Narrow Results

The shape phase transition between spherical U(5) and axially deformed SU(3) nuclei is investigated systemically for the rare-earth region nuclei by the constrained relativistic mean field theory with the interactions NL3. The properties of ground state for Nd, Gd and Dy isotopes are described fairly well as compared with experiments. By examining the potential energy curve and quadruple deformation β₂ obtained with this microscopic approach, the possible critical point nuclei are suggested to be ^148,150Nd for Nd isotopes, but ¹⁴⁸Nd is the best candidate, and ¹⁵⁰Nd is slightly to the rotor side of the phase transition. For Gd and Dy isotopes, ^150,152Gd and ^152,154Dy are suggested to be the critical point nuclei. Similar conclusions are also drawn from the microscopic neutron single particle spectra.

The collective multipole excitations are studied in the framework of relativistic random-phase approximation with the vacuum polarization. First, we show for the nuclear ground state that the leading order of derivative expansion of the effective action arising from the vacuum correction agrees with the exact calculation using the Green function method very well. The derivative expansion makes us easy to perform a fully self-consistent calculation, even for the random-phase approximation. A remarkable effect of the inclusion of the vacuum polarization is the increase of the effective mass m_eff/m_N ~ 0.9, which gives, for all multipole modes, smaller energy-weighted sum rule values than those of the typical relativistic model. Also, the large effective mass constrained by the vacuum polarization can give an excellent agreement with experimental data on the excitation energy for the isoscalar quadrupole resonances. It is shown, further, that the change of the shell structure due to the vacuum polarization plays an important role in the dipole compression modes.

The pion was introduced by Yukawa as the mediator of nucleon-nucleon interaction to bind nucleons in nucleus. Due to its characteristic properties, however, the pion had not be used until recent years for description of nuclei. We present here a newly developed method to treat the pion exchange interaction in nuclei. We study nuclear structure by using the chiral sigma model lagrangian in the relativistic chiral mean field model with projection. The pion develops mean field and provides a magic number effect. We demonstrate also the ability of treating tensor interaction due to pion exchange in terms of tensor optimized shell model.

Single-particle resonant states in Ca isotopes are studied systematically by real stabilization method (RSM) in coordinate space within the framework of the self-consistent relativistic mean field (RMF) theory. Phase shifts are obtained by scattering phase shift method. The resonant parameters (the energies, widths) are extracted by fitting energy and phase shift. Wave functions of resonances are obtained by matching conditions of bound and scattering states. Taking ⁶⁰Ca as an example, results are compared with corresponding results obtained from the analytic continuation in the coupling constant approach and the scattering phase shift method. Satisfied agreements are found. The rules of resonant parameters changing in Ca isotopes are also analyzed.

The systematic investigation of shape evolution between spherical U(5) and γ-unstable O(6) for Mo isotopes has been carried out by the microscopic quadrupole constrained relativistic mean field model plus BCS method with all the most used interactions, i.e. PK1, NL3, TM1 and NLSH. The calculated potential energy surfaces show a clear shape evolution for the even–even Mo isotopes with N = 50~64 and ⁹⁴Mo is suggested to be the γ-unstable nucleus, which is favored by the experimental data. Similar conclusion is also drawn from the neutron single particle spectra.

In the framework of the relativistic mean field theory, the stability of thermal protoneutron stars is investigated. There is a highest possible temperature for a stable protoneutron star. A stable protoneutron star may be a metastable one if its mass is too large. As the temperature increases, the metastable mass range of protoneutron stars narrows. With the increase of temperature, the probability that a stable protoneutron star is a metastable one increases. A really stable protoneutron star with higher temperature can contain more species of hyperons. The case of SN 1987A is analyzed connected with the results in this article.

We have calculated astrophysical reaction cross-sections for $(\gamma ,\alpha )$ reactions of some nuclei important for the calculation of p-process reaction-decay network. Reaction rates for $\alpha$-induced reactions are calculated with the semi-microscopic optical potential constructed using double folding method, where nuclear density distributions for finite nuclei along with the effective nucleon–nucleon interaction are the important components of the folded potential. For this purpose, density distributions of target nuclei are obtained from relativistic mean field approach. Astrophysical reaction cross-section for elastic scattering of $\alpha$-particle from ${}^{92}\mathrm{\text{Mo}}$ target is compared with the existing experimental results to constrain the newly formed potential. Further, to check the credibility of the present theoretical framework, the astrophysical S-factor for $(\alpha ,\gamma )$ reactions are compared with the experimental observation, wherever available. Finally, an estimate of dominant photodisintegration channels at various astrophysical temperature is discussed for p-nuclei ${}^{74}\mathrm{\text{Se}}$ and ${}^{96}\mathrm{\text{Ru}}$.

