Spin, iso-spin dependence of nucleon-nucleon effective interaction in nuclear matter calculations

A set of density dependent nucleon-nucleon (N-N) interactions has been examined in nuclear matter calculations by varying spin-isospin contributions. Two sets of potentials have been considered. One having a density dependentσ-function type short range part followed by one term long range Gaussian part while the other having a density dependentσ-function part followed by two Gaussian terms. The strength parameters of the potential have been fitted to the saturation properties of nuclear matter, i.e. binding energy per particle of 15.5 MeV atk _F=1.35 fm⁻¹. Several sets of these two potentials have been generated by varying the strength parameterM of Majorana exchange operatorP _M. It is seen thatM indirectly controls the spin, iso-spin contribution to the interaction potential and thus affects the nuclear matter properties such as compressibility and symmetry energy considerably, while variation of these quantities with the range parameterμ for givenM is moderate at lowM values while at higherM values it is quite large.     

Zero-range density dependence in effective interaction

A class of approximate interactions ZRA, having contact density dependence and microscopically derived density independent part, is constructed. Such an approximation retains all physical virtues of non-contact density dependent interactions and simplifies numerical calculations considerably. ZRA is tested and compared with similar interactions in nuclear matter and in s-d shell. The spurious selfscreening rearrangement termS and a shape transition in³²S are studied.     

On the energy dependence of the effective interaction

The Schrödinger equation is studied in a finite subspace of the Hilbert space. The truncation of the configuration space makes the (effective) interaction energy-dependent. This dependency is investigated. An analytic expression for the matrix elements of the effective interaction is established for the schematic model, for the displaced harmonic oscillator, for a simple random-phase problem and for a pairing force model. Thereby the phase transitions from bound to unbound states and from normal to superconducting states are analysed.     

Low energy effective interaction of XXZ spin interaction in the two-dimensional quantum dot

We investigate the low-energy behavior of the two-dimensional quantum dot. By using the renormalization group analysis with the random matrix theory, we examine the role of anisotropy of the electron–electron interaction and demonstrate the induced instabilities in the universal Hamiltonian. As a result, it is found that anisotropy in general gives rise to four additional phases (eight phases as total), and in certain regions, the anisotropy becomes amplified at low temperature.     

Ground state energy of spin polarized hard core neutron matter

The expansion of the ground state energy of spin polarized hard core neutron matter in powers of x =k_Fc (k_F = Fermi momentum, c = hardcoreradius) is calculated up to terms ≈x⁸.     

Microscopic calculations of spin polarized neutron matter at finite temperature

The properties of spin polarized neutron matter are studied both at zero and finite temperature within the framework of the Brueckner–Hartree–Fock formalism, using the Argonne v18 nucleon–nucleon interaction. The free energy, energy and entropy per particle are calculated for several values of the spin polarization, densities and temperatures together with the magnetic susceptibility of the system. The results show no indication of a ferromagnetic transition at any density and temperature.     

Polarization of high spin nuclear levels via tilted multifoil interaction

It has been demonstrated that with suitably spaced carbon foils, tilted with respect to the particle momentum, a large polarization can be generated in high spin nuclei by the tilted foil atomic polarization. Two experiments have been carried out with such polarized high spin isomers: a measurement of the sign of the quadrupole moment of the 10⁺ isomer in⁵⁴Fe, and a new attempt of higher sensitivity at detecting a possible positive parity admixture to the 17/2^– isomer in⁹³Tc.On leave from the Hahn-Meitner Institut, Berlin, W. Germany.On leave from Physics Department, Brooklyn College of the City of New York, Brooklyn, New York.     

The effective neutron—proton interaction in rare-earth nuclei

The available experimental information concerning the low-lying rotational-band energies in rare-earth nuclei with odd neutron and proton numbers is analysed within the framework of the unified model. We extract 69 empirical values for 51 two-particle matrix elements of the effective neutron—proton interaction in 16 nuclei. This information deals with 43 two-quasi-particle configurations. Strength and range parameters for various types of effective interaction are determined from least-squares fits of calculated matrix elements to the empirical values. We find a significant improvement in the fit when spin-polarized and long-range components are included in the effective force, indicating the importance of core-polarization effects. We investigate the sensitivity of the calculation to the choice of experimental information, to the single-particle model, and to the radial shape of the force. Some predictions are made concerning as yet unconfirmed or unobserved configurations.     

Enhanced isospin dependence of the empirical particle-hole effective interaction

The separation betweenT=0 andT=1 centroids of the empirical effective interaction is fairly large for the (d ₃ ^2/−1 f _7/2)JT particle-hole interaction as compared to nearby (f _7/2)² JT and (d _5/2)² JT particle-particle interactions. This interesting feature of the empirical effective interaction is shown to arise as a consequence of renormalization of the effective interaction as one truncates the configuration space from (s−d)⁻¹(f−p)¹ to (d ₃ ^2/−1 f _7/2) and from (f−p)² and (s−d)² configurations to (f _7/2)² and (d _5/2)² respectively.     

The spin structure of charmonium and the quark-gluon effective interaction

The large S-state hyperfine splittings and the spacing of the P-states of charmonium can be explained qualitatively by an effective quark-gluon anomalous magnetic moment of 1 quark magneton within the context of a nonrelativistic linear potential model.     

Relativistic mean-field parametrization of effective interaction in nuclear matter

The results of the modern relativistic Dirac-Brueckner calculations of nuclear matter are parametrized in terms of the relativistic- mean-field theory with scalar and vector nonlinear selfinteractions. It is shown that the inclusion of the isoscalar vector-meson quartic selfinteraction is essential for obtaining a proper density dependence of the vector potential in the mean-field model. The obtained mean-field parameters represent a simple parametrization of effective interaction in nuclear matter. This interaction may be used in the mean-field studies of the structure of finite nuclei without the introduction of additional free parameters.This work was supported in part by the Grant Agency of the Slovak Academy of Sciences under Grant No. GA SAV-517/1991.     

