We study bottomonium $b\overline{b}$ production in $pp$ collisions as well as in heavy-ion collisions, using a quantal density matrix approach. The initial bottom (anti)quarks are provided by the pythia event generator. We solve the Schrödinger equation for the $b\overline{b}$ pair, identifying the potential with the free energy, calculated with lattice QCD, to obtain the temperature dependent $b\overline{b}$ density matrix as well as the dissociation temperature. The formation of bottomonium is given by projection of the bottomonium density matrix onto the density matrix of the system. With this approach we describe the rapidity and transverse momentum distribution of the $\mathrm{{\rm Y}}$ ($n\mathrm{S}$) in pp collisions at $\sqrt{s_{NN}}=5.02$ TeV, extending a similar calculation for the charmonium states [T. Song, J. Aichelin, and E. Bratkovskaya, Phys. Rev. C 96, 014907 (2017)]. We employ the Remler formalism to study the $b\overline{b}$ production in heavy ion collisions in which the heavy quarks scatter elastically with partons from the quark-gluon plasma (QGP). The elastic scattering of heavy (anti)quark in QGP is realized by the dynamical quasiparticle model (DQPM) and the expanding QGP is modeled by parton-hadron-string dynamics (PHSD). We find that a reduction to 10% of the scattering cross section for a (anti)bottom quark with a QGP parton reproduces the experimental data. This suggests that due to color neutrality the scattering cross section of the small $b\overline{b}$ system with a parton is considerably smaller than twice the bottom-parton scattering cross section.

We explore the theoretical possibility of ${}^{3}P_0$ neutron superfluid in dilute spin-polarized neutron matter, which may be relevant to the crust region of a magnetized neutron star. In such a dilute regime where the neutron Fermi energy is less than 1 MeV, the ${}^{1}S_0$ neutron superfluid can be suppressed by a strong magnetic field of the compact star. In the low-energy limit relevant for dilute neutron matter, the ${}^{3}P_0$ interaction is stronger than the ${}^{3}P_2$ one which is believed to induce the triplet superfluid in the core. We present the ground-state phase diagram of dilute neutron matter with respect to the magnetic field and numerically estimate the critical temperature of the ${}^{3}P_0$ neutron superfluid, which is found to exceed ${10}^7$ K.

An investigation of the quasiprojectile breakup channel in semiperipheral and peripheral collisions of ${}^{58,64}\mathrm{Ni}+{}^{58,64}\mathrm{Ni}$ at 32 and 52 MeV/nucleon is presented. Data have been acquired in the first experimental campaign of the INDRA-FAZIA apparatus in GANIL. The effect of isospin diffusion between projectile and target in the two asymmetric reactions has been highlighted by means of the isospin transport ratio technique, exploiting the neutron-to-proton ratio of the quasiprojectile reconstructed from the two breakup fragments. We found evidence that, for the same reaction centrality, a higher degree of relaxation of the initial isospin imbalance is achieved in the breakup channel with respect to the more populated binary output, possibly indicating the indirect selection of specific dynamical features. We have proposed an interpretation based on different average projectile-target contact times related to the two exit channels under investigation, with a longer interaction for the breakup channel. The time information has been extracted from antisymmetrized molecular dynamics simulations of the studied systems coupled to $\mathrm{Gemini}++$: the model calculations support the hypothesis hereby presented.

Relativistic corrections have been made in the nonrelativistic antisymmetrized molecular dynamics (amd) simulations to apply to the high-energy neutron production in the ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ and ${}^{16}\mathrm{O}+{}^{12}\mathrm{C}$ collisions at incident energies of 290 and 400 MeV/nucleon. The corrections are made in kinematics alone and neither nucleon-nucleon inelastic scatterings nor meson productions are taken into account, and amd with the relativistic corrections is called semirelativistic amd. The three-nucleon collision ($3N\text{C}$) and Fermi boost in the collision processes are taken into account in the nonrelativistic amd. Since the relativistic corrections tend to compensate in each other, the difference between the semirelativistic and nonrelativistic results become small. High-energy tails of the available experimental neutron double-differential cross sections, especially at larger angles, are well reproduced by amd with the $3N\mathrm{C}$ term both with nonrelativistic and semirelativistic simulations. These results indicate that the high-energy neutrons are dominantly produced by the $3N\mathrm{C}$ process in this incident energy range.

