Finite-range Effective Interaction Research Articles

Relativistic approach to the nuclear breathing mode

Microscopic theory of the nuclear response based on the relativistic meson-nucleon Lagrangian is applied to the description of the isoscalar giant monopole resonance (ISGMR) in a variety of nuclear systems. It is shown that the parameter-free inclusion of beyond-mean-field correlations of the quasiparticle-vibration coupling (qPVC) type in the leading approximation allows for a simultaneous realistic description of the ISGMR in nuclei of lead, tin, zirconium, and nickel mass regions, which is difficult on the mean-field level. The calculations employ the finite-range effective meson-nucleon interaction, which, in combination with the qPVC, has consistently demonstrated the ability to reliably describe many other nuclear structure phenomena. Systematic calculations of the isoscalar monopole response for nickel isotopes help reveal the central role of the coupling between the ISGMR and the low-energy quadrupole states in the placement of the ISGMR centroids.

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.

Theoretical Study of the Role of Symmetry Energy as Well as Its Density Slope and Curvature on Neutron Star Core Crust Transition Density Using Finite Range Effective Interaction

Theoretical Study of the Role of Symmetry Energy as Well as Its Density Slope and Curvature on Neutron Star Core Crust Transition Density Using Finite Range Effective Interaction

Charge radii of Ca isotopes and correlations

We study the effects of short- and long-range correlations on the charge radii of Ca isotopes. We start our investigation with an independent particle model consisting in Hartree-Fock plus Bardeen-Cooper-Schrieffer calculations with finite-range effective nucleon-nucleon interactions of Gogny type. The short-range correlations effects are evaluated by considering all the terms of a cluster expansion containing a single correlation line. The long-range correlations are taken into account by including the coupling with the quasi-particle random phase approximation phonons. While the effects of the short-range correlations are negligible, those of the long-range correlations largely modify the independent particle model results and improve the agreement with the experimental data.

Nuclear symmetry energy parameters from neutron skin thickness in 208Pb and electric dipole polarizability in 68Ni , 120Sn and 208Pb

Observables like neutron skin thickness and electric dipole polarizability in heavy nuclei are considered as most effective probes for the density dependence of nuclear symmetry energy at subsaturation density region. In the present work, within the framework of droplet model, we use finite range effective interactions to calculate the neutron skin thickness in 208Pb and the electric dipole polarizability in 68Ni, 120Sn and 208Pb. We correlate these quantities with the parameters of nuclear symmetry energy. Available experimental data on the neutron skin thickness in 208Pb and electric dipole polarizability in 68Ni, 120Sn and 208Pb are used to deduce information on the density slope parameter of nuclear symmetry energy at saturation and at subsaturation densities. Constraints such as 35.2 ≤ L(ρ 0) ≤ 64.4 MeV and 43 ≤ L(ρ c ) ≤ 55 MeV are obtained using experimental values for neutron skin thickness.

Regularized pseudopotential for mean-field calculations

We present preliminary results obtained with a finite-range two-body pseudopotential complemented with zero-range spin-orbit and density-dependent terms. After discussing the penalty function used to adjust parameters, we discuss predictions for binding energies of spherical nuclei calculated at the mean-field level, and we compare them with those obtained using the standard Gogny D1S finite-range effective interaction.

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.

The fourth-order symmetry energy of nuclear matter and symmetry energy coefficients of finite nuclei using extended semi-empirical mass formula

An extended nuclear mass formula has been used by considering the bulk, surface and coulomb contributions to the nuclear mass. In this mass formula, the fourth-order symmetry energy coefficient [Formula: see text] of finite nuclei and fourth-order symmetry energy [Formula: see text] of nuclear matter (NM) are related explicitly to the characteristic parameters of NM equation of state (EOS) using finite range effective interaction. The calculations are carried out with Yukawa form of exchange interaction having the same range but with different strengths for interaction between like and unlike nucleon. In this extended mass formula, by approximating [Formula: see text] to a constant [Formula: see text] an explicit relation between [Formula: see text] and fourth-order symmetry energy [Formula: see text] is obtained, which provides the possibility to extract information on [Formula: see text].

Zero-Temperature Equation of State of a Two-Dimensional Bosonic Quantum Fluid with Finite-Range Interaction

We derive the two-dimensional equation of state for a bosonic system of ultracold atoms interacting with a finite-range effective interaction. Within a functional integration approach, we employ a hydrodynamic parameterization of the bosonic field to calculate the superfluid equations of motion and the zero-temperature pressure. The ultraviolet divergences, naturally arising from the finite-range interaction, are regularized with an improved dimensional regularization technique.

