Density-dependent Effective Interaction Research Articles

Low energy α+16O scattering in the orthogonality condition model

The orthogonality condition model (OCM) is used to describe α+16O scattering at low energies. A double folding potential with density-dependent effective NN interactions is used as the local potential of the model. The energies and widths of α-cluster resonances and differential cross sections are calculated. The results are compared to one obtained using the standard potential approach, without the nonlocal interaction of the OCM.

Radiative proton capture cross sections in the mass range 40–54

Proton capture cross sections in the energy range of astrophysical interest for mass region 40-54 have been calculated in the Hauser-Feshbach formalism with reaction code TALYS1.6. The density dependent M3Y effective nucleon-nucleon interaction folded with target radial matter densities from relativistic mean field approach is used to obtain the semi-microscopic optical potential. A definite normalization of potential-well depths has been used over the entire mass region. The $(p,\gamma)$ rates of some reactions, important in the astrophysical scenario, are calculated using the potential in the relevant mass region.

Nuclear symmetry energy in terms of single-nucleon potential and its effect on the proton fraction of β-stable npeμ matter

Momentum and density dependence of single-nucleon potential uτ (k, ρ, β) is analyzed using a density dependent finite range effective interaction of the Yukawa form. Depending on the choice of the strength parameters of exchange interaction, two different trends of the momentum dependence of nuclear symmetry potential are noticed which lead to two opposite types of neutron and proton effective mass splitting. The 2nd-order and 4th-order symmetry energy of isospin asymmetric nuclear matter are expressed analytically in terms of the single-nucleon potential. Two distinct behavior of the density dependence of 2nd-order and 4th-order symmetry energy are observed depending on neutron and proton effective mass splitting. It is also found that the 4th-order symmetry energy has a significant contribution towards the proton fraction of β-stable npeμ matter at high densities.

Investigation of 17F+p elastic scattering at near-barrier energies

The 17F +p elastic scattering at two near-barrier energies of 3.5 and 4.3 MeV/nucleon, have been analyzed in the framework of the single folding approach. The folded potentials are constructed by folding the density-dependent (DDM3Y) effective nucleon-nucleon interaction over the nuclear density of the one-proton halo nucleus 17F. Two versions of the density are considered. In addition, two versions of the one-nucleon knock-on exchange potentials are introduced to construct the real microscopic potentials. The derived potentials supplemented by phenomenological Woods-Saxon imaginary and spin-orbit potentials produced excellent description of the differential elastic scattering cross sections at the higher energy without need to introduce any renormalization. At the lower energy, however, in order to successfully reproduce the data, it is necessary to reduce the strength of the constructed real DDM3Y potential by about 25% of its original value. Furthermore, good agreement with data is obtained using the extracted microscopic DDM3Y potentials for both real and imaginary parts. Moreover, the interesting notch test is applied to investigate the sensitivity of the elastic scattering cross section to the radial distribution of the constructed microscopic potentials. The extracted reaction (absorption) cross sections are, also, investigated.

Density dependent effective interactions and recollections of the Rutgers-Princeton years

The density-dependent effective interactions given by the new Brown-Rho (new- BR) scalings and chiral three-nucleon force V3N are compared with the empirical density- dependent force of the Skyrme interactions. The new-BR scaling is based on a Skyrmion- half-Skyrmion model where nuclear matter is treated as a Skyrmion matter for density smaller than a transition density n1/2 ≊ 0.32 fm−3 while a half-Skyrmion matter for density greater. In this model, the meson mass, nucleon mass and meson-nucleon coupling are all scaled with density, making the resulting two-nucleon interaction density dependent. By integrating out a participating nucleon over the Fermi sea, Holt, Kaiser and Weise have obtained an effective three-nucleon force V̄3N which is also a density-dependent two-nucleon interaction. The equation of state for symmetric nuclear matter given by the new-BR-scaled V2N, V̄3N, and (unscaled-V2N + a Skyrme-type density-dependent force) are all found to be closely similar to each other.

Semicontact three-body interaction for nuclear density functional theory

To solve difficulties related to the use of nuclear density functional theory applied in its beyond mean-field version, we introduce a semi-contact 3-body effective interaction. We show that this interaction is a good candidate to replace the widely used density dependent effective interaction. The resulting new functionals are able to describe symmetric, neutron, polarized and neutron polarized nuclear matter as well as the effective mass properties simultaneously.

