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.     

Bonding potential between two12C nuclei

The potential between two¹²C nuclei in linear chain configuration has been calculated microscopically using the Ali-Bodmerα-α potential. This potential shows a pocket and compares well in the tail region with the phenomenological potential extracted before, from the data on the quasi-molecular resonances of the¹²C +¹²C system. This provides support to the diatomic like rotation-vibration picture of quasi-molecular states.     

On the nuclear matter approach to the heavy-ion optical potential

A simple theory of the heavy-ion optical potential oV, based on the local density approximation, is presented. The colliding ions are described locally as two slabs of nuclear matter. The real part of the energy density of the two slabs is derived from the properties of nuclear matter, and for the imaginary part the “frivolous model” is applied. Results for oV in the case of two slabs are presented and compared with results of other calculations. Arguments are given in favour of using the frivolous model in the optical potential and the VUU calculations for heavy-ion collisions.     

Analysis of elastic scattering of pi-mesons by nuclei within the microscopic optical potential

The microscopic pion-nucleus optical potential defined by the pion-nucleon scattering amplitude and the density distribution function of the target nucleus is applied to obtain the differential cross section of the elastic pion-nucleus scattering based on the solution to the relativistic wave equation. This allow one to account for effects of the relativization and distortion by the potential field. Data on π^±-meson scattering on ²⁸Si, ⁵⁸Ni, and ²⁰⁸Pb nuclei at T _lab = 291 MeV are analyzed and the parameters of the in-medium πN-amplitude are obtained. The parameters are compared with similar parameters for scattering on free nucleons.     

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.     

On the relation between Brueckner theory and Jastrow theory of nuclear matter

The two- and three-hole-line contributions to the ground state energy as calculated from Brueckner theory are derived from a cluster expansion followed by variation of the trial function. The implications of that derivation both for Brueckner theory and for Jastrow theory are worked out in detail. It is argued that the Jastrow theory is able to give simpler methods to calculate the ground state energy which may be of the same accuracy as current Brueckner calculations. It is shown that the single-particle potential of Brueckner theory is intimately related to a subsidiary condition used in the variation of the trial function. The main steps which have to be taken in a derivation of the general hole-line expansion from Jastrow theory are indicated. It is shown that the hole-line expansion is not a cluster expansion in the sense of Jastrow theory, and an interpretation is given of the “self-consistent choice” of the single-particle potential advocated in Brueckner theory.     

An equation of state for nuclear and higher-density matter based on relativistic mean-field theory

A model stress tensor for high-density matter based on a linearized relativistic quantum field theory is examined. The two coupling constants are fit to nuclear matter. Other properties of nuclear and neutron matter and neutron stars are then implied.     

Interplay between two- and three-body interaction in light nuclei and nuclear matter

A recent study of different models of three-nucleon interaction (TNI) in ³He, ³H, ⁴He and nuclear matter is extended to study the influence of different choices of the accompanying two-body interaction. A new two-body potential, Argonne υ₁₄, is coupled with both the Tucson and isobar intermediate-state models of two-pion-exchange TNI, with a phenomenological intermediate-range repulsive TNI added to the latter. Variational calculations are carried out for these systems, and compared to the earlier work. We find that a stronger tensor component in the two-body potential, as typified by a larger deuteron D-state percentage, gives more attraction for the TNI, counteracting the saturation effect obtained when only two-body forces are considered.     

Self-consistent calculation of the optical potential and ground-state properties of nuclear matter

On the basis of the Green-function formalism, we performed a self-consistent calculation of the self-energy ∑(k, ω) of a particle interacting with the infinite nuclear medium. The function ∑(k, ω) was mapped out in the energy-momentum plane, and the single-particle energy ω(k), momentum distribution ?(k) and the “on-shell” part of the self-energy, ∑(k, ω(k)), were defined, from which all physical properties followed. In particular we investigated the ground-state properties of nuclear matter in two Λ-approximations of the T-matrix. In one, the intermediate two-particle propagator, Λ₀₀, represented free-particle propagation; in the other, called Λ₁₁, intermediate states included both interacting particles and holes. Pauli principle effects were included in both approximations. The second approximation was expected to be conserving because it included a large part of the rearrangement effects which, we found, contributed ～6 MeV per particle to the average energy and ～28 MeV to the singleparticle energy at zero momentum. The Hugenholtz-van Hove theorem was nearly satisfied, with only 1 MeV separating the chemical potential from the average energy. We also studied, in the Λ₀₀-approximation, the optical potential for the scattering of a particle by a large nucleus; it was directly related to the “on-shell” part of the self-energy. It was found that, below 100 MeV, the real part varied as (?90 + 0.584E) [MeV], and the imaginary part as (2.4 + 0.009 E) [MeV].     

