The nuclei ${}^{151}\mathrm{Sm}$ and ${}^{171}\mathrm{Tm}$ have been identified as attractive candidates for the detection of the cosmic neutrino background. Both isotopes undergo first-forbidden nonunique beta decays, which inhibits a prediction of their spectral shape using symmetries alone, and this has, so far, obstructed a definitive prediction of their neutrino capture cross sections. In this work we point out that for both elements the so-called $\xi$ approximation is applicable and this effectively limits the spectral shape to a deviation of at most $1\%$ from the one that would arise if beta decays were of the allowed type. Using measured half-lives we extract the relevant nuclear matrix element and predict the neutrino capture cross sections for both isotopes at the $1\%$ level, accounting for a number of relevant effects including radiative corrections and the finite size of the nuclei. We obtained $(1.12\pm 0.01)\times {10}^{-46}{\mathrm{cm}}^2$ for ${}^{171}\mathrm{Tm}$ and $(4.77\pm 0.01)\times {10}^{-48}{\mathrm{cm}}^2$ for ${}^{151}\mathrm{Sm}$. This method is robust as it does not rely on the data points near the endpoint of the beta spectrum, which may be contaminated by atomic physics effects, namely shakeup and shakeoff. Finally, we calculate the target mass which is necessary for cosmic neutrino discovery and discuss several bottlenecks and respective solutions associated to the experimental program. We conclude that the detection of cosmic neutrino background by neutrino capture on ${}^{151}\mathrm{Sm}$ and ${}^{171}\mathrm{Tm}$ is achievable and free from theoretical limitations but still subject to technical issues that should be further investigated by the experimentalists in the context of the proposed PTOLEMY project.

We study a family of equations of state (EOS) for hybrid neutron star matter. The hybrid EOS are obtained by a Maxwell construction of the first-order phase transition between a hadronic phase described by the relativistic density-functional EOS of the “DD2” class with excluded volume effects and a deconfined quark matter phase modeled by an instantaneous nonlocal version of the Nambu–Jona-Lasinio model in $\text{SU}{\left(2\right)}_f$ with vector interactions and color superconductivity. The form factor in the nonlocal quark matter model is fitted to lattice QCD results in the Coulomb gauge. Owing to strong coupling in the vector meson and diquark channels, a coexistence phase of color superconductivity and chiral symmetry breaking occurs. Our results show an approximately constant behavior for the squared speed of sound with values of 0.4–0.6 in the density region relevant for neutron star interiors. To simultaneously fulfill the constraints from the Neutron Star Interior Composition Explorer radius measurement for PSR $\mathrm{J}0740+6620$ and tidal deformability from GW170817 it is necessary to consider a $\mu$-dependent bag pressure that mimics confinement.

Background: The cluster radioactivity from the neutron-deficient trans-tin region of the nuclear landscape has given immediate attention in the nuclear structure studies. Recent prediction of the emitting clusters from the ground and intrinsic excited states of proton-rich Ba isotopes opens the direction to explore the corresponding decay characteristics. A theoretical probe is necessary for understanding the cluster decays of Ba isotopes.

Purpose: In the present study, cluster-decay half-lives are calculated and their decay characteristics are investigated for even-even ${}^{112–122}\mathrm{Ba}$ isotopes in both ground and intrinsic excited states along the proton drip line.

Method: The preformed-cluster-decay model (PCM) is employed for estimating the decay half-lives. The preformation probability $\left(P_0\right)$ of the cluster decay from the parent nuclei is calculated by using the well-known phenomenological formula of Blendowske and Walliser [Phys. Rev. Lett. 61, 1930 (1988)], supplemented with the newly proposed $Q$-value-based preformation factor for the cluster with mass $A_c>28$. The penetration probability is calculated from the interaction potential using the Wentzel-Kramers-Brillouin (WKB) approximation. The nucleon-nucleon ($NN$) potential and individual binding energy (BE) of the cluster and daughter nuclei are estimated from the microscopic relativistic mean-field formalism (RMF) and compared with those from experiments and the finite-range-droplet model for the estimation of the $Q$ values of the cluster decays. The nonlinear RMF Lagrangian from which the effective relativistic R3Y $NN$ potential is derived using the $\mathrm{NL}{3}^{*}$ parameter set is employed for the calculation of the nuclear matter densities. The R3Y and well-known M3Y potential are employed to obtain the cluster-daughter interaction potential using the double-folding procedure along with their corresponding RMF densities. The total potential along with their respective cluster decay $Q$ values are used as input in the PCM to obtain the half-lives ($T_{1/2}$) of ${}^{112–122}\mathrm{Ba}$ isotopes in their ground and intrinsic excited states.

