Density Dependent Version Research Articles

Probing nuclear equation of state with the cdm3y version of B3y-fetal effective interaction

This paper is a study of the nuclear Equation of State (EOS) of cold nuclear matter with the B3Y-Fetal effective interaction in its CDM3Y density-dependent version within the framework of Hartree-Fock approximation. The well-known saturation properties of both symmetric and asymmetric nuclear matter are well-reproduced in this work. Using the CDM3Y-K approach, this study has evolved a new set of user interactions, some of which are CDB3Y1-, CDB3Y2-, CDB3Y3-, CDB3Y4-, CDB3Y5-, CDB3Y6-Fetal interactions with corresponding incompressibilities K0 = 188, 204, 217,228, 241 and 252 MeV respectively, in excellent agreement with those of the M3Y-Paris and M3Y-Reid effective interactions. For asymmetric nuclear matter, the new set of interactions has produced the symmetry energy Esym = 32.00 MeV with an associated slope parameter L = 55 MeV at a saturation density ρ = 0.17fm−3 and asymmetry parameter δ = 1.00 (pure neutron matter) in good agreement with the standard values obtained from coupled channel analysis of charge exchange reactions, statistical multifragmentation model and terrestrial Nuclear Physics experimental analyses. Furthermore, the new set of interactions has been found to have bright prospects in a nuclear reaction as the real folded potential computed with the CDB3Y6-Fetal interaction within the framework of double folding potential has been found to be good and similar to that of CDB3Y6-Paris whose optical potential has a repulsive direct component.

Management strategy of the naked carp (Gymnocypris przewalskii) in the Qinghai lake using matrix population modeling

Naked carp (Gymnocypris przewalskii) is the only fish species commercially harvested in Qinghai Lake, which is the largest inland saltwater lake in China. Multiple ecological stresses such as long-term overfishing, drying-up of riverine inflows, and decreases in spawning habitat caused the naked carp population to decrease from 320,000 tons before the 1950s to only 3000 tons by the early 2000s. We used matrix projection population modeling to quantitatively simulate the dynamics of the naked carp population from the 1950s to the 2020s. Five versions of the matrix model were developed from the field and laboratory information that represented different population states (high but declining, low abundance, very low abundance, initial recovery, pristine). Equilibrium analysis was applied to density-independent versions of the matrices and population growth rate, age composition, and elasticities were compared among versions. Stochastic, density-dependent version of the most recent decade (recovering) version was used to simulate the time-dependent responses to a range of levels of artificial reproduction (addition of age-1 from hatchery) and of the pristine version to simulate combinations of fishing rate and minimum age of harvest. Results showed the major role of overfishing in the population decline and that the population growth rate was most sensitive to the survival of juveniles and the spawning success of early-age adults. Dynamic simulations showed a rapid population response to artificial reproduction when population abundance was low and that if artificial reproduction continues at its current level, then population biomass would reach 75% of its pristine biomass after 50 years. Simulations with the pristine version identified sustainable fishing levels and the importance of protecting the first few ages of maturity. Overall, modeling results showed that artificial reproduction under conditions of no fishing is an effective approach to restoring the naked carp population. Further effectiveness should consider maximizing survival in the months just after release and maintaining genetic and phenotypic diversity. More information on density-dependent growth, survival, and reproduction, as well as on the genetic diversity and growth and migratory behavior (phenotypic variation) of released and native-spawned fish, would help inform management and conservation strategies and practices going forward.

Analysis of the 28Si(α,α)28Si elastic scattering at energies from 12.7 to 50.5 MeV

The available experimental elastic scattering angular distributions data of α-particles on 28Si nucleus have been reanalyzed in the energy range from 12.7 to 50.5 MeV. The analysis performed within the context of optical model (OM) potential. In the framework of double-folding model (DFM), we created the real part of optical potential using a density dependent version BDM3Y1-Paris interaction model.

