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 $\ell$-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.

We have measured the branching ratio for the superallowed $0^{+}\to$ $0^{+}\beta$ transition from ${}^{34}\mathrm{Ar}$ to be 0.9448(8), and determined its $ft$ value to be 3058.1(28) s, a result with $\pm 0.09$% precision, which is a factor of 3 improvement over the previous result based on current world data. The $ft$-value ratio for the mirror pair of superallowed transitions ${}^{34}\mathrm{Ar}$ $\to {}^{34}\mathrm{Cl}$ and ${}^{34}\mathrm{Cl}$ $\to {}^{34}\mathrm{S}$ becomes the most precise yet measured and, in a sensitive test of the method used to calculate the isospin-symmetry-breaking correction, ${\delta }_C$, it agrees well with the ratio as calculated with Woods-Saxon radial wave functions. This confirms the method used in the most recent survey of superallowed decays to extract $V_{\text{ud}}$, the up-down quark-mixing element of the Cabibbo-Kobayashi-Maskawa matrix. In addition, our branching-ratio results for the four observed Gamow-Teller branches to $1^{+}$ states in ${}^{34}\mathrm{Cl}$ are shown to agree well with shell-model calculations based on the same effective interactions that were used in the determination of ${\delta }_C$.

We investigate possible production of neutron-rich isotopes of nobelium. We calculate the production cross sections of ${}^{261–266}\mathrm{No}$ in the multinucleon transfer reactions of the same projectiles (${}^{36}\mathrm{S},{}^{40}\mathrm{Ar},{}^{48}\mathrm{Ca}$, and ${}^{50}\mathrm{Ti}$) and targets (${}^{254}\mathrm{Es}$ and ${}^{248–251}\mathrm{Cf}$) that were used in the previous study for the possible production of neutron-rich isotopes of Md. We find that the production cross sections of neutron-rich No isotopes are about an order of magnitude smaller than those for neutron-rich Md isotopes. By combining the results for the production of neutron-rich No and Md isotopes, we suggest simple expressions which can trace the isotopic trends of the production cross sections of heavy neutron-rich isotopes. The logarithm of the production cross section is proportional to isospin of projectile or target and the $Q$ value.

It is shown that recently observed $\alpha$ cluster states a few MeV above the $\alpha$ threshold energy in ${}^{52}\mathrm{Ti}$ correspond to the higher nodal band states with the $\alpha +{}^{48}\mathrm{Ca}$ cluster structure, i.e., a vibrational mode in which the intercluster relative motion is excited. The existence of the higher nodal states in the ${}^{48}\mathrm{Ca}$ core region in addition to the well-known higher nodal states in ${}^{20}\mathrm{Ne}$ and ${}^{44}\mathrm{Ti}$ reinforces the importance of the concept of vibrational motion due to clustering even in medium-weight nuclei with a $jj$-shell closed core. The higher nodal band and the shell-like ground band in ${}^{52}\mathrm{Ti}$ are described in a unified way by a Luneburg lenslike deep local potential due to the Pauli principle, which explains the emergence of backward angle anomaly (anomalous large angle scattering) at low energies, prerainbows at intermediate energies, and nuclear rainbows at high energies in the $\alpha +{}^{48}\mathrm{Ca}$ scattering. The existence of a $K=0^{-}\alpha$ cluster band analog to ${}^{44}\mathrm{Ti}$ midway between the ground band and the higher nodal band is inevitably predicted.

Excited states in ${}^{160}\mathrm{Gd}$ were populated via $\beta$ decay from the low- and high-spin isomers in ${}^{160}\mathrm{Eu}$. The high-spin, $K^{\pi }=5^{-}$ state feeds several two-quasiparticle levels, as well as a sequence associated with a $\gamma$ vibration and a $K^{\pi }=4^{+}$, hexadecapole vibrational structure. The decay scheme was significantly improved with the observation of new transitions and states when compared with the two competing level schemes from over four decades ago. Configuration assignments for some of the multiquasiparticle levels have been suggested, based upon decay properties, systematics from neighboring nuclei, and comparisons with theoretical calculations. In addition, 15 new low-spin states and approximately 60 new transitions were observed resulting from the decay of the low-spin ${}^{160}\mathrm{Eu}$ isomer.

