Similarities between the lattice gas model and some other models of nuclear multifragmentation

We continue our development of the nuclear lattice gas model by exploring links and similarities with other theoretical approaches to nuclear multifragmentation: the percolation model and the statistical multifragmentation model. It is shown that there exists a limit where the lattice gas model reduces to the percolation model. The similarity between the lattice gas model and the statistical multifragmentation model is more indirect and we utilize the equations of state in the two models. By using the law of partial pressures we obtain P-ϱ diagrams for the statistical multifragmentation model and find that these are remarkably similar to those obtained in the lattice gas model via an exact evaluation of the nuclear partition function on the lattice. For completeness, we also compute the P-ϱ diagram for a system obeying pure classical molecular dynamics with a simple two-body force.     

The pion propagator in relativistic quantum field theories of the nuclear many-body problem

Pion interactions in the nuclear medium are studied using renormalizable relativistic quantum field theories. Previous studies using pseudoscalar πN coupling encountered difficulties due to the large strength of the πNN vertex. We therefore formulate renormalizable field theories with pseudovector πN coupling using techniques introduced by Weinberg and Schwinger. Calculations are performed for two specific models: the scalar-vector theory of Walecka, extended to include π and ρ mesons in a non-chiral fashion, and the linear σ-model with an additional neutral vector meson. Both models qualitatively reproduce low-energy πN phenomenology and lead to nuclear matter saturation in the relativistic Hartree formalism, which includes baryon vacuum fluctuations. The pion propagator is evaluated in the onenucleon-loop approximation, which corresponds to a relativistic random-phase approximation built on the Hartree ground state. Virtual $\text{N}\text{N}$ loops are included, and suitable renormalization techniques are illustrated. The local-density approximation is used to compare the threshold pion self-energy to the s-wave pion-nucleus optical potential. In the non-chiral model, s-wave pion-nucleus scattering is too large in both pseudoscalar and pseudovector calculations, indicating that additional constraints must be imposed on the lagrangian. In the chiral model, the threshold self-energy vanishes automatically in the pseudovector case, but does so for pseudoscalar coupling only if the baryon effective mass is chosen self-consistently. Since extrapolation from free space to nuclear density can lead to large effects, pion propagation in the medium can determine which πN coupling is more suitable for the relativistic nuclear many-body problem. Conversely, pion interactions constrain the model lagrangian and the nuclear matter equation of state. An approximately chiral model with pseudovector coupling is favored. The techniques developed here allow for a consistent treatment of these models using renormalizable relativistic quantum field theores.     

A semimicroscopic model of nuclear vibrations with separable forces and the giant dipole resonance of 12C

In the generalized ph basis generated for the realistic nuclear ground state, the nuclear hamiltonian is approximated by an expression containing the separable effective forces and terms which can be estimated from the spectroscopic data. The model hamiltonian obtained is used to describe normal nuclear vibrations. The application of this approach in the shell-model theory of nuclear reactions is discussed. The S-matrix for nucleon-nucleus scattering is calculated explicitly. The ¹²C photodisintegration calculation is made as a test example.     

Nuclear matter in the skyrme model

The applicability of the Skyrme model to the analysis of nuclear matter is discussed. Constraints on an ansatz that describes a cubic skyrmion crystal are presented. Properties of this ansatz are studied numerically. Results are used to discuss nuclear matter in the large-N limit and at N = 3.     

Hypernuclear binding energies in the α-particle model

The binding energies B_Λ for the hypernuclei with baryon number A = 4N + 1 up to_Λ²⁵Mg have been calculated by the variational method in the framework of Brink's α-particle model. The central ΛN potential is adjusted to the binding energy of_Λ⁵He. Due to their strong dependence on the nuclear density, the B_Λ energies are very sensitive to the choice of the effective nuclear interaction and have reasonable values for large A with the potential B1 of Brink and Boeker. The comparison with the B_Λ values obtained in the limiting shell model and the consideration of two different Λ-particle wave functions both indicate that the effect of nuclear clustering on B_Λ is significant only for_Λ⁹Be and_Λ¹³C. The nuclear distortion due to the Λ-particle binding is also evaluated in this calculation.     

Central depression of the nuclear charge distribution

As a systematic feature of all measured charge distributions we find a shift in the form-factor zeroes as compared to a simple folding model. To first order, this shift can be interpreted as resulting from the central depression w, caused by the Coulomb repulsion. Accounting for it leads to an increase in the surface width of nuclear charge distributions by 0.105 fm. This interpretation of the experimental findings is compared with the droplet model, which relates w with the compression modulus K and the asymmetry energy J. Accounting for w leads to an increase in the extrapolated nuclear matter density by 7.5%. However, this macroscopic model is not able to describe the experimental results in detail since w is also influenced by shell effects. HF + BCS calculations with effective Skyrme-type interactions reproduce part of the data, revealing the influence of shells on w. Here, too, there remain discrepancies in details. A level of accuracy is reached at which most probably also the skewness of the charge distribution must be taken into account.     

Reflection asymmetry in the calculations of nuclear mass parameters in terms of the modified oscillator model

The cranking model has been adapted to the four dimentional (?₂, ?₃, ?₄, ?₅) nuclear shape parametrization of the Nilsson model. Some advantages of the nuclear shape parametrization in terms of Legendre polynomials are pointed out. The most characteristic properties of the mass parameters and their dependence upon the shell structure are illustrated and discussed for some actinide nuclei.     