Nuclear structure properties and decay rates of molybdenum isotopes

Electron capture and $\beta ^{-}$ decay are the dominant decay processes during late phases of evolution of heavy stars. Previous simulation results show that weak rates on isotopes of Molybdenum (Mo) have a meaningful contribution during the development of phases of stars before they go supernova. The relative abundance coupled with the stellar weak rates on Mo isotopes may change the lepton-to-baryon content of the core material. Here we report on the calculation of nuclear structure properties of 82−138Mo isotopes employing the RMF model. Later we calculate the weak decay rates of these isotopes. We use the pn-QRPA model to compute these rates. In the first step, the ground-state nuclear properties of Mo isotopes such as binding energy per nucleon, neutron and proton separation energies, charge radii, total electric quadrupole moments and deformation parameter of electric quadrupole moments have been calculated using density dependent version of RMF model with DD-PC1 and DD-ME2 functionals. The calculated electric quadrupole deformation parameters have been used in a deformed pn-QRPA calculation in the second phase of this work to calculate half-lives and weak decay rates for these Mo isotopes in stellar matter. We calculate the electron capture and $\beta $-decay rates over an extensive range of temperature ($0.01\times 10^{9}$ K to $30\times 10^{9}$ K) and density (10 to $10^{11}$) g/cm3. Our study can prove useful for simulation of presupernova evolution processes of stars.

Symmetric nuclear matter calculations: A variational approach

We have studied nuclear matter with a new M3Y-type effective nucleon-nucleon interaction based on the lowest order constrained variational approach (LOCV) as the principal investigating tool. The chosen interaction, called B3Y-Fetal, has been used in its DDM3Y1, BDM3Y0, BDM3Y1, BDM3Y2, and BDM3Y3 density-dependent versions to reproduce the saturation properties of cold nuclear matter at the saturation density, $\ensuremath{\rho}=0.17\phantom{\rule{0.28em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}3}$. Such properties as the binding energy per nucleon, also called the equation of state (EOS), and the incompressibility of symmetric nuclear matter have been computed, with results proving to be acceptably in agreement with previous work done with the M3Y-Paris and M3Y-Reid interactions by other researchers. Insightful information on symmetric nuclear matter obtained from the folding analysis in this work has shown it to be possibly governed by a soft EOS.

Analysis of heavy-ion fusion reactions using new parameterized form of the universal function of nuclear proximity potential

In the present work, we modify the original version of this formalism (Prox. 77) using a new analytical form of the universal function which is formulated based on the double-folding model with three density-dependent versions of the M3Y-type interactions, namely DDM3Y1, CDM3Y3 and BDM3Y1, for 46 fusion systems with condition 48≤Z1Z2≤2460 for charge product of their participant nuclei. It is found that when the Prox. 77 potential is accompanied by each of the formulated universal functions, the agreement between the theoretical and experimental data of the fusion barrier heights increase for our selected systems. The obtained results of this study reveal that the saturation property of cold nuclear matter plays a key role in the calculations of the fusion cross sections. We conclude that the Prox. 77 model with universal function based on the BDM3Y1 interactions provides the best results for fusion barrier heights and cross sections. On the basis of the prox. 77(BDM3Y1) potential model, we present the parameterized formulas for fusion barrier heights VB and positions RB. These formulas can calculate the values of RB andVB with good accuracy in comparison with the experimental data. A comparison is also presented among the theoretical results of the present work and those obtained by the modified form of the original version of proximity approach through the universal function and surface energy coefficients available in the literature.

The energy balance relation for weak solutions of the density-dependent Navier–Stokes equations

We consider the incompressible inhomogeneous Navier–Stokes equations with constant viscosity coefficient and density which is bounded and bounded away from zero. We show that the energy balance relation for this system holds for weak solutions if the velocity, density, and pressure belong to a range of Besov spaces of smoothness 1/3. A density-dependent version of the classical Kármán–Howarth–Monin relation is derived.

