The continuum Faddeev equations for the neutron-neutron-alpha ($n+n+\alpha$) system are formulated for a general interaction as well as for finite rank forces. In addition, the capture process $n+n+\alpha \to {}^6\mathrm{He}+\gamma$ is derived.

The isotopic dependencies of one-quasiparticle states in Es and Md are treated. In ${}^{253,255}\mathrm{Lr}$, the energies of the lowest one-quasiproton states are calculated. The one-quasiparticle isomer states are revealed in the nuclei of an $\alpha$-decay chain starting from ${}^{269}\mathrm{Rg}$. The $\alpha$ decays from some isomer states are predicted. The population of isomer states in the complete fusion reactions is discussed.

A fully consistent relativistic continuum random phase approximation (RCRPA) is constructed, where the contribution of the continuum spectrum to nuclear excitations is treated exactly by the single-particle Green’s function technique. The full consistency of the calculations is achieved that the same effective Lagrangian is adopted for the ground state and the excited states. The negative energy states in the Dirac sea are also included in the single-particle Green’s function in the no-sea approximation. The currents from the vector meson and photon exchanges and the Coulomb interaction in RCRPA are treated exactly. The spin-orbit interaction is included naturally in the relativistic frame. Numerical results of the RCRPA are checked with the constrained relativistic mean-field theory. We study the effects of the inconsistency, particularly the currents and Coulomb interaction in various collective multipole excitations.

Present applications of the dispersive-optical-model analysis are restricted by the use of a local but energy-dependent version of the generalized Hartree-Fock potential. This restriction is lifted by the introduction of a corresponding nonlocal potential without explicit energy dependence. Such a strategy allows for a complete determination of the nucleon propagator below the Fermi energy with access to the expectation value of one-body operators (like the charge density), the one-body density matrix with associated natural orbits, and complete spectral functions for removal strength. The present formulation of the dispersive optical model (DOM) therefore allows the use of elastic electron-scattering data in determining its parameters. Application to ${}^{40}\mathrm{Ca}$ demonstrates that a fit to the charge radius leads to too much charge near the origin using the conventional assumptions of the functional form of the DOM. A corresponding incomplete description of high-momentum components is identified, suggesting that the DOM formulation must be extended in the future to accommodate such correlations properly. Unlike the local version, the present nonlocal DOM limits the location of the deeply bound hole states to energies that are consistent with ($e,e$${}^{\prime }$$p$) and ($p,2p$) data.

Charged reaction products originated from the interaction of the loosely bound radioactive ion beam ${}^{17}\mathrm{F}$ ($S_p=600$ keV) with the proton-shell closed ${}^{58}\mathrm{Ni}$ target were measured at two colliding energies slightly above the Coulomb barrier. The collected data were analyzed within the framework of the optical model to deduce the reaction cross section and to investigate the role played by inelastic excitations, transfer channels, and the breakup process ${}^{17}\mathrm{F}\to {}^{16}\mathrm{O}+p$ at near-barrier energies. The reaction cross section at the lower ${}^{17}\mathrm{F}$ energy showed a moderate enhancement ($~$$20\%$) with respect to that of the system ${}^{16}\mathrm{O}+{}^{58}\mathrm{Ni}$. At this energy direct reaction channels were also found to be more relevant than those for the reaction induced from the tightly bound projectile ${}^{16}\mathrm{O}$ on the same target. Both features could be strongly related to the very low binding energy of the ${}^{17}\mathrm{F}$ valence proton.

We present a novel method of smoothing discrete breakup cross sections calculated by the method of continuum-discretized coupled channels. The smoothing method based on the complex scaling method is tested with success for a ${}^{58}\mathrm{Ni}$($d,\mathit{pn}$) reaction at $80$ MeV as an example of three-body breakup reactions and applied to a ${}^{12}\text{C}({}^6\text{He},\mathit{nn}\hspace{0.5em}{}^4\text{He})$ reaction at $229.8$ MeV as an example of four-body breakup reactions. Fast convergence of the breakup cross section with respect to extending the model space is confirmed. The method is also applied to ${}^{12}\text{C}({}^6\text{He},\mathit{nn}\hspace{0.5em}{}^4\text{He})$ and ${}^{208}\text{Pb}({}^6\text{He},\mathit{nn}\hspace{0.5em}{}^4\text{He})$ reactions at $240$ MeV/$A$ and compared with the experimental data.

