We elucidate the fate of two and three neighboring $\alpha$ particles in cold neutron matter by focusing on an analogy between such $\alpha$ systems and Fermi polarons realized in ultracold atoms. We describe in-medium excitation properties of an $\alpha$ particle and neutron-mediated two- and three-$\alpha$ interactions using theoretical approaches developed for studies of cold atomic systems. We numerically solve the few-body Schrödinger equation of $\alpha$ particles within standard $\alpha$ cluster models combined with in-medium properties of $\alpha$ particles. We point out that the resultant two-$\alpha$ ground state and three-$\alpha$ first excited state, which correspond to ${}^8\mathrm{Be}$ and the Hoyle state, respectively, known as main components in the triple-$\alpha$ reaction, can become bound states in such a many-neutron background although these states are unstable in vacuum. Our results suggest a significance of these in-medium cluster states not only in astrophysical environments such as core-collapsed supernova explosions and neutron star mergers but also in neutron-rich nuclei.

Single-nucleon knockout reaction studies of the proton-dripline nuclei ${}^9\mathrm{C}$ and ${}^{13}\mathrm{O}$ suggest an appreciable suppression of spectroscopic factors. In this work, we calculate the one-neutron and one-proton spectroscopic factors for the mirror pair ${}^9\mathrm{C}\text{−}{}^9\mathrm{Li}$ and ${}^{13}\mathrm{O}$ using two variants of the continuum shell model: the complex-energy Gamow shell model and the real-energy shell model embedded in the continuum. Our results indicate that the continuum effects strongly suppress the spectroscopic factors of well-bound orbits in the dripline systems but have less impact on the spectroscopic factors of weakly bound states.

A systematic analysis of the $\alpha$ $+$ core structure is performed in the ground state bands of even-even nuclei of the $22\le Z\le 42$ region in terms of the local potential model. The $\alpha$ $+$ core interaction is described by the nuclear potential of $(1+\text{Gaussian})\times (\text{W.S.}+{\text{W.S.}}^3)$ shape with two free parameters. Properties such as energy levels, reduced $\alpha$ widths, $B\left(E2\right)$ transition rates, and rms charge radii are calculated and compared with experimental data. A good agreement with the experimental data is obtained in general, even for the nuclei without the $\alpha$ $+$ {doubly closed shell core} configuration. The analysis of the selected nuclei in the $22\le Z\le 42$ region indicates that ${}^{44}\mathrm{Ti}$ and ${}^{94}\mathrm{Mo}$ have a greater $\alpha$-clustering degree in comparison with their respective neighboring nuclei of this set. In addition, the model points to the existence of nuclei without the $\alpha$ $+$ {doubly closed shell core} configuration with a significant $\alpha$-clustering degree compared to ${}^{44}\mathrm{Ti}$, ${}^{60}\mathrm{Zn}$, and ${}^{94}\mathrm{Mo}$. The study shows that the $\alpha$ $+$ core approach is satisfactorily applicable to nuclei other than those with $\alpha$ clustering above double-shell closures.

The finite-temperature linear response theory based on the finite-temperature relativistic Hartree-Bogoliubov (FT-RHB) model is developed in the charge-exchange channel to study the temperature evolution of spin-isospin excitations. Calculations are performed self-consistently with relativistic point-coupling interactions DD-PC1 and DD-PCX. In the charge-exchange channel, the pairing interaction can be split into isovector $(T=1)$ and isoscalar $(T=0)$ parts. For the isovector component, the same separable form of the Gogny D1S pairing interaction is used both for the ground-state calculation as well as for the residual interaction, while the strength of the isoscalar pairing in the residual interaction is determined by comparison with experimental data on Gamow-Teller resonance (GTR) and isobaric analog resonance (IAR) centroid energy differences in even-even tin isotopes. The temperature effects are introduced by treating Bogoliubov quasiparticles within a grand-canonical ensemble. Thus, unlike the conventional formulation of the quasiparticle random-phase approximation (QRPA) based on the Bardeen-Cooper-Schrieffer (BCS) basis, our model is formulated within the Hartree-Fock-Bogoliubov (HFB) quasiparticle basis. Implementing a relativistic point-coupling interaction and a separable pairing force allows for the reduction of complicated two-body residual interaction matrix elements, which considerably decreases the dimension of the problem in the coordinate space. The main advantage of this method is to avoid the diagonalization of a large QRPA matrix, especially at finite temperature where the size of configuration space is significantly increased. The implementation of the linear response code is used to study the temperature evolution of IAR, GTR, and spin-dipole resonance (SDR) in even-even tin isotopes in the temperature range $T=0\text{–}1.5$ MeV.

