Relativistic Mean Field Densities Research Articles

Isotopic Shift in Hg-Isotopes within Brückner versus Relativistic Energy Density Functional

The present study is focused on revealing a characteristic kink of the neutron shell closure N = 126 across the Hg-isotopic chain within the relativistic mean-field (RMF) approach with the IOPB-I, DD-ME2, DD-PC1 and NL3 parameter sets. The RMF densities are converted to their spherical equivalence via the Wood–Saxon approximation and used as input within the parametrization procedure of the coherent density fluctuation model (CDFM). The nuclear matter symmetry energy is calculated using the Brückner energy density functional, and its surface, as well as volume components, are evaluated within Danielwicz’s liquid drop prescription. In addition, a comparison between Brückner and relativistic energy density functionals using the NL3 parameter set is shown as a representative case. The binding energy, charge distribution radius and symmetry energy are used as indicators of the isotopic shift in both ground and isomeric states. We have found the presence of a kink at the shell/sub-shell closure at N = 126 for neutron-rich 206Hg. The formation of the kink is traceable to the early filling of the 1i11/2 orbitals rather than 2g9/2, due to the large spin-orbit splitting. As such, the link between the occupational probability and the magicity of nuclei over the Hg-isotopic chain is established.

Theoretical Investigation of α-decay Chains of Fm-isotopes

Background: The theoretical and experimental investigations of decay properties of heavy and superheavy nuclei are crucial to explore the nuclear structure and reaction dynamics.
 Purpose: The aim of this study is to probe the α-decay properties of 243Fm and 245Fm isotopic chains using relativistic mean-field (RMF) approach within the framework of preformed cluster-decay model (PCM).
 Methods: The RMF densities are folded with the relativistic R3Y NN potential to deduce the nuclear interaction potential between the α particle and daughter nucleus. The penetration probability is calculated within the WKB approximation.
 Results: The α-decay half-lives of even-odd 243Fm and 245Fm isotopes and their daughter nuclei are obtained from the preformed cluster-decay model. These theoretically calculated half-lives are found to be in good agreement with the recent experimental measurements.
 Conclusions: The novel result here is the applicability of the scaling factor within the PCM as a signature for shell/sub-shell closures in α-decay studies. As such, we have also demonstrated that N=137, 139 and Z=94 corresponding to 231,233Pu could be shell/sub-shell closures. The least T1/2 is found at 243,245Fm which indicate their individual stability and α-decay as their most probable decay mode.

Investigation of Astrophysical S-Factor for 12C + 16O and 16O + 16O Reactions Within the Relativistic Mean-Field Approach

The fusion dynamics of 12C + 16O and 16O + 16O astrophysical reactions is investigated using the relativistic mean-field (RMF) formalism for the non-linear NL3* parameter set. The RMF densities, along with the widely adopted M3Y and relativistic R3Y nucleon-nucleon (NN) interaction potentials, are used to obtain the nuclear potential within the double folding approach. The ℓ-summed Wong model is used to obtain the fusion cross-section. The ℓmax values are extracted from the sharp cut-off model. The fusion cross-section is also represented in terms of the astrophysical S-factor, and the results are compared with the available experimental data. The microscopic R3Y NN potential is observed to give a reasonable fit to the experimental cross-section.

Fusion cross section of α -induced reactions for heavy target nuclei

The fusion reactions induced by $^{4}\mathrm{He}$ projectiles on heavy target nuclei provide the reference to study the reaction dynamics of exotic halo nuclei. The present analysis aims to probe the effects of different nuclear density distributions and the effective nucleon-nucleon ($NN$) interaction potentials on the fusion cross section of $^{4}\mathrm{He}$-induced reactions for heavy target nuclei. The nuclear densities for the heavy nuclei are obtained within the well-known Skyrme-Hartree-Fock model and the relativistic mean-field (RMF) approach for the $\mathrm{NL}{3}^{*}$ parameter set. These densities are integrated with the density-dependent M3Y and the relativistic R3Y nucleon-nucleon ($NN$) potentials to obtain the nuclear interaction potential. The fusion cross section and the astrophysical $S$ factor are obtained for $^{4}\mathrm{He}+^{208}\mathrm{Pb}, ^{4}\mathrm{He}+^{209}\mathrm{Bi}, ^{4}\mathrm{He}+^{235}\mathrm{U}$, and $^{4}\mathrm{He}+^{238}\mathrm{U}$ systems within the $\ensuremath{\ell}$-summed Wong model. The relativistic R3Y $NN$ potential folded with RMF densities are observed to give a better fit to the available experimental data. Furthermore, a comparison is made for the results obtained using Hill-Wheeler and Wentzel-Kramers-Brillouin transmission coefficients for $^{4}\mathrm{He}+^{208}\mathrm{Pb}$ system. We found a reasonable fit in the cross section at around the Coulomb-barrier energies for both the approximations and also similar predictions can be drawn for all considered systems.