Many-body approaches for atomic nuclei generally rely on a basis expansion of the nuclear states, interactions, and current operators. In this work, we derive the representation of the magnetic dipole operator in plane-wave and harmonic-oscillator basis states, as needed for Faddeev calculations of few-body systems or many-body calculations within, e.g., the no-core shell model, the in-medium similarity renormalization group, coupled-cluster theory, or the nuclear shell model. We focus in particular on the next-to-leading-order two-body contributions derived from chiral effective field theory. We provide detailed benchmarks and also comparisons with quantum Monte Carlo results for three-body systems. The derived operator matrix elements represent the basic input for studying magnetic properties of atomic nuclei based on chiral effective field theory.

The atomic masses of ${}^{111,113}\mathrm{Ag}$, ${}^{111–113}\mathrm{Pd}$, ${}^{111–113}\mathrm{Rh}$, ${}^{111–113}\mathrm{Ru}$, and ${}^{111,112}\mathrm{Mo}$ have been measured during the online commissioning experiments of the ZeroDegree multi-reflection time-of-flight Mass Spectrograph (ZD MRTOF-MS) at the RIKEN RI beam factory. The mass of ${}^{112}\mathrm{Mo}$ has been determined. For the previously known masses, a good agreement between our results and the 2020 Atomic Mass Evaluation has been observed in most cases. The determined two-neutron separation energies for Mo isotopes up to $N=70$ show a smooth trend. In this work, the performed experiment and analysis procedure are presented. The theoretical interest in the measured region is highlighted, and the results are discussed in terms of the various mass surface formulas including the new mass data. Furthermore, a comparison between our results and global theoretical mass models is given, and we provide a benchmark for results from a Bayesian machine learning algorithm for future mass extrapolation.

Nuclear $\beta$ spectrum and the corresponding (anti)neutrino spectrum play important roles in many aspects of nuclear astrophysics, particle physics, nuclear industry, and nuclear data. In this work we propose a projected shell model (PSM) to calculate the level energies as well as the reduced one-body transition density (ROBTD) by the Pfaffian algorithm for nuclear $\beta$ decays. The calculated level energies and ROBTD are inputted to the beta spectrum generator (BSG) code to study the high precision $\beta$ spectrum of allowed one-to-one transitions. When experimental level energies are adopted, the calculated $\beta$ spectrum by ROBTD of the PSM deviates from the one by the extreme simple particle evaluation of the BSG by up to $10\%$, reflecting the importance of nuclear many-body correlations. When calculated level energies are adopted, the calculated $\beta$ spectrum shows sensitive dependence on the reliability of calculated level energies. The developed method for ROBTD by the PSM will also be useful for study of the first-forbidden transitions, the isovector spin monopole resonance, etc., in a straightforward way.

The neutron emission, extensively used as a clock to measure fission delay, is not fully understood. There are ambiguities in interpretation of experimental results at higher energies and a dearth of information at low energies. In order to address these issues, a measurement of pre-scission neutron multiplicity $\left({\nu }_{\mathrm{pre}}\right)$ for ${}^7\mathrm{Li}+{}^{203}\mathrm{Tl}$ at low energy $(E^{*}=43.7\mathrm{MeV})$ have been carried out. The statistical model calculations incorporating shell corrections, constrained by fitting fission excitation functions down to energies near fission threshold, underestimate the experimental ${\nu }_{\mathrm{pre}}$ values. At the energy of the present measurement, dynamical effects are found to be negligible. This would imply large emission of neutrons at the instant of neck rupture. More theoretical and experimental investigations are required to understand the behavior of low density neutron rich nuclear matter at the neck region.