The calculations of the potential-energy surface are essential in the theoretical description of the fission process. In the constrained self-consistent approach, the smooth evolution of nuclear shape is described from the ground state until a very elongated one with a narrow neck. In all microscopic calculations, the rupture of the neck at scission is associated with a substantial change of nuclear matter density distribution and rapid energy decrease. In this paper, we show that there is no discontinuity of the potential-energy surface at scission when multiconstrained calculations are applied with the neck constraint. An early rupture of the neck at lower quadrupole and octupole moments is discussed as competitive with the conventional fission path. We discuss the neck properties in the scission configuration. We find that the neck radius in the asymmetric fission mode cannot decrease below 2 fm, and the nuclear matter density cannot decrease below the saturation density. In the compact fission mode, nuclear density may go down to half of the saturation density before the rupture of the neck.

We investigate the fusion and scattering of a ${}^{16}\mathrm{O}$ projectile on ${}^{152,154}\mathrm{Sm}$ targets using the time-dependent coupled-channels wave-packet method. We benchmark calculations of the $S$-matrix elements, fusion cross sections, and scattering differential cross sections with those from the time-independent coupled-channels method, and compare the results to experimental data. We find that our time-dependent method and the time-independent method produce quantitatively similar results for the $S$-matrix elements and fusion cross sections, but our method cannot quantitatively explain the experimental scattering differential cross sections, mainly due to the low maximum number of partial waves produced by the time-dependent method. Nevertheless, the strong agreements between our method and the time-independent method demonstrates that the time-dependent coupled-channels wave-packet method can be used to address fusion reactions for a wide range of energies, with the advantage of being able to extend to time-dependent Hamiltonians for more advanced modeling of nuclear reactions.

Combining laser spectroscopy in a Versatile Arc Discharge and Laser Ion Source (VADLIS) with Penning-trap mass spectrometry at the CERN-ISOLDE facility, this work reports on mean-square charge radii of neutron-rich mercury isotopes across the $N=126$ shell closure, the electromagnetic moments of ${}^{207}\mathrm{Hg}$, and more precise mass values of ${}^{206\text{–}208}\mathrm{Hg}$. The odd-even staggering (OES) of the mean square charge radii and the kink at $N=126$ are analyzed within the framework of covariant density functional theory (CDFT), with comparisons between different functionals to investigate the dependence of the results on the underlying single-particle structure. The observed features are defined predominantly in the particle-hole channel in CDFT, since both are present in the calculations without pairing. However, the magnitude of the kink is still affected by the occupation of the $\nu 1i_{11/2}$ and $\nu 2g_{9/2}$ orbitals with a dependence on the relative energies as well as pairing.

Background: Superdeformed (SD) bands are suggested by theory around ${}^{40}\mathrm{Ca}$ and in lighter alpha-conjugate nuclei such as ${}^{24}\mathrm{Mg}$, ${}^{28}\mathrm{Si}$, and ${}^{32}\mathrm{S}$. Such predictions originate from a number of theoretical models including mean-field models and antisymmetrized molecular dynamics (AMD) calculations. While SD bands have been identified in ${}^{40}\mathrm{Ca}$ and its near neighbors, evidence of their existence in the lighter, midshell nuclei is circumstantial at best. The key evidence of superdeformation would be the observation of transitions with high $B$($E2)$ transition strengths connecting states in a rotational sequence. This is challenging information to obtain since the bands lie at a high excitation energy and competition from out-of-band decay is dominant.