Results: The calculated half-lives ($T_{1/2}$) for relativistic R3Y $NN$ potential and $Q$ values are found to deviate slightly compared to the ones from the M3Y due to the difference in their barrier characteristics. We notice that at elongated neck configuration a minimum neck-length parameter $\mathrm{\Delta }R=1.0\text{fm}$ is required for R3Y potential due to its repulsive nature, whereas the value is $0.5\text{fm}$ is suitable for the M3Y case. However, the estimated decay half-lives for both the potentials are in reasonably good agreement with the experimental lower limit of ${}^{114}\mathrm{Ba}$. In contrast with the ground-state decays, the inclusion of intrinsic excitation reduces the corresponding half-life values considerably but does not rule out the role of magicity.

Conclusions: The sensitivity of the decay half-lives to $Q$ values and neck-length parameter has also been demonstrated. The decay half-lives are predicted for various cluster decays from neutron-deficient Ba isotopes. Since none of the experimental half-lives for the examined clusters is precisely known yet, further studies with available observed half-lives will be needed to substantiate our findings.

The formation of deuterons in heavy-ion collisions at relativistic energies is investigated by employing two recently advanced models—the minimum spanning tree (MST) method and the coalescence model—by embedding them in the parton-hadron quantum molecular dynamics (PHQMD) and the ultrarelativistic quantum molecular dynamics (UrQMD) transport approaches. While the coalescence mechanism combines nucleons into deuterons at the kinetic freeze-out hypersurface, the MST identifies the clusters during the different stages of time evolution. We find that both clustering procedures give very similar results for the deuteron observables in the UrQMD as well as in the PHQMD environment. Moreover, the results agree well with the experimental data on deuteron production in Pb$+$Pb collisions at $\sqrt{s_{NN}}=8.8$ GeV (selected for the comparison of the methods and models in this study). A detailed investigation shows that the coordinate space distribution of the produced deuterons differs from that of the free nucleons and other hadrons. Thus, deuterons are not destroyed by additional rescattering.

In this work, we assess the importance of nonequilibrium dynamics in the production of photons from the late stages of relativistic heavy-ion collisions. The $p_{\mathrm{T}}$-differential spectra and $v_2$ of photons from the late hadronic stage are computed within a nonequilibrium hadron transport approach, and compared to the results of a local equilibrium evolution using ideal relativistic hydrodynamics. It is found that nonequilibrium dynamics enhance the late-stage photon production at low $p_{\mathrm{T}}$ and decreases it at higher $p_{\mathrm{T}}$ compared to the estimate from hydrodynamics. This same comparison points to a significant increase in the momentum anisotropies of these photons due to nonequilibrium dynamics. Once combined with photons produced above the particlization temperature in the hydrodynamics evolution, the differences between the two approaches appear modest for the $p_{\mathrm{T}}$ differential spectra, but are clearly noticeable at low $p_{\mathrm{T}}$ for the elliptic flow: nonequilibrium dynamics enhance the photon $v_2$ below $p_{\mathrm{T}} \approx 1.4$ GeV.

The thermodynamic properties of a system of interacting boson particles and antiparticles at finite temperatures are studied within the framework of the thermodynamically consistent Skyrme-like mean-field model. The mean field contains both attractive and repulsive terms. Self-consistency relations between the mean field and thermodynamic functions are derived. We assume a conservation of the isospin density for all temperatures. It is shown that, independently of the strength of the attractive mean field, at the critical temperature $T_{\mathrm{c}}$ the system undergoes the phase transition of second order to the Bose-Einstein condensate, which exists in the temperature interval $0\le T\le T_{\mathrm{c}}$. We obtained that the condensation represents a discontinuity of the derivative of the heat capacity at $T=T_{\mathrm{c}}$, and condensate occurs only for the component with a higher particle-number density in the particle-antiparticle system.

