nuclear matter in different spin-isospin channels

We investigate the neutron and proton single particle (s.p.) potentials of asymmetric nuclear matter and their isospin dependence in various spin-isospin ST channels within the framework of the Brueckner-Hartree-Fock approach. It is shown that in symmetric nuclear matter, the s.p. potentials in both the isospin-singlet T=0 channel and isospin-triplet T=1 channel are essentially attractive, and the magnitudes in the two different channels are roughly the same. In neutron-rich nuclear matter, the isospin-splitting of the proton and neutron s.p. potentials turns out to be mainly determined by the isospin-singlet T=0 channel contribution which becomes more attractive for the proton and more repulsive for the neutron at higher asymmetries.     

Single particle properties in asymmetric nuclear matter and TBF rearrangement effect

We have developed the formula and the numerical code for calculating the rearrangement contribution to the single particle (s.p.) properties in asymmetric nuclear matter induced by three-body forces within the framework of the Brueckner theory extended to include a microscopic three-body force (TBF). We have investigated systematically the TBF-induced rearrangement effect on the s.p. properties and their isospin-behavior in neutron-rich nuclear medium. It is shown that the TBF induces a repulsive rearrangement contribution to the s.p. potential in nuclear medium. The repulsion of the TBF rearrangement contribution increases rapidly as a function of density and nucleon momentum. It reduces largely the attraction of the BHF s.p. potential and enhances strongly the momentum dependence of the s.p. potential at large densities and high-momenta. The TBF rearrangement effect on symmetry potential is to enhances its repulsion (attraction) on neutrons (protons) in dense asymmetric nuclear matter.     

Relation between nuclear matter and nuclear potential in inelastic alpha—nucleus scattering

Inelastic transition form factors for alpha—nucleus collective excitations are derived from deformed matter distributions by averaging an effective alpha nucleus interaction over the nucleons in the nucleus. The method is an extension of the procedure of calculating the real part of elastic alpha—nucleus potentials from nuclear matter distributions. Numerical examples for the nuclei of ⁴²Ca and ¹⁴²Nd are given. The resulting inelastic form factors depend on the multipolarity of the inelastic excitation and differ from those conventionally derived from a deformed optical potential.     

Incompressibility and single-particle potential for asymmetric nuclear matter with Skyrme potential

The incompressibility and the single-particle potential of asymmetric nuclear matter have been investigated in the framework of the Skyrme interaction. These parameters have been studied as functions of the nuclear density, the neutron excess parameter, and the temperature. The ratio of the isothermal incompressibility of hot nuclear matter to the incompressibility of cold nuclear matter for different values of neutron excess as a function of temperature is calculated. It is observed that this ratio decreases with temperature increasing apart from pure neutron matter when the growth of temperature leads to the growth of incompressibility. The symmetry incompressibility has been calculated as a function of density for different values of temperature. The text was submitted by the authors in English.     

Nucleon-nucleus optical potential in a relativistic theory of nuclear matter

From a relativistic model of nuclear matter the optical potentials for nucleon scattering from ⁴⁰Ca and ⁹⁰Zr are obtained. These potentials are derived from the properties of the target nucleus and are essentially universal. This means that the integrated strength of the optical potential $\text{J}{}_{\mathrm{A}}\text{= (}\text{1}\text{A}\text{) ∫}\text{d}{}^3\text{r U}{}_{\mathrm{<mtext>op</mtext>}}\text{(r)}$ is very weakly dependent on A. The optical potential for antiparticle-nucleus scattering is also computed.     

Semi-microscopic optical potential calculation by the nuclear matter approach

In this paper the semi-microscopic nuclear matter approach has been introduced to calculate the microscopic optical potential. The first- and second-order mass operators in asymmetric nuclear matter have been derived with Skyrme effective interactions and the real and imaginary parts of the optical potential for finite nuclei have been obtained by applying a local density approximation. Five Skyrme interactions II–VI have been used and compared with the experimental data to determine how well these Skyrme interaction function for our purposes. Our results obtained in this simple way are to some extent comparable with those obtained with the “nuclear matter” and “nuclear structure” approaches without adjusting the parameters of the Skyrme interactions.     

The meson propagator in nuclear matter

We present a formal device for calculation of a meson propagator in infinite nuclear matter, through the calculation of the ground state energy of the system in the presence of external, static meson fields, using a pseudo-Hamiltonian simply related to the actual Hamiltonian. This approach is particularly well adapted for dealing with some effects that are not taken into account at all in multiple scattering approaches, for example, the effects of nuclear forces on the intermediate states which are involved in the meson-single-nucleon scattering. A theorem is proved about limiting conditions under which the charged pion propagator is independent of the nuclear forces. These conditions are nearly enough realized in π-nucleus scattering (sufficiently below the energy of the first resonance) so that we can evaluate the corrections perturbatively. The (virtually unknown) two-body force between the 3-3 resonance and nucleons is shown to be of considerable importance in determining the π-meson propagator.     

Single particle energies of nuclear matter and the reference spectrum method

The single particle energies and the ground state energy of a superfluid system of nuclear matter are investigated. There are two difficulties in calculating these quantitites in the t-matrix approximation: (1) On account of the structure of thet-matrix equation the single particle energy is a very complicated expression, which cannot be evaluated explicitly in general. (2) Due to the superfluidity of nuclear matter, there are singularities in thet-matrix. — To overcome these difficulties we apply the reference spectrum method, recently proposed byBethe, et al. The most important properties of a superfluid medium, the shift of the ground state energy and the gap in the single particle spectrum can then be very well described qualitatively. The quantitative results, however, are not satisfying. Furthermore, the estimation of the single particle potential is very much simplified. However, this is useful only for hole states. For particle statesk>k _F , the single particle energy cannot be calculated with sufficient accuracy on account of new complications coming from the rearrangement energy.     

The disassembly of nuclear matter

A statistical model is applied for multi-fragment final states in nuclear collisions with bombarding energies E/A ≈ 100 MeV. A portion of the intermediate system formed is assumed to decay according to the available classical non-relativistic phase space, calculated in a grand canonical ensemble. The model correlates and predicts many experimental observables in terms of three parameters: the available energy per nucleon, the isospin asymmetry, and the effective interaction volume.     

The theory of nuclear matter

This article is an account of the present position of theories of nuclear matter initiated some years ago mainly by Jastrow and Brueckner. Section 1 introduces the basic ideas. Section 2 discusses the variational approach. Section 3 develops methods involving partial summations in perturbation theory. The difficulties confronting the latter approach, and their partial resolution by ideas from superconductivity theory, are analysed in § 4.

Much of the formalism is relevant also in the theory of individual nuclei (see for example the review by Eden 1959) and in fields other than nuclear physics (see for example The Many Body Problem, Les Houches, 1958). However, in the selection of material our criterion has been relevance for the ground state of nuclear matter.