Calculation of excitation functions of the 5 4 , 5 6 , 5 7 , 5 8 Fe(p,n) reaction from threshold to 30 MeV

The cross-sections for the formation of ^54,56,57,58Co in the ^54,56,57,58Fe(p, n) reaction from threshold to 30 MeV protons have been theoretically calculated using the TALYS-1.4 nuclear model code, whereby we have studied major nuclear reaction mechanisms, including direct, pre-equilibrium and compound nuclear reaction. Subsequently, the level density and shell damping parameters have been adjusted and at the same time, the odd–even effects are well comprehended. The excitation functions have been compared with experimental nuclear data. It is observed that the theoretical cross-sections match fairly well. Proton-induced reaction cross-sections provide clues to understand the nuclear structure and offers a good testing ground for ideas about nuclear forces. In addition, complete information in this field is very much required for application in accelerator-driven subcritical system.     

The anomalous behaviour of nuclear structure functions revisited

The anomalous behaviour of the nuclear structure functions is discussed in the framework of a simple statistical parton model, where the nucleus is treated as a bag of uncorrelated partons. We show that the model reproduces correctly the main features of the effect and, to some extent, it is even successful at the numerical level. The characteristic prediction of the model (to be tested experimentally) is a saturation law: for largeA (=nuclear mass number) the anomalous nuclear behaviour of the structure functions is described by a universal (i.e.A-independent) function of the Bjorken variable.     

A continuum calculation for the giant dipole resonance in28Si including the effect of collective correlations

Continuum shell model calculations for the giant dipole resonance in²⁸Si based on both the 1p 1h model and the collective correlation model are described and the results compared with experiment. The eigenchannel theory of nuclear reactions has been used to include the effect of the particle continuum.     

Study of the hadronization process in cold nuclear medium

The improved two-scale model is used to perform the fit to the semi-inclusive deep-inelastic scattering (SIDIS) data of HERMES experiment at DESY on nuclear targets. The ratio of hadron multiplicity on nuclear target to the deuterium one is chosen as observable, as usually. The two-parameter’s fit gives satisfactory agreement with the data in term of χ ² criterium. Best values of parameters are then used to calculate the nuclear multiplicity ratio for the hadrons not included in the fit procedure.     

Self-consistent calculations of hypernuclear properties with the Skyrme interaction

An extension of the Skyrme-Hartree-Fock formalism is proposed for calculating Λ binding energies (B_Λ) in hypernuclei throughout the periodic table. The calculation includes the self-consistent nuclear polarization by the Λ hyperon. Realistic estimates for ground state B_Λ's are obtained with a simple effective ΛN force and are compared with a Λ-nucleus potential model. The Λ particle excitation spectra have also been calculated. They are discussed in the context of strangeness analog state formation and the emphasis is put on the symmetry between Λ and nuclear states.     

Systematic study of the heavy-ion fusion barrier in the frozen approximation

The height and position of the fusion barrier for the real part of the interaction potential between two colliding nuclei are studied as a function of the Coulomb strength. The calculations are performed in the framework of the spherical constrained HF + BCS formalism using the frozen approximation. The effective Skyrme type force SKa is used. The model contains no free parameters. For the height of the fusion barrier good agreement is found with the values obtained using the empirical Bass potential that is known to reproduce well the data for many nuclear systems. In contrast, the recently observed apparent rise of the fusion barrier (‘extra-extra-push’) for very massive nuclear systems with a product of nuclear chargesZ ₁ xZ ₂ above 1600 cannot be reproduced. We also give estimations for the overlap of the mass densities of both colliding nuclei at the fusion barrier distance.     

Microscopical structure of the states of deformed nuclei in the neighborhood of the yrast line

A simple model is derived which allows one to study the structure of the nuclear states in the neighborhood of the “yrast” band. In the present scheme the precession motion plays a role of one of the normal modes of oscillations. (The structure of the dispersion equation for this mode corresponds to the well known classical formula.) Vibrational states associated with quadrupole oscillations of the nuclear shape are determined from a general equation. At slow rotation this equation breaks up into the known equations for β-, Δ- and γ-vibrations and non-collectivized K^π = 1⁺ excitations.     

Nuclear physics aspects of the astrophysical <Emphasis Type="Italic">p</Emphasis>-process

An overview is given on the experimental nuclear physics aspects of the astrophysical p-process that is responsible for the production of the heavy proton-rich nuclei known as p-nuclei. The nuclear physics input of the p-process scenario involves the knowledge of radiative capture cross sections, mostly calculated by the Hauser-Feshbach statistical model. Our experiments test the reliability of the model calculations in the proton-rich region as well as provide experimental information on the cross sections relevant to the p-process.     

Simple microscopic model for the scalar-isoscalar component of the Landau-Migdal amplitude

A simple microscopic model is proposed that describes the coordinate dependence of the zeroth harmonic f ₀(r) of the scalar-isoscalar component of the Landau-Migdal amplitude. In the theory of finite Fermi systems due to Migdal, such a dependence was introduced phenomenologically. The model presented in this study is based on a previous analysis of the Brueckner G matrix for a planar slab of nuclear matter; it expresses the function f ₀(r) in terms of the off-mass-shell T matrix for free nucleon-nucleon scattering. The result involves the T matrix taken at the negative energy value equal to the doubled chemical potential μ of the nucleus being considered. The amplitude f ₀(r) found in this way is substituted into the condition that, in the theory of finite Fermi systems, ensures consistency of the self-energy operator, effective quasiparticle interaction, and the density distribution. The calculated isoscalar component of the mean nuclear field V(r) agrees fairly well with a phenomenological nuclear potential. Owing to a strong E dependence of the T matrix at low energies, the potential-well depth V(0) depends sharply on μ, increasing as |μ| is reduced. This effect must additionally stabilize nuclei near the nucleon drip line, where μ vanishes.