Density-dependent Effective Interaction Research Articles

Semi-microscopic optical-model with channel coupling analysis to describe neutron-nucleus scattering of light and heavy nuclei

Many studies utilizing various potential models have been conducted on the scattering of nucleons from nuclei. In our study, we added channel coupling to a semi-microscopic optical model. With incident energies between 10 and 30 MeV, we sought to compare the predicted reaction observables for the neutron scattering of the following nuclei: 12C, 16O, 54Fe, 58Ni, 120Sn, and 208Pb. We did this twice, once using the density-dependent M3Y-Reid nucleon-nucleon effective bare interaction and once using the density-independent M3Y-Reid effective bare interaction. The remaining terms of the optical potential model take the form of Woods-Saxon and its derivatives, and the real volume term is obtained by folding the NN effective bare potential over the density of the nuclear target using the density-dependent M3Y-Reid NN effective bare interaction and density-independent M3Y-Reid NN effective bare interaction. To investigate how the potential characteristics depend on energy, the ground state is connected to a select few low-lying collective excited states. The density-dependent M3Y-Reid NN effective bare interaction-based semi-microscopic model reproduces the reaction features and forecasts the experimental total cross sections. The parameters of potential depth exhibit a linear energy dependence. We contrast the outcomes of the M3Y-Reid density-dependent model with those attained using the M3Y-Reid nucleon-nucleon effective bare interaction, which is density-independent. The M3Y Reid density-dependent model performs well when the two models are compared.

Relativistic and nonrelativistic mean field analysis of the shell evolution in 44−52Ar isotopes

The systematic search of axial ground state and the emergence of new gaps in neutron-rich [Formula: see text]Ar isotopes are the challenging of current calculations of relativistic and nonrelativistic mean field models. For this purpose, we have employed the model based on Relativistic Hartree–Bogoliubov (RHB) with the density-dependent effective interaction of point coupling DD-PCX type. However, the nonrelativistic mean field calculations based on Hartree-Fock model were carried out with Skyrme SV-min parametrization. All the present calculations were performed within axial symmetries. The results provide that most of isotopes show an oblate-deformed ground state. In particular, [Formula: see text]Ar and [Formula: see text]Ar display a spherical shape in their ground states with SV-Min calculations. There is a notable signature of the sub-shell closure at neutron number [Formula: see text], whereas [Formula: see text] is expected to be nearly quenched in the spherical ground. Furthermore, coexistence features are predicted in the neutron-rich [Formula: see text]Ar isotope. We have also studied the neutron axial densities and its central depletion in the well-deformed grounds for the first time. In addition to these, the proton single-particle evolution and bubble-like structure at [Formula: see text]Ar are very well reproduced with DD-PCX calculations.

Stellar electron-capture rates based on finite-temperature relativistic quasiparticle random-phase approximation

The electron capture process plays an important role in the evolution of the core collapse of a massive star that precedes the supernova explosion. In this study, the electron capture on nuclei in stellar environment is described in the relativistic energy density functional framework, including both the finite temperature and nuclear pairing effects. Relevant nuclear transitions $J^\pi = 0^\pm, 1^\pm, 2^\pm$ are calculated using the finite temperature proton-neutron quasiparticle random phase approximation with the density-dependent meson-exchange effective interaction DD-ME2. The pairing and temperature effects are investigated in the Gamow-Teller transition strength as well as the electron capture cross sections and rates for ${}^{44}$Ti and ${}^{56}$Fe in stellar environment. It is found that the pairing correlations establish an additional unblocking mechanism similar to the finite temperature effects, that can allow otherwise blocked single-particle transitions. Inclusion of pairing correlations at finite temperature can significantly alter the electron capture cross sections, even up to a factor of two for ${}^{44}$Ti, while for the same nucleus electron capture rates can increase by more than one order of magnitude. We conclude that for the complete description of electron capture on nuclei both pairing and temperature effects must be taken into account.