Neutron-proton effective mass splitting in terms of symmetry energy and its density slope

Using a simple density-dependent finite-range effective interaction having Yukawa form, the density dependence of isoscalar and isovector effective masses is studied. The isovector effective mass is found to be different for different pairs of like and unlike nucleons. Using HVH theorem, the neutron-proton effective mass splitting is represented in terms of symmetry energy and its density slope. It is again observed that the neutron-proton effective mass splitting has got a positive value when isoscalar effective mass is greater than the isovector effective mass and has a negative value for the opposite case. Furthermore, the neutron-proton effective mass splitting is found to have a linear dependence on asymmetry β. The second-order symmetry potential has a vital role in the determination of density slope of symmetry energy but it does not have any contribution on neutron-proton effective mass splitting. The finite-range effective interaction is compared with the SLy2, SKM, f−, f0, and f+ forms of interactions.

Stability ofβ-equilibrated dense matter and core-crust transition in neutron stars

The stability of the $\beta$-equilibrated dense nuclear matter is analyzed with respect to the thermodynamic stability conditions. Based on the density dependent M3Y effective nucleon-nucleon interaction, the effects of the nuclear incompressibility on the proton fraction in neutron stars and the location of the inner edge of their crusts and core-crust transition density and pressure are investigated. The high-density behavior of symmetric and asymmetric nuclear matter satisfies the constraints from the observed flow data of heavy-ion collisions. The neutron star properties studied using $\beta$-equilibrated neutron star matter obtained from this effective interaction for a pure hadronic model agree with the recent observations of the massive compact stars. The density, pressure and proton fraction at the inner edge separating the liquid core from the solid crust of neutron stars are determined to be $\rho_t=$ 0.0938 fm$^{-3}$, P$_t=$ 0.5006 MeV fm$^{-3}$ and x$_{p(t)}=$ 0.0308, respectively.

The effect of Fermi momentum cutoff on the binding energy of closed shell nuclei in the LOCV framework

The ground state binding energies of the light symmetric closed-shell nuclei, i.e., 4He, 12C, 16O and 40Ca and the heavy asymmetric ones, i.e., 48Ca, 90Zr and 120Sn are calculated in the harmonic oscillator (HOS) basis, by imposing the relative Fermi momentum cutoff of two point-like interacting nucleons on the density dependent average effective interactions (DDAEI). The DDAEI are generated through the lowest order constrained variational (LOCV) method calculations for the asymmetric nuclear matter with the operator and the channel dependent type bare nucleon-nucleon potentials, such as the Argonne \(Av_{18}^{j_{\max } = 2}\) and the Reid soft core, Reid68, interactions. In the framework of harmonic oscillator shell model, the cutoff is imposed by defining the maximum value of the relative quantum numbers (RQNmax) in two ways: (1) The RQNmax of the last shell and (2) the RQNmax of each shell, in the ground state of the nucleus. It is shown that present results on the binding energies and the root means square radius are closer to the corresponding experimental data than, our previous works with the same DDAEI potentials, but without the cutoff constraint. However, for the light symmetric nuclei, the second scheme gives less binding energy and larger root mean square radius compare to the first one. While the situation is reversed for the heavier nuclei.

Effective interaction: From nuclear reactions to neutron stars

An equation of state (EoS) for symmetric nuclear matter is constructed using the density dependent M3Y effective interaction and extended for isospin asymmetric nuclear matter. Theoretically obtained values of symmetric nuclear matter incompressibility, isobaric incompressibility, symmetry energy and its slope agree well with experimentally extracted values. Folded microscopic potentials using this effective interaction, whose density dependence is determined from nuclear matter calculations, provide excellent descriptions for proton, alpha and cluster radioactivities, elastic and inelastic scattering. The nuclear deformation parameters extracted from inelastic scattering of protons agree well with other available results. The high density behavior of symmetric and asymmetric nuclear matter satisfies the constraints from the observed flow data of heavy-ion collisions. The neutron star properties studied using $\beta$-equilibrated neutron star matter obtained from this effective interaction reconcile with the recent observations of the massive compact stars.

From nuclear reactions to compact stars: A unified approach

An equation of state (EoS) for symmetric nuclear matter is constructed using the density dependent M3Y effective interaction and extended for isospin asymmetric nuclear matter. Theoretically obtained values of symmetric nuclear matter incompressibility, isobaric incompressibility, symmetry energy and its slope agree well with experimentally extracted values. Folded microscopic potentials using this effective interaction, whose density dependence is determined from nuclear matter calculations, provide excellent descriptions for proton, alpha and cluster radioactivities, elastic and inelastic scattering. The nuclear deformation parameters extracted from inelastic scattering of protons agree well with other available results. The high density behavior of symmetric and asymmetric nuclear matter satisfies the constraints from the observed flow data of heavy-ion collisions. The neutron star properties studied using $\beta$-equilibrated neutron star matter obtained from this effective interaction for pure hadronic model agree with the recent observations of the massive compact stars such as PSR J1614-2230, but if a phase transition to quark matter is considered such agreement is no longer possible.

