The energies and widths of $DNN$ quasibound states with isospin $I=1/2$ are evaluated in two methods, the fixed center approximation to the Faddeev equation and the variational method approach to the effective one-channel Hamiltonian. The $DN$ interactions are constructed so they dynamically generate the ${\Lambda }_c\left(2595\right)$ ($I=0$, $J^{\pi }=1/2^{-}$) resonance state. We find that the system is bound by about 250 MeV from the $DNN$ threshold, $\sqrt{s}\sim 3500$ MeV. Its width, including both the mesonic decay and the $D$ absorption, is estimated to be about 20–40 MeV. The $I=0$ $DN$ pair in the $DNN$ system is found to form a cluster that is similar to the ${\Lambda }_c\left(2595\right)$.

Recent prompt $\gamma$-ray spectroscopy studies of ${}^{149,151}$Pr have revealed weak octupole correlations. These are manifested by the absence of strong intraband $E1$ transitions between bands of opposite parities. On the other hand, in their isotones ${}^{151,153}$Pm, which have only two additional protons, the $E1$ transition rates are several orders of magnitude stronger, indicating enhanced octupole correlations. The quasiparticle phonon model combined with the particle-rotor model, which allows octupole correlations and Coriolis mixing to be taken into account, has been applied to calculate the $E1$ transition rates between low-lying states of the nuclei ${}^{149,151}$Pr and ${}^{151,153}$Pm. The dependence of the $E1$ rates on the magnitude of the quadrupole deformation, the magnitude and sign of the hexadecapole deformation parameter, the Coriolis and recoil attenuation parameters, the energies of the vibrational bandheads, and the parameters of the Nilsson Hamiltonian have been thoroughly investigated. From this investigation an overall conclusion can be drawn that, even if the intrinsic quasiparticle structure of the bandheads and the octupole correlations vary as the parameters of the model are changed, the octupole correlations in the odd Pr isotopes are much weaker than those in the odd Pm isotopes. Moreover, the experimental $E1$ transition rates can be satisfactorily described with the values of the quadrupole and hexadecapole deformation parameters expected in this region. In the case of ${}^{151}$Pr, two possible dominant configurations have been assigned to the 35.1-keV isomeric state, namely, the 3/2[422] and 1/2[420] orbitals. Our calculations show that the first assignment provides an $E1$ value closer to the experimental observations.

Effects of the collision geometry on experimental observables that are known to be sensitive to the high-density behavior of nuclear symmetry energy are examined in U $+$ U collisions at 0.52 GeV/nucleon using an isospin- and momentum-dependent interaction within the framework of the isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model. It is found that the neutron-proton differential flow in tip-tip collisions and the difference of neutron and proton elliptic flow in body-body collisions are more sensitive to the symmetry energy at suprasaturation densities compared with collisions of spherical nuclei of the same masses. In addition, the $n/p$ ratio of preequilibrium nucleons is found to be slightly more sensitive to the symmetry energy in tip-tip collisions, and the collision geometry affects the ${\pi }^{-}/{\pi }^{+}$ ratio significantly.

The new excluded-volume hadron gas model by Singh et al. is critically discussed. We demonstrate that in this model the results obtained from relations between thermodynamical quantities disagree with the corresponding results obtained by statistical ensemble averaging. Thus, the model does not satisfy the requirements of thermodynamical consistency.

We determine the nonlinear hydrodynamic response to geometrical fluctuations in heavy ion collisions using ideal and viscous hydrodynamics. This response is characterized with a set of nonlinear response coefficients that determine, for example, the $v_5$ that is produced by an ${\epsilon }_2$ and an ${\epsilon }_3$. We analyze how viscosity damps both the linear and nonlinear response coefficients, and provide an analytical estimate that qualitatively explains most of the trends observed in more complete simulations. Subsequently, we use these nonlinear response coefficients to determine the linear and nonlinear contributions to $v_1$, $v_4$, and $v_5$. For viscous hydrodynamics the nonlinear contribution is dominant for $v_4$, $v_5$, and higher harmonics. For $v_1$, the nonlinear response constitutes an important $\sim 25\%$ correction in midcentral collisions. The nonlinear response is also analyzed as a function of transverse momentum for $v_1$, $v_4$, and $v_5$. Finally, recent measurements of correlations between event planes of different harmonic orders are discussed in the context of nonlinear response.