A microscopic,anharmonic quasiparticle-phonon coupling theory for vibrational nuclei

A microscopic method of describing quasiparticle-phonon coupling, based upon an equation-of-motion technique for the pairing plus quadrupole Hamiltonian, retaining anharmonic terms, is used to calculate the spectra of both even and odd isotopes of paladium and cadmium. The spurious states in the odd nucleus calculation are removed before diagonalization. The basis is up to three phonons for even nuclei and up to two phonons plus a quasiparticle for odd nuclei.     

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.     

Complex coupled-mode theory for tapered optical waveguides

A coupled-mode formulation based on complex local modes is developed for tapered and longitudinally varying optical waveguides. Different from the conventional coupled-mode theory that requires integration over the entire spectrum of radiation modes, the new formulation treats the radiation fields via discrete complex modes similarly to the guided modes. Accuracy, convergence, and scope of validity for the solutions of the complex coupled-mode equations are investigated in detail for a typical single-mode waveguide taper. It is demonstrated that the complex coupled-mode theory has overcome the difficulties of the conventional theory in simulation of radiation field effects while preserving the simplicity and intuitiveness of this popular method.     

Comparison of neutron resonance spacings with microscopic theory for spherical nuclei

The nuclear level spacings determined from neutron resonance experiments for nuclei with 20 ≦ A ≦ 148 and 181 ≦ A ≦ 209 are compared with spacings calculated for spherical nuclei with a microscopic theory which includes the nuclear pairing interaction. Single particle levels of Seeger et al. and Nilsson et al. are used in the calculations. The gross features of the experimental data due to nuclear shells are reproduced with the microscopic theory. In addition, the absolute agreement between experiment and theory is reasonable (67 % of the 151 cases examined agree to within a factor of 2) in view of uncertainties in the experimental data, the theoretical single particle levels and the pairing strength. Values of the spin cutoff parameter σ²(E), calculated with a microscopic theory, are included also for several doubly even nuclei and discussed in terms of nuclear shells.     

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.     

A relativistic quantum field theory for rotating nuclear matter

The relativistic quantum field theory of Walecka is extended to rotating nuclear systems using a mean-field Thomas-Fermi approximation. Self-bound systems exhibit centrifugal stretching and a maximum angular frequency. Systems constrained to a cylindrical box develop central holes for large angular frequencies.     

Effective mass enhancement and the imaginary part of the optical potential in nuclear matter

We demonstrate that the Correlated Basis Function (CBF) approach allows for an efficient quantitative determination of the optical-model potential in nuclear matter.     

Infinite nuclear matter model and a new mass formula for atomic nuclei

The ground-state energy of an atomic nucleus with asymmetryβ is considered to be equivalent to the energy of a perfect sphere made up of the infinite nuclear matter of the same asymmetry plus a residual energyη called the local energy,η represents the energy due to shell, deformation, diffuseness and exchange Coulomb effect etc. Using this picture and the generalized Hugenholtz- Van Hove theorem of many-body theory a new mass formula has been developed. Based on this, a mass table containing the mass excesses of 3481 nuclei in the range 18 ⩽A ⩽ 267 has been made. This mass formula is compared with other mass models.     

Critical analysis of quark-meson coupling models for nuclear matter and finite nuclei

Three versions of the quark-meson coupling (QMC) model are applied to describe properties of nuclear matter and finite nuclei. The models differ in the treatment of the bag constant and in terms of non-linear scalar self-interactions. In two versions of the model the bag constant is held fixed at its free-space value whereas in the third model it depends on the density of the nuclear environment. As a consequence opposite predictions for the medium modifications of the internal nucleon structure arise. After calibrating the model parameters at equilibrium nuclear matter density, binding energies, charge radii, single-particle spectra and density distributions of spherical nuclei are analyzed and compared with QHD calculations. For the models which predict a decreasing size of the nucleon in the nuclear environment, unrealistic features of the nuclear shapes arise.