Imposing Fermi momentum cut-off on the channel- and density-dependent effective interaction and the ground-state properties of closed shell nuclei

The ground-state properties of light-moderate symmetric closed shell nuclei, i.e. 4He, 12C, 16O, 28Si, and 40Ca, and moderate-heavy asymmetric ones, i.e. 48Ca, 90Zr, and 120Sn, are calculated using the channel- and density-dependent effective interaction with the imposed Fermi momentum cut-off (CDDEI+FMC). CDDEI+FMC are generated through the lowest-order constrained variational (LOCV) nuclear matter calculations with the $ Av_{18}(j_{max}=2)$ nucleon-nucleon bare potential. FMC is considered by defining the maximum value of the relative quantum numbers according to the last shell in the ground state of a nucleus. The Hamiltonian matrix of the truncated effective interactions is diagonalized in the harmonic oscillator basis, regarding the nucleon configurations. The FMC effect on the different interaction channels is considered by comparing the contributions of each channel in the binding energies of the sample nuclei. CDDEI+FMC are replaced by the density-dependent average effective interactions with the imposed FMC (DDAEI+FMC) for the channels with $ j > j_{max}$ . For the light nuclei, the results show that the nuclei are more binding relative to the CDDEI-FMC case. The 4He nucleus is about 1.4MeV more binding per nucleon, and the root mean square of its radius equals the experimental data exactly. For the moderate-heavy closed shell nuclei, there are no significant differences between the results of the two cases, both with FMC and without it.

Role of symmetry potential in nuclear symmetry energy and its density slope parameter

Using a density dependent finite-range effective interaction of Yukawa form the nuclear mean field in asymmetric nuclear matter is expanded in terms of power series of asymmetry β ( = ρ n − ρ p ρ ) as u τ ( k , ρ , β ) = u 0 ( k , ρ ) ± u sym , 1 ( k , ρ ) β + u sym , 2 ( ρ ) β 2 . The behavior of nuclear symmetry potential u sym , 1 ( k , ρ ) around the Fermi momentum k f is found to be connected to the density dependence of symmetry energy E sym ( ρ ) and nucleon effective mass m 0 ⁎ m ( k = k f , ρ ) in symmetric nuclear matter. Two different trends of momentum dependence for nuclear symmetry potential is observed depending on the choice of strength parameters of exchange interaction, but at Fermi momentum it is found to be independent of the choice of parameters. The nuclear symmetry energy E sym ( ρ ) and its slope L ( ρ ) are expressed analytically in terms of nuclear mean field in isospin asymmetric nuclear matter using the same interaction. We find that the second order nuclear symmetry potential u sym , 2 ( ρ ) cannot be neglected while calculating the density slope of symmetry energy L ( ρ ) as well as the nuclear mean field in extremely neutron (proton) rich nuclear matter.

An effective Nuclear Model: from Nuclear Matter to Finite Nuclei

The momentum and density dependence of mean fields in symmetric and asymmetric nuclear matter are analysed using the simple density dependent finite range effective interaction containing a single Gaussian term alongwith the zero-range terms. Within the formalism developed, it is possible to reproduce the various diverging predictions on the momentum and density dependence of isovector part of the mean field in asymmetric matter. The finite nucleus calculation is formulated for the simple Gaussian interaction in the framework of quasilocal density functional theory. The prediction of energies and charge radii of the interaction for the spherical nuclei compares well with the results of other effective theories.

Anti-analog giant dipole resonances and the neutron skin of nuclei

We examine a method to determine the neutron-skin thickness of nuclei using data on the charge-exchange anti-analog giant dipole resonance (AGDR). Calculations performed using the relativistic proton–neutron quasiparticle random-phase approximation (pn-RQRPA) reproduce the isotopic trend of the excitation energies of the AGDR, as well as that of the spin-flip giant dipole resonances (IVSGDR), in comparison to available data for the even–even isotopes 112–124Sn. It is shown that the excitation energies of the AGDR, obtained using a set of density-dependent effective interactions which span a range of the symmetry energy at saturation density, supplemented with the experimental values, provide a stringent constraint on value of the neutron-skin thickness. For 124Sn, in particular, we determine the value ΔRpn=0.21±0.05 fm. The result of the present study shows that a measurement of the excitation energy of the AGDR in (p,n) reactions using rare-isotope beams in inverse kinematics, provides a valuable method for the determination of neutron-skin thickness in exotic nuclei.

