The hydrodynamic model including the spin degree of freedom and the electromagnetic field is discussed. In this derivation, we apply electromagnetism for a macroscopic medium proposed by Minkowski. For the equation of motion of spin, we assume that the hydrodynamic representation of the Pauli equation is reproduced when the many-body effect is neglected. Then the spin-magnetic interaction in the Pauli equation is converted to a part of the magnetization. The fluid and spin stress tensors induced by the many-body effect are obtained by employing the algebraic positivity of the entropy production in the framework of the linear irreversible thermodynamics, including the mixing effect of the irreversible currents. We further construct the constitutive equation of the polarization and the magnetization. Our polarization equation is more reasonable compared to another result obtained using electromagnetism for a macroscopic medium proposed by de Groot-Mazur.

Our earlier Faddeev three-body study in the $K^{-}$-deuteron scattering length, $A_{K^{-}d}$, is revisited here in light of the recent developments on two fronts: (i) the improved chiral unitary approach to the theoretical description of the coupled $\overline{K}N$ related channels at low energies, and (ii) the new and improved measurement from SIDDHARTA Collaboration of the strong interaction energy shift and width in the lowest $K^{-}$-hydrogen atomic level. Those two, in combination, have allowed us to produce a reliable two-body input to the three-body calculation. All available low-energy $K^{-}p$ observables are well reproduced and predictions for the $\overline{K}N$ scattering lengths and amplitudes, ${\left(\pi \Sigma \right)}^{\circ }$ invariant-mass spectra, as well as for $A_{K^{-}d}$ are put forward and compared with results from other sources. The findings of the present work are expected to be useful in interpreting the forthcoming data from CLAS, HADES, LEPS, and SIDDHARTA Collaborations.

We derive the node structure of the radial functions which are solutions of the Dirac equation with scalar $S$ and vector $V$ confining central potentials, in the conditions of exact spin or pseudospin symmetry, i.e., when one has $V=\pm S+C$, where $C$ is a constant. We show that the node structure for exact spin symmetry is the same as the one for central potentials which go to zero at infinity but for exact pseudospin symmetry the structure is reversed. We obtain the important result that it is possible to have positive energy bound solutions in exact pseudospin symmetry conditions for confining potentials of any shape, including naturally those used in hadron physics, from nuclear to quark models. Since this does not occur for potentials going to zero at large distances, which are used in nuclear relativistic mean-field potentials or in the atomic nucleus, this shows the decisive importance of the asymptotic behavior of the scalar and vector central potentials on the onset of pseudospin symmetry and on the node structure of the radial functions. Finally, we show that these results are still valid for negative energy bound solutions for antifermions.

The character of the low-energy $E1$ excitations is investigated by analyzing transition densities obtained from the RPA calculations in the doubly magic nuclei. We propose a decomposition method of the $E1$ excitations into the $pn$ mode (i.e., oscillation between protons and neutrons) and the skin mode (i.e., oscillation of the neutron skin against the inner core) via the transition densities, by which their mixing is handled in a straightforward manner. Crossover behavior of the $E1$ excitations is found, from the skin mode at low energy to the $pn$ mode at higher energy. The ratio of the skin-mode strength to the full strength turns out to be insensitive to the nuclides and to the effective interactions in the energy region of the crossover. Depending on the excitation energy, the observed low-energy $E1$ excitations are not necessarily dominated by the skin mode, as exemplified for ${}^{90}$Zr.

Background: The resonance structure in ${}^{11}$C is of particular interest with regard to the astrophysical ${}^7$Be($\alpha ,\gamma$) reaction, relevant at high temperature, and to the $\alpha$-cluster structure in ${}^{11}$C.

Purpose: The measurement was made to determine the unknown resonance parameters for the high excited states of ${}^{11}$C. In particular, the $\alpha$-decay width can be useful information to discuss the $\alpha$-cluster structure in ${}^{11}$C.

Methods: New measurements of ${}^7\mathrm{Be}+\alpha$ resonant scattering and the ${}^7$Be($\alpha ,p$)${}^{10}$B reaction in inverse kinematics were performed for center-of-mass energy up to 5.5 MeV, and the resonances at excitation energies of 8.9–12.7 MeV in the compound ${}^{11}$C nucleus were studied. Inelastic scattering of ${}^7\mathrm{Be}+\alpha$ and the ${}^7$Be($\alpha ,p$${}_1$)${}^{10}$B${}^{*}$ reaction were also studied with a simultaneous $\gamma$-ray measurement. The measurements were performed at the low-energy radioactive ion beam facility CRIB (CNS Radioactive Ion Beam separator) of the Center for Nuclear Study, the University of Tokyo.

