arXiv subjects
Publications and source records attributed to M. Hjorth-Jensen.
We discuss various properties of singlet S pairing in neutron and nuclear matter in terms of the bare nuclon-nucleon interaction. Relations to the NN phase shifts are discussed, as well as various properties of the BCS wave function and the coherence length for fermion superfluids in infinite matter.
We present solutions of the coupled, non-relativistic $^3S_1$-$^3D_1$ gap equations for neutron-proton pairing in symmetric nuclear matter, and estimate relativistic effects by solving the same gap equations modified according to minimal relativity and using single-particle energies from a Dirac-Brueckner-Hartree-Fock calculation. As a main result we find that relativistic effects decrease the value of the gap at the saturation density $k_F=1.36 fm^{-1}$ considerably, in conformity with the lack of evidence for strong neutron-proton pairing in finite nuclei.
The microscopic quasiparticle-phonon model, MQPM, is used to study the energy spectra of the odd $Z=53 - 63$, N=82 isotones. The results are compared with experimental data, with the extreme quasiparticle-phonon limit and with the results of an unrestricted $2s1d0g_{7/2}0h_{11/2}$ shell model (SM) calculation. The interaction used in these calculations is a realistic two-body G-matrix interaction derived from modern meson-exchange potential models for the nucleon-nucleon interaction. For the shell model all the two-body matrix elements are renormalized by the $\hat{Q}$-box method whereas for the MQPM the effective interaction is defined by the G-matrix.
We consider 1S0 pairing in infinite neutron matter and nuclear matter and show that in the lowest order approximation, where the pairing interaction is taken to be the bare nucleon-nucleon (NN) interaction in the 1S0 channel, the pairing interaction and the energy gap can be determined directly from the 1S0 phase shifts. This is due to the almost separable character of the NN interaction in this partial wave. Since the most recent NN interactions are charge-dependent, we have to solve coupled gap equations for proton-proton, neutron-neutron, and neutron-proton pairing in nuclear matter. The results, however, are found to be close to those obtained with charge-independent potentials.
We calculate the low-lying spectra of heavy tin isotopes from A=120 to A=130 using the 2s1d0g_{7/2}0h_{11/2} shell to define the model space. An effective interaction has been derived using 132Sn as closed core employing perturbative many-body techniques. We start from a nucleon-nucleon potential derived from modern meson exchange models. This potential is in turn renormalized for the given medium, 132Sn, yielding the nuclear reaction matrix, which is then used in perturbation theory to obtain the shell model effective interaction.
We study the symmetry energy in infinite nuclear matter employing a non-relativistic Brueckner-Hartree-Fock approach and using various new nucleon-nucleon (NN) potentials, which fit np and pp scattering data very accurately. The potential models we employ are the recent versions of the Nijmegen group, Nijm-I, Nijm-II and Reid93, the Argonne $V_{18}$ potential and the CD-Bonn potential. All these potentials yield a symmetry energy which increases with density, resolving a discrepancy that existed for older NN potentials. The origin of remaining differences is discussed.
In this work we investigate the so-called model-space Brueckner-Hartree-Fock (MBHF) approach for nuclear matter as well as for neutron matter and the extension of this which includes the particle-particle and hole-hole (PPHH) diagrams. A central ingredient in the model-space approach for nuclear matter is the boundary momentum $k_M$ beyond which the single-particle potential energy is set equal to zero. This is also the boundary of the model space within which the PPHH diagrams are calculated. It has been rather uncertain which value should be used for $k_M$. We have carried out model-space nuclear matter and neutron matter calculations with and without PPHH diagrams for various choices of $k_M$ and using several modern nucleon-nucleon potentials. Our results exhibit a saturation region where the nuclear and neutron matter matter energies are quite stable as $k_M$ varies. The location of this region may serve to determine an "optimum" choice for $k_M$. However, we find that the strength of the tensor force has a significant influence on binding energy variation with $k_M$. The implications for nuclear and neutron matter calculations are discussed.
The coherence length of superfluid neutron matter is calculated from the microscopic BCS wavefunction of a Cooper pair in momentum space making use of the Bonn meson-exchange potential. We find that the coherence length is proportional to the Fermi momentum-to pairing gap ratio, in good agreement with simple estimates used in the literature, and we establish the appropriate fitting constants using our numerical data. Our calculations can be applied to the problem of inhomogeneous superfluidity of hadronic matter in the crust of a neutron star.
The shell model within the $2s1d0g_{7/2}0h_{11/2}$ shell is applied to calculate nuclear structure properties of the even Z=52 - 62, N=82 isotones. The results are compared with experimental data and with the results of a quasiparticle random-phase approximation (QRPA) calculation. The interaction used in these calculations is a realistic two-body G-matrix interaction derived from modern meson-exchange potential models for the nucleon-nucleon interaction. For the shell model all the two-body matrix elements are renormalized by the $\hat{Q}$-box method whereas for the QRPA the effective interaction is defined by the G-matrix.
The yrast generalized seniority states are compared with the corresponding shell model states for the case of the Sn isotopes $^{104-112}$Sn. For most of the cases the energies agree within 100 keV and the overlaps of the wave functions are greater than 0.7.