Purpose: The purpose of the present study is to establish a new methodology to circumvent the difficulties in identifying and quantifying in-band transitions through directly populating candidate states in the SD band in ${}^{28}\mathrm{Si}$ through inelastic alpha scattering, selecting such states with a spectrometer, and measuring their gamma-ray decay with a large array of high-purity germanium detectors, allowing direct access to electromagnetic transition strengths.

Methods: Excited states in ${}^{28}\mathrm{Si}$ were populated in the ${}^{28}\mathrm{Si}(\alpha ,{\alpha }^{\prime })$ reaction using a 130-MeV ${}^4\mathrm{He}$ beam from the K140 AVF cyclotron at the Research Center for Nuclear Physics. Outgoing alpha particles were analyzed using the Grand Raiden spectrometer positioned at an angle of $9.1^{\circ }$ to favor the population of states with $J\approx 4$. Coincident gamma rays were detected with the CAGRA array of 12 HPGe clover detectors augmented by a set of four large ${\mathrm{LaBr}}_3$ detectors.

Results: Data analysis showed that it was possible to identify additional low-energy transitions in competition with high-energy decays from excited states in ${}^{28}\mathrm{Si}$ in the vicinity of 10 MeV. However, while the candidate $4^{+}$ SD state at 10.944 MeV was populated, a 1148-keV transition to the candidate $2^{+}$ SD state at 9.796 MeV was not observed, and only an upper limit for its transition strength of $B\left(E2\right)<43$ W.u. could be established. This contradicts AMD predictions of $\approx 200$ W.u. for such a transition.

Conclusion: The present study strongly rejects the hypothesis that the candidate set of states identified in ${}^{28}\mathrm{Si}$ represents an SD band, which demonstrates the potential of the methodology devised here.

Within a Bayesian statistical framework using the standard Skyrme-Hartree-Fock model, the maximum a posteriori (MAP) values and uncertainties of nuclear matter incompressibility and isovector interaction parameters are inferred from the experimental data of giant resonances and neutron-skin thicknesses of typical heavy nuclei. With the uncertainties of the isovector interaction parameters constrained by the data of the isovector giant dipole resonance and the neutron-skin thickness, we have obtained $K_0={223}_{-8}^{+7}$ MeV at 68% confidence level using the data of the isoscalar giant monopole resonance in ${}^{208}\mathrm{Pb}$ measured at the Research Center for Nuclear Physics (RCNP), Japan, and at the Texas A&M University, USA. Although the corresponding ${}^{120}\mathrm{Sn}$ data gives a MAP value for $K_0$ about 5 MeV smaller than the ${}^{208}\mathrm{Pb}$ data, there are significant overlaps in their posterior probability distribution functions.

Background: The $\left(N<82\right)\mathrm{Xe}$ isotopes with only four valence protons are known to be γ soft and to have the spectrum similar to the O(6) limiting symmetry.

Purpose: Study the validity of the $\mathrm{O}\left(6\right)\supset \mathrm{O}\left(5\right)$ symmetry in the various vibrational bands of the $N=72 {}^{126}\mathrm{Xe}$ isotope.

Methods: Comparison of the ${}^{126}\mathrm{Xe}$ spectrum with O(6) symmetry. Apply the microscopic theory of dynamic pairing plus quadrupole (DPPQ) model and the interacting boson model (IBM-1). The energy spectrum, absolute $B\left(\mathrm{E}2\right)$ values and E2 transition ratios are evaluated. The odd-even spin staggering in the γ band is displayed, and the potential-energy plot is used to determine the shape of the nucleus.

Results: The predictions of the eigenvalues and the $B\left(\mathrm{E}2\right)$ values and the interband $B\left(\mathrm{E}2\right)$ ratios extended over the five excited bands up to $\tau =5$ in the O(6) multiplet view. The O(5) symmetry is well preserved, and the O(6) symmetry is slightly broken.

Conclusions: The predictions in the DPPQ model provide an alternative framework to the fluctuations in the O(6) quantum numbers in the IBM framework. The DPPQ model predictions are in fair agreement with experiment. The IBM-1 predictions provide a complementary view.