We analyze the production and freeze-out of the isomer ${}^{180}\mathrm{Ta}$${}^m$ in the $\nu$-process. We consider the influence of a possible low-lying intermediate ($J=5$) state at $592$ keV using a transition width estimated from the measured half-life. This more realistic width is much smaller than the previous estimate. We find that the $592$-keV state leads only to a small reduction of the residual isomer population ratio from the previous result; that is, considering this better estimate for the transition width, the isomer population ratio changes from $\mathcal{R}=0.39$ to $\mathcal{R}=0.38$, whereas previously it was estimated that this transition could reduce the ratio to $\mathcal{R}=0.18$. This finding strengthens the evidence that ${}^{138}\mathrm{La}$ and ${}^{180}\mathrm{Ta}$ are coproduced by neutrino nucleosynthesis with an electron neutrino temperature of $\mathit{kT}\approx 4$ MeV.

Heavy-ion fusion reactions ${}^{122}\mathrm{Sn}$(${}^{14,15}\mathrm{N}$, $\mathit{xn}$)${}^{132}\mathrm{La}$ have been utilized for the lifetime measurements using the recoil distance method. The lifetimes of seven low-lying excited states were obtained. In addition, the lifetimes of two states belonging to a band, which was identified as a decoupled band, were obtained. The decoupling behavior in ${}^{132}\mathrm{La}$ has been theoretically investigated using the particle-rotor model in the model space of $\pi h_{11/2}$ and ($\nu s_{1/2},$ $\nu d_{3/2}$). The pseudospin coupling model was also utilized to understand the decoupling behavior in terms of the valence-particle configuration $\pi h_{11/2}({\Omega }_{\pi }=\frac{1}{2})\otimes \nu [\mathrm{411̃}]({\Omega }_{\nu }=\frac{1}{2},\frac{3}{2})$, and a reasonable agreement with the experiment was obtained.

We study low-energy shape oscillations of negative parity in the first and second (isomeric) minima in actinides. As a main tool, we use the phenomenological Woods-Saxon potential with a variety of shape deformations. This allows including a mixing of various multipolarities when considering oscillations with a fixed $K$ quantum number. The phonon energies are determined either from the collective Hamiltonian with the microscopic-macroscopic energy and cranking mass parameters, or from its simplified version with the constant-mass parameters. The results for $K^{\pi }=0^{-},1^{-}$ in the first minima are in reasonable agreement with experimental data, which include predicted $E1$ transitions; the $K^{\pi }=2^{-}$ energies are systematically overestimated. In the second minimum, as compared to the data for ${}^{240}\mathrm{Pu}$ and ${}^{236}\mathrm{U}$, our calculated $K=1,2$ energies are overestimated, while the $K=0$ energies are three or more times too large. This signals either a noncollective character of the experimentally assigned $K=0$ states or a serious flaw of the model in the second minimum. More data on the $K=0$, $I^{\pi }=1^{-}$ collective states in the second minima of other nuclei are necessary to resolve this issue.

Isotope yield distributions in the multifragmentation regime were studied with high-quality isotope identification, focusing on the intermediate mass fragments (IMFs) produced in semiviolent collisions. The yields were analyzed within the framework of a modified Fisher model. Using the ratio of the mass-dependent symmetry energy coefficient relative to the temperature, $a_{\mathrm{sym}}/T$, extracted in previous work and that of the pairing term, $a_{\mathrm{p}}/T$, extracted from this work, and assuming that both reflect secondary decay processes, the experimentally observed isotope yields were corrected for these effects. For a given $I=N-Z$ value, the corrected yields of isotopes relative to the yield of ${}^{12}\mathrm{C}$ show a power law distribution $Y(N,Z)/Y({}^{12}\mathrm{C})~A^{-\tau }$ in the mass range $1⩽A⩽30$, and the distributions are almost identical for the different reactions studied. The observed power law distributions change systematically when $I$ of the isotopes changes and the extracted $\tau$ value decreases from $3.9$ to $1.0$ as $I$ increases from $-1$ to $3$. These observations are well reproduced by a simple deexcitation model, with which the power law distribution of the primary isotopes is determined to be ${\tau }^{\mathrm{prim}}=2.4\pm 0.2$, suggesting that the disassembling system at the time of the fragment formation is indeed at, or very near, the critical point.