In a previous work, we presented data for the ${}^{10}\mathrm{B}+{}^{197}\mathrm{Au}$ system, corresponding to quasielastic and elastic scattering, ${}^{197}\mathrm{Au}$ inelastic excitation, and one neutron pickup transfer, measuring the angular distribution of scattered beam-like ejectiles at several energies around the Coulomb barrier. In this paper, we present data for the fusion process of the same system, at several energies around the Coulomb barrier, as well as new data for one neutron pickup and stripping transfer. In this case, we detected offline $\gamma$ rays stemming from the $\beta$-delayed decay chain of fusion-evaporation residues and heavy transfer products. As in our previous work, we analyzed this data set with coupled reaction channels calculations using the São Paulo potential. We show that the coupling to the one neutron transfer channel is quite important to describe the fusion data at the sub-barrier energy region. We also provide a comparison of the experimental fusion cross sections obtained for ${}^{10}\mathrm{B}+{}^{197}\mathrm{Au}$ with data for several other systems involving the same target nucleus.

The most strange dibaryon $\mathrm{\Omega }\mathrm{\Omega }$ with quantum numbers $S=-6$, $I=0$, and $J^P=0^{+},1^{-},2^{+},3^{-}$ is reanalyzed in the framework of a quark delocalization color screening model (QDCSM) and chiral quark model (ChQM). The $\mathrm{\Omega }\mathrm{\Omega }$ dibaryon with $J^P=0^{+}$ is bound, and the one with other quantum numbers $J^P=1^{-},2^{+},3^{-}$ are all unbound in our calculation. The low-energy scattering phase shifts, the scattering length, and the effective range of the $\mathrm{\Omega }\mathrm{\Omega }$ dibaryon with $J^P=0^{+}$ also support the existence of such strange dibaryon. This dibaryon is showed to be a shallow bound state in QDCSM, while the binding energy becomes much larger in the ChQM by including the effect of the hidden color channels coupling. And the scalar nonet meson exchange in the ChQM also provides more attraction for the $\mathrm{\Omega }\mathrm{\Omega }$ system. Experimental search for such most strange dibaryon will provide much information for understanding the hadron-hadron interactions in different quark models.

We report measurement of the $g$-factor for the ${11/2}^{-}$ isomeric state at 535 keV in ${}^{133}\mathrm{La}$, employing the time differential perturbed angular distribution technique (TDPAD). This isomer was populated in the reaction ${}^{126}\mathrm{Te}({}^{11}\mathrm{B}$, $4n){}^{133}\mathrm{La}$ at beam energy of 52 MeV. From the observed nuclear spin precession, analysed through combined, magnetic dipole and electric quadrupole hyperfine interactions, we obtain the $g$ factor for the $11/2^{-}$ state as $g=1.16\pm 0.07$. In addition, this analysis provides the spectroscopic quadrupole moment $\left|Q\right|=1.71\pm 0.34b$, yielding the deformation parameter $\beta =0.28\pm 0.10$. Further, we have performed theoretical calculations using the large-scale shell model and the Monte Carlo shell model. The results successfully describe the low-lying levels and the band structures of ${}^{133}\mathrm{La}$, and the calculated $g$ factor compares well with the values obtained from our experiment. The dominant configuration of $11/2^{-}$ isomeric state in ${}^{133}\mathrm{La}$ is inferred to be $\pi \left(h_{11/2}\right)\otimes {}^{132}\mathrm{Ba}\left(0^{+}\right)$.