Antiferromagnetism of nuclear matter in the model with effective Gogny interaction

The possibility of ferromagnetic (FM) and antiferromagnetic (AFM) phase transitions in symmetric nuclear matter is analyzed within the framework of a Fermi liquid theory with effective Gogny interaction. It is shown that, at some critical density, nuclear matter with the D1S effective force undergoes a phase transition to the AFM spin state (opposite directions of neutron and proton spins). The self-consistent equations of spin-polarized nuclear matter with the D1S force have no solutions corresponding to FM spin ordering (the same direction of neutron and proton spins) and, hence, the FM transition does not appear. The AFM spin polarization parameter is found for zero and finite temperature. It is shown that the AFM spin polarization parameter of partially polarized nuclear matter at low enough temperatures increases with temperature. The entropy of the AFM spin state for some temperature range is larger than the entropy of the normal state. Nevertheless, the free energy of the AFM spin state is always less than the free energy of the normal state, and the AFM spin-polarized state is preferable for all temperatures below the critical temperature. The text was submitted by the authors in English.     

Polarization contributions to the vacancy binding energy in doped oxides

An effective medium theory due to Onsager is generalized to yield the macroscopic dielectric constant of a random assembly of associated vacancy-dopant bound pairs embedded in a dielectric host. The model is then further developed to give the vacancy-dopant binding energy, employing concepts long-established in electrolyte theory. The results of this analysis are used to compute the activation enthalpy for electrical conduction in the ionic conduction regime. The values so found are in reasonable accord with experimental data from various sources on Ce_1?xCa_xO_2?x, with x?0.02, assuming a vacancy migration enthalpy of 0.71 eV. The latter is the only adjustable parameter in the theory here developed. With this same value, the predicted variation of the low-temperature conduction activation enthalpy in Ce_1?2xY_2xO_2?x and Ce_1?2xGd_2xO_2?x (again at small x) are acceptably reproduced, although more experimental data would be desirable. The dielectric constant of the yttria-doped material is also described by the present model, again with no adjustable parameters. Several different features of the theory lead to its loss of validity in more concentrated mixtures. These are examined in detail.     

Valence and sea contributions to the nucleon spin

The first moments of the polarized valence parton distribution functions (PDFs) truncated to the wide Bjorken x region 0.004<x<0.7 are directly (without any fitting procedure) extracted in the next to leading order (NLO) QCD from both COMPASS and HERMES data on pion production in polarized semi-inclusive DIS (SIDIS) experiments. The COMPASS and HERMES data are combined in two ways and two scenarios for the fragmentation functions (FFs) are considered. Two procedures are proposed for an estimation of light sea quark contributions to the proton spin. Both lead to the conclusion that these contributions are compatible with zero within the errors.     

Electromagnetic contributions to the nucleon-nucleon interaction

The helicity amplitudes of the nucleon-nucleon one-photon exchange interaction are calculated. The anomalous magnetic moments of the proton and neutron are included in the calculations. The formalism is especially suitable for the small angle proton-proton interaction at intermediate energies. The electromagnetic phase shifts in the Born approximation are defined and calculated. The three cases of the proton-proton, the neutron-proton and the neutron-neutron interactions are dealt with separately. Analytic expressions are given for sums defined by divergent partial waves. We indicate the pecularities of the neutron-proton interaction: the singlet-triplet transitions and the t⁻¹ singularity in the differential cross section. These peculiarities require an improved treatment of the neutron-proton interaction. A modified formalism is suggested.     

Tensor quasiparticle interaction and spin—isospin sound in nuclear matter

The effect of the tensor components of the quasiparticle interaction in nuclear matter on the spin—isospin sound type excitations is studied. Numerical results are obtained using a simplified model of the quasiparticle interaction in nuclear matter. The quasiparticle distribution matrix corresponding to the spin—isospin sound is found to be qualitatively different from that obtained for purely central quasiparticle interaction. The macroscopic effects, however, are restricted to a small change in the phase velocity of the spin—isospin sound.     

Properties of nuclear matter using the velocity-dependent effective potential ofs-wave interaction

Two forms of a velocity-dependent effective potential are used. The binding energy and the incompressibility of the nuclear matter are calculated. These are found to be in a good agreement with those obtained by others and with the experimental results. The single-particle potential, the effective massM ^* and the nuclear surface energy are also discussed and compared with those obtained by the others.     

Dilute neutron matter on the lattice at next-to-leading order in chiral effective field theory

We discuss lattice simulations of the ground state of dilute neutron matter at next-to-leading order in chiral effective field theory. In a previous paper the coefficients of the next-to-leading-order lattice action were determined by matching nucleon-nucleon scattering data for momenta up to the pion mass. Here the same lattice action is used to simulate the ground state of up to 12 neutrons in a periodic cube using Monte Carlo simulations. We explore the density range from 2% to 8% of normal nuclear density and analyze the ground-state energy as an expansion about the unitarity limit with corrections due to finite scattering length, effective range, and P -wave interactions.     

Knock-on type exchange and the density dependence of an effective interaction

We investigate the origin of the density-dependence of the strength of an effective interaction previously derived from a Brueckner-Hartree-Fock calculation of the optical-model potential in nuclear matter. From the analysis of a model based on the Hartree-Fock approximation and on a Yukawa interaction with a Majorana exchange component, we study to what extent this dependence derives from the momentum-dependence of the exchange contribution of the knock-on type. The model is also used to discuss zero-range pseudopotential methods for including this knock-on contribution.