Narrow Results

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 analytical expression of the density-dependent binding energy per nucleon for the relativistic mean field (RMF), the so-called relativistic energy density functional (Relativistic-EDF), is used to obtain the isospin-dependent symmetry energy and its components for the isotopic chain of Sc-, Ti-, V- and Cr-nuclei. The procedure of the coherent density fluctuation model is employed to formulate the Relativistic-EDF and Brüeckner energy density functional (Brüeckner-EDF) at local density. A few signatures of shell and/or sub-shell closure are observed in the symmetry energy and its components, i.e. surface and volume symmetry energy, far from the $\beta$-stable region for odd-$A$ Sc- and V-, and even–even Ti- and Cr- nuclei with nonlinear NL3 and G3 parameter sets. A comparison is made with the results obtained from Relativistic-EDF and Brüeckner-EDF with both NL3 and G3 for the considered isotopic chains. We find Relativistic-EDF outperforms the Brüeckner-EDF in predicting the shell and/or sub-shell closure of neutron-rich isotopes at $N=50$ for these atomic nuclei. Moreover, a relative comparison has been made for the results obtained with the nonlinear NL3 and G3 parameter sets.

The neutron skin of atomic nuclei impacts the structure of neutron-rich nuclei, but its accurate measurement is quite challenging. We present predictions for neutron skins and proton radii for light to medium mass nuclei by employing Covariant Density Functional Theory (CDFT) based on density-dependent meson-exchange interaction. Using our microscopic predictions, we find a linear correlation between the neutron skin and the isospin asymmetry. The calculations are also extended to find a linear relationship between proton and neutron radii of mirror nuclei. Using the charge symmetry property of nuclear forces, a correlation between the neutron skin of neutron-rich nuclei and difference between the proton radii of the corresponding mirror pair has also been investigated. The inclusion of ISB term is found to affect the mirror difference charge radii of ${}^{48}$Ca-${}^{48}$Ni mirror pair.

The extra contributions due to an extra generation of vector-like quarks to the isospin symmetry breaking observable associated with the radiative B → K*γ decay is obtained. It is shown that this additional contribution is sensitive to the nonunitarity parameter U^sb, which is a measure of the the strength of the non-zero tree-level flavor changing neutral current in this model. The significance of this result is that, once accurate experimental results on the isospin asymmetry becomes available, one can constrain the U^sb independent of the mass of the extra quarks and so a much more stringent acceptable model parameter space could be obtained.

The proposal of the present work is to study the difference between the strange quark–antiquark amount in the proton and neutron. For this purpose, the possible nucleon–hyperon–kaon fluctuations are analyzed with the effective chiral theory. The small difference of particle masses is shown to be in the origin of this isospin asymmetry. The dependence of the results on the mass cutoff parameter and with the coupling constants is analyzed.

We study the effects of the scalar-isovector light mesons on the isospin asymmetry and phase transition of hadronic matter to hadronic matter with a condensate of antikaons, using an effective model with derivative couplings. In our formalism, nucleons interact through the exchange of σ, ω, ϱ, δ, and ς mesons in the presence of electrons and muons to accomplish electric charge neutrality and beta equilibrium. The phase transition to the antikaons condensate was implemented through the Gibbs conditions combined with the mean-field approximation, giving rise to a mixed phase of coexistence between nucleon matter and the condensed antikaons. As expected, our results indicate that the scalar-isovector mesons increase the range of the mixed phase–space, they operate for restoring isospin symmetry and they reduce the value of the effective nucleon mass, independently of the depth of the optical potential for antikaons. Also as expected the increase of the depth of optical potential favors the population of antikaons. Our results predict the density threshold of birth of the K-antikaons. The most expressive result of our calculation is the abrupt change in the isospin asymmetry due to the presence of the condensate. Moreover, we have found that scalar-isovector mesons increase the fraction of protons and reduced the fraction of neutrons in the system, since these mesons couple with the conserved isovector current of baryons and thus the minimum in the energy of the system corresponds to saturated isospin states (symmetric in isospin). Finally, we have found as expected that these mesons produce the stiffness of the EoS.

Symmetry energy coefficients of explicitly isospin asymmetric nuclear matter at variable densities (from 0.5ρ₀ up to 2ρ₀) are studied as generalized screening functions. An extended stability condition for asymmetric nuclear matter is proposed. We find the possibility of obtaining stable asymmetric nuclear matter even in some cases for which the symmetric nuclear matter limit is unstable. Skyrme-type forces are extensively used in analytical expressions of the symmetry energy coefficients derived as generalized screening functions in the four channels of the particle hole interaction producing alternative behaviors at different ρ and b (respectively, the density and the asymmetry coefficient). The spin and spin-isospin coefficients, with corrections to the usual Landau Migdal parameters, indicate the possibility of occurring instabilities with common features depending on the nuclear density and n–p asymmetry. Possible relevance for high energy heavy ions collisions and astrophysical objects is discussed.

Based on the similarity renormalization group (SRG) method, proton and neutron asymmetry in the nuclear pseudospin is investigated for the deformed system. We have checked influences of every term on the proton pseudospin splitting and their correlation with nuclear deformation. Further, we have found that dynamical term always made a similar effect on the proton pseudospin symmetry (PSS), which is different from the neutron case. By exerting its influence on the dynamical term, the vector–isovector $V_{\rho }$ potential gives the main contribution to the isospin asymmetry in the PSS except for several deeply bound states. The phenomenon that isospin asymmetry in the PSS becomes worse for the levels closer to the continuum and its reasons is disclosed.

Following a paper [R. Lisboa, Phys. Rev. C 67 054305 (2003)], we reinvestigate the role of the Coulomb and ρ potentials in the isospin asymmetry of nuclear pseudospin. By comparing the contributions of these potentials to the splitting of pseudospin doublets, we found the effect of the ρ potential is small and the Coulomb potential gives the main contribution to the observed isospin asymmetry of the psuedospin wavefunction splittings.