Ground state properties of nuclear matter

The ground state properties of nuclear matter are calculated in theΛ ₁₁-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.     

A Separable Pairing Force in Nuclear Matter

The method introduced by Duguet is adopted to derive a separable form of the pairing interaction in the ^1So channel from a bare or an effective nucleon-nucleon （NN） interaction in nuclear matter. With this approach the separable pairing interaction reproduces the pairing properties provided by its corresponding NN interaction. In this work, separable forms of pairing interactions in the ^1So channel for the bare NN interaction, Bonn potential and the Gogny effective interaction are obtained. It is found that the separable force of the Gogny effective interaction in the 1So channel has a clear link with the bare NN interaction. With such a simple separable form pairing properties provided by the Gogny force in nuclear matter can be reproduced.     

The properties of nuclear matter at zero and finite temperatures

The properties of nuclear matter are studied in the frame of the Brueckner theory. The Brueckner-Hartree-Fock approximation plus two-body density-dependent Skyrme potential which is equivalent to three-body interaction are used. Various modern nucleon-nucleon potentials are used in the framework of the Brueckner-Hartree-Fock approximation, e.g.: CD-Bonn potential, Nijm1 potential, and Reid 93 potential. These modern nucleon-nucleon potentials fit the deuteron properties and are phase shifts equivalent. The equation of state at T = 0, pressure at T = 0, 8, and 12 MeV, free energy at T = 8 and 12 MeV, nuclear matter incompressibility, and the symmetry energy calculation are presented. The hot properties of nuclear matter are calculated using T ²-approximation method at low temperatures. Good agreement is obtained in comparison with previous theoretical estimates and experimental data, especially at low densities.     

Quasimolecular nuclear optical potentials

A theory is presented to calculate potentials for the elastic nuclear heavy-ion scattering in a phenomenological way. The density properties of finite nuclei are derived with a schematic ansatz for the interaction energy between nuclear matter. The same interaction energy is applied to the calculation of the real part of the heavy-ion potential, which is of the quasimolecular type. The imaginary part is connected with the outflow time of nuclear matter out of compressed regions of overlapping nuclei. The resulting cross section for the elastic O¹⁶-O¹⁶ scattering reproduces the experiment up to 30 MeV quite well. An effective compression modulus of the S³² compound system can be deduced from the scattering experiment. It results to be about 200 MeV.     

Approximation of the microscopic effective pairing interaction by the off-shell T matrix for free nucleon-nucleon scattering

The effective pairing interaction in the ¹ S ₀ channel as calculated microscopically within the Brueckner method for a planar slab of nuclear matter by using the separable version of the Paris nucleon-nucleon potential is investigated. The effective interaction is determined for the model space including all negative-energy single-particle states. An analysis is performed for two values of the chemical potential, μ=?8 and ?4 MeV. It is shown that, to a high precision, the effective interaction can be approximated by the off-shell T matrix for free nucleon-nucleon interaction, the T matrix in question being taken at a negative value of the total energy of two nucleons E=2μ.     

Equation of state of asymmetric nuclear matter: a VMC study

A Variational Monte Carlo (VMC) method is employed to investigate the properties of symmetric and asymmetric nuclear matter. The realistic Urbana V ₁₄ twonucleon interaction potential of Lagaris and Pandharipande was used to describe the microscopic interactions. Also, many body interactions are included as a density dependent term in the potential. Total kinetic and potential energies per particle are calculated for asymmetric nuclear matter by VMC method at various densities and isospin asymmetry parameters. The results are compared with data found in literature, and it was observed that the results obtained in this study reasonably agree with the results found in the literature. Also, the symmetry energy and incompressibility factor of the nuclear matter were obtained. The results obtained are in good agreement with those obtained by various authors with different methods and techniques.     

Thermodynamic properties of superconducting nuclear matter

Phase diagrams of superconducting nuclear matter are calculated by solving a set of finite temperature gap equations, using several Skyrme effective interactions. Our results indicate that nuclear matter may have a superconducting phase in a small region with density near one half of the normal nuclear matter density and temperature k_BT ≲ 1.4 MeV. Our calculation is based on a finite temperature Green's function method with an abnormal pair cutoff approximation. The same approximation is employed in deriving the internal energy, entropy and chemical potential of superconducting nuclear matter. In this way, its equation of state is obtained, and compared with that of normal nuclear matter. The energy gap of superconducting nuclear matter is found to depend rather sensitively on both density and temperature. This dependence is analysed in terms of the Skyrme interaction parameters. The correlation effect on chemical potential is found to be important at high density, and its inclusion is essential in determining the equation of state of superconducting nuclear matter.     