Understanding the explosion mechanism of a core-collapse supernova (CCSN) is important to accurately model CCSN scenarios for different progenitor stars using model-observation comparisons. The uncertainties of various nuclear reaction rates relevant for CCSN scenarios strongly affect the accuracy of these stellar models. Out of these reactions, the ${}^{13}\mathrm{N}(\alpha ,p){}^{16}\mathrm{O}$ reaction has been found to affect various stages of a CCSN at varying temperatures. This work presents the first direct measurement of the ${}^{13}\mathrm{N}(\alpha ,p){}^{16}\mathrm{O}$ reaction performed using a 34.6 MeV beam of radioactive ${}^{13}\mathrm{N}$ ions and the active-target detector MUSIC (MUlti-Sampling Ionization Chamber) at Argonne National Laboratory. The resulting total ${}^{13}\mathrm{N}(\alpha ,p){}^{16}\mathrm{O}$ reaction cross sections from this measurement in the center-of-mass energy range of 3.26–6.02 MeV are presented and compared with calculations using the Hauser-Feshbach formalism. Uncertainties in the reaction rate have been dramatically reduced at CCSN temperatures.

We study the energy spectra of $\mathrm{\Xi }$ hypernuclei ${}_{\mathrm{\Xi }}{}^{15}\mathrm{C}$ and ${}_{\mathrm{\Xi }}{}^{12}\mathrm{Be}$ with a relativistic mean field (RMF) model with meson exchange $\mathrm{\Xi }N$ interactions. The RMF parameters are optimized to reproduce the average energy of KINKA and IRRAWADDY events for the ground state and also the average energy of KISO and IBUKI events for the excited state in ${}_{\mathrm{\Xi }}{}^{15}\mathrm{C}$. The potential depth of the average $\mathrm{\Xi }N$ mean field potential is found to be about $-12$ MeV in the nuclear matter limit. We further introduce the two-body $s$- and $p$-wave interactions between valence nucleons and $\mathrm{\Xi }$ particle. We found that the $s$-wave interaction deduced from the HAL lattice QCD results is rather weak to obtain the energy difference between IRRAWADDY and KINKA events. The $p$-wave interaction is added and fitted to reproduce the energy difference. The resulting interaction together with the $s$-wave one gives a reasonable energy simultaneously for IBUKI event as an excited ${\mathrm{\Xi }}_p$ state. The model is further applied to predict the energy spectrum of ${}_{\mathrm{\Xi }}{}^{12}\mathrm{Be}$.

Structure of the neutron-rich $N=86$ isotope ${}^{140}\mathrm{Xe}$, located northeast of a doubly-magic nucleus ${}^{132}\mathrm{Sn}$, is investigated by $\beta \text{−}\gamma$ spectroscopy. Two $\beta$-decay isomers in ${}^{140}\mathrm{I}$ are newly found in the study of two different $\beta$ decays of ${}^{140}\mathrm{I}$ which were produced by two reactions (i) direct in-flight fission at a primary target and (ii) $\beta$ decay of ${}^{140}\mathrm{Te}$ at an active stopper. Half-lives of the $\beta$ decays of the ground state, the low-spin isomer, and the high-spin isomer are determined to be 0.38(2), 0.91(5), and 0.47(4) s, respectively. Decay schemes of the $\beta$ decay of the high-spin isomer and of the mixed $\beta$ decays of the ground state and the low-spin isomer in ${}^{140}\mathrm{I}$ to ${}^{140}\mathrm{Xe}$ are constructed using the information on $\gamma$-ray coincidence relation and $\gamma$-ray intensity. Nuclear structures of the low-lying states in ${}^{140}\mathrm{Xe}$ and ${}^{140}\mathrm{I}$ are discussed by comparing the experimental results to two theoretical calculations based on a large-scale shell model and the deformed Skyrme Hartree-Fock-Bogoliubov plus deformed quasiparticle-random-phase approximation. Possible candidates for (quasi-)$\gamma$-band members of $2^{+}$ and $4^{+}$ states and the octupole collective $1^{-}$ state are proposed in ${}^{140}\mathrm{Xe}$. Increase of quadrupole, triaxial, and octupole collectivities is discussed with the increase of neutron and proton numbers.

The Skyrme energy density formalism is applied to address the capture cross sections of ${}_{112}{}^{286}\mathrm{Cn}^{*}$, ${}_{114}{}^{