Divergence in the Relativistic Mean Field Formalism: A Case Study of the Ground State Properties of the Decay Chain of 214,216,218U Isotopes

A new α-emitting 214U has been recently observed experimentally. This opens the window to theoretically investigate the ground-state properties of the lightest known even–even neutron deficient 214,216,218U isotopes and to examine α-particle clustering around the shell closure. The decay half-lives are calculated within the preformed cluster-decay model (PCM). To obtain the α-daughter interaction potential, the RMF densities are folded with the newly developed R3Y and the well-known M3Y NN potentials for comparison. The alpha preformation probability (Pα) is calculated from the analytic formula of Deng and Zhang. The WKB approximation is employed for the calculation of the transmission probability. The individual binding energies (BE) for the participating nuclei are estimated from the relativistic mean-field (RMF) formalism and those from the finite range droplet model (FRDM) as well as WS3 mass tables. In addition to Z=84, the so-called abnormal enhancement region, i.e., 84≤Z≤90 and N<126, is normalised by an appropriately fitted neck-parameter ΔR. On the other hand, the discrepancy sets in due to the shell effect at (and around) the proton magic number Z=82 and 84, and thus a higher scaling factor ranging from 10−8–10−5 is required. Additionally, in contrast with the experimental binding energy data, large deviations of about 5–10 MeV are evident in the RMF formalism despite the use of different parameter sets. An accurate prediction of α-decay half-lives requires a Q-value that is in proximity with the experimental data. In addition, other microscopic frameworks besides RMF could be more reliable for the mass region under study. α-particle clustering is largely influenced by the shell effect.

Surface properties for Ne, Na, Mg, Al, and Si isotopes in the coherent density fluctuation model using the relativistic mean-field densities

We have systematically studied the surface properties, such as symmetry energy, neutron pressure, and symmetry energy curvature coefficient for Ne, Na, Mg, Al, and Si nuclei from the proton to neutron drip lines. The coherent density fluctuation model (CDFM) is used to estimate these quantities taking the relativistic mean-field densities as inputs. The Brückner energy density functional is taken for the nuclear matter binding energy and local density approximation is applied for its conversion to coordinate space. The symmetry energy again decomposed to the volume and surface components within the liquid drop model formalism to the volume and surface parts separately. Before calculating the surface properties of finite nuclei, the calculated bulk properties are compared with the experimental data, whenever available. The NL3* parameter set with the Bardeen–Cooper–Schrieffer (BCS) pairing approach in an axially deformed framework is used to take care of the pairing correlation when needed. The deformed density is converted to its spherical equivalent with a two-Gaussian fitting, which is used as an input for the calculation of weight function in the CDFM approximation. With the help of the symmetry energy, the isotopes 29F, 28Ne, 29,30Na, and 31,35,36Mg are considered to be within the island of inversion (Han et al. Phys. Lett. B, 772, 529 (2017). doi:10.1016/j.physletb.2017.07.007). Although we get large symmetry energies corresponding to a few neutron numbers for this isotopic chain as expected, an irregular trend appears for all these considered nuclei. The possible reason behind this abnormal behavior of symmetry energy for these lighter mass nuclei is also included in the discussion, which gives a direction for future analysis.