Off-shell effects in O

We calculate the binding energy of ¹⁶O for a set of phase-shift-equivalent potentials previously studied in nuclear matter. Off-shell variations of up to 2.8 MeV per particle occur compared with about a 10 MeV per particle variation in nuclear matter. As in nuclear matter calculations a nearly linear relation exists between the variations in the binding-energy results and the wound integral k. We compare the ¹⁶O results with a nuclear matter calculation at the “equivalent” nuclear matter density of k_F = 1.13 fm⁻¹. This “equivalent” density reflects the fact that ¹⁶O has a surface and hence a lower average density than nuclear matter. The ¹⁶O and nuclear matter off-shell variations are comparable once one takes into account the lower average density of ¹⁶O and the suppression of the relative D-wave interaction — also a surface effect. We present a method of computing the correlated wave functions of finite nuclear systems and display such wave functions for ¹⁶O. The correlated wave functions of ¹⁶O and of nuclear matter are strikingly similar for all of the potentials studied.     

A relativistic approach to the equation of state of asymmetric nuclear matter

The properties of asymmetric nuclear matter for a wide range of densities and asymmetric parameters are investigated within the lowest-order-constrained variational (LOCV) method by employing the relativistic Hamiltonian with a potential which has been fitted relativistically to N-N phase shifts ( [(v)\tilde]₁₄ \tilde{{v}}_{{14}}^{} and to the AV₁₄interaction. Like our previous work on symmetric nuclear matter, the boost interaction corrections as well as the relativistic one-body and two-body kinetic corrections are calculated. The various properties of asymmetric nuclear matter such as the symmetry energy, the saturation energy and the validity of the a² \alpha^{2}_{} law, etc., are examined. The symmetry energy is reduced by about 7MeV when we use [(v)\tilde]₁₄ \tilde{{v}}_{{14}}^{} instead of its non-relativistic version, i.e. the AV₁₄interaction. The results are compared with other many-body calculations.     

Neutron Matter Properties Using Skyrme Interaction

The purpose of the present work is to extend earlier nuclear matter calculations to study the properties of neutron matter. The binding energy per particle, symmetry energy, single particle potential, effective mass, and magnetic susceptibility are calculated using a modified Skyrme interaction. These are calculated as a function of the Fermi momentum k_f in the range 0 < k_f < 2 fm^?1. Two sets of the interaction parameters are obtained by fitting the interaction parameters using the available information on neutron matter. Relativistic corrections to the order 1/c² are also calculated. The relativistic corrections are very small and they increase as k_f is increased.     

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.     

Fission of a slab of charged nuclear matter in the time-dependent hartree fock (TDHF) theory

The time evolution of a slab of charged nuclear matter is studied within the TDHF method as a function of the initial conditions. The effective interaction is of Skyrme type plus a repulsive Yukawa interaction representing the Coulomb repulsion. The implications on the time evolution of specific collective as well as intrinsic excitations are investigated. Fission is found to occur at large enough excitation energies for a variety of initial conditions after timest _fi ≈(1–3)·10^?21 s. The final disintegration of the slab (“snatching”) is characterized by arapid rise of a potential barrier between the nascent fragments, the rise occurring int _sn≈0.2·10^?21 s. The importance for the fission process of the reflection symmetry of the occupied single particle states is demonstrated.     

Effects of nuclear structure in the spin-dependent scattering of weakly interacting massive particles

We present calculations of the nuclear from factors for spin-dependent elastic scattering of dark matter WIMPs from¹²³Te and¹³¹Xe isotopes, proposed to be used for dark matter detection. A method based on the theory of finite Fermi systems was used to describe the reduction of the single-particle spin-dependent matrix elements in the nuclear medium. Nucleon single-particle states were calculated in a realistic shell model potential; pairing effects were treated within the BCS model. The coupling of the lowest single-particle levels in¹²³Te to collective 2⁺ excitations of the core was taken into account phenomenologically. The calculated nuclear form factors are considerably less then the single-particle ones for low momentum transfer. At high momentum transfer some dynamical amplification takes place due to the pion exchange term in the effective nuclear interaction. But as the momentum transfer increases, the difference disappears, the momentum transfer increases and the quenching effect disappears. The shape of the nuclear form factor for the¹³¹Xe isotope differs from the one obtained using an oscillator basis.     