The quasi-elastic excitation function for the ${}^{17}\mathrm{O}$ $+$ ${}^{64}\mathrm{Zn}$ system was measured at energies near and below the Coulomb barrier, at the backward angle ${\theta }_{\mathrm{lab}}={161}^{°}$. The corresponding quasi-elastic barrier distribution was derived. The excitation function for the neutron stripping reactions was also measured, at the same angle and energies, and the experimental values of the spectroscopic factors were deduced by fitting the data. A reasonably good agreement was obtained between the experimental quasi-elastic barrier distribution with the coupled-channel calculations including a very large number of channels. Of the channels investigated, three dominated the coupling matrix: two inelastic channels, ${}^{64}\mathrm{Zn}$(2${}_1^{+}$) and ${}^{17}\mathrm{O}$(1/2${}^{+}$), and one-neutron transfer channel, particularly the first one. On the other hand, a very good agreement is obtained when we use a nuclear diffuseness for the ${}^{17}\mathrm{O}$ nucleus larger than the one for ${}^{16}\mathrm{O}$. We verify that quasi-elastic barrier distribution is a sensitive tool for determining nuclear matter diffuseness.

The relativistic mean field approach including isovector-scalar channel (i.e., exchanging $\delta$ mesons) interaction is taken to study the properties of neutron star matter including hyperons and antikaon condensation. For hyperonic neutron stars, it shows that the $\delta$-meson channel interaction stiffens the equation of state at lower densities but it softens the equation of state after hyperons appear. This leads to the neutron star having a lower central density and a larger radius than the one with the same mass but without the $\delta$-meson channel interaction. For neutron star matter including both hyperons and antikaon condensation, the $\delta$-meson channel interaction increases the onset density of the antikaon condensation. At the same time, the stability of the kaonic neutron star and its dependence on the kaon optical potential are discussed. For stable kaonic neutron stars with larger radii, those with the inclusion of the $\delta$-meson channel interaction have larger masses than those without the $\delta$-meson interaction, but the result is reversed for those with smaller radii. Calculated results are also compared with neutron star observations. Constraints on the model parameters are then provided.

A microscopic state-of-the-art calculation of the nuclear matrix element for neutrinoless double-$\beta$ decay of ${}^{150}\mathrm{Nd}$ with an account for nuclear deformation is performed. The proton-neutron quasiparticle random phase approximation (QRPA) with a realistic residual interaction [the Brueckner $G$ matrix derived from the charge-dependent Bonn (Bonn-CD) nucleon-nucleon potential] is used as the underlying nuclear structure model. The present calculated matrix element is suppressed by about $40\%$ as compared with our previous QRPA result for ${}^{150}\mathrm{Nd}$ obtained with neglect of deformation. By making use of this newest nuclear matrix element, one may conclude that neutrinoless double-$\beta$ decay of ${}^{150}\mathrm{Nd}$, to be measured soon by the SNO$+$ collaboration, provides one of the best probes of the Majorana neutrino mass.

Future exact many-body theory will allow us to calculate nuclear reactions based on the adopted $\mathit{NN}$ and many-body nuclear potentials. But $\mathit{NN}$ potentials are not observable and there are an infinite number of the phase-equivalent $\mathit{NN}$ potentials related via finite-range unitary transformations. We show that asymptotic normalization coefficients, which are the amplitudes of the asymptotic tails of the overlap functions, are invariant under finite-range unitary transformations but spectroscopic factors are not. We prove also that the exact amplitudes for the $(d,p),(d,\mathit{pn})$, and $(e,e^{\prime }p)$ reactions determining the asymptotic behavior of the exact scattering wave functions in the corresponding channels, in contrast to spectroscopic factors, are invariant under finite-range unitary transformations. Moreover, the exact reaction amplitudes are not parametrized in terms of the spectroscopic factors and nuclear reactions in the exact approach cannot provide a tool to determine spectroscopic factors which are not observable.

The mass of ${}^{31}\mathrm{S}$ has been measured with the JYFLTRAP double Penning trap mass spectrometer. The new mass excess value of $-19\hspace{0.5em}042.55(24)\hspace{0.5em}\mathrm{keV}$ deviates from the adopted value of $-19\hspace{0.5em}044.6(15)\hspace{0.5em}\mathrm{keV}$ by $1.4\sigma$. The mass value of ${}^{32}\mathrm{Cl}$ has been revised with the new ${}^{31}\mathrm{S}$ result and the latest data from $\beta$-delayed proton decay of ${}^{32}\mathrm{Cl}$. The new mass excess value for ${}^{32}\mathrm{Cl}$ is $-13\hspace{0.5em}334.88(65)\hspace{0.5em}\mathrm{keV}$, which is the most precise value for ${}^{32}\mathrm{Cl}$ so far and in agreement with the recent (${}^3\mathrm{He},t$) data. The isobaric multiplet mass equation has been tested in the $T=2$ quintet at $A=32$, and the cubic form of the equation has been found to agree with the experimental data. The $Q_{\mathit{EC}}$ value for the $\beta$ decay of $T=1/2$ mirror nucleus ${}^{31}\mathrm{S}$ has been determined as $Q_{\mathit{EC}}=5397.99(24)\hspace{0.5em}\mathrm{keV}$, which slightly deviates from the previously adopted value.