Results: We obtained excitation functions of ${}^7$Be($\alpha ,{\alpha }_0$)${}^7$Be (elastic scattering), ${}^7$Be($\alpha ,{\alpha }_1$)${}^7$Be${}^{*}$ (inelastic scattering), ${}^7$Be($\alpha ,p$${}_0$)${}^{10}$B, and ${}^7$Be($\alpha ,p$${}_1$)${}^{10}$B${}^{*}$. Many resonances including a new one were observed and their parameters were determined by using an $R$-matrix analysis.

Conclusions: The resonances we observed possibly enhance the ${}^7$Be($\alpha ,\gamma$) reaction rate but with a smaller magnitude than the lower-lying resonances. A new negative-parity cluster band, similar to the one previously suggested in the mirror nucleus ${}^{11}$B, is proposed.

Total cross sections for proton- and deuteron-induced-fission of ${}^{208}$Pb and ${}^{238}$U have been determined in the energy range between 500 MeV and 1 GeV. The experiment has been performed in inverse kinematics at GSI Darmstadt, facilitating the counting of the projectiles and the identification of the reaction products. High precision between 5$\%$ and 7$\%$ has been achieved by individually counting the beam particles and by registering both fission fragments in coincidence with high efficiency and full $Z$ resolution. Fission was clearly distinguished from other reaction channels. The results were found to deviate by up to 30$\%$ from Prokofiev's systematics on total fission cross sections. There is good agreement with an elaborate experiment performed in direct kinematics.

Two cluster structures of ${}^9$Be, namely, ${}^5$He + ${}^4$He and ${}^8$Be + $n$, have been considered for its breakup to describe the available data on elastic scattering for a ${}^9$Be projectile with ${}^{28}$Si, ${}^{64}$Zn, and ${}^{144}$Sm targets. The results of these calculations suggest that the breakup coupling effects are significant for the ${}^5$He + ${}^4$He cluster model above the barrier energies, while they are dominant at relatively lower energies for the ${}^8$Be + $n$ model. The addition of a one-neutron stripping channel in the ${}^8$Be + $n$ model gives an overall good description of the elastic data for all the systems considered. The couplings generated by breakup in the ${}^8$Be + $n$ model have a behavior different from the coupling effects obtained within the ${}^5$He + ${}^4$He model, the former being more prominent at lower energies and for the heavier target systems. The behavior of extracted dynamic polarization potentials generated due to breakup and one-neutron transfer coupling has been investigated.

Results from searches of double $K$ capture in ${}^{78}$Kr in an experiment with the large-volume copper proportional counter, using data samples corresponding of two independent series of measurements with different intrinsic radioactivity background are presented. The total exposure of the low-background measurements is 0.343 $\mathrm{kg}\times \mathrm{y}$. A combination of methods of selection of useful events with a unique set of characteristics and wavelet analysis of events allowed a reduction of the background by $\sim$2000 times in the energy region of interest. The statistical significance of combined data from two stages of operation equals $2.5\sigma$. Corresponding to such effect, the half-life of ${}^{78}$Kr relative to $2\nu 2K$ capture equals $T_{1/2}=[9.2_{-2.6}^{+5.5}\left(\mathrm{stat}\right)\pm 1.3\left(\mathrm{syst}\right)]\times {10}^{21}$ y. Half-life limits for other $2K$ transitions to the excited states in ${}^{78}$Se are obtained at the level of ${10}^{21}$ y in the first time. In particular, limits on $2\nu 2K$ capture to the excited level $0_1^{+}$ (1499 keV) and resonant neutrinoless double $K$ capture to the level $2^{+}$ (2838 keV) have been defined on the level of $T_{1/2}\ge 5.4\times {10}^{21}$ y at 90$\%$ C.L.

Recent improvements in the experimental determination of properties of the isovector giant quadrupole resonance (IVGQR), as demonstrated in the $A=208$ mass region, may be instrumental for characterizing the isovector channel of the effective nuclear interaction. We analyze properties of the IVGQR in ${}^{208}$Pb, using both macroscopic and microscopic approaches. The microscopic method is based on families of nonrelativistic and covariant energy density functionals (EDF), characterized by a systematic variation of isoscalar and isovector properties of the corresponding nuclear matter equations of state. The macroscopic approach yields an explicit dependence of the nuclear symmetry energy at some subsaturation density, for instance $S(\rho =0.1$ fm${}^{-3})$, or the neutron skin thickness $\Delta r_{np}$ of a heavy nucleus, on the excitation energies of isoscalar and isovector GQRs. Using available data it is found that $S(\rho =0.1$ fm${}^{-3})=23.3\pm 0.6$ MeV. Results obtained with the microscopic framework confirm the correlation of the $\Delta r_{np}$ to the isoscalar and isovector GQR energies, as predicted by the macroscopic model. By exploiting this correlation together with the experimental values for the isoscalar and isovector GQR energies, we estimate $\Delta r_{np}=0.14\pm 0.03$ fm for ${}^{208}$Pb, and the slope parameter of the symmetry energy: $L=37\pm 18$ MeV.