Properties of nuclear matter andN=Z closed-shell nuclei

A simple three-parameter density dependent effective interaction is used to study the properties of nuclear matter, neutron matter and some bulk properties such as ground state energies and rms charge radii of three double-closed shell nuclei⁴He,¹⁶O and⁴⁰Ca. The three parameters of the effective interaction are determined by requiring to fit the binding energy and density of infinite nuclear matter at saturation density as well as ground state energy of¹⁶O in the first order perturbation theory. This interaction gives correct saturation in nuclear matter with a value of 283 MeV for compressibility. The symmetry coefficienta _T atk _F=1·36 fm^–1 is 28·58 MeV. The energy per particle in neutron matter is calculated in the range of nuclear matter densities and it compares well with those ofNemeth andSprung. Groundstate energies and rms charge radii of⁴He,¹⁶O and⁴⁰Ca are calculated using oscillator eigen functions as single particle wave functions. Results for ground state energies are in good agreement with empirical values and rms charge radii are slightly better than those obtained byMoszkowski with the MDI.The authors are thankful to the Computer Centre, Utkal University, Bhubaneswar for providing computational facilities for this work.     

Complex microscopic optical potential between two nuclei based on Dirac-Brueckner theory for nuclear matter

The real and imaginary parts of the optical-model potential between two nuclei are calculated in the energy density formalism. The energy density is derived from the Dirac-Brueckner approach to nuclear matter. In this approach, both free NN scattering and the saturation properties of nuclear matter can be explained starting from a realistic NN interaction. The relativistic features incorporated in the Dirac-Brueckner approach make the real part of the optical potential less attractive than that obtained in a non-relativistic calculation while the imaginary part is enhanced. The comparison of the calculated differential cross section for elastic ¹²C-¹²C scattering with the experimental data suggests that the enhancement of the imaginary part due to the relativistic treatment is favourable while its repulsive contribution to the real part is unfavourable.     

Summation of ring diagrams of nuclear thermodynamic potential

Using an imaginary-time linked diagram expansion of the thermodynamic potential Ω, we derive methods by which the particle-particle (hole-hole) and the particle-hole ring diagrams of Ω can each be summed up to all orders in a rather convenient way. A model space P and a corresponding finite temperature reaction matrix K are introduced in order to take care of the strong short-range correlations between nucleons. Methods of the finite temperature Green functions are employed. The contribution from the particle-particle (hole-hole) ring diagrams to Ω is given in terms of simple integrals of the form ∝₀¹dλ tr_p {M(λ)K} where λ is a strength parameter, and M a thermal transition matrix which is calculated from a finite-temperature RPA-type secular equation. Solutions of this equation are derived, and their possible connections with phase transitions are discussed. The particle-hole ring diagrams are treated in a similar way. Applications of the present approach and prospects for formulating a Brueckner-type theory of nuclear matter at finite temperature are discussed.     

Theory of kaonic atoms

A nonlocal energy-dependent self-consistent kaon-nucleus optical potential is derived for kaonic atoms. Energy level shifts and widths are calculated for several light nuclei, and the results are compared with experiment. The sensitivity of the results to changes in parameters of the nuclear matter distribution is studied. Nonlocality and off-energy-shell effects are examined.The optical potential is derived by means of a Brueckner-type many-body theory with the independent pair approximation for the kaon and the nucleon. The two-body interaction on which the optical potential depends is represented by separable potentials of the Yamaguchi form. Coupled channels ($\text{K}\text{N}$ and Σπ) are used for the I = 0 states, which are dominated by the $\text{Y}{}_0{}^1$ resonance, and only a single channel ($\text{K}\text{N}$) is used for the I = 1 state.Calculations are carried out in three levels of approximation of the nonlocal energy-dependent optical potential. In no approximation is the potential found to be proportional to the nuclear density. Indeed, the real part of the potential changes sign in the nuclear surface. Sensitivity of the results to variations in the nuclear matter distribution is investigated and found to be on the order of experimental error. Nonlocality and off-energy-shell effects are estimated to be at least as large as this error, so that these effects must be included if one wishes to extract information about the nuclear surface from the existing experimental data. The use of correct nucleon wavefunctions and binding energies is similarly found to be essential in the calculation.     

The spectrum of hot hadronic matter and finite-temperature QCD sum rules

The sum rules method, which is widely used for the investigation of the resonance physics within the QCD framework, is generalized to the case of finite temperatures and densities. Conditions are formulated under which this method is quite efficient for the determination of the spectrum of hadronic matter at T ≠ 0. The finite-temperature QCD sum rules are analysed in the vector channel J^PC = 1⁻⁻. Sharp and qualitative changes in the spectrum are found in the temperature interval T = 130–150 MeV. It is naturally explained as a consequence of the disappearance of confinement at the temperature T_c = 140±10 MeV. The finite-temperature QCD sum rules also show that the restoration of chiral symmetry at some temperature T_F cannot precede deconfinement. In the case T_F⪢T_c the sum rules indicate that the intermediate phase at T_c<T<T_F is dominated by quasi-free quarks with nonzero dynamical mass m_q^T ≈ 300 MeV.