We determined the matter density distributions and root-mean-square radii of ${}^{12,13}\mathrm{C}$, ${}^{14}\mathrm{N}$, ${}^{20,22}\mathrm{Ne}$, ${}^{24,26}\mathrm{Mg}$, ${}^{30}\mathrm{Si}$, ${}^{40,42,44,48}\mathrm{Ca}$, ${}^{46,48}\mathrm{Ti}$, ${}^{54}\mathrm{Fe}$, ${}^{58,64}\mathrm{Ni}$, ${}^{90,92}\mathrm{Zr}$, ${}^{116,124}\mathrm{Sn}$, and ${}^{208}\mathrm{Pb}$ through fitting the relative and the absolute small-angle differential cross sections of proton-nucleus elastic scattering at 0.8 GeV with the Glauber model, respectively. Compared to the absolute cross section analysis method, the radius systematic errors originating from the absolute cross section normalization factors were obviously reduced by the relative cross section analysis method. In particular, with the obtained matter density of the soft nucleus ${}^{30}\mathrm{Si}$, an impact of the dynamical correlations on the diffuse density distribution caused by the deformation mixing configurations was discussed. The theoretical calculations were performed within the framework of the particle-number and angular-momentum projected generator coordinate method (PNAMP + GCM) based on the deformed relativistic mean field plus the Bardeen-Cooper-Schrieffer (RMF + BCS) model.

Significant excesses of $e^{+}{e}^{-}$ pair production at very low transverse momentum $(p_T<0.15 \mathrm{GeV}/c)$ were observed by the STAR collaboration in hadronic heavy-ion collisions. Such enhancement is assumed to be a sign of photon-photon production in heavy-ion collisions with hadronic overlap, based on comparisons with model calculations for spherical Au $+$ Au collisions. However, there is a lack of calculations for $e^{+}{e}^{-}$ pair production from coherent photon-photon interactions in hadronic $\mathrm{U} + \mathrm{U}$ collisions, due to the deformity of uranium nuclei. In this article, we present calculations for $e^{+}{e}^{-}$ pair photoproduction at $\sqrt{s_{NN}}=193$ GeV in both spherical and deformed $\mathrm{U} + \mathrm{U}$ collisions within STAR detector acceptance using the equivalent photon approximation. We conduct event-by-event analysis to investigate the effects of initial nuclear deformation on pair production. Our numerical results show good agreement with experimental data for the 40%–60% and 60%–80% centrality classes in $\mathrm{U} + \mathrm{U}$ collisions, and the differences between spherical and deformed configurations are approximately 3%. We also calculate the yields of the photoproduced $e^{+}{e}^{-}$ pair in hadronic deformed $\mathrm{Ru} + \mathrm{Ru}$ and $\mathrm{Zr} + \mathrm{Zr}$ collisions at $\sqrt{s_{NN}}=200 \mathrm{GeV}$. The results reveal that the ratios of the yields of Ru to Zr exhibit very small differences $(<1\%)$ between spherical and deformed cases.

The properties of a nanosecond isomer in ${}^{32}\mathrm{Si}$, disputed in previous studies, depend on the evolution of proton and neutron shell gaps near the island of inversion. We have placed the isomer at 5505.2(2) keV with $J^{\pi }=5^{-}$, decaying primarily via an $E3$ transition to the $2_1^{+}$ state. The $E3$ strength of 0.0841(10) W.u. is unusually small and suggests that this isomer is dominated by the ${\left(\nu d_{3/2}\right)}^{-1}\otimes {\left(\nu f_{7/2}\right)}^1$ configuration, which is sensitive to the $N=20$ shell gap. A newly observed $4_1^{+}$ state is placed at 5881.4(13) keV; its energy is enhanced by the $Z=14$ subshell closure. This indicates that the isomer is located in a yrast trap, a feature rarely seen at low mass numbers.

Background: The existence of a tetraneutron comprising four neutrons has long been debated.