An extensive study of $\alpha$-decay half-lives for various decay chains of isotopes of $Z=120$ is performed within the axially deformed relativistic mean-field (RMF) formalism by employing the NL3, NL3${}^{\ast }$, and DD-ME2 parameter set. The structural properties of the nuclei appearing in the decay chains are explored. The binding energy, quadrupole deformation parameter, root-mean-square charge radius, and pairing energy are calculated for the even–even isotopes of $Z=100\text{–}120$, which are produced in five different $\alpha$-decay chains, namely, ${}^{296}120\to {}^{260}\mathrm{\text{No}}$, ${}^{298}120\to {}^{262}\mathrm{\text{No}}$, ${}^{300}120\to {}^{264}\mathrm{\text{No}}$, ${}^{302}120\to {}^{266}\mathrm{\text{No}}$, and ${}^{304}120\to {}^{268}\mathrm{\text{No}}$. A superdeformed prolate ground state is observed for the heavier nuclei, and gradually the deformation decreases towards the lighter nuclei in the considered decay chains. The RMF results are compared with various theoretical predictions and experimental data. The $\alpha$-decay energies are calculated for each decay chain. To determine the relative numerical dependency of the half-life for a specific $\alpha$-decay energy, the decay half-lives are calculated using four different formulas, namely, Viola–Seaborg, Alex–Brown, Parkhomenko–Sobiczewski and Royer for the above said five $\alpha$-decay chain. We notice a firm dependency of the half-life on the $\alpha$-decay formula in terms of $Q_{\alpha }$-values for all decay chains. Further, this study also strengthens the prediction for the island of stability in terms of magic number at the superheavy valley in the laboratories.

The ground state nucleon (neutron and proton) distributions for A=20 isobars (Z=6–12) are investigated. For this purpose, the relativistic mean field equations are solved in the coordinate space and also by using the conventional basis expansion method. The pairing is treated in the simple constant gap approximation and also self consistently through the Bogoliubov transformation employing the realistic Gogny D1S interaction as well as the zero range density dependent effective interaction. The comparative study of the results thus obtained indicates the level and the extent of differences in the physical observables like binding energies, sizes, densities, etc. of these nuclei, arising due to the use of these different variants of solving the RMF/RHB equations. Though the results are qualitatively similar, the deviations do appear at a finer level, especially for large T_z (²⁰O and ²⁰N). The calculations also reveal mirror symmetry about T_z=0 for all physical observables, which is in accordance with the experiment. The calculated nucleon densities are compared with those obtained by using a semi-phenomenological model that incorporates correctly the asymptotic behavior. The reaction cross-sections with these A=20 isobars as projectiles incident on a ¹²C target at 950 A MeV incident energy, calculated within the Glauber model using the RMF/RHB and model densities agree well with the experiment.

The ground state properties of even mass Cr and Fe isotopes are studied using the generalized hybrid derivative coupling model. The energy surface of each isotope is plotted as a function of the mass quadrupole moment. The neutron numbers N=20 and N=40 are seen to remain magic numbers but N=28 and 50 are predicted to be non-magic. The neutron number N=70 turns out to be a magic number according to the present calculation. In all the isotopes studied the calculated binding energy values are less than those obtained from experiment while the deformation is in better agreement.

Pseudospin symmetry is an approximate relativistic symmetry of the nucleus as demonstrated by experimental data. This symmetry follows from the fact that the vector and scalar potentials of nucleons moving in a relativistic mean field are approximately equal in magnitude and opposite in sign. QCD sum rules in nuclear matter support this conclusion. Such an observation suggests a fundamental reason for pseudospin symmetry. We review the status of pseudospin symmetry conservation in the nucleon–nucleon interaction.

The superheavy nucleus ²⁹⁴118 and its α-decay chain have been investigated systematically in the relativistic mean-field (RMF) theory with the interactions NL3, TMA, PK1 and NLZ. The properties of ground state have been described well with the binding energies per nucleon and α-decay energies, which are reproduced as compared with the experimental data. It shows that the RMF theory is effective for studying not only the stable nuclei but also the superheavy nuclei presented here. In particular, the prolate shape predicted in the ground state of these superheavy nuclei is in agreement with the experimental data as well as other theoretical calculations.