A Comprehensive Theoretical Analysis of 6,7Li + 64Zn Elastic Scattering in a Wide Angular Range Around the Coulomb Barrier

In this paper, the elastic scattering angular distributions of 6,7Li on 64Zn have been investigated by using various nuclear potentials. For this, we use the phenomenological Woods-Saxon potential, the real double folding potential with the density-independent M3Y effective interaction supplemented with an imaginary part in Woods-Saxon form and the double folding potentials multiplied with a normalization factor of the real and imaginary parts via the density-independent and CDM3Y6 density-dependent versions of the M3Y effective interaction have been used. The results have been compared with each other as well as with the experimental data. It has been observed that the agreement between the theoretical results and earlier reported data is perfect. Finally, the change of the total reaction cross sections with energy has been investigated.

Extended Hartree-Fock study of the single-particle potential: The nuclear symmetry energy, nucleon effective mass, and folding model of the nucleon optical potential

The nucleon mean-field potential has been thoroughly investigated in an extended Hartree-Fock (HF) calculation of nuclear matter (NM) using the CDM3Y3 and CDM3Y6 density dependent versions of the M3Y interaction. The single-particle (SP) energies of nucleons in NM are determined according to the Hugenholtz--Van Hove theorem, which gives rise naturally to a rearrangement term (RT) of the SP potential at the Fermi momentum. Using the RT obtained exactly at the different NM densities and neutron-proton asymmetries, a consistent method is suggested to take into account effectively the momentum dependence of the RT of the SP potential within the standard HF scheme. To obtain a realistic momentum dependence of the nucleon optical potential (OP), the high-momentum part of the SP potential was accurately readjusted to reproduce the observed energy dependence of the nucleon OP over a wide range of energies. The impact of the RT and momentum dependence of the SP potential on the density dependence of the nuclear symmetry energy and nucleon effective mass has been studied in detail. The high-momentum tail of the SP potential was found to have a sizable effect on the slope of the symmetry energy and the neutron-proton effective mass splitting at supranuclear densities of the NM. Based on a local density approximation, the folding model of the nucleon OP of finite nuclei has been extended to take into account consistently the RT and momentum dependence of the nucleon OP in the same mean-field manner, and successfully applied to study the elastic neutron scattering on the lead target at the energies around the Fermi energy.

Folding Model Study of the Elastic Alpha-alpha Scattering at Low Energies

The folding model analysis of the elastic \(\alpha + \alpha\) scattering at the incident energies below the reaction threshold of 34.7 MeV (in the lab system) has been done using the well-tested density dependent versions of the M3Y interaction and realistic choices for the \(^4\)He density. Because the absorption is negligible at the energies below the reaction threshold, we were able to probe the \(\alpha + \alpha\) optical potential at low energies quite unambiguously and found that the α + α overlap density used to construct the density dependence of the M3Y interaction is strongly distorted by the Pauli blocking. This result gives possible explanation of a long-standing inconsistency of the double-folding model in its study of the elastic \(\alpha + \alpha\) and \(\alpha\)-nucleus scattering at low energies using the same realistic density dependent M3Y interaction.

Equation of state of neutron star matter, and the nuclear symmetry energy

The nuclear mean-field potentials obtained in the Hartree-Fock method with different choices of the in-medium nucleon-nucleon (NN) interaction have been used to study the equation of state (EOS) of the neutron star (NS) matter. The EOS of the uniform NS core has been calculated for the $\mathit{npe}\ensuremath{\mu}$ composition in the $\ensuremath{\beta}$ equilibrium at zero temperature, using version Sly4 of the Skyrme interaction as well as two density-dependent versions of the finite-range M3Y interaction (CDM3Y$n$ and M3Y-P$n$), and versions D1S and D1N of the Gogny interaction. Although the considered effective NN interactions were proven to be quite realistic in numerous nuclear structure and/or reaction studies, they give quite different behaviors of the symmetry energy of nuclear matter at supranuclear densities that lead to the soft and stiff scenarios discussed recently in the literature. Different EOS's of the NS core and the EOS of the NS crust given by the compressible liquid drop model have been used as input of the Tolman-Oppenheimer-Volkov equations to study how the nuclear symmetry energy affects the model prediction of different NS properties, like the cooling process as well as the gravitational mass, radius, and moment of inertia.