Proximity effect of pair correlation in the inner crust of neutron stars

Abstract We study the proximity effect of pair correlation in the inner crust of neutron stars by means of the Skyrme–Hartree–Fock–Bogoliubov theory formulated in coordinate space. We describe a system composed of a nuclear cluster immersed in neutron superfluid confined in a spherical box. Using a density-dependent effective pairing interaction that reproduces both the pair gap of neutron matter obtained in ab initio calculations and that of finite nuclei, we analyze how the pair condensate in a neutron superfluid is affected by the presence of the nuclear cluster. It is found that the proximity effect is characterized by the coherence length of the neutron superfluid measured from the edge position of the nuclear cluster. The calculation predicts that the proximity effect has a strong density dependence. In the middle layers of the inner crust with baryon density $5 \times 10^{-4}$ fm$^{-3} \mathop < \limits_ \sim \ \rho_b \mathop < \limits_ \sim \ 2\times 10^{-2}$ fm$^{-3}$, the proximity effect is strongly limited in the vicinity of the nuclear cluster, i.e., in a sufficiently smaller area than the Wigner–Seitz cell. In contrast, the proximity effect is predicted to extend to the whole volume of the Wigner–Seitz cell in shallow layers of the inner crust with $\rho_b \mathop < \limits_ \sim \ 2 \times 10^{-4}$ fm$^{-3}$, and in deep layers with $\rho_b \mathop > \limits_ \sim \ 5 \times 10^{-2}$ fm$^{-3}$.

Analysis of strong refractive effect within 11Li projectile structure

In the context of the double folding optical model, the strong refractive effect for elastic scattering of 11Li + 12C and 11Li + 28Si systems at incident energies of 29, 50, and 60 MeV/n is studied. Real folded potentials are generated based on a variety of nucleon-nucleon interactions with the suggested density distributions for the halo structure of 11Li nuclei. The rearrangement term (RT) of the extended realistic density dependent CDM3Y6 effective interaction is considered. The imaginary potential was taken in the traditional standard Woods-Saxon form. Satisfactory results for the calculated potentials are obtained, with a slight effect of the RT in CDM3Y6 potential. Successful reproduction with a normalization factor close to one for the observed angular distributions of the elastic scattering differential cross section has been achieved using the derived potentials. The obtained reaction cross-section is studied as a guide by extrapolating our calculations and previous results.

Microscopic study of the shell structure evolution in isotopes of light to middle mass range nuclides

Shell structure evolution in isotopes (even Z and even N) of Silicon (Si), Sulphur (S), Argon (Ar) and Calcium (Ca) has been analysed. We have used both Relativistic Hartree-Bogoliubov theory and Non-Relativistic Hartree-Fock-Bogoliubov theory for the theoretical calculations of the physical observables of interest. We have employed the model based on Relativistic Hartree-Bogoliubov theory with the density dependent effective interactions of meson exchange and point coupling types. Calculations based on Hartree-Fock-Bogoliubov theory are carried out with different skyrme forces and their sensitivity has been tested. Physical observables of interest include binding energies, single neutron separation energies, two-neutron separation energies, shell closure parameter Dn(Z, N) and differential variation dS2n(Z, N) based on two neutron separation energy. Our theoretical results gives indication of shell closure at neutron number N =14 and neutron number N = 20 for the nuclei of Silicon (Si). Shell closures at neutron numbers N = 14, 20 and neutron number N = 28 are observed for Sulphur (S) nuclides. Argon (Ar) and Calcium (Ca) isotopes also provides the signature of shell closures at neutron numbers N = 20 and neutron number N = 28.

