Narrow Results

An extensive theoretical search for the proton magic number in the superheavy valley beyond Z = 82 and the corresponding neutron magic number after N = 126 is carried out. For this we scanned a wide range of elements Z = 112–130 and their isotopes. The well-established non-relativistic Skryme–Hartree–Fock and Relativistic Mean Field formalisms with various force parameters are used. Based on the calculated systematics of pairing gap, two-neutron separation energy and the shell correction energy for these nuclei, we find Z = 120 as the next proton magic and N = 172, 182/184, 208 and 258 the subsequent neutron magic numbers.

We have studied nuclear structure and reaction properties of Ne, Mg and Si isotopes, using relativistic mean field (RMF) densities, in the framework of Glauber model. Total reaction cross-section σ_R for Ne isotopes on ¹²C target have been calculated at incident energy 240 MeV. The results are compared with the experimental data and with the recent theoretical study [W. Horiuchi et al., Phys. Rev. C 86, 024614 (2012)]. Study of σ_R using deformed densities have shown a good agreement with the data. We have also predicted total reaction cross-section σ_R for Ne, Mg and Si isotopes as projectiles and ¹²C as target at different incident energies.

We study the interaction of Λ-hyperon with proton and neutron inside a nucleus within the framework of relativistic mean field (RMF) formalism. The single-particle energy levels for some of the specific proton and neutron orbits are analyzed with the addition of Λ-successively. The neutron energy level is more deeper, because of decrease in symmetry energy due to substitution of neutron by Λ-hyperon.

Within the framework of relativistic Thomas–Fermi (RTF) and relativistic extended Thomas–Fermi (RETF) approximations, we calculate the giant monopole resonance (GMR) excitation energies for Sn and related nuclei. A large number of nonlinear relativistic force parameters are used in these calculations. We find a parameter set is capable to reproduce the experimental monopole energy of Sn isotopes, when its nuclear matter compressibility lies within 210–230 MeV, however, it fails to reproduce the GMR energy of other nuclei. That means, simultaneously a parameter set cannot reproduce the GMR values of Sn and other nuclei.

The effect of the nucleon coupling constants on the mass radius ratio (further, the surface gravitational redshift) of proto neutron star (PNS) PSR J0737-3039A is examined with relativistic mean field theory in consideration of a baryon octet. Here, five sets of nucleon coupling constants DD-MEI, GL85, GL97, GM1 and NL2 are used. The PNS’s temperature is assumed to be $T=20$ MeV and the mass the PNS PSR J0737-3039A is chosen as $M=1.338M_{\odot }$. The radius and the mass radius ratio of the PNS PSR J0737-3039A calculated by the five groups of nucleon coupling constants above are $R=15.693\text{–}18.846$ km and $M/R=0.071\text{–}0.085M_{\odot }$/km, respectively. The surface gravitational redshift $z$ of the PNS PSR J0737-3039A calculated from the above five groups of nucleon coupling constants is $z=0.125\text{–}0.156$.

The nuclear matter density at finite temperature was evaluated analytically in the relativistic mean field theory using Sommerfeld approximation at low temperature. These analytical results are interesting since they allow a more transparent analysis of the contributions of the involved parameters.

The properties of massive protoneutron stars (PNSs) are of great significance for the study of supernova and the evolution of neutron stars or black holes. The mass of the massive neutron star PSR J1614-2230 is fitted by selecting the nuclear coupling constants and adjusting the hyperon coupling constants in the framework of the relativistic mean field (RMF) theory. The model is then extrapolated to calculate the properties of massive PNS with the trapped neutrinos. The effects of different trapped neutrinos on the composition and structure of massive PNSs are discussed for entropy per baryon $S=1$. Results show that the presence of trapped neutrinos increase the energy density. Moreover, the significant neutrinos trapped, such as electron leptons number $Y_L=0.4$, reduces the pressure of massive PNSs in the density region 0.2–0.5fm${}^{-3}$, that is to say, the equation-of-state (EOS) is softened in this region. The maximum masses and corresponding radii of massive PNSs are calculated to be 2.110$M_{\odot }$, 2.106$M_{\odot }$, 2.095$M_{\odot }$, 2.082$M_{\odot }$ and 12.19, 11.88, 11.75 and 11.81 km for the electron leptons number $Y_L=0.1,0.2,0.3,0.4$. We calculate the distribution of the internal temperature, and get the effects of the trapped neutrinos on the internal temperature of massive PNSs for the first time. For the different electron leptons number $Y_L=0.1,0.2,0.3,0.4$, the central temperatures of the massive PNS, when the mass is taken to be the same as that of the observed neutron star PSR J1614-2230$(1.97\pm 0.04M_{\odot })$, are $19.57_{-0.19}^{+0.32}$, $22.55_{-0.25}^{+0.36}$, $25.48_{-0.45}^{+0.68}$, $27.47_{-0.83}^{+0.93}$MeV, respectively.