Exact calculation of three-body contact interaction to second order

For a system of fermions with a three-body contact interaction the second-order contributions to the energy per particle $\bar E(k_f)$ are calculated exactly. The three-particle scattering amplitude in the medium is derived in closed analytical form from the corresponding two-loop rescattering diagram. We compare the (genuine) second-order three-body contribution to $\bar E(k_f)\sim k_f^{10}$ with the second-order term due to the density-dependent effective two-body interaction, and find that the latter term dominates. The results of the present study are of interest for nuclear many-body calculations where chiral three-nucleon forces are treated beyond leading order via a density-dependent effective two-body interaction.

Saturation properties of isospin asymmetric nuclear matter

Abstract The saturation properties of the isospin asymmetric nuclear matter, ANM, are studied microscopically using the density dependent M3Y-Paris and M3Y-Reid effective interactions in their CDM3Y- K versions. To do so, two-dimensional expansion of the energy per nucleon of ANM with respect to its density, ρ , and isospin asymmetry, I ≡ ( ρ n − ρ p ) / ρ , has been used within a suitable density range. Within this framework, the ANM saturation density, energy per nucleon and incompressibility as functions of the isospin asymmetry, I , up to its eighth order are derived in simple analytical formulas. These formulas link explicitly the ANM saturation properties to the CDM3Y- K density dependence forms through 24 characteristic quantities and coefficients which represent the different order partial derivatives of the energy with respect to ρ and I . The results show that the different terms up to I 8 , but with only 18 characteristic coefficients, are needed to describe reasonably the different ANM saturation properties. Up to four times the saturation density of nuclear matter, some properties such as the energy per nucleon of ANM and pure neutron matter are well expressed by their expansion up to only the quadratic term in I . Based on both Paris and Reid effective interactions and within the symmetric nuclear matter saturation incompressibility range of K 0 = 220 – 250 MeV , the different coefficients of the ANM incompressibility are obtained with the values of K 02 = − 348 ± 57 MeV , K 04 = 35 ± 31 MeV and K 06 = 4 ± 13 MeV .

On the unabridged 7D-folding structure of the optical model potential for nucleon-nucleus scattering

Microscopic optical model potentials for nucleon-nucleus collisions, based on density-dependent effective interactions, involve multi-dimensional integrals to ac- count for the Fermi motion of the bound nucleons of the target. If a spherical matter distribution is assumed, each matrix element of the optical potential in momentum space requires the evaluation of seven-dimensional integrals. Here we describe the structure of these potentials and report results from their actual evaluation. Results for the scatter- ing observables are compared with those based on alternative approximations, observing moderate sensitivity. These findings validate the use of simpler expressions to evaluate folding optical potentials, from which higher-order or unconventional effects in the effec- tive interaction can safely be investigated.

Absence of a maximum in theSfactor at deep sub-barrier energies in the fusion reaction40Ca + 40Ca

The fusion reaction ${}^{40}$Ca + ${}^{40}$Ca was very recently reinvestigated by the Legnaro group and cross sections down to $\ensuremath{\mu}$b were measured. In the present work this reaction is analyzed within the coupled-channel formalism including ${2}^{+}$, ${3}^{\ensuremath{-}}$, and ${5}^{\ensuremath{-}}$ phonon states. The heavy-ion entrance channel potential is calculated within the double-folding prescription and comprises a direct local term and a local equivalent of the nonlocal knock-on exchange component. The single-particle densities entering the folding integrals are prescribed according to the density matrix expansion. Coupling potentials are calculated from the $G$-matrix Michigan three-range Yukawa-type semirealistic nucleon-nucleon interaction (M3Y) as well as one modern parametrization of the density-dependent Gogny effective interaction. Realistic deformation parameters are used. The best fit to the data is not pointing to a possible maximum in the astrophysical $S$-factor as in a previous study on sub-barrier fusion involving ${}^{48}$Ca projectiles.

The ground state binding energy of the closed shell nuclei with the density dependent Av18 effective interaction in LOCV method

This work presents the calculation of the ground state binding energy of some light closed shell nuclei such as 4He, 12C, 16O, 28Si, 32S, 40Ca and 56Ni. We use our channel-dependent effective two-body interactions data that are produced through the lowest order constrained variational (LOCV) method for asymmetric nuclear matter with the charge-dependent Av18 bare NN potential up to Jmax = 2 and Jmax = 5. The local density approximation approach in the harmonic oscillator basis and Brody-Moshinsky coefficients are used to produce the relative and center of mass dependent effective two-body potentials. We show that the ground state energies of the closed shell nuclei with Av18 (Jmax = 2) gives more binding with respect to Reid68 bare NN potential as well as Δ – Reid68. However, there is not much difference between the Av18 (Jmax = 5) and Reid68Day which has been defined up to Jmax=5. We conclude that the contributions of higher partial waves (J > 2) are not very important and two-body kinetic energy in J=1 channel is twice as that of J=0 which is not the case for the two-body potential energy. Finally, our work results are compared with other theoretical approaches and experimental data.