On the symmetry energy and deformed magic number at N = 100 in rare earth nuclei

The exotic nuclei are a fertile source of new features of nuclear structure. The evolution of new shell gaps accompanied by quenching of classical magic numbers is one of the marked features in these nuclei. These studies aimed to search and explore such behavior and find major significance on both the experimental and theoretical fronts. Here, we present an inclusive study and significant evidence of the existence of deformed shell closure at the neutron number N = 100 in rare earth Nd, Sm, Gd and Dy nuclei, obtained from the persistence of a peak in the analysis of symmetry energy and its bulk and surface components, over the isotopic chains of these nuclei, within the coherent density fluctuation model (CDFM). The relativistic mean field densities, employing the NL3 and recently developed IOPB-I parameter sets, have been used as an input within CDFM. This result is in excellent agreement with our earlier prediction of deformed magic shell closure at N = 100 in rare earth nuclei [Satpathy et al (2004 J. Phys. G 30 771); Ghouri et al (2012 Phys. Rev. C 85 064327)] and further reinforced by the experimental confirmation of deformed magicity at N = 100 in 162Sm and 164Gd nuclei [Patel et al (2014 Phys. Rev. Lett. 113 262502)]. An important consequence of the work is that N = 100 isotopes of these nuclei can serve as a waiting point in r-process nucleosynthesis and influence the heavy nuclei formation in astrophysical entities.

Effect of density and nucleon-nucleon potential on the fusion cross section within the relativistic mean field formalism

We have studied the effect of density and the nucleus-nucleus interaction potential on the fusion reaction cross section for the synthesis of heavy and superheavy nuclei within the relativistic mean field formalism. The double-folding procedure is used to obtain the nuclear interaction potential for the well-known M3Y and recently developed R3Y nucleon-nucleon potential for relativistic mean field densities. The $\mathrm{NL}{3}^{*}$ parameter set is used to calculate the density distributions for targets and projectiles and is further used to obtain the nuclear potential. The $\ensuremath{\ell}$-summed Wong formula is used to provide a transparent and analytic way to formulate the fusion cross sections for even-even $^{48}\mathrm{Ca}+^{154}\mathrm{Sm}$, $^{48}\mathrm{Ca}+^{238}\mathrm{U}$, $^{48}\mathrm{Ca}+^{248}\mathrm{Cm}$, $^{64}\mathrm{Ni}+^{238}\mathrm{U}$, $^{26}\mathrm{Mg}+^{248}\mathrm{Cm}$; even-odd $^{46}\mathrm{K}+^{181}\mathrm{Ta}$; and odd-odd $^{31}\mathrm{Al}+^{197}\mathrm{Au}$ and $^{39}\mathrm{K}+^{181}\mathrm{Ta}$ systems. The structural effects are also correlated with the fusion cross section through the equivalent diffuseness parameter using the densities of interacting nuclei for all nuclei (projects and targets) involved in the reactions just listed.

Investigation of proton emission using deformed relativistic mean field densities

The proton emission in neutron deficient nuclei with [Formula: see text] has been investigated within the framework of axially deformed relativistic mean field (RMF) theory using NL3 and density-dependent DD-ME1 and DD-ME2 parameters. The quasi-bound states from which the proton emission is probable are determined. The RMF densities are folded with the M3Y effective nucleon–nucleon interaction to obtain the nuclear potential. The total interaction potential consisting of nuclear, Coulomb and centrifugal potentials is used to calculate the proton decay half-lives using the Wentzel–Kramers–Brillouin (WKB) approximation. For this, we have used the [Formula: see text], [Formula: see text] being the single-particle energy of the decaying proton near the Fermi surface. The calculated proton decay half-lives for different nuclei are in consonance with experimental data.

Above-barrier heavy-ion fusion cross-sections using the relativistic mean-field approach: Case of spherical colliding nuclei

In the present work, the influence of the nuclear matter density on the DF potential and on the Coulomb barrier parameters is studied systematically for collisions of spherical nuclei. The value of the parameter BZ=ZPZT/(AP1/3+AT1/3) (estimating the Coulomb barrier height) varies in these calculations from 10 MeV up to 150 MeV. We have introduced self-consistent relativistic mean field (RMF) density in the present analysis. For the nucleon-nucleon effective interaction, the M3Y forces with the finite range exchange term and density dependence are employed. The above barrier fusion cross sections are calculated within the framework of the trajectory model with surface friction. Results are compared with the previous study in which the nuclear density came from the Skyrme Hartree-Fock (HF) calculations and with the high precision experimental data. This comparison demonstrates that i) agreement between the theoretical and experimental cross sections obtained with RMF and HF densities is of the same quality and ii) the values of the only adjustable parameter (friction strength) obtained with RMF and HF densities strongly correlate with each other.