Similarity renormalization group (SRG) flow equations can be used to unitarily soften nuclear Hamiltonians by decoupling high-energy intermediate-state contributions to low-energy observables while maintaining the natural hierarchy of many-body forces. Analogous flow equations can be used to consistently evolve operators so that observables are unchanged if no approximations are made. The question in practice is whether the advantages of a softer Hamiltonian and less-correlated wave functions might be offset by complications in approximating and applying other operators. Here we examine the properties of SRG-evolved operators, focusing in this article on applications to the deuteron but leading toward methods for few-body systems. We find the advantageous features generally carry over to other operators with additional simplifications in some cases from factorization of the unitary transformation operator.

The complete and incomplete fusion cross sections for ${}^9\mathrm{Be}+{}^{124}\mathrm{Sn}$ reaction have been deduced using the online $\gamma$-ray measurement technique. Complete fusion at energies above the Coulomb barrier was found to be suppressed by $~28\%$ compared to the coupled-channels calculations and is in agreement with the systematics of L. R. Gasques et al. [Phys. Rev. C 79, 034605 (2009)]. Study of the projectile dependence for fusion on a ${}^{124}\mathrm{Sn}$ target shows that, for ${}^9\mathrm{Be}$ nuclei, the enhancement at below-barrier energies is substantial compared to that of tightly bound nuclei.

Decay processes of ground and excited bottom baryons are studied in the ${}^3{P}_0$ nonrelativistic quark model with all model parameters fixed in the sector of light quarks. Using as an input the recent mass of ${\Xi }_b$ and the theoretical masses of ${\Xi }_b^{*}$ and ${\Xi }_b^{\prime }$, narrow decay widths are predicted for the ground-state bottom baryons ${\Xi }_b^{*}$ and ${\Xi }_b^{\prime }$. The work predicts large decay widths, about $100$ MeV for the $\rho$-type orbital excitation states of ${\Xi }_b$.

We examine the nuclear liquid-gas phase transition at a large number of colors ($N_c$) within the framework of the van der Waals (VdW) We argue that the VdW equation is appropriate for describing internucleon forces, and discuss how each parameter scales with $N_c$. We demonstrate that $N_c=3$ (our world) is not large with respect to the other dimensionless scale relevant to baryonic matter, the number of neighbors in a dense system $N_N$. Consequently, we show that the liquid-gas phase transition looks dramatically different at $N_c\to \infty$ with respect to our world: The critical-point temperature becomes of the order of ${\Lambda }_{\mathrm{QCD}}$ rather than below it. The critical-point density becomes of the order of the baryonic density, rather than an order of magnitude below it. These are precisely the characteristics usually associated with the “quarkyonic phase.” We therefore conjecture that quarkyonic matter is simply the large-$N_c$ limit of the nuclear liquid, and the interplay between $N_c$ and $N_N$ is the reason that the nuclear liquid in our world is so different from quarkyonic matter. We conclude by suggesting ways in which our conjecture can be tested in future lattice measurements.

We study the development of collectivity in the neutron-rich nuclei around $N=40$, where the experimental and theoretical evidence suggest a rapid shape change from the spherical to the rotational regime, in analogy to what happens at the island of inversion surrounding ${}^{31}\mathrm{Na}$. Theoretical calculations are performed within the interacting shell-model framework in a large valence space, based on a ${}^{48}\mathrm{Ca}$ core, which encompasses the full $\mathit{pf}$ shell for the protons and the $0f_{5/2}$, $1p_{3/2}$, $1p_{1/2}$, $0g_{9/2}$, and $1d_{5/2}$ orbits for the neutrons. The effective interaction is based on a G matrix obtained from a realistic nucleon-nucleon potential whose monopole part is corrected empirically to produce effective single-particle energies compatible with the experimental data. We find a good agreement between the theoretical results and the available experimental data. We predict the onset of deformation at different neutron numbers for the various isotopic chains. The maximum collectivity occurs in the chromium isotopes where the large deformation regime already starts at $N=38$. The shell evolution responsible for the observed shape changes is discussed in detail, in parallel to the situation in the $N=20$ region.