The property difference between the neutron star PSR J0348$+$0432 and its proto neutron star is studied in the framework of the relativistic mean field theory considering neutrino trapping. We see that the central baryon number density of the proto neutron star PSR J0348+0432 is in the range ${\rho }_{c,\mathrm{\text{PNS}}}=0.539\text{–}0.698$fm${}^{-3}$, which is smaller than that of the neutron star PSR J0348$+$0432 ${\rho }_{c,\mathrm{\text{NS}}}=0.634\text{–}0.859$fm${}^{-3}$. Inside the neutron star PSR J0348$+$0432, only the neutrons, protons, $\mathrm{\Lambda }$ and ${\mathrm{\Xi }}^{-}$ produce, whereas the hyperons ${\mathrm{\Sigma }}^{-},{\mathrm{\Sigma }}^0,{\mathrm{\Sigma }}^{+}$ and ${\mathrm{\Xi }}^0$ all do not appear. But in the proto neutron star PSR J0348$+$0432, hyperons ${\mathrm{\Sigma }}^{-}$, ${\mathrm{\Sigma }}^0$, ${\mathrm{\Sigma }}^{+}$ and ${\mathrm{\Xi }}^0$ all will produce, though their relative particle number density is still very small, no more than 2%. This shows that higher temperature will be advantageous to the hyperon production.

The relativistic mean field (RMF) theory is used to examine the effect of the meson-$\mathrm{\Xi }$ coupling constants on the properties of the neutron star (NS) PSR J0348+0432 when the hyperon potential of $\mathrm{\Xi }$ is fixed. It is found that the greater the $x_{\sigma \mathrm{\Xi }}$ and $x_{\omega \mathrm{\Xi }}$, the stronger the repulsive interaction. The potential field strengths of mesons $\omega$ and $\rho$ and the chemical potentials of neutron n and electron e increase, whereas the potential field strengths of mesons $\sigma$ decrease with the increase of the meson-$\mathrm{\Xi }$ coupling constants. It is also found that the relative particle number density of neutron ${\rho }_n/\rho$ and hyperon $\mathrm{\Lambda }$ in the NS PSR J0348+0432 increase, whereas that of hyperon ${\mathrm{\Xi }}^{-}$ decrease as the meson-$\mathrm{\Xi }$ coupling constants increase. In our calculations, hyperon ${\mathrm{\Xi }}^0$, ${\mathrm{\Sigma }}^{-}$, ${\mathrm{\Sigma }}^0$ and ${\mathrm{\Sigma }}^{+}$ all do not appear. Our results show that the meson-$\mathrm{\Xi }$ coupling constants cannot be uniquely determined as the hyperon-potential of $\mathrm{\Xi }$ is determined. Therefore, the related properties of NS cannot be uniquely determined only by the determined hyperon potential of $\mathrm{\Xi }$.