Proton emission from the drip-line nuclei I-Bi using the WKB approximation with relativistic mean-field densities * * Supported by the Department of Science and Technology, Govt. of India (EMR/2015/002517)

We study the properties of proton rich nuclei reported as proton emitters in the region from I to Bi with Z = 53 to 83 and N = 56 to 102 as a crucial application to the existence of exotic nuclei. The effective relativistic mean-field formalism (E-RMF), with NL3, FSUGarnet, G3 and IOPB-I interactions, is adopted for analysis of the ground state properties of proton emitters. Furthermore, in the E-RMF background, the Wentzel-Karmers-Brillouin (WKB) barrier penetration method is used for the calculation of proton emission half-lives. It is found that the calculated half-lives are in good agreement with the experimental results for all emitters considered in this study.

Effect of deformation on structure and reaction of Al isotopes using relativistic mean field densities in Glauber model

We have examined the ground state properties of Al isotopes towards the proton rich side from A = 22 to 28 using the well known relativistic mean field (RMF) formalism with NLSH parameter set. The calculated results are compared with the predictions of finite range droplet model and experimental data. The calculation is extended to estimate the reaction cross section for $$^{22-28}$$ Al as projectiles with $$^{12}$$ C as target. The incident energy of the projectiles are taken as 950 MeV/nucleon, for both spherical and deformed RMF densities as inputs in the Glauber model approximation. Further investigation of enhanced values of total reaction cross section for $$^{23}$$ Al and $$^{24}$$ Al in comparison to rest of the isotopes indicates the proton skin structure of these isotopes. Specifically, the large value of root mean square radius and total reaction cross section of $$^{23}$$ Al could not be ruled out the formation of proton halo.

Effects of NN potentials on p Nuclides in the A ∼100–120 region

Microscopic optical potentials for low-energy proton reactions have been obtained by folding density dependent M3Y (DDM3Y) interaction derived from nuclear matter calculation with densities from mean field approach to study astrophysically important proton rich nuclei in mass 100–120 region. We compare [Formula: see text] factors for low-energy [Formula: see text] reactions with available experimental data and further calculate astrophysical reaction rates for [Formula: see text] and [Formula: see text] reactions. Again, we choose some nonlinear R3Y (NR3Y) interactions from relativistic mean field (RMF) calculation and folded them with corresponding RMF densities to reproduce experimental [Formula: see text]-factor values in this mass region. Finally, the effect of nonlinearity on our result is discussed.

Study of Reaction Cross Section of Light Mass Nuclei Using Glauber Formalisms

We study the reaction dynamics of some light mass nuclei (Be-Ar isotopes). We use the well-known Glauber formalism with densities obtained from a recently developed simple effective interaction, in the frameword of the microscopic non-relativistic Hartree–Fock formalisms. For comparison, we used also densities from the relativistic mean field formalism. In general, the study of the reaction dynamics suggests that both formalisms reproduce well the experimental data, with a slight superiority of the relativistic mean field densities over those of non-relativistic Hartree–Fock. This is so for the majority of the chosen cases, except for a few nuclear halo systems.

Interaction cross sections for neon isotopes in the Glauber model and the halo structure ofNe31

In this work we calculate the interaction cross sections of neon isotopes (${}^{17--32}$Ne) on ${}^{12}\mathrm{C}$ at 240 and 950 MeV/nucleon within the framework of the Coulomb-modified correlation expansion for the Glauber model $S$ matrix. The calculations involve (i) up to the two-body density term in the correlation expansion, (ii) the relativistic mean-field (RMF) densities for the colliding nuclei, and (iii) the single Gaussian approximation for the nucleon-nucleon (NN) amplitude. To test the halo structure, the extended neutron density distribution for $^{31}\mathrm{Ne}$ is also used. Our results, using RMF densities, are in close agreement with the available experimental data at 240 MeV/nucleon except for $^{31}\mathrm{Ne}$, for which the extended neutron density distribution is found to play an important role in explaining the data, thereby supporting a halo structure in $^{31}\mathrm{Ne}$. The corresponding results at 950 MeV/nucleon are, however, not as satisfactory as those obtained at 240 MeV/nucleon. The results also demonstrate the importance of the two-body density term in the present calculations.