Neutron star cooling: A challenge to the nuclear mean field

The two recent density-dependent versions of the finite-range M3Y interaction (CDM3Y$n$ and M3Y-P$n$) have been probed against the bulk properties of asymmetric nuclear matter (NM) in the nonrelativistic Hartree Fock (HF) formalism. The same HF study has also been done with the famous Skyrme (SLy4) and Gogny (D1S and D1N) interactions which were well tested in the nuclear structure calculations. Our HF results are compared with those given by other many-body calculations like the Dirac-Brueckner Hartree-Fock approach or ab-initio variational calculation using free nucleon-nucleon interaction, and by both the nonrelativistic and relativistic mean-field studies using different model parameters. Although the two considered density-dependent versions of the M3Y interaction were proven to be quite realistic in the nuclear structure or reaction studies, they give two distinct behaviors of the NM symmetry energy at high densities, like the Asy-soft and Asy-stiff scenarios found earlier with other mean-field interactions. As a consequence, we obtain two different behaviors of the proton fraction in the $\beta$-equilibrium which in turn can imply two drastically different mechanisms for the neutron star cooling. While some preference of the Asy-stiff scenario was found based on predictions of the latest microscopic many-body calculations or empirical NM pressure and isospin diffusion data deduced from heavy-ion collisions, a consistent mean-field description of nuclear structure database is more often given by some Asy-soft type interaction like the Gogny or M3Y-P$n$ ones. Such a dilemma poses an interesting challenge to the modern mean-field approaches.

Maximization principles for frequency-dependent selection II: the one-locus multiallele case

In this article we study a single-locus multiallele version of the pairwise-interaction model (PIM) in discrete and continuous time and a density-dependent version of this model (D-PIM) in continuous time. The PIM assumes that the fitnesses of genotypes are proportional to the average amount of competition resulting from pairwise interactions. Hence, fitness is frequency dependent. Our main aim is to provide necessary and sufficient conditions for the validity of maximization principles analogous to Fisher's Fundamental Theorem for constant selection. We provide a systematic analysis and illustrate our results by concrete examples. We show that in discrete time the mean fitness is nondecreasing along every trajectory provided the interaction coefficients are nonnegative and symmetric. For asymmetric interactions this is in general not true. However, for what we call pseudo-symmetric interactions a function similar to, but in general not identical to, the mean fitness: the adjusted-mean fitness, is nondecreasing along trajectories. For asymmetric interactions, we also provide sufficient conditions for the mean fitness, and more generally for the adjusted-mean fitness, to be nondecreasing and sufficient conditions when it is not. In continuous time, we provide similar but stronger results. If the interaction coefficients are pseudo-symmetric, the adjusted-mean fitness is nondecreasing in the D-PIM.

Effect of octupole and higher deformations on Coulomb barrier

The effect of octupole deformation, β 3 , and the higher multipole deformations, β 6 and β 8 , on the distribution of barriers in orientation degrees of freedom, is studied. Coulomb barriers are derived in the frame work of the double folding model with the realistic M3Y nucleon–nucleon interaction and its density dependent version. 48Ca + 244Pu spherical-deformed nuclear interacting pair is considered, as an example, to study the effect of deformation parameters on the height and position of the Coulomb barrier. Although the dependence of the Coulomb barrier parameters on the higher deformations is complicated, numerically, if it is treated in microscopic way, we found a simple linear variation of barrier parameters with the different orders of deformation. We found that the variation of the barrier parameters with deformation exactly follows the change of the half density radius of the deformed nucleus in the direction of the separation vector between the centers of mass of the interacting nuclei. This suggests a simple and straightforward way to predict the behavior of the barrier parameters with different orders of deformations. We compared the results of present work with a similar recent study of the same quantities based on simple expression derived by Wong for the Coulomb part and proximity approach for the nuclear part of heavy ion potential, respectively.