In this work we present results for pairing gaps in $β$--stable neutron star matter with electrons and muons using a relativistic Dirac--Brueckner--Hartree--Fock approach, starting with modern meson--exchange models for the nucleon--nucleon interaction. Results are given for superconducting $^1S_0$ protons and $^3P_2$ and $^1D_2$ neutron superfluids. A comparison is made with recent non--relativistic calculations and the implications for neutron star cooling are discussed.
$^{3}P_{2}$ pairing in neutron matter is investigated using the Bonn potential models. We find pairing energy gaps in pure neutron matter comparable to the results of previous investigators when the attractive tensor coupling is included. However, taking into account that in a neutron star we have matter at $β$ equilibrium, we find that the $^{3}P_{2}$-$^{3}F_{2}$ energy gap is reduced considerably.
In this work we calculate neutron and proton energy gaps in neutron star matter, using the Bonn meson--exchange interactions and a model--space approach to the gap equation. This approach allows a consistent calculation of energy gaps and single particle energies with the model--space Brueckner--Hartree--Fock (MBHF) method, without double counting of two--particle correlations. Neutron energy gaps are calculated at zero and finite temperature. Proton energy gaps are calculated at beta equilibrium, and it is shown that the inclusion of muons has a significant effect. The results are compared with those of other works, and the implications for neutron star physics are briefly discussed.
In this work we consider the role of muons in various URCA processes relevant for neutrino emissions in the core region of neutron stars. The calculations are done for $β$--stable nuclear matter with and without muons. We find muons to appear at densities $ρ= 0.15$ fm$^{-3}$, slightly around the saturation density for nuclear matter $ρ_0 =0.16$ fm$^{-3}$. The direct URCA processes for nucleons are forbidden for densities below $ρ= 0.5$ fm$^{-3}$, however the modified URCA processes with muons $(n+N\rightarrow p+N +μ+\overlineν_μ, p+N+μ\rightarrow n+N+ν_μ$), where $N$ is a nucleon, result in neutrino emissivities comparable to those from $(n+N\rightarrow p+N +e +\overlineν_e, p+N+e \rightarrow n+N+ν_e$). This opens up for further possibilities to explain the rapid cooling of neutrons stars. Superconducting protons reduce however these emissivities at densities below $0.4$ fm$^{-3}$.
In this work we study properties of neutron star crusts, where matter is expected to consist of nuclei surrounded by superfluid neutrons and a homogeneous background of relativistic electrons. The nuclei are disposed in a Coulomb lattice, and it is believed that the structure of the lattice influences considerably the specific heat of the neutronic matter inside the crust of a neutron star. Using a modern meson--exchange potential in the framework of a local--density approximation we calculate the neutronic specific heat accounting for various shapes of the Coulomb lattice, from spherical to non--spherical nuclear shapes. We find that a realistic nucleon--nucleon potential leads to a significant increase in the neutronic specific heat with respect to that obtained assuming a uniform neutron distribution. The increase is largest for the non--spherical phase of the crust. These results may have consequences for the thermal history of young neutron stars.
In this work we calculate the total mass, radius, moment of inertia, and surface gravitational redshift for neutron stars using various equations of state (EOS). Modern meson-exchange potential models are used to evaluate the $G$-matrix for asymmetric nuclear matter. We calculate both a non-relativistic and a relativistic EOS. Of importance here is the fact that relativistic Brueckner-Hartree-Fock calculations for symmetric nuclear matter fit the empirical data, which are not reproduced by non-relativistic calculations. Relativistic effects are known to be important at high densities, giving an increased repulsion. This leads to a stiffer EOS compared to the EOS derived with a non-relativistic approach. Both the non-relativistic and the relativistic EOS yield moments of inertia and redshifts in agreement with the accepted values. The relativistic EOS yields, however, too large mass and radius. The implications are discussed.
The convergence of the perturbation expansion for the effective interaction to be used in shell-model calculations is investigated as function of the mass number $A$, from $A=4$ to $A=208$. As the mass number increases, there are more intermediate states to sum over in each higher-order diagram which contributes to the effective interaction. Together with the fact that the energy denominators in each diagram are smaller for larger mass numbers, these two effects could largely enhance higher-order contributions to the effective interaction, thereby deteriorating the order-by-order convergence of the effective interaction. This effect is counterbalanced by the short range of the nucleon-nucleon interaction, which implies that its matrix elements are weaker for valence single-particle states in ``large'' nuclei with large mass number as compared to those in light nuclei. These effects are examined by comparing various mean values of the matrix elements. It turns out that the contributions from higher-order terms remain fairly stable as the mass number increases from $A=4$ to $A=208$. The implications for nuclear structure calculations are discussed.
Using the Color-Dielectric model to describe quark confinement, including strange quarks and accounting for beta--equilibrium, we get masses for a static neutron star in the range $1.3\leq M/M_{\odot}\leq 1.54 $ for a radius $R\approx 9$ km. Rapid cooling through the direct URCA mechanism is obtained. The implications for the composition of neutron stars is discussed.