Neutron skin thickness of finite nuclei with finite range effective interaction in droplet model

We analyze the relation between the symmetry energy coefficient [Formula: see text] of finite nuclei with mass number [Formula: see text] in the semi-empirical mass formula. The nuclear matter symmetry energy [Formula: see text] at reference density [Formula: see text] in the subsaturation density region can be determined by the symmetry energy [Formula: see text] and its density slope [Formula: see text] at the saturation density [Formula: see text]. From this relation, the neutron skin thickness ‘[Formula: see text]’ in finite nuclei with droplet model are correlated to the various symmetry energy parameters. A prominent role of the bulk symmetry energy [Formula: see text] to the so-called surface stiffness coefficient [Formula: see text] is observed in deriving the size of the neutron skin. Two types of neutron skins are distinguished: the “surface” and the “bulk”. The linear dependence of the neutron skin thickness for different stable nuclei ([Formula: see text]) on the slope [Formula: see text] of the symmetry energy as well as on the relative neutron excess [Formula: see text] is observed. Though the value of the surface width is found to be limited within 0.1[Formula: see text]fm, its contribution should not be neglected to measure neutron skin thickness.

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.

Topical Issue on Finite Range Effective Interactions and Associated Many-Body Methods - A Tribute to Daniel Gogny

Topical Issue on Finite Range Effective Interactions and Associated Many-Body Methods - A Tribute to Daniel Gogny

Thermal field theory of bosonic gases with finite-range effective interaction

We study a dilute and ultracold Bose gas of interacting atoms by using an effective field theory which takes account finite-range effects of the inter-atomic potential. Within the formalism of functional integration from the grand canonical partition function we derive beyond-mean-field analytical results which depend on both scattering length and effective range of the interaction. In particular, we calculate the equation of state of the bosonic system as a function of these interaction parameters both at zero and finite temperature including one-loop Gaussian fluctuation. In the case of zero-range effective interaction we explicitly show that, due to quantum fluctuations, the bosonic system is thermodynamically stable only for very small values of the gas parameter. We find that a positive effective range above a critical threshold is necessary to remove the thermodynamical instability of the uniform configuration. Remarkably, also for relatively large values of the gas parameter, our finite-range results are in quite good agreement with recent zero-temperature Monte Carlo calculations obtained with hard-sphere bosons.

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.

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.

Partial-wave decomposition of the finite-range effective tensor interaction

We perform a detailed analysis of the properties of the finite-range tensor term associated with the Gogny and M3Y effective interactions. In particular, by using a partial wave decomposition of the equation of state of symmetric nuclear matter, we show how we can extract their tensor parameters directly from microscopic results based on bare nucleon-nucleon interactions. Furthermore, we show that the zero-range limit of both finite-range interactions has the form of the N3LO Skyrme pseudo-potential, which thus constitutes a reliable approximation in the density range relevant for finite nuclei. Finally, we use Brueckner-Hartree-Fock results to fix the tensor parameters for the three effective interactions.

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.

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.

On the properties ofN= 50 isotones from78Ni to100Sn

By using the self-consistent approach based on the Skyrme functional and with account of pairing correlations, we calculate global properties of nuclei, such as binding energies, one and two-neutron separation energies, density distributions of nucleons, root-mean-square radii of nucleon distributions. For description of excitation energies and transition rates we apply the RPA+BCS approach based on the finite range effective interaction defined by us before. Everywhere, where it is possible, we perform comparison of theoretical results with the experimental data.

Microscopic positive-energy potential based on the Gogny interaction

We present a nucleon elastic scattering calculation based on Green's function formalism in the random-phase approximation. For the first time, the finite-range Gogny effective interaction is used consistently throughout the whole calculation to account for the complex, nonlocal, and energy-dependent optical potential. Effects of intermediate single-particle resonances are included and found to play a crucial role in the account for measured reaction cross sections. Double counting of the particle-hole second-order contribution is carefully addressed. The resulting integro-differential Schr\"odinger equation for the scattering process is solved without localization procedures. The method is applied to neutron and proton elastic scattering from $^{40}\mathrm{Ca}$. A successful account for differential and integral cross sections, including analyzing powers, is obtained for incident energies up to 30 MeV. Discrepancies at higher energies are related to a much-too-high volume integral of the real potential for large partial waves. This work opens the way to simultaneously assess effective interactions suitable for both nuclear structure and reactions.