Optical model potentials involving loosely boundp-shell nuclei around 10 MeV/nucleon

We present the results of a search for optical model potentials for use in the description of elastic scattering and transfer reactions involving stable and radioactive p-shell nuclei. This was done in connection with our program to use transfer reactions to obtain data for nuclear astrophysics, in particular for the determination of the astrophysical ${S}_{17}$ factor for ${}^{7}\mathrm{Be}(p,\ensuremath{\gamma}{)}^{8}\mathrm{B}$ using two ${(}^{7}\mathrm{Be}{,}^{8}\mathrm{B})$ proton transfer reactions. Elastic scattering was measured using ${}^{7}\mathrm{Li},$ ${}^{10}\mathrm{B},$ ${}^{13}\mathrm{C},$ and ${}^{14}\mathrm{N}$ projectiles on ${}^{9}\mathrm{Be}$ and ${}^{13}\mathrm{C}$ targets at or about $E/A=10\mathrm{M}\mathrm{e}\mathrm{V}/\mathrm{n}\mathrm{u}\mathrm{c}\mathrm{l}\mathrm{e}\mathrm{o}\mathrm{n}.$ Woods-Saxon type optical model potentials were extracted and are compared with potentials obtained from a microscopic double folding model. Several nucleon-nucleon effective interactions were used: M3Y with zero range and finite range exchange term, two density dependent versions of M3Y and the effective interaction of Jeukenne, Lejeune, and Mahaux. We find that the latter one, which has an independent imaginary part, gives the best description. Furthermore, we find the renormalization constant for the real part of the folding potential to be nearly independent of the projectile-target combination at this energy and that no renormalization is needed for the imaginary part. From this analysis, we are able to eliminate an ambiguity in optical model parameters and thus better determine the asymptotic normalization coefficient for ${}^{10}{\stackrel{\ensuremath{\rightarrow}}{\mathrm{B}}}^{9}\mathrm{B}+p.$ Finally we use these results to find optical model potentials for unstable nuclei with emphasis on the reliability of the description they provide for peripheral proton transfer reactions. We discuss the uncertainty introduced by the procedure in the prediction of the distorted wave Born approximation cross sections for the ${(}^{7}\mathrm{Be}{,}^{8}\mathrm{B})$ reactions used in extracting the astrophysical factor ${S}_{17}(0).$

Modelling of the effect of a sea-level rise and land subsidence on the evolution of the groundwater density in the subsoil of the northern part of the Netherlands

The Province of Friesland is conducting a study on possible future changes in the surface water and groundwater systems of Friesland. The aim of the study is to assess what changes might be caused by land subsidence and a rise in sea level—focusing in particular on the salinization of the surface water—by modelling the flow of groundwater in the coastal zone of the Province of Friesland. A three-dimensional density distribution of groundwater (based on the chloride distribution in the groundwater) can be projected by using the density dependent version of the MLAEM software: MVAEM (Strack, O.D.L., 1989. Multi-layer aquifer modeling using the analytical element method. Proc. 4th Int. Conf. on the use of models to findworking solutions to groundwater problems, National Water Well Association, Dublin, Ohio, USA, 1995). Construction of a fully three-dimensional density distribution is based on irregularly spaced chloride concentration data points. These are interpolated using a three-dimensional multi-quadric interpolator (in MVAEM). For some parts of the model area, chloride data were not available (e.g. the Wadden Sea); for these regions chloride concentrations were estimated (based on geo-electric and other information) and assigned to artificial data points, which were added to the data set. The techniques used for this process were developed during the construction of the coastal elements in NAGROM—the NAtional GROundwater Model for The Netherlands (De Lange, W.J., van der Meij, J.L., 1995. NAGROM (National GROundwater Model). RIZA, Lelystad, TNO-GG, Delft, The Netherlands; De Lange, W.J., 1996. Groundwater modeling of large domains with analytic elements. Delft University of Technology, Delft, The Netherlands). The influences of a sea-level rise and land subsidence on the groundwater system were simulated by computational modelling of density-driven groundwater flow. The groundwater model that was used is a refined version of the regional model contained in NAGROM, based on the analytic element method ( Strack, 1989). NAGROM is a national water management tool for evaluating different water conservation and distribution policies. It was developed by the Institute for Inland Water Management and Waste Water Treatment in co-operation with The Netherlands Institute of Applied Geoscience TNO (NITG-TNO). The effect of a sea-level rise and land subsidence was calculated for a 50-year period. Salinization of the surface waters by discharged groundwater in the Northern part of The Netherlands was compared with the evolution of the region not including sea-level rise and land subsidence. The amount of saline discharge as part of the surface water balance was calculated under special boundary conditions set according to the proposed sea-level rise and land subsidence in a semi-unsteady state.