A simultaneous description of hadronic yields; pion, kaon, and proton spectra; elliptic flows; and femtoscopy scales in the hydrokinetic model of $A+A$ collisions is presented at different centralities for the top BNL Relativistic Heavy Ion Collider (RHIC) and CERN Large Hadron Collider (LHC) 2.76-TeV energies. The initial conditions are based on the Monte Carlo Glauber simulations. When going from RHIC to LHC energy in the model, the only parameters changed are the normalization of the initial entropy defined by the number of all charged particles in most central collisions, contribution to entropy from binary collisions, and barionic chemical potential. The hydrokinetic model is used in its hybrid version, which provides the correct match (at the isochronic hypersurface) of the decaying hadron matter evolution with hadronic ultrarelativistic quantum molecular dynamics cascade. The results are compared with the standard hybrid models where hydrodynamics and hadronic cascade are matching just at the non-space-like hypersurface of chemical freeze-out or on the isochronic hypersurface. The modification of the particle-number ratios at LHC caused, in particular, by the particle annihilations at the afterburn stage is also analyzed.

We have calculated the proton charge radius by assuming that the real proton radius is not unique and the radii are randomly distributed in a certain range. This is performed by averaging the elastic electron-proton differential cross section over the form factor cutoff. By using a dipole form factor and fitting the middle value of the cutoff to the low-$Q^2$ Mainz data, we found the lowest ${\chi }^2/N$ for a cutoff $\Lambda =0.8203\pm 0.0003$ GeV, which corresponds to a proton charge radius $r_E=0.8333\pm 0.0004$ fm. The result is compatible with the recent precision measurement of the Lamb shift in muonic hydrogen as well as recent calculations using more sophisticated techniques. Our result indicates that the relative variation of the form factor cutoff should be around 21.5$\%$. Based on this result we have investigated effects of the nucleon radius variation on the symmetric nuclear matter (SNM) and the neutron star matter (NSM) by considering the excluded volume effect in our calculation. The mass-radius relation of a neutron star is found to be sensitive to this variation. The nucleon effective mass in the SNM and the equation of state of both the SNM and the NSM exhibit a similar sensitivity.

The newly developed multichannel cluster model (MCCM), based on the coupled-channel Schrödinger equation with outgoing wave boundary conditions, is extended to study the $\alpha$-decay fine structure in heavy odd-odd nuclei. Calculations are performed for the $\alpha$ transitions to favored rotational bands where the unpaired nucleons remain unchanged. The simple WKB barrier penetration formula is also used to evaluate the branching ratios for various daughter states. It is found that the WKB formula seems to overestimate the branching ratios for the second and third members of the favored rotational band, while the MCCM gives a precise description of them without any adjustable parameters. Moreover, the experimental total $\alpha$-decay half-lives are well reproduced within the MCCM.

Exclusive photoproduction of vector mesons in the perturbative two-gluon exchange formalism depends significantly on nucleon and nuclear gluon distributions. In the present study we calculate total cross sections and rapidity distributions of $J/\psi \left(1s\right)$, $\psi \left(2s\right)$, ${\rm Y}\left(1s\right)$, ${\rm Y}\left(2s\right)$, and ${\rm Y}\left(3s\right)$ in ultraperipheral proton-lead ($p$Pb) and lead-lead (PbPb) collisions at the CERN Large Hadron Collider (LHC) at $\sqrt{s_{{}_{NN}}}=5$ TeV and $\sqrt{s_{{}_{NN}}}=2.76$ TeV, respectively. Effects of gluon shadowing are investigated and potentials for constraining nuclear gluon modifications are discussed.

We calculate the strong couplings of pions to the $\Delta \left(1232\right)$ resonance using a QCD parametrization method that includes in addition to the usual one-quark also two-quark and previously uncalculated three-quark operators. We find that three-quark operators are necessary to obtain results consistent with the data and other QCD based baryon structure models. Our results are also in quantitative agreement with a model employing large $D$-state admixtures to the $N$ and $\Delta$ wave functions indicating that the $\pi N$ and $\pi \Delta$ couplings are sensitive to the spatial shape of these baryons.

