Finite Range Simple Effective Interaction Research Articles

Nuclear Matter Properties and Neutron Star Phenomenology Using the Finite Range Simple Effective Interaction

The saturation properties of symmetric and asymmetric nuclear matter have been computed using the finite range simple effective interaction with Yukawa form factor. The results of higher-order derivatives of the energy per particle and the symmetry energy computed at saturation, namely, Q0, Ksym, Kτ, Qsym, are compared with the corresponding values extracted from studies involving theory, experiment and astrophysical observations. The overall uncertainty in the values of these quantities, which results from a wide spectrum of studies described in earlier literature, lies in the ranges −1200≲Q0≲400 MeV, −400≲Ksym≲100 MeV, −840≲Kτ≲−126 MeV and −200≲Qsym≲800 MeV, respectively. The ability of the equations of state computed with this simple effective interaction in predicting the threshold mass for prompt collapse in binary neutron star merger and gravitational redshift has been examined in terms of the compactness of the neutron star and the incompressibility at the central density of the maximum mass star. The correlations existing between neutron star properties and the nuclear matter saturation properties have been analyzed and compared with the predictions of other model calculations.

Finite-range simple effective interaction including tensor terms

The prediction of single particle level crossing phenomenon between $2p_{3/2}$ and $1f_{5/2}$ orbitals in $Ni$- and $Cu$-isotopic chains by the finite range simple effective interaction without requiring the tensor part is discussed. In this case the experimentally observed crossing could be studied as a function of nuclear matter incompressibility, $K(\rho_0)$. The estimated crossing for the neutron number $N$=46 could be reproduced by the equation of state corresponding to $K(\rho_0)$=240 MeV. However, the observed proton gaps between the $1h_{11/2}$ and $1g_{7/2}$ shells in $Sn$ and $Sb$ isotopic chain, and the neutron gaps between the $1i_{13/2}$ and $1h_{9/2}$ shells in $N$=82 isotones, as well as the shell closure properties at $N$=28 require explicit consideration of a tensor part as the central contribution is not enough to initiate the required level splittings.

Influence of direct Urca on the r-mode spin down features of newborn neutron star pulsars

We perform a study on the time duration, final frequency, and exit temperature of the r-mode instability in newborn neutron stars of normal fluid composition under the assumption that the r-mode is the dominating spin-down mechanism. It is found that these spin-down features will vary widely depending on the star mass when direct Urca becomes operative. The occurrence of direct Urca is decided from the stiffness of the symmetry energy of the underlying equation of state, which is still uncertain. The change in the spin-down features in stars of different masses has been studied by computing the magnitude of the bulk viscosity due to the extent of direct Urca coverage in the core. The range for the variation of the symmetry energy stiffness, characterized by the slope parameter L, is decided from the tidal deformability data of the GW170817 event and the maximum mass constraint. The study is done by applying a family of equation of states obtained with the finite range simple effective interaction, constrained at low and intermediate densities by nuclear data and the flow analysis in heavy-ion collisions and at high densities by causality.

Nuclear symmetry energy and neutron skin thickness of 208Pb using a finite range effective interaction

We use a finite range simple effective interaction to construct nuclear equations of state for the study of the density dependence of the nuclear symmetry energy. The EoSs provide good descriptions of the nuclear symmetry energy at a subsaturation density ρc = 0.11 fm−3 and at a density around two times the saturation density ρ0. We obtain a correlation between the neutron skin thickness in 208Pb and the density slope parameter at the subsaturation density. A linear relation is obtained between the neutron skin thickness and the parameter , where Es(ρ0) and L(ρc) are respectively the nuclear symmetry energy at saturation density and the density slope parameter at the subsaturation density.

Influence of the nuclear matter equation of state on the r-mode instability using the finite-range simple effective interaction

The characteristic physical properties of rotating neutron stars under the r-mode oscillation are evaluated using the finite-range simple effective interaction. Emphasis is given on examining the influence of the stiffness of both the symmetric and asymmetric parts of the nuclear equation of state on these properties. The amplitude of the r-mode at saturation is calculated using the data of particular neutron stars from the considerations of ‘spin equilibrium’ and ‘thermal equilibrium’. The upper limit of the r-mode saturation amplitude is found to lie in the range 10−8–10−6, in agreement with the predictions of earlier work.