Prediction of VL and VLL equilibria of mixtures containing petroleum reservoir fluids and methanol with a cubic EoS

Abstract Avlonitis, D., Danesh, A. and Todd, A.C., 1994. Prediction of VL and VLL equilibria of mixtures containing petroleum reservoir fluids and methanol with cubic EoS. Fluid Phase Equilibria, 94: 181-216. A cubic equation of state, with simple non-density-dependent mixing rules, is used to represent the phase behaviour of multicomponent mixtures containing hydrocarbons up to n -octane, nitrogen, carbon dioxide, hydrogen sulphide, water and methanol. The reliability of the model is tested against diverse experimental VL and VLL equilibrium data of multicomponent systems. The proposed correlation can be applied for efficient design and operation of transfer lines and processing units. The practical value of the theoretically correct concept of density dependence is tested on a density-dependent version of the above mixing rules. It is demonstrated that while both mixing rules produce very similar results when only one polar component is present, the density-dependent mixing rules may be inferior for mixtures containing both water and methanol, owing to an inherent deficiency. It is also demonstrated that an invariant version of the proposed non-density-dependent mixing rule may not lead to indisputably improved predictions for the studied systems.

ATDHF fission paths in some actinide nuclei

A method of computing fission paths by the ATDHF theory of Villars, developed in earlier papers by the author and his collaborator, has been applied to four actinide nuclei. The calculations are fully microscopic and use a density-dependent version of the two-nucleon effective interaction supplemented with a residual Yukawa potential. Results are presented in detail.

A nuclear matter study using the density dependent M3Y interaction

The basic nuclear matter properties are calculated within the standard Hartree-Fock scheme using a Michigan version of the in-medium NN interaction (the so-called M3Y interaction). Due to the attractive character of the M3Y interaction, the saturation requirement for the nuclear matter is not fulfilled and the nuclear matter generated with this interaction is unstable against collapse. This necessitates the introduction of an appropriate density dependence into the original M3Y interaction. Our density dependent versions of the M3Y interaction consistently reproduce the equilibrium density and binding energy of the normal nuclear matter as well as the microscopic results (obtained by Jeukenne, Lejeune and Mahaux) for the nucleon optical potential. They can be used in the folding model to calculate the nucleon-nucleus and nucleus-nucleus potentials. A possible study of the cold nuclear equation of state through heavy-ion scattering, which is based on the use of the new interaction to calculate the heavy-ion optical potential, is also discussed.

Even parity states of16O

The even parity states arising from 2h(cross) omega excitations in 16O are investigated using the shell model. As a residual interaction the authors employ the density-dependent version of the Skyrme interaction SIII and treat the density as an input. Apart from states belonging to the Kpi =0+ rotational band, which are assumed to be beyond the present model, the results are quite satisfactory and the number of levels below 25 MeV as well as their distribution in energy is in overall agreement with experiment.