Purpose: Motivated by a recent observation of particle-stable tetraneutrons, we investigated potential particle-stable tetraneutron emission in thermal neutron-induced ${}^{235}\mathrm{U}$ fission using a nuclear research reactor.

Methods: We performed $\gamma$-ray spectroscopy for a ${}^{88}{\mathrm{SrCO}}_3$ sample irradiated in a reactor core. Stable ${}^{88}\mathrm{Sr}$ was expected to produce ${}^{91}\mathrm{Sr}$ by a tetraneutron-induced $({}^4\mathrm{n},n)$ reaction; hence, observation of $\gamma$ rays followed by $\beta$ decay of ${}^{91}\mathrm{Sr}$ would indicate particle-stable tetraneutron emission.

Results: The $\gamma$-ray spectrum of an irradiated ${}^{88}{\mathrm{SrCO}}_3$ sample did not show any photopeak for ${}^{91}\mathrm{Sr}$.

Conclusion: The emission rate of particle-stable tetraneutrons, if they exist, is estimated to be lower than $8\times {10}^{-7}$ per fission at the 95% confidence level, assuming the cross sections of reactions induced by hypothetical particle-stable tetraneutrons.

Background: Asymmetric fission is known to occur in two regions, the actinides and sublead, and is dependent on the fissioning system excitation energy. Experimental evidence in the sublead region show that this mode is surprisingly persistent with increasing energy and its origin is not fully understood.

Purpose: To experimentally study the fusion-fission reaction of ${}^{215}\mathrm{Fr}$ at moderate excitation energy and determine previously unknown independent fission yields and other properties.

Method: The compound nucleus was formed in the reaction ${}^{18}\mathrm{O}+{}^{197}\mathrm{Au}$. The prompt $\gamma$ rays emitted during the reaction were measured with the high efficiency and high granularity $\nu$-ball-2 spectrometer. Independent fission yields of even-even nuclei were determined by detecting triple-gamma cascades in the fission fragments.

Results: The observed yields, although dominated by a symmetric peak, show maxima for heavy fragment of $Z\approx 54–56$, which is consistent with the known results in the actinide region but unexpected for the nuclide of interest, and at the studied excitation energy.

Conclusions: The mode of asymmetric fission is present even at relatively high excitation energies in the system studied. This observation matches experimental findings in the sublead region, contrary to the actinides, and so far there is no well-developed explanation of this phenomenon.

We study the effect of the isovector-scalar meson $a_0$(980) on the properties of nuclear matter and the neutron star (NS) matter by constructing a parity doublet model with including the $a_0$ meson based on the chiral SU(2)${}_L\times {\text{SU}\left(2\right)}_R$ symmetry. We also include the $\omega -\rho$ mixing contribution to adjust the slope parameter at the saturation. We find that, when the chiral invariant mass of nucleon $m_0$ is smaller than about 800 MeV, the existence of $a_0$(980) enlarges the symmetry energy by strengthening the repulsive $\rho$ meson coupling. On the other hand, for large $m_0$ where the Yukawa coupling of $a_0$(980) to nucleon is small, the symmetry energy is reduced by the effect of $\omega -\rho$ mixing. We then construct the equation of state (EoS) of a neutron star matter to obtain the mass-radius relation of NS. We find that, in most choices of $m_0$, the existence of $a_0$(980) stiffens the EoS and makes the radius of NS larger. We then constrain the chiral invariant mass of nucleon from the observational data of NS, and find that $580\text{MeV}\lesssim m_0\lesssim 860\text{MeV}$ for $L_0=57.7$ MeV.

The uncertainty in the nuclear matrix elements (NMEs) of $0\nu \beta \beta$ decay for ${}^{76}\mathrm{Ge}$, ${}^{82}\mathrm{Se}$, ${}^{128}\mathrm{Te}$, ${}^{130}\mathrm{Te}$, and ${}^{136}\mathrm{Xe}$ in the self-consistent quasiparticle random phase approximation (QRPA) method is investigated by using eighteen Skyrme interactions supplemented with either a volume or surface type of pairing interactions. The NMEs for the isotopes concerned (except ${}^{136}\mathrm{Xe}$) are less sensitive to the particle-hole (ph) interactions, while they are strongly dependent on the employed isovector particle-particle (pp) pairing interactions even though the pairing strengths are optimized to the same pairing gap. The results indicate that a precise determination of the isovector pp pairing interaction in the Skyrme energy density functional is of importance to reduce the uncertainty in the NMEs within the QRPA framework.