As an extension of previous work, we calculate the production cross section of heavy neutron-rich isotopes by employing the quantal diffusion description to ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U}$ collisions. The quantal diffusion is deduced from stochastic mean-field approach, and transport properties are determined in terms of time-dependent single-particle wave functions of the time-dependent Hartree-Fock theory. As a result, the approach allows for prediction of production cross sections without any adjustable parameters. The secondary cross sections by particle emission are calculated with the help of the statistical gemini$++$ code.

We calculate the forward unpolarized doubly-virtual Compton scattering (VVCS) off the deuteron in the framework of pionless effective field theory, up to next-to-next-to-next-to-leading order (N3LO) for the longitudinal and next-to-leading order for the transverse amplitude. The charge elastic form factor of the deuteron, obtained from the residue of the longitudinal VVCS amplitude, is used to extract the value of the single unknown two-nucleon one-photon contact coupling that enters the longitudinal amplitude at N3LO. We also study the lowest spin-independent generalized polarizabilities of the deuteron. The calculated unpolarized VVCS amplitude provides a high-precision model-independent input for a future calculation of the two-photon-exchange correction to the Lamb shift of muonic deuterium.

A $\gamma$-ray spectroscopic study of ${}^{212}\mathrm{Po}$ was performed at the Grand Accélérateur National d'Ions Lourds, using the inverse kinematics $\alpha$-transfer reaction ${}^{12}\mathrm{C}({}^{208}\mathrm{Pb},{}^{212}\mathrm{Po}){}^8\mathrm{Be}$ and the AGATA spectrometer. A careful analysis based on $\gamma \gamma$ coincidence relations allowed us to establish 14 new excited states in the energy range between 1.9 and 3.3 MeV. None of these states, however, can be considered as candidates for the levels with spins and parities of $1^{-}$ and $2^{-}$ and excitation energies below 2.1 MeV, which have been predicted by recent $\alpha$-cluster model calculations. A systematic comparison of the experimentally established excitation scheme of ${}^{212}\mathrm{Po}$ with shell-model calculations was performed. This comparison suggests that the six states with excitation energies (spins and parities) of 1744 ($4^{-}$), 1751 ($8^{-}$), 1787 ($6^{-}$), 1946 ($4^{-}$), 1986 ($8^{-}$), and 2016 ($6^{-}$) keV, which previously were interpreted as $\alpha$-cluster states, may in fact be of positive parity and belong to low-lying shell-model multiplets. This reinterpretation of the structure of ${}^{212}\mathrm{Po}$ is supported by experimental information with respect to the linear polarization of $\gamma$ rays, which suggests a magnetic character of the 432-keV $\gamma$ ray decaying from the state at an excitation energy of 1787 keV to the $6_1^{+}$ yrast state, and exclusive reaction cross sections.

The generator coordinate method begins with the variational construction of a set of nonorthogonal mean-field states that span a subspace of the full many-body Hilbert space. These states are then often projected onto states with good quantum numbers to restore symmetries, leading to a set with members that can be similar to one another, and it is sometimes possible to reduce this set without greatly affecting results. Here, we propose a greedy algorithm that we call the energy-transition-orthogonality procedure (ENTROP) to select subsets of important states. As applied here, the approach selects on the basis of diagonal energy, orthogonality, and contribution to the matrix element that governs neutrinoless double-$\beta$ decay. We present both shell-model and preliminary ab initio calculations of this matrix element for the decay of ${}^{76}\mathrm{Ge}$, with quadrupole deformation parameters and the isoscalar pairing strength as generator coordinates. ENTROP converges quickly, reducing significantly the number of basis states needed for an accurate calculation.