We investigate the hadronic reactions $\pi N\to \eta N$ and $\pi N\to K\Lambda$ via single-energy partial-wave analyses in the c.m. energy range 1080 to 2100 MeV. Our results for the $K\Lambda$ channel are consistent with prior works; however, for the $\eta N$ channel our results differ significantly from previous energy-dependent partial-wave analyses that violate the $S$-matrix unitarity. We present results of $\eta N$ and $K\Lambda$ partial-wave amplitudes constrained by a unitary energy-dependent model. We obtain excellent predictions of integrated cross sections for the two reactions from a global energy-dependent solution. Our results imply that the region just above $S_{11}\left(1535\right)$ has a major contribution from $P_{11}\left(1710\right)$ for ${\pi }^{-}p\to \eta n$, whereas the large peak near 1700 MeV in ${\pi }^{-}p\to K^0\Lambda$ is dominated by contributions from both $S_{11}\left(1650\right)$ and $P_{11}\left(1710\right)$.

We study the melting of a $K^{-}$ condensate in hot and neutrino-trapped protoneutron stars. In this connection, we adopt relativistic field theoretical models to describe the hadronic and condensed phases. It is observed that the critical temperature of antikaon condensation is enhanced as baryon density increases. For a fixed baryon density, the critical temperature of antikaon condensation in a protoneutron star is smaller than that of a neutron star. We also exhibit the phase diagram of a protoneutron star with a $K^{-}$ condensate.

We study different scenarios of topological phase transitions in the vicinity of the ${\pi }^0$ condensation point in neutron matter. The transitions occur between the Fermi-liquid state and a topologically different one with two sheets of the Fermi surface. Two possibilities of a rearrangement of quasiparticle degrees of freedom are shown: the first-order topological phase transition and the second-order one. The order of the phase transition is found to be strongly dependent on the value of the critical wave vector of the soft ${\pi }^0$ mode. The thermodynamics of the system is also studied. It is shown that the topology of the quasiparticle momentum distribution is mainly determined by the neutron matter density, while the temperature $T$ is essential in a narrow density region. A simple explanation of the first-order topological phase transition at $T=0$ is given.

The thermal pairing gap obtained by embedding the exact solutions of the pairing problem into the canonical ensemble is employed to calculate the width and strength function of the giant dipole resonance (GDR) within the phonon damping model. The results of calculations describe reasonably well the data for the GDR width as well as the GDR linearized strength function, recently obtained for ${}^{201}$Tl in the temperature region between 0.8 and 1.2 MeV, for which other approaches that neglect the effect of nonvanishing thermal pairing fail to describe.

Recently the identity method was proposed to calculate second moments of the multiplicity distributions from event-by-event measurements in the presence of the effects of incomplete particle identification. In this paper the method is extended for higher moments. The moments of smeared multiplicity distributions are calculated using single-particle identity variables. The problem of finding the moments of the multiplicity distributions is reduced to solving a system of linear equations.

Background: Measurements of neutron radii provide important constraints on the isovector sector of nuclear density functionals and offer vital guidance in areas as diverse as atomic parity violation, heavy-ion collisions, and neutron-star structure.

Purpose: We assess the impact of spin-orbit currents on the electromagnetic- and weak-charge radii of a variety of nuclei. Special emphasis is placed on the experimentally accessible electroweak skin, defined as the difference between weak-charge and electromagnetic-charge radii.