We study the role of pions in hot dense matter encountered in astrophysics. We find that strong interactions enhance the number density of negatively charged pions and that this enhancement can be calculated reliably for a relevant range of density and temperature by using the virial expansion. We assess the influence of pions and muons on the equation of state (EOS) and weak-interaction rates in hot dense matter. We find that thermal pions increase the proton fraction and soften the EOS. We also find that charged current weak reactions involving pions and muons ${\overline{\nu }}_{\mu }+{\mu }^{-}\to \pi$ and ${\nu }_{\mu }+{\pi }^{-}\to {\mu }^{-}$ make an important contribution to the opacity of muon neutrinos. This could influence the dynamics of core-collapse supernovae and neutron-star mergers. Finally, we note that pion-nucleon reactions can alter the evolution of the proton fraction when weak interactions are not in equilibrium.

The structures of the neutron-rich ${}^{69,71,73}\mathrm{Co}$ isotopes were investigated via $(p,2p)$ knockout reactions at the Radioactive Isotope Beam Factory, RIKEN. Isotopes of interest were studied using the DALI2 $\gamma$-ray detector array combined with the MINOS target and tracker system. Level schemes were reconstructed using the $\gamma \text{−}\gamma$ coincidence technique, with tentative spin-parity assignments based on the measured inclusive and exclusive cross sections. Comparison with shell-model calculations using the Lenzi-Nowacki-Poves-Sieja LNPS and PFSDG-U interactions suggests coexistence of spherical and deformed shapes at low excitation energies in the ${}^{69,71,73}\mathrm{Co}$ isotopes. The distorted-wave impulse approximation (DWIA) framework was used to calculate the single-particle cross sections. These values were compared with the experimental findings.

Differential cross sections for elastic Compton scattering from ${}^4\mathrm{He}$ have been measured with high statistical precision at the High Intensity $\gamma$-ray Source at laboratory scattering angles of ${55}^{\circ }$, ${90}^{\circ }$, and ${125}^{\circ }$ using a quasi-monoenergetic photon beam with a weighted mean energy value of 81.3 MeV. The results are compared to previous measurements and similar fore-aft asymmetry in the angular distribution of the differential cross sections is observed. This experimental work is expected to strongly motivate the development of effective-field-theory calculations of Compton scattering from ${}^4\mathrm{He}$ to fully interpret the data.

Using the Brink-Axel hypothesis we derive the rate $R$ for nuclear dipole excitation by a laser pulse carrying $N\gg 1$ photons with average energy $\hslash {\omega }_0\approx 5$ MeV. As expected $R\propto {\left(\hslash {\omega }_0\right)}^3$. The rate is also proportional to the aperture $\alpha$ of the laser pulse. Perhaps less expected is the fact that $R\propto N$, irrespective of the degree of coherence of the laser pulse. The expression for $R$, derived for a nearly stationary laser pulse, is valid also for short times and can, thus, be used in simulations via rate equations of multiple nuclear dipole excitations by a single pulse. The explicit dependence of $R$ on the parameters of the laser pulse and on nuclear parameters given in the paper should help to optimize experiments on laser-nucleus reactions.

Within the ultrarelativistic quantum molecular dynamics model, in which the Lorentz covariant treatment of nuclear mean-field potential is considered, the fluctuations of net-baryon, net-charge, and deuteron multiplicity distributions in $\mathrm{Au}+\mathrm{Au}$ head-on collisions at $\sqrt{s_{NN}}=3.0–5.0$ GeV are calculated. The results show that the nuclear mean-field potential can significantly enhance the magnitude of baryon number fluctuations in narrow rapidity windows, and this enhancement rapidly weakens with increasing beam energy. However, for proton and net-charge number fluctuations, the mean-field effects are less noticeable than that for baryon number. In addition, for net-charge number fluctuations, the negative binomial distribution agrees well with the calculated results at the midpseudorapidity window. Finally, the event-by-event fluctuations of deuteron number in the coalescence production picture are calculated as well, and it is found that its cumulant ratios decrease linearly with increasing the average multiplicity of deuterons per event, i.e., increase with increasing beam energy.