Low-energy proton reactions of astrophysical interest in theA∼90–100 region

Semimicroscopic optical potentials for low energy proton reactions in mass 90-100 region have been obtained by folding the density dependent M3Y interaction with relativistic mean field densities. Certain parameters in the potential have been deduced by comparing calculated results with the data for elastic scattering. Low energy proton reactions in this mass region have been studied in the formalism with success. Rates of important astrophysical reaction in the mass region have been calculated.

Optical potential obtained from relativistic-mean-field theory-based microscopic nucleon–nucleon interaction: applied to cluster radioactive decays

A microscopic nucleon–nucleon (NN) interaction is derived from the popular relativistic-mean-field (RMF) theory Lagrangian and used to obtain the optical potential by folding it with the RMF densities of cluster and daughter nuclei. The NN-interaction is remarkably related to the inbuilt fundamental parameters of RMF theory, and the results of the application of the so obtained optical potential, made to exotic cluster radioactive decays and α+α scattering, are found comparable to that for the well-known, phenomenological M3Y effective NN-interaction. The RMF-based NN-interaction can also be used to calculate a number of other nuclear observables.

IMPORTANCE OF PREFORMATION PROBABILITY IN CLUSTER RADIOACTIVE-DECAYS USING RELATIVISTIC MEAN FIELD THEORY WITHIN THE PREFORMED CLUSTER MODEL

Using the preformed cluster model (PCM) of Gupta and collaborators, we have deduced empirically the preformation probability P0emp from experimental data on both the α and exotic-cluster radioactive decays in the trans-lead region having doubly magic 208 Pb or its neighboring nuclei as daughters, using the spherical and (in some cases) deformed relativistic mean field (RMF) densities. For spherical considerations, the P0α(emp) for alpha-decays is almost constant ~ 10-2 - 10-3 for all the parent nuclei studied, and P0c(emp) for cluster-decays of the same parents decrease with increasing size of cluster. The results obtained for spherical P0c(emp) are within two to three orders of magnitude of the well accepted phenomenological formula of Blendowske-Walliser (BW), which led us to propose a new empirical formula. The use of deformed RMF densities, however, tend to bring the results closer to BW formula.

Neutron density distribution and the halo structure ofC22

The recently measured reaction cross sections for the neutron-rich carbon isotopes ($^{19}\mathrm{C}$, $^{20}\mathrm{C}$, and $^{22}\mathrm{C}$) on a proton target at 40 A MeV are analyzed using the finite range Glauber model (FRGM) and the microscopic optical potential calculated within the Brueckner-Hartree-Fock formalism (BHF). In FRGM nucleon-nucleon cross sections are used, while in the latter (BHF), Hamada-Johnston, Urbana v-14, and the Argonne v-18 internucleon potentials are employed to calculate the microscopic optical potential. The required nucleon density distributions are calculated within the relativistic mean-field (RMF) framework. To test the halo structure, the extended neutron density distribution for $^{22}\mathrm{C}$ is also used. The analysis reveals that the BHF results of all three internucleon potentials are very close to each other, and also agree with the corresponding results of the FRGM. Our results, using RMF densities, are in agreement with the experimental data for all isotopes of carbon except $^{22}\mathrm{C}$, for which we require extended neutron density distribution, indicating a halo structure.

Nuclear reaction cross sections of exotic nuclei in the Glauber model for relativistic mean field densities

We have calculated the total nuclear reaction cross sections of exotic nuclei in the framework of the Glauber model, using as inputs the standard relativistic mean field (RMF) densities and the densities obtained from the more recently developed effective-field-theory-motivated RMF (the E-RMF). Both light and heavy nuclei are taken as the representative targets, and the light neutron-rich nuclei as projectiles. We found the total nuclear reaction cross section to increase as a function of the mass number, for both the target and projectile nuclei. The differential nuclear elastic scattering cross sections are evaluated for some selected systems at various incident energies. We found a large dependence of the differential elastic scattering cross section on incident energy. Finally, we have applied the same formalism to calculate both the total nuclear reaction cross section and the differential nuclear elastic scattering cross section for the recently discussed superheavy nucleus with atomic number Z = 122.