Methods: Two accurately calibrated relativistic mean-field models are used to compute proton, neutron, charge, and weak-charge radii of a variety of nuclei.

Results: We find that spin-orbit contributions to the electroweak skin of light neutron-rich nuclei, such as ${}^{22}$O and ${}^{48}$Ca, are significant and result in a substantial increase in the size of the electroweak skin relative to the neutron skin.

Conclusions: Given that spin-orbit contributions to both the charge and weak-charge radii of nuclei are often as large as present or anticipated experimental error bars, future calculations must incorporate spin-orbit currents in the calculation of electroweak form factors.

Measurements of kaon production at subthreshold energies in heavy-ion collisions point to a soft nuclear equation of state for densities up to two to three times nuclear matter saturation density. We apply these results to study the implications on compact star properties, especially in the context of the recent measurement of the two solar mass pulsar PSR J1614-2230. The implications are twofold: First, the heavy-ion results constrain nuclear matter at densities relevant to light neutron stars. Hence, a radius measurement could provide information about the density dependence of the symmetry energy which is a crucial quantity in nuclear physics. Second, the information on the nucleon potential obtained from the analysis of the heavy-ion data can be combined with restrictions from causality on the nuclear equation of state. From this we can derive a limit for the highest allowed compact star mass of three solar masses.

A $\gamma$-ray spectroscopy study of ${}^{30}$S is presented. Excitation energies have been determined with improved precision over previous studies and firm spin-parity assignments have been made for key ${}^{29}\text{P}+p$ resonant states. An evaluation of the ${}^{29}$P($p,\gamma$)${}^{30}$S reaction for $T=0.08$–2.5 GK shows that the 3${}^{+}$ and 2${}^{+}$ resonant states located at $E_r=289\left(3\right)$ and 410(3) keV, respectively, dominate the ${}^{29}$P($p$,$$$\gamma$)${}^{30}$S reaction rate in ONe novae, while the 410-keV resonance is expected to govern the rate in x-ray burster environments. These new, precise resonance energy measurements and firm spin-parity assignments have significantly reduced uncertainties in the ${}^{29}$P($p$,$$$\gamma$)${}^{30}$S reaction in ONe novae and x-ray bursts. In particular, the reaction rate is now specified precisely enough for calculations of isotopic abundances in ONe novae ejecta.

Background: The reduced, level-independent, Bardeen-Cooper-Schrieffer Hamiltonian is exactly diagonalizable by means of a Bethe ansatz wave function, provided the free variables in the ansatz are the solutions of the set of Richardson-Gaudin equations. On the one side, the Bethe ansatz is a simple product state of generalized pair operators. On the other hand, the Richardson-Gaudin equations are strongly coupled in a nonlinear way, making them prone to singularities. Unfortunately, it is nontrivial to give a clear physical interpretation to the Richardson-Gaudin variables because no physical operator is directly related to the individual variables.

Purpose: The purpose of this paper is to shed more light on the singular behavior of the Richardson-Gaudin equations, and how this is related to the product wave structure of the Bethe ansatz.

Method: A pseudodeformation of the quasispin algebra is introduced, leading towards a Heisenberg-Weyl algebra in the contraction limit of the deformation parameter. This enables an adiabatic connection of the exact Bethe ansatz eigenstates with pure bosonic multiphonon states. The physical interpretation of this approach is an adiabatic suppression of the Pauli exclusion principle.

Results: The method is applied to a so-called “picket-fence” model for the BCS Hamiltonian, displaying a typical critical behavior in the Richardson-Gaudin variables. It was observed that the associated bosonic multiphonon states change collective nature at the critical interaction strengths of the Richardson-Gaudin equations.

Conclusions: The Pauli exclusion principle is the main responsible for the critical behavior of the Richardson-Gaudin equations, which can be suppressed by means of a pseudodeformation of the quasispin algebra.