$\beta$-decay properties of nuclei are investigated within the relativistic nuclear energy density functional framework by varying the temperature and density, conditions relevant to the final stages of stellar evolution. Both thermal and nuclear pairing effects are taken into account in the description of nuclear properties and in the finite-temperature proton-neutron relativistic quasiparticle random-phase approximation (FT-PNRQRPA) to calculate the relevant allowed and first-forbidden transitions in the $\beta$ decay. The temperature and density effects are studied on the $\beta$-decay half-lives at temperatures $T=0$–$1.5\mathrm{MeV}$ and at densities $\rho Y_e={10}^7\mathrm{g}/{\mathrm{cm}}^3$ and ${10}^9\mathrm{g}/{\mathrm{cm}}^3$. The relevant Gamow-Teller transitions are also investigated for Ti, Fe, Cd, and Sn isotopic chains at finite-temperatures. We find that the $\beta$-decay half-lives increase with increasing density $\rho Y_e$, whereas half-lives generally decrease with increasing temperature. It is shown that the temperature effects decrease the half-lives considerably in nuclei with longer half-lives at zero temperature, while only slight changes for nuclei with short half-lives are obtained. We also show the importance of including the de-excitation transitions in the calculation of the $\beta$-decay half-lives at finite-temperatures. Comparing the FT-PNQRPA results with the shell-model calculations for $pf$-shell nuclei, a reasonable agreement is obtained for the temperature dependence of $\beta$-decay rates. Finally, large-scale calculations of $\beta$-decay half-lives are performed at temperatures $T_9\left(\text{K}\right)=5$ and $T_9\left(\text{K}\right)=10$ and densities $\rho Y_e={10}^7$ and ${10}^9\mathrm{g}/{\mathrm{cm}}^3$ for even-even nuclei in the range $8\le Z\le 82$, relevant for astrophysical nucleosynthesis mechanisms.

We investigate the robustness of “noncollective” rotational behavior for nuclei with random two-body interactions in the framework of nuclear shell model. The normal $I(I+1)$ behavior of average excitation energy of yrast states is universal for both even-nucleon and odd-nucleon systems by two-body random ensemble. In some special random samplings, especially the samplings with spin-$I_{\max }$ ground state, the inverse noncollective rotational behavior is found for both even-nucleon and odd-nucleon systems in this paper. Interestingly, above rotational behaviors are still robust in the presence of random two-body interactions plus realistic single-particle energies.

The evolution of quadrupole and octupole collectivity in neutron-deficient Xe, Ba, Ce, and Nd nuclei near the “octupole magic” neutron number $N=56$ is investigated within the mapped $sdf$-IBM framework. Microscopic input is obtained via quadrupole and octupole constrained Hartree-Fock-Bogoliubov calculations, based on the parametrization D1M of the Gogny energy density functional. Octupole-deformed mean-field ground states are predicted for Ba and Ce isotopes near $N=56$. Excitation energies of positive- and negative-parity states as well as electric transition rates are computed with wave functions resulting from the diagonalization of the mapped IBM Hamiltonian. The parameters of the Hamiltonian are determined via the mapping of the mean-field potential energy surfaces onto the expectation value of the Hamiltonian in the condensate state of the $s$, $d$, and $f$ bosons. Enhanced octupolarity is predicted for Xe, Ba, and Ce isotopes near $N=56$. The shape/phase transition from octupole-deformed to strongly quadrupole-deformed near $N=60$ is analyzed in detail.

New effective $\mathrm{\Lambda }N$ interactions are proposed for the density-dependent relativistic mean-field model. The multidimensionally constrained relativistic mean-field model is used to calculate ground-state properties of eleven known $\mathrm{\Lambda }$ hypernuclei with $A\ge 12$ and the corresponding core nuclei. Based on effective $NN$ interactions DD-ME2 and PKDD, the ratios $R_{\sigma }$ and $R_{\omega }$ of scalar and vector coupling constants between $\mathrm{\Lambda }N$ and $NN$ interactions are determined by fitting calculated $\mathrm{\Lambda }$ separation energies to experimental values. We propose six new effective interactions for $\mathrm{\Lambda }$ hypernuclei: DD-ME2-Y1, DD-ME2-Y2, DD-ME2-Y3, PKDD-Y1, PKDD-Y2, and PKDD-Y3 with three ways of grouping and including these eleven hypernuclei in the fitting. It is found that the two ratios $R_{\sigma }$ and $R_{\omega }$ correlate well and a good linear relation exists between them. The statistical errors of the ratio parameters in these effective interactions are analyzed. These new effective interactions are used to study the single-$\mathrm{\Lambda }$ excited states, the equation of state of hypernuclear matter, and neutron-star properties with hyperons.