Hyperon–nucleon three-body forces and strangeness in neutron stars

Three-body forces acting on a $\Lambda$ hyperon in a nuclear medium are investigated, with special focus on the so-called hyperon puzzle in neutron stars. The hyperon-nucleon two-body interaction deduced from SU(3) chiral effective field theory is employed at next-to-leading order. Hyperon-nucleon three-body forces are approximated using saturation by decuplet baryons and are transcribed to density-dependent effective two-body interactions. These together are taken as input in a Brueckner-Bethe-Goldstone equation with explicit treatment of the $\Lambda N\leftrightarrow\Sigma N$ and $\Lambda NN\leftrightarrow\Sigma NN$ coupled channels. Single-particle potentials of a $\Lambda$ hyperon in symmetric nuclear matter and neutron matter are calculated. With parameters of the $\Lambda NN$ three-body force constrained by hypernuclear phenomenology, extrapolations to high baryon density are performed. By comparison of the $\Lambda$ and neutron chemical potentials at densities characteristic of the core of neutron stars it is found that the combined repulsive effects of two- and three-body correlations makes the appearance of $\Lambda$ hyperons in neutron stars energetically unfavourable, thus offering a possible solution to a longstanding question.

Gravitational waves from non-radial perturbations in neutron stars

In the present work, we explore the Rossby mode perturbations in case of neutron stars as sources of continuous gravitational waves. The intensity and time evolution of the emitted gravitational waves in terms of the amplitude of the strain tensor are estimated in the slow rotation approximation using β-equilibrated neutron star matter obtained from density dependent M3Y effective interaction. For a wide range of neutron star masses, the fiducial gravitational and various viscous time scales, the critical frequencies and the time evolutions of the frequencies are calculated. Unlike other non-radial perturbations, amplitude of Rossby mode perturbation increases due to the emission of gravitational waves which carry angular momentum of the star to infinity. Hence, existence of such perturbation in a star implies a positive rate of change in the angular momentum transfer. It, therefore, implies that for a particular neutron star, the intensity of gravitational wave emission increases with time until the angular frequency reduces down to a critical value below which the star stops emitting radiation.

Ground state properties and shape evolution in Pt isotopes within the covariant density functional theory

In this work, the ground state properties of the platinum isotopic chain, [Formula: see text]Pt are studied within the covariant density functional theory. The calculations are carried out for a large number of even–even Pt isotopes by using the density-dependent point-coupling and the density-dependent meson-exchange effective interactions. All ground state properties such as the binding energy, separation energy, two-neutron shell gap, root mean square (rms)-radii for neutrons and protons and quadrupole deformation are discussed and compared with available experimental data, and with the predictions of some nuclear models such as the Relativistic Mean Field (RMF) model with NL3 functional and the Hartree–Fock–Bogoliubov (HFB) method with SLy4 Skyrme force. The shape phase transition for Pt isotopic chain is also studied. Its corresponding total energy curves as well as the potential energy surfaces confirm the transition from prolate to oblate shapes at [Formula: see text]Pt contrary to some studies predictions and in agreement with others. Overall, a good agreement is found between the calculated and experimental results wherever available.

Nuclear structure investigation of even-even Sn isotopes within the covariant density functional theory

The current investigation aims to study the ground-state properties of one of the most interesting isotopic chains in the periodic table, 94−168Sn, from the proton drip line to the neutron drip line by using the covariant density functional theory, which is a modern theoretical tool for the description of nuclear structure phenomena. The physical observables of interest include the binding energy, separation energy, two-neutron shell gap, rms-radii for protons and neutrons, pairing energy and quadrupole deformation. The calculations are performed for a wide range of neutron numbers, starting from the proton-rich side up to the neutron-rich one, by using the density-dependent meson-exchange and the density dependent point-coupling effective interactions. The obtained results are discussed and compared with available experimental data and with the already existing results of relativistic Mean Field (RMF) model with NL3 functional. The shape phase transition for Sn isotopic chain is also investigated. A reasonable agreement is found between our calculated results and the available experimental data.