The probability $P_n$ of emitting a neutron following $\beta$ decay is critical in many areas of nuclear science, from understanding nucleosynethesis during the $r$ process to control of reactor power levels and nuclear waste management. As it is not always easy to measure or calculate, indirect empirical approaches have been developed to estimate the $P_n$ value from the decay $Q_{\beta }$ value and the neutron separation energy S${}_n$. Here, we present a new prescription incorporating also the half-life $T_{1/2}$, which correlates the known data better and thus improves an estimation of $P_n$ when only $T_{1/2}$, $Q_{\beta }$, and S${}_n$ are known. This new relation can be used to predict $P_n$ values for cases where the half-life is known, thus it can be useful in $r$-process network calculations and in modeling advanced fuel cycles.

I describe the computation of energy widths of nuclear states using an integral over the interaction region of ab initio variational Monte Carlo wave functions, and I present calculated widths for many states. I begin by presenting relations that connect certain short-range integrals to widths. I then present predicted widths for $5⩽A⩽9$ nuclei, and I compare them against measured widths. They match the data more closely and with less ambiguity than estimates based on spectroscopic factors. I consider the consequences of my results for identification of observed states in ${}^8$B, ${}^9$He, and ${}^9$Li. I also examine failures of the method and conclude that they generally involve broad states and variational wave functions that are not strongly peaked in the interaction region. After examining bound-state overlap functions computed from a similar integral relation, I conclude that overlap calculations can diagnose cases in which computed widths should not be trusted.

We perform three-body model calculations for a $sd$-shell hypernucleus ${}_{\Lambda }^{19}$F (${}_{\Lambda }^{17}\mathrm{O}+p+n$) and its core nucleus ${}^{18}$F (${}^{16}\mathrm{O}+p+n$), employing a density-dependent contact interaction between the valence proton and neutron. We find that the $B\left(E2\right)$ value from the first excited state (with spin and parity of $I^{\pi }=3^{+}$) to the ground state ($I^{\pi }=1^{+}$) is slightly changed by the addition of a $\Lambda$ particle, which exhibits the so called shrinkage effect of $\Lambda$ particle. We also show that the excitation energy of the $3^{+}$ state is reduced in ${}_{\Lambda }^{19}$F compared to ${}^{18}$F, as is observed in a $p$-shell nucleus ${}^6$Li. We discuss the mechanism of this reduction of the excitation energy, pointing out that it is caused by a different mechanism from that in ${}_{\Lambda }^7$Li.

The low-spin level scheme of ${}^{68}$Ni was investigated with the Gammasphere array following reactions between a ${}^{70}$Zn beam and ${}^{238}$U, ${}^{208}$Pb, and ${}^{197}$Au targets. Spin assignments for some states have been verified through $\gamma$-ray angular correlations, including the $0^{+}$ assignment for the 2511-keV level. Two previously unknown states at 3302 and 3405 keV have been identified. No evidence was found for a recently reported 216-ns, $0^{+}$ isomer at 2202 keV that was attributed to a proton two-particle, two-hole intruder configuration, despite experimental conditions similar to those used in the measurement reporting its discovery.

The microscopic description of neutron scattering by ${}^{16}$O below 30 MeV is carried out by means of the continuum particle-vibration coupling (cPVC) method with the Skyrme nucleon-nucleon ($NN$) effective interaction. In the cPVC method, a proper boundary condition on a nucleon in continuum states is imposed, which enables one to evaluate the transition matrix in a straightforward manner. Experimental data of the total and total-elastic cross sections are reproduced quite well by the cPVC method. An important feature of the result is the fragmentation of the single-particle resonance into many peaks as well as the shift of its centroid energy. Thus, some part of the fine structure of the experimental cross sections at lower energies is well described by the cPVC framework. The cPVC method based on a real $NN$ effective interaction is found to successfully explain about 85$\%$ of the reaction cross section, through explicit channel-coupling effects.