Several aspects about Λ-hypernuclei in the relativistic mean field theory, including the effective Λ-nucleon coupling strengths based on the successful effective nucleon-nucleon interaction PK1, hypernuclear magnetic moment and -hypernuclei, have been presented. The effect of tensor coupling in Λ-hypernuclei and the impurity effect of to nuclear structure have been discussed in detail.

Two parameter sets (Set 1 and Set 2) of the standard relativistic mean field (RMF) model plus additional vector isoscalar nonlinear term, which are constrained by a set of criteria²⁰ determined by symmetric nuclear matter stabilities at high densities due to longitudinal and transversal particle–hole excitation modes are investigated. In the latter parameter set, δ meson and isoscalar as well as isovector tensor contributions are included. The effects in selected finite nuclei and nuclear matter properties predicted by both parameter sets are systematically studied and compared with the ones predicted by well-known RMF parameter sets. The vector isoscalar nonlinear term addition and instability constraints have reasonably good effects in the high-density properties of the isoscalar sector of nuclear matter and certain finite nuclei properties. However, even though the δ meson and isovector tensor are included, the incompatibility with the constraints from some experimental data in certain nuclear properties at saturation point and the excessive stiffness of the isovector nuclear matter equation of state at high densities as well as the incorrect isotonic trend in binding the energies of finite nuclei are still encountered. It is shown that the problem may be remedied if we introduce additional nonlinear terms not only in the isovector but also in the isoscalar vectors.

Analysis of the parameters adjustment effects in isovector as well as in isoscalar sectors of effective field based relativistic mean field (E-RMF) model in the symmetric nuclear matter and neutron-rich matter properties has been performed. The impacts of the adjustment on slowly rotating neutron star are systematically investigated. It is found that the mass–radius relation obtained from adjusted parameter set G2** is compatible not only with neutron stars masses from 4U 0614+09 and 4U 1636-536, but also with the ones from thermal radiation measurement in RX J1856 and with the radius range of canonical neutron star of X7 in 47 Tuc, respectively. It is also found that the moment inertia of PSR J073-3039A and the strain amplitude of gravitational wave at the Earth's vicinity of PSR J0437-4715 as predicted by the E-RMF parameter sets used are in reasonable agreement with the extracted constraints of these observations from isospin diffusion data.

We compare the systematics of binding energies computed within the standard and extended versions of the relativistic mean-field (RMF) model and the Skyrme–Hartree–Fock (SHF) model. The general trends for the binding energies for super-heavy nuclei are significantly different for these models. The SHF models tend to underbind the superheavy nuclei, while RMF models show just the opposite trend. The extended RMF model seems to provide remarkable improvements over the results obtained for the standard RMF model.

The effects of auxiliary contribution in forms of electromagnetic tensors and relativistic electromagnetic exchange in local density approximation as well as δ meson and isovector density-dependent nonlinear terms in standard relativistic mean field model constrained by nuclear matter stability criteria in some selected finite nuclei and nuclear matter properties are studied. It is found that in the case of finite nuclei, the electromagnetic tensors play the most dominant part compared to other auxiliary terms. Due to the presence of electromagnetic tensors, the binding energies prediction of the model can be improved quite significantly. However, these terms do not yield demanded effects for rms radii prediction. In the case of nuclear matter properties, the isovector density-dependent nonlinear term plays the most crucial role in providing predictions which are quite compatible with experimental constraints. We have also shown these auxiliary contributions are indeed unable to improve the single particle spectrum results of the model.

Densities from relativistic mean field calculations are applied to construct the optical potential and, hence calculate the endpoint of the rapid proton capture (rp) process. Mass values are taken from a new phenomenological mass formula. Endpoints are calculated for different temperature-density profiles of various X-ray bursters. We find that the rp process can produce significant quantities of nuclei upto around mass 95. Our results differ from existing works to some extent.

We study the extremely neutron-rich nuclei for Z = 17–23, 37–40 and 60–64 regions of the periodic table by using axially deformed relativistic mean field formalism with NL3* parametrization. Based on the analysis of binding energy, two neutron separation energy, quadrupole deformation and root mean square radii, we emphasized the speciality of these considered regions which are recently predicted islands of inversion.

This paper refers to another attempt to search for spherical double shell closure nuclei beyond Z = 82, N = 126. All calculations and results are based on a newly developed approach entitled as simple effective interaction (SEI). Our results predict that the combination of magic nucleus occurs at N = 182 (Z = 114, 120, 126). All possible evidences for the occurrence of magic nuclei are discussed systematically. And, the obtained results for all observables are compared with the relativistic mean field theory for NL3 parameter.