Background: The reactions with the neutron-rich ${}^{48}\mathrm{Ca}$ beam and actinide targets resulted in the detection of new superheavy (SH) nuclides with $Z=104–118$. The unambiguous identification of the new isotopes, however, still poses a problem because their $\alpha$-decay chains terminate by spontaneous fission (SF) before reaching the known region of the nuclear chart. The understanding of the competition between $\alpha$-decay and SF channels in SH nuclei is, therefore, of crucial importance for our ability to map the SH region and to assess its extent.

Purpose: We perform self-consistent calculations of the competing decay modes of even-even SH isotopes with $108\le Z\le 126$ and $148\le N\le 188$.

Methods: We use the state-of-the-art computational framework based on self-consistent symmetry-unrestricted nuclear density functional theory capable of describing the competition between nuclear attraction and electrostatic repulsion. We apply the SkM* Skyrme energy density functional. The collective mass tensor of the fissioning superfluid nucleus is computed by means of the cranking approximation to the adiabatic time-dependent Hartree-Fock-Bogoliubov (HFB) approach. This paper constitutes a systematic self-consistent study of spontaneous fission in the SH region, carried out at a full HFB level, that simultaneously takes into account both triaxiality and reflection asymmetry.

Results: Breaking axial symmetry and parity turns out to be crucial for a realistic estimate of collective action; it results in lowering SF lifetimes by more than 7 orders of magnitude in some cases. We predict two competing SF modes: reflection symmetric modes and reflection asymmetric modes.

Conclusions: The shortest-lived SH isotopes decay by SF; they are expected to lie in a narrow corridor formed by ${}^{280}\mathrm{Hs}$, ${}^{284}\mathrm{Fl}$, and ${}_{118}^{284}\mathrm{Uuo}$ that separates the regions of SH nuclei synthesized in “cold-fusion” and “hot-fusion” reactions. The region of long-lived SH nuclei is expected to be centered on ${}^{294}\mathrm{Ds}$ with a total half-life of $\sim 1.5\mathrm{days}$. Our survey provides a solid benchmark for the future improvements of self-consistent SF calculations in the region of SH nuclei.

Starting from the extended Nambu-Jona-Lasinio (ENJL) model, we show that in nuclear matter the Lifshitz phase transition (LPT) takes place at suprasaturation density and zero temperature, while it is subsaturation transition in neutron matter. At finite temperature $T$ and nucleon chemical potential $\mu$ the phase diagram in the $(T,\mu )$ plane for nuclear and neutron matters is established with the existence of corresponding tricritical points (TCP) which separate the first- and half-order from the second-order phase transitions. Many properties of the LPT are cleared up throughout the investigation of equations of state and other thermodynamic quantities. How to experimentally identify the LPT in nuclear matter is discussed.

We present for the first time many types of empirical evidence that point to the existence of preferred neutron/proton numbers for superdeformed (SD) shapes. We use a simple premise based on the pairing correlations to obtain the proposed empirical evidence. In particular, plots of γ-ray energy ratio such as $R$($I$) $=$ $E_{\gamma }$($I$ → $I$-2)/ $E_{\gamma }$($I$-2 → $I$-4) vs $N$ and $Z$, $R$($I$) vs $I$ plots, nuclear softness parameter values, and the number of SD bands for a given $N$ and $Z$ are used to pinpoint the $N$, $Z$ numbers that are most favored as the deformed magic numbers. The proton and neutron magic numbers so obtained not only confirm the earlier theoretical predictions made for the chain of particle numbers corresponding to the SD shapes but also verify the increase in deformation with the particle number within each chain. The analysis also leads to several new predictions for the occurrence of the SD bands.

A study on the surface diffuseness parameter of the nuclear potential for the reactions of ${}^{208}$Pb with ${}^{48}$Ti, ${}^{54}$Cr, ${}^{56}$Fe, ${}^{64}$Ni, and ${}^{70}$Zn is performed using large-angle quasi-elastic scattering experimental data. Diffuseness parameters that are considerably lower than the standard value of around 0.63 fm are required in order to fit the experimental data at deep sub-barrier energies, except for the ${}^{54}$Cr+${}^{208}$Pb system, where the required diffuseness parameter is in satisfactory agreement with (but still lower than) the standard value. Furthermore, when the energies of the experimental data used in the fittings are increased from the deep sub-barrier region to the energies closer to the Coulomb barrier height, the best fitted diffuseness parameters also increase. The increase in the obtained diffuseness parameters as the energies are increased also seems to have a possible tendency to be a function of the charge product of the target and projectile nuclei. We find that the phenomenon of threshold anomaly might explain our findings here. The increase in the diffuseness parameters could also due to dynamical effects, for example, due to neutron movements.