The dark matter admixed neutron stars (DANSs) are studied using the two-fluid TOV equations separately, in which the normal matter (NM) and dark matter (DM) are simulated by the relativistic mean field theory and self-interacting fermionic model, respectively. A universal relationship $M_D^{max}=(0.269\frac{m_f}{m_I}+0.627){(\frac{1\mathrm{\text{GeV}}}{m_f})}^2{\mathrm{\text{M}}}_{\odot }$ is suggested, where $M_D^{max}$ is the maximum mass of DM existing in DANSs, $m_f$ is the particle mass of DM ranging from 5GeV to 1TeV, $m_I$ is the interaction mass scale with the value 300GeV (0.1GeV) for weak (strong) interaction DM model. This simple formula connects directly the microcosmic nature of DM particle with its macrocosmic mass existing in DANSs. Meanwhile, such a formula exhibits that the existence of NM has little effect on $M_D^{max}$. It is found that the ratio of radius of DM in DANSs over $M_D^{max}$ is a constant with the value about 12$\frac{\mathrm{\text{km}}}{{\mathrm{\text{M}}}_{\odot }}$ (7$\frac{\mathrm{\text{km}}}{{\mathrm{\text{M}}}_{\odot }}$) for weak (strong) interaction DM cases. According to the calculated results, only for the strong interaction DM cases with $m_f=5$ to $10$GeV and central energy density ${𝜀}_D>10^3$MeV/fm³, DM has obvious effect on the mass of compact star. Compared with the energy density of DM in the Milky Way galaxy, $\sim 10^{-36}$MeV/fm³, the existence of DM might hardly affect the mass of compact stars in the Milky Way galaxy.

The properties of proto neutron star (PNS) PSR J0740+6620 are studied with the relative mean field theory. In our calculations, we find that five nucleon coupling parameters (DD-MEI, NL1, NL2, TW99 and GM1) can give the mass of the PNS PSR J0740+6620. The radius of PNS PSR J0740+6620 calculated by GM1 is the smallest, $R=14.63$–$13.44$km, and that calculated by TW99 is the largest, $R=17.46$–$17.07$km. The radius calculated by other nucleon coupling parameters is between the two. We find that properties of PNS PSR J0740+6620 calculated by different nucleon coupling parameters are different. The central baryon density ${\rho }_c$, the central field strength ${\sigma }_{0c}$, ${\omega }_{0c}$, ${\sigma }_{0c}^{\ast }$ and ${\varphi }_{0c}$ of mesons $\sigma$, $\omega$, ${\sigma }^{\ast }$ and $\varphi$, the central energy density ${𝜀}_c$, and the central pressure $p_c$ calculated by GM1 are all the largest among the five sets of nucleon coupling parameters. The calculations with DD-MEI, TW99 and GM1 show that eight baryons (n, p, $\mathrm{\Lambda }$, ${\mathrm{\Sigma }}^{-}$, ${\mathrm{\Sigma }}^0$, ${\mathrm{\Sigma }}^{+}$, ${\mathrm{\Xi }}^{-}$ and ${\mathrm{\Xi }}^0$) appear inside PNS PSR J0740+6620 whereas those with NL1 and NL2 show that hyperon ${\mathrm{\Sigma }}^{+}$ does not appear. The relative particle density of baryons inside PNS PSR J0740+6620 is also very different as the PNS is calculated with different nucleon coupling constants.

The binding energies per-nucleon for 1654 nuclei, whose mass numbers range from 16 to 263 and charge numbers range from 8 to 106, are calculated by the relativistic mean field theory, with finite nucleon size effect being taken into account. The calculated energy surface goes through the middle of experimental points, and the root mean square deviation for the binding energies per-nucleon is 0.08163 MeV. The numerical results may be well simulated by a droplet model type mass formula. The droplet model is therefore put on the relativistic mean field theoretical foundations.

Nuclear matter incompressibility is calculated in the framework of the relativistic mean field theory. Asymmetry reduces the incompressibility. The isothermal incompressibility decreases with increasing temperature, and the isentropic one decreases with increasing entropy. Attention is given to the incompressibility at supernova collapse conditions.

Relativistic mean field theory is used to produce potential energy surfaces (PESs) for Ti isotopes. The relatively flat PESs suggest that ^{48, 52, 60}Ti, being on the way from vibrations to γ-unstable behavior, are the possible examples with the transitional dynamical symmetry E(5). Especially for ⁴⁸Ti, PES shows that it is a better candidate with E(5) symmetry. These conclusions are supported by the experimental data via the observed ratios of excitation energies.