Elastic scattering of one-proton halo nucleus 17F on different mass targets using semi microscopic potentials

The elastic scattering of 17F have been studied for different mass targets (e.g. 12C, 14N, 58Ni, 208Pb) at different energies. We used the double folding optical model potential based on the density-dependent DDM3Y effective nucleon-nucleon interaction. Both version of the density distribution of the one-proton halo 17F nucleus has been taken into account in the above mentioned potential. The data for angular distributions of the elastic scattering differential cross section and reaction cross sections has been successfully reproduced at different energies using the above potentials. The energy dependence and the target mass number dependence of scattering in the imaginary volume integrals and the total reaction cross sections has also been studied.

Nuclear structure study of some tin isotopes using the self-consistent mean field method

Hartree-Fock calculations for even-even Tin isotopes usingSkyrme density dependent effective nucleon-nucleon interaction arediscussed systematically. Skyrme interaction and the general formulafor the mean energy of a spherical nucleus are described. The chargeand matter densities with their corresponding rms radii and thenuclear skin for Sn isotopes are studied and compared with theexperimental data. The potential energy curves obtained withinclusion of the pairing force between the like nucleons in Hartree-Fock-Bogoliubov approach are also discussed.

Gravitational waves from isolated neutron stars: Mass dependence of r -mode instability

In this work we study the r-mode instability windows and the gravitational wave signatures of neutron stars in the slow rotation approximation using the equation of state obtained from the density dependent M3Y effective interaction. We consider the neutron star matter to be $\beta$-equilibrated neutron-proton-electron matter at the core with a rigid crust. The fiducial gravitational and viscous timescales, the critical frequencies and the time evolutions of the frequencies and the rates of frequency change are calculated for a range of neutron star masses. We show that the young and hot rotating neutron stars lie in the r-mode instability region. We also emphasize that if the dominant dissipative mechanism of the r-mode is the shear viscosity along the boundary layer of the crust-core interface, then the neutron stars with low $L$ value lie in the r-mode instability region and hence emit gravitational radiation.

Skyrme density functional description of the double magic Ni78 nucleus

We calculate the single particle spectrum of the double magic nucleus $^{78}$Ni in a Hartree-Fock approach using the Skyrme density-dependent effective interaction containing central, spin-orbit and tensor parts. We show that the tensor part has an important effect on the spin-orbit splitting of the proton $1f$ orbit which may explain the survival of magicity so far from the stability valley. We confirm the inversion of the $1f5/2$ and $2p3/2$ levels at the neutron number 48 in the Ni isotopic chain expected from previous Monte Carlo shell model calculations and supported by experimental observation.

Concentration-dependent swelling and structure of ionic microgels: simulation and theory of a coarse-grained model.

We study swelling and structural properties of ionic microgel suspensions within a comprehensive coarse-grained model that combines the polymeric and colloidal natures of microgels as permeable, compressible, charged spheres governed by effective interparticle interactions. The model synthesizes the Flory-Rehner theory of cross-linked polymer gels, the Hertz continuum theory of effective elastic interactions, and a theory of density-dependent effective electrostatic interactions. Implementing the model using Monte Carlo simulation and thermodynamic perturbation theory, we compute equilibrium particle size distributions, swelling ratios, volume fractions, net valences, radial distribution functions, and static structure factors as functions of concentration. Trial Monte Carlo moves comprising particle displacements and size variations are accepted or rejected based on the total change in elastic and electrostatic energies. The theory combines first-order thermodynamic perturbation and variational free energy approximations. For illustrative system parameters, theory and simulation agree closely at concentrations ranging from dilute to beyond particle overlap. With increasing concentration, as microgels deswell, we predict a decrease in the net valence and an unusual saturation of pair correlations. Comparison with experimental data for deionized, aqueous suspensions of PNIPAM particles demonstrates the capacity of the coarse-grained model to predict and interpret measured swelling behavior.