Exact versus Taylor-expanded energy density in the study of the neutron star crust–core transition

The importance of the fourth and higher order terms in the Taylor series expansion of energy of isospin asymmetric nuclear matter in studies of the neutron star crust–core phase transition is investigated using the finite-range simple effective interaction. Analytic expressions for the evaluation of the second and fourth order derivative terms in the Taylor series expansion for any general finite-range interaction of Yukawa, exponential or Gaussian form have been obtained. The effect of the nuclear matter incompressibility, symmetry energy and slope parameters on the predictions for the crust–core transition density is examined. The crustal moment of inertia is calculated and the prediction for the radius of the Vela pulsar is analyzed using different equations of state.

Deformation properties with a finite-range simple effective interaction

Deformed and spherical even–even nuclei are studied using a finite-range simple effective interaction within the Hartree–Fock–Bogoliubov mean-field approach. Different parameter sets of the interaction, corresponding to different incompressibility, are constructed by varying the exponent γ of the density in the traditional density-dependent term. Ten of the 12 parameters of these interactions are determined from properties of asymmetric nuclear matter and spin-polarized pure neutron matter. The two remaining parameters are fitted to reproduce the experimental binding energies known in 620 even–even nuclei using several variants of the rotational energy correction. The rms deviations for the binding energy depend on the value of γ and the way the rotational energy correction is treated but they can be as low as 1.56 MeV, a value competitive with other renowned effective interactions of Skyrme and Gogny type. Charge radii are compared to the experimental values of 313 even–even nuclei and the rms deviation is again comparable and even superior to the one of popular Skyrme and Gogny forces. Emphasis is given to the deformation properties predicted with these interactions by analyzing the potential energy surfaces for several well deformed nuclei and the fission barriers of some nuclei. Comparison of the results with the experimental information, where available, as well as with the results of the Gogny D1S force, shows satisfactory agreement.

Properties of nuclear matter and finite nuclei with finite range simple effective interaction

The nuclear mean field as a function of momentum and density is the quantity of crucial relevance in the study of nuclear matter and the equation of state can be obtained from it at momentum equals to Fermi momentum. In order to simulate the momentum dependence of the mean field, the effective interaction is constructed in the simplest form and the parameters are fixed with proper care on the momentum dependent aspects of the mean fields in different kinds of nuclear matter. By fixing the parameters of the interaction, as discussed in the work, microscopic trends of nuclear matter properties and predictions in finite nuclei, not less than any other conventional interaction, could be obtained.

Study of spin polarized nuclear matter and finite nuclei with finite range simple effective interaction

The properties of spin polarized pure neutron matter and symmetric nuclear matter (SNM) are studied using the finite range simple effective interaction, upon its parametrization revisited. Out of the total twelve parameters involved, we now determine ten of them from nuclear matter (NM), against the nine parameters in our earlier calculation, as required in order to have predictions in both spin polarized NM and finite nuclei in unique manner being free from uncertainty found using the earlier parametrization. The information on the effective mass splitting in polarized neutron matter of the microscopic calculations is used to constrain the one more parameter, that was earlier determined from finite nucleus, and in doing so the quality of the description of finite nuclei is not compromised. The interaction with the new set of parameters is used to study the possibilities of ferromagnetic and antiferromagnetic transitions in completely polarized SNM. Emphasis is given to analyse the results analytically, as far as possible, to elucidate the role of the interaction parameters involved in the predictions.

Speed of sound in nuclear matter using the finite-range simple effective interaction

The speed of sound is calculated in both symmetric nuclear matter and neutron matter through equations of state using the finite-range effective interaction SEI suggested by Satpathy and collaborators. It is found that in symmetric nuclear matter, the speed of sound becomes superluminous far beyond the normal nuclear matter density π 0 for two given temperatures with internal energies of 100 and 200 MeV, unlike the Skyrme force (SK-III) where superluminosity occurs at density ∼ π 0. In neutron matter, the occurrence of superluminosity is further shifted from the region of the normal nuclear-matter density. These observations confirm the suitability of SEI for calculating properties of nuclei at finite temperatures and hence there is no need to either readjust the interaction parameters or to make them density dependent.