We investigate the effect of the scalar-isovector δ-meson field on the equation of state (EOS) and composition of hyperonic neutron star matter, and the properties of hyperonic neutron stars within the framework of the relativistic mean field theory. The influence of the δ-field turns out to be quite different and generally weaker for hyperonic neutron star matter as compared to that for npeμ neutron star matter. We find that inclusion of the δ-field enhances the strangeness content slightly and consequently moderately softens the EOS of neutron star matter in its hyperonic phase. As for the composition of hyperonic star matter, the effect of the δ-field is shown to shift the onset of the negatively-charged (positively-charged) hyperons to slightly lower (higher) densities and to enhance (reduce) their abundances. The influence of the δ-field on the maximum mass of hyperonic neutron stars is found to be fairly weak, whereas inclusion of the δ-field turns out to enhance sizably both the radii and the moments of inertia of neutron stars with given masses. It is also shown that the effects of the δ-field on the properties of hyperonic neutron stars remain similar in the case of switching off the Σ hyperons.

Working within the framework of relativistic mean field theory, we study for the first time the clustering structure (nuclear sub-structure) of ^112–122Ba nuclei in an axially deformed cylindrical coordinate. We calculate the individual neutrons and protons density distributions for Ba-isotopes. From the analysis of the clustering configurations in total (neutrons-plus-protons) density distributions for various shapes of both the ground and excited states, we find different sub-structures inside the Ba nuclei considered here. The important step, carried out here for the first time, is the counting of number of protons and neutrons present in the clustering region(s). ¹²C is shown to constitute the cluster configuration in prolate-deformed ground-states of ^112–116Ba and oblate-deformed first excited states of ^118–122Ba nuclei. Presence of other lighter clusters such as ²H, ³H and nuclei in the neighborhood of N = Z, ¹⁴N, ^34–36Cl, ³⁶Ar and ⁴²Ca are also indicated in the ground and excited states of these nuclei. Cases with no cluster configuration are shown for ^112–116Ba in their first and second excited states. All these results are of interest for the observed intermediate-mass-fragments and fusion–fission processes, and the so far unobserved evaporation residues from the decaying Ba* compound nuclei formed in heavy ion reactions.

We study the binding energy, root-mean-square radius and quadrupole deformation parameter for the synthesized superheavy element Z = 115, within the formalism of relativistic mean field theory. The calculation is dones for various isotopes of Z = 115 element, starting from A = 272 to A = 292. A systematic comparison between the binding energies and experimental data is made.The calculated binding energies are in good agreement with experimental result. The results show the prolate deformation for the ground state of these nuclei. The most stable isotope is found to be ²⁸²115 nucleus (N = 167) in the isotopic chain. We have also studied Q_α and T_α for the α-decay chains of ^{287, 288}115.

The ground state properties namely the binding energy, the root mean square (rms) radius (neutron, proton and charge) and the deformation parameter of 45 newly identified neutron-rich isotopes in the A~71–152 mass region have been predicted in the relativistic mean filed (RMF) framework along with the Bardeen–Cooper–Schrieffer (BCS) type of pairing. Validity of the RMF results with the NL3 effective force are tested for odd-A Zn and Rh isotopic chains without taking the time reversal symmetry breaking effects into consideration. The RMF prediction on the binding energies are in good agreement with the empirical/finite-range droplet model calculation. The shell effects on the rms radii of odd-A Zn and Rh isotopes are nicely reproduced. The possibility of shape-coexistence in the newly identified nuclei is discussed.

We have studied the ground state bulk properties of magnesium isotopes using axially symmetric relativistic mean field formalism. The BCS pairing approach is employed to take care of the pairing correlation for the open shell nuclei. The contour plot of the nucleons distribution are analyzed at various parts of the nucleus, where clusters are located. The presence of an ¹⁶O core along bubble like α-particle(s) and few nucleons are found in the Mg isotopes.

Adopting the equation of states (EOSs) from the relativistic mean field (RMF) theory, the relationships among the keplerian frequency f_K, gravitational mass M and radius R for the rapidly rotating neutron stars with and without hyperons are presented and analyzed. For various RMF EOSs, the empirical formula , proposed by P. Haensel et al. [Astron. Astrophys.502 (2009) 605], is found to be an approximation with the error at most 13% and such approximation is worse for the neutron stars with hyperons. It indicates that the errors should be considered when the empirical formula is used to discuss the properties of neutron stars.