The ${}^{20}\mathrm{Ne}{(p,\gamma )}^{21}\mathrm{Na}$ reaction is the slowest in the NeNa cycle and directly affects the abundances of the Ne and Na isotopes in a variety of astrophysical sites. Here we report the measurement of its direct capture contribution, for the first time below $E_{\mathrm{c}.\mathrm{m}.}=352$ keV, and of the contribution from the $E_{\mathrm{c}.\mathrm{m}.}=368$ keV resonance, which dominates the reaction rate at $T=0.03$–1.00 GK. The experiment was performed deep underground at the Laboratory for Underground Nuclear Astrophysics, using a high-intensity proton beam and a windowless neon gas target. Prompt $\gamma$ rays from the reaction were detected with two high-purity germanium detectors. We obtain a resonance strength $\omega \gamma =(0.112\pm 0.{002}_{\mathrm{stat}}\pm 0.{005}_{\mathrm{sys}})\mathrm{meV}$, with an uncertainty a factor of 3 smaller than previous values. Our revised reaction rate is 20% lower than previously adopted at $T<0.1$ GK and agrees with previous estimates at temperatures $T\ge 0.1$ GK. Initial astrophysical implications are presented.

Background: Precise understanding of nuclear fission is crucial for experimental and theoretical nuclear physics, astrophysics, and industrial applications; however, the complete physical mechanism is unresolved due to the complexities.

Purpose: In this study, we present a new method to describe the dynamical-fission process and following prompt-neutron emission, where we combine the dynamical fission calculation based on the Langevin method and the Hauser-Feshbach statistical model.

Methods: Two methods are connected smoothly within the universal charge distribution and the energy conservation, allowing us to calculate a sequence of fission dynamics and postfission phase, including prompt neutron emission.

Results: Using a certain set of model parameters, we successfully reproduce the experimental primary-fission yields, total kinetic energy, independent-fission yields, and prompt neutron emissions for the neutron-induced fission of ${}^{236}\mathrm{U}$, a compound nucleus of $n+{}^{235}\mathrm{U}$. We elucidate the physical mechanism of the characteristic features observed in previous experiments, such as shell properties. Additionally, we apply our calculation to two very neutron-rich uranium isotopes, i.e., ${}^{250}\mathrm{U}$ and ${}^{255}\mathrm{U}$, which are not experimentally confirmed but are important for r-process nucleosynthesis. Theoretical results indicate that ${}^{250}\mathrm{U}$ exhibits an asymmetric multiple-peak fission yield distribution, while the neutron-rich ${}^{255}\mathrm{U}$ has a single peak due to symmetric fission. Our method predicts postneutron emission fragments, where ${}^{250}\mathrm{U}$ shows a stronger neutron emissivity than ${}^{255}\mathrm{U}$.

Conclusions: Our framework is highly reproducible in the experiments and shows that the number of emitted neutrons after fission differs significantly in neutron-rich uranium fission depending on distributions of fission variables.

It is shown that the proton formation probabilities, extracted from experimental decay half-lives, can be well reproduced by a simple multilinear formula with only three parameters. The parameters obtained by considering the standard root mean square deviation and the mini-max criteria are very similar to each other. In addition, we applied Bayesian analysis to study the uncertainties of the parameters and the model predictions. In this way we explain the systematics of proton decay half-lives. The multilinearity of the model also provides a way to classify the relative hindrance of different proton decays. All the recent experimental data agree very well with the model prediction. Our Bayesian analysis suggests that those new data do help constrain the uncertainty of the model parameters.