Microscopic optical potentials within the weak density dependent nucleon-nucleon effective interactions

<p class="tomtat1">The microscopic optical potentials have been investigated in the framework of the nuclear structure approach based on the energy-density functional approaches. The effective phenomenological nucleon-nucleon interaction SLy5 is consistently used to obtain the Hartree-Fock single particle states, the collective motion at small amplitudes of the target, and the coupling between the particle and phonons. The role of the weak density dependent interaction is showed. </p>

Limiting symmetry energy elements from empirical evidence

In the framework of an equation of state (EoS) constructed from a momentum and density-dependent finite-range two-body effective interaction, the quantitative magnitudes of the different symmetry elements of infinite nuclear matter are explored. The parameters of this interaction are determined from well-accepted characteristic constants associated with homogeneous nuclear matter. The symmetry energy coefficient [Formula: see text], its density slope [Formula: see text], the symmetry incompressibility [Formula: see text] as well as the density-dependent incompressibility [Formula: see text] evaluated with this EoS are seen to be in good harmony with those obtained from other diverse perspectives. The higher order symmetry energy coefficients [Formula: see text], etc., are seen to be not very significant in the domain of densities relevant to finite nuclei, but gradually build up at supra-normal densities. The analysis carried out with a Skyrme-inspired energy density functional (EDF) obtained with the same input values for the empirical bulk data associated with nuclear matter yields nearly the same results.

On the applicability of density dependent effective interactions in cluster-forming systems.

We systematically studied the validity and transferability of the force-matching algorithm for computing effective pair potentials in a system of dendritic polymers, i.e., a particular class of ultrasoft colloids. We focused on amphiphilic dendrimers, macromolecules which can aggregate into clusters of overlapping particles to minimize the contact area with the surrounding implicit solvent. Simulations were performed for both the monomeric and coarse-grained models in the liquid phase at densities ranging from infinite dilution up to values close to the freezing point. The effective pair potentials for the coarse-grained simulations were computed from the monomeric simulations both in the zero-density limit (Φeff0) and at each investigated finite density (Φeff). Conducting the coarse-grained simulations with Φeff0 at higher densities is not appropriate as they failed at reproducing the structural properties of the monomeric simulations. In contrast, we found excellent agreement between the spatial dendrimer distributions obtained from the coarse-grained simulations with Φeff and the microscopically detailed simulations at low densities, where the macromolecules were distributed homogeneously in the system. However, the reliability of the coarse-grained simulations deteriorated significantly as the density was increased further and the cluster occupation became more polydisperse. Under these conditions, the effective pair potential of the coarse-grained model can no longer be computed by averaging over the whole system, but the local density needs to be taken into account instead.

Nuclear Energy Density Functional for KIDS

The density functional theory (DFT) is based on the existence and uniqueness of a universal functional $E[\rho]$, which determines the dependence of the total energy on single-particle density distributions. However, DFT says nothing about the form of the functional. Our strategy is to first look at what we know, from independent considerations, about the analytical density dependence of the energy of nuclear matter and then, for practical applications, to obtain an appropriate density-dependent effective interaction by reverse engineering. In a previous work on homogeneous matter, we identified the most essential terms to include in our "KIDS" functional, named after the early-stage participating institutes. We now present first results for finite nuclei, namely the energies and radii of $^{16,28}$O, $^{40,60}$Ca.

Nuclear constraints on the core-crust transition and crustal fraction of moment of inertia of neutron stars

The crustal fraction of moment of inertia in neutron stars is calculated using $\beta$-equilibrated nuclear matter obtained from density dependent M3Y effective interaction. The transition density, pressure and proton fraction at the inner edge separating the liquid core from the solid crust of the neutron stars determined from the thermodynamic stability conditions are found to be $\rho_t=$ 0.0938 fm$^{-3}$, P$_t=$ 0.5006 MeV fm$^{-3}$ and $x_{p(t)}=$ 0.0308, respectively. The crustal fraction of the moment of inertia can be extracted from studying pulsar glitches and is most sensitive to the pressure as well as density at the transition from the crust to the core. These results for pressure and density at core-crust transition together with the observed minimum crustal fraction of the total moment of inertia provide a new limit for the radius of the Vela pulsar: $R \geq 4.10 + 3.36 M/M_\odot$ kms.