The optimized perturbation theory (OPT) is confronted to first-principle lattice simulations. We compare results from the Polyakov linear-sigma model (PLSM) in OPT with the conventional mean-field approximation (MFA). At finite temperatures and chemical potentials, the chiral condensates and the decofinement order parameters, the thermodynamic pressure, the pseudocritical temperatures, the subtracted condensates, the second- and high-order moments of various conserved charges (cumulants) obtained in MFA are compared with OPT and also confronted to available lattice quantum chromodynamics (QCD) simulations. We conclude that when moving from lower- to higher-order moments of different quantum charges, OPT becomes more closer to lattice QCD simulations. The higher-order moments of conserved charges, such as baryon, strange, and electric charge, are proportional to powers of the correlation length and thus expected to diverge at the critical endpoint of the QCD phase boundary. Making sure that one approximate approach is more sensitive than another, even slightly, is crucial for implementing PLSM, for instance, in positioning critical endpoint and providing an important signature for the possible experimental detection.

The equilibrium distributions of the different pasta geometries and their linear sizes are calculated from the mean field Gibbs energy functional in symmetric nuclear matter at finite temperature. The average sizes and shapes coincide approximately with the ones predicted by a standard pasta calculation in the coexisting phase approximation, but fluctuations are additionally calculated and seen to increase with temperature and baryonic density. The different pasta shapes are shown to coexist in a wide domain of density and temperature, in qualitative agreement with the findings of large scale molecular dynamics simulations, but with a much less expensive computational cost.

Various mechanisms may contribute to neutrinoless double beta decay in the left-right symmetric model. The interference between these mechanisms also contribute to the overall decay rate. The analysis of the contributions of these interference terms is important for disentangling different mechanisms. In the present paper we study interference effects contributing to the decay rate for neutrinoless double-$\beta$ decay in the left-right symmetric model. The numerical values for maximum interference for several nuclides are calculated. It is observed that, for most of the interference terms, the contribution is smaller than $20\%$ for all the nuclei considered in the study. However, the interference between the mass mechanisms (light and heavy) and $\eta$ mechanism is observed to be in the range $30\%–50\%$. The variation of the interference effect with the $Q$ values is also studied.

The only way neutron matter can couple to the electromagnetic field is through an anomalous coupling, which plays an important role in the thermodynamics of pure neutron matter. Such theories are, however, perturbatively non-renormalizable, which presents a difficulty in terms of the unambiguous treatment of the divergencies in a perturbative approach. Here, we show that despite this, an unambiguous expression can be obtained for the vacuum energy contribution to the grand canonical potential in the case of a constant magnetic field. We find that this contribution is quite small, which justifies the no-sea approximation usually made. We also discuss the density and temperature dependence of the full grand canonical potential.

The superfluid tunneling model is applied to the calculation of ground-state–to–ground-state α decay in the even-even neutron-deficient Te-Ba nuclei. We show that there is a larger α-particle formation probability in nuclei of this region above ${}^{100}\mathrm{Sn}$ when compared to analogous nuclei above ${}^{208}\mathrm{Pb}$. This is consistent with the expected systematic variation of the pair gap $\mathrm{\Delta }$ as a function of mass number. The recent experimental data on the α decay of the $N=Z$ nuclei ${}^{104}\mathrm{Te}$ and ${}^{108}\mathrm{Xe}$ are shown to leave open the possibility of enhanced α-particle formation involving nucleon correlations beyond the standard treatment of like-nucleon pairing, which is the mechanism suggested as underlying “superallowed” α decay.

The $K$-matrix formalism is applied to a schematic model for nuclear fission. The purpose is to explore the dependence of observables on the assumptions made about the configuration space and nucleon interaction in the Hamiltonian of the fissile nucleus. As expected, branching ratios in induced fission are found to depend sensitively on the character of the residual interaction, whether it is pairing in form or taken from a random ensemble. On the other hand, the branching ratio is not much affected by the presence of additional configurations that do not introduce new fission paths.