Symmetry energies of nuclear matter and the spin and isospin dependence of the nuclear single-particle potential in the Landau theory

The spin and spin-isospin symmetry energies of nuclear matter and the spin and isospin dependent terms of the nuclear single-particle potential at the Fermi surface are calculated within the frame of the Landau theory of the normal Fermi liquid from the existing sets of the Landau parameters. The possibility of the relation of these parameters to the experimental energies of certain collective nuclear excited states is pointed out. The results are also applied to the calculation of the symmetry and the spin-spin terms in the low energy nuclear optical model potential.     

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.     

Symmetry energy from neutron-rich fragments in heavy-ion collisions, and its dependence on incident energy, and impact parameters

The yields of fragments produced in the 60Ni+ 12C reactions at 80 A and 140 A MeV, and with maximum impact parameters of 1.5, 2 and 7.3 fm at 80 A MeV are calculated by the statistical abrasion-ablation model. The yields of fragments are analyzed by the isobaric yield ratio (IYR) method to extract the coefficient of symmetry energy to temperature (asym/T ). The incident energy is found to influence asym/T very little. It’s found that asym/T of fragments with the same neutron-excess I = N-Z increases when A increases, while asym/T of isobars decreases when A increases. The asym/T of prefragments is rather smaller than that of the final fragments, and the asym/T of fragments in small impact parameters is smaller than that of the larger impact parameters, which both indicate that asym/T decreases when the temperature increases. The choice of the reference IYRs is found to have influence on the extracted a sym /T of fragments, especially on the results of the more neutron-rich fragments. The surface-symmetry energy coefficient (bs/T ) and the volume-symmetry energy coefficient (bv/T) are also extracted, and the bs/bv is found to coincide with the theoretical results.     

Causality and the energy dependence of microscopic nucleus-nucleus potential

Microscopic nucleus-nucleus potentials have been calculated by the Tübingen Group, using the energy-density formalism, for several systems. If these potentials are to be interpreted as optical potentials which generate the elastic-scattering wave function and phase shifts, they would be expected to satisfy causality. It is shown by investigations of the energy dependence of the real and imaginary parts of the microscopic potentials that they are consistent with causality requirements.     

Optical-model potential and broad single-particle resonances

The dynamical energy dependence of the optical-model potential is studied in the case of a broad single-particle resonance. It is found that the optical-model potential is slowly energy-varying. The optical phase shift and the transmission coefficient are shown to display a resonance.     

Pressure dependence of the compressibility of alkali halides

The parameterC ₁=[(1/K _T )/P] _T , which describes the pressure variation of the compressibility, has been examined correlating the thermodynamical and interatomic potential approaches employing fewer approximations than has been usual heretofore. General expressions have been derived forC ₁ by including the thermal correction terms, which have generally been ignored in previous studies concerning thermal properties of ionic crystals. The parameterC ₁ has also been related to the Grüneisen parameter, , using a relation given earlier. The applicability of the derived equations is investigated and discussed for alkali halides employing few realistic potential forms. A good general accord is found with the available experimental data, which exhibits an essential improvement over other theoretical determinations.     

On the single-particle potential of renormalized Brueckner theory

Evaluating the set of all factorizable insertions, we derive closed expressions for the single-particle potential of renormalized Brueckner theory. The implications of these results are discussed. In this way we derive a number of results previously established by diagrammatic methods. We establish bounds on the single-particle energies and we prove the existence of solutions of the self-consistency problem. The solution can be made unique by requiring maximum occupation of the subspace of hole states.     

Dynamic polarizability,dispersion coefficient C6 and dispersion energy in the effective fragment potential method

The development of a fragment–fragment dispersion energy expression, for the general effective fragment potential (EFP2) method is presented. C₆ dispersion coefficients, expressed in terms of the dynamic polarizabilties over the imaginary frequency range (α(iν)), were calculated for a set of homo and hetero dimers. Using these coefficients the dispersion energy has been calculated. The dispersion energy is expressed using a simple London series expansion terminated after the n=6 term and implemented using distributed localized molecular orbitals (LMOs). The EFP2 dispersion energy is compared to symmetry adapted perturbation theory (SAPT) values. From this comparison, it is apparent that one needs to include higher order terms in the dispersion energy. Adding an estimated C₈ term to the C₆ energy greatly improves the agreement with the benchmark SAPT energies.     

Study of the single-particle energy spectrum of disordered systems

In this paper the recursion method is applied to the study of the energy spectrum of strongly disordered systems. The real spatial atomic configuration of amorphous semiconductors is the foundation the theory is based on. The presence of partial disorder (short-range order) is shown to be the reason for the existence of a mobility edge whose position is determined by the asymptotic behaviour of the recursion coefficients of a weakly disordered substitution structure. An analytical expression for the local density of states (LDS) is found consisting of contributions from a point and a continuous spectrum. Strong distortions of the local atomic structure are shown to be the origin of localized states. The spectral strength is defined as the weight factor a localized level has in the LDS. The concept of local resonance states is introduced into the theory of disordered solids. Resonances put structure on the LDS of the continuum. Near isolated sharp resonances an analytical representation of the LDS is found. Both localized levels, spectral strengths, resonance energies and widths, and LDS's are numerically calculated for simple models. The theory is applied tod-electrons on a fcc-lattice.     

On the energy spectra of single-particle states in nuclei

The single-particle spectra of ¹⁶O, ⁴⁰Ca, ⁴⁸Ca and ⁵⁶Ni have been studied using self- consistent field methods and a quadratically velocity-dependent two-nucleon effective (reaction- matrix) interaction. The self-consistent field equations are derived in some detail for the spin- independent interaction which is used. A one-body spin-orbit interaction of the Thomas form is added.     

Collective and single-particle states at high excitation energy

Damping of high-lying single-particle states was investigated by the study of decay by proton emission from high-lying states in ⁹¹Nb, populated by the ⁹⁰Zr(α, t) reaction at E_α=180 MeV. In addition to decay to the ground state of ⁹⁰Zr, semi-direct decay was observed to the low-lying (2⁺/5^? and 3^?) phonon states, confirming the conclusion from other experiments that phonon states play an important role in the damping process of the single-particle states. Furthermore, the population and decay of isobaric analogue states of ⁹¹Zr, which are located at an excitation energy of about 10–12 MeV in ⁹¹Nb, has been studied in the same reaction.     

Temperature dependence of the compressibility of two-dimensional electron systems with long-range potential fluctuations in the quantum Hall effect regime

The temperature dependence of the compressibility of two-dimensional electron systems (2DESs) in GaAs/AlGaAs heterostructures in the quantum Hall effect regime have been studied both experimentally and theoretically. The compressibility was determined using the capacitance spectroscopy technique and the measurements of a low-frequency electric field penetrating through the 2DES. The measured temperature dependences of the 2DES compressibility are quantitatively described using a model taking into account inhomogeneity of the electron density at a finite temperature. Changes in the chemical potential of the 2DES in the vicinity of even filling factors determined from the capacitive and transport measurements are mutually consistent and agree with the results of finite-temperature calculations.     

Variational definition of the single-particle potential in the Brueckner-Hartree-Fock approach

The consequences of the variational definition of the self-consistent potential in Brueckner-Hartree-Fock theory are explored to higher orders even summing up some classes of diagrams to infinity. The consistency of this definition with a diagrammatic expansion are checked. Overcounting terms in the variational approach are pointed out and their numerical influence on the ground state properties of nuclei is checked at the example of¹⁶O. Ambiguities of the potential defined by the variational procedure stemming from the property of the Pauli-operatorQ ² =Q are studied diagrammatically and numerically. The application to¹⁶O shows that the influence of the Pauli rearrangement term is partially cancelled by the higher order starting energy rearrangement terms discussed in this work.     

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.     

On the energy dependence of the real part of the heavy-ion optical potential

The energy dependence of the real part of the heavy-ion optical potential is attributed to the J(J + 1) dependence of the-potential which is caused by the rotation induced during the collision. The magnitude and the form of the energy dependence are calculated for several light nucleus-nucleus systems with the use of the distortion potential which is defined by the diagonalization of the coupling interaction. It is shown that the heavy-ion scatterings with the inelastic channels of high and low excitation energies lead to weak and strong energy dependence of the potential, respectively.     

On the various derivations of the energy dependence of the empirical optical potential

The predictions of the energy dependence of the real part of the empirical optical potential implied by the formulations based on nuclear reaction theories and on the multiple scattering approach are compared. The recent data on the nucleon-nucleon forward scattering amplitude obtained from phase-shift analyses, direct measurements and dispersion relations are used. The meaning of the local expression obtained in the multiple scattering formalism is discussed and it is shown that its implications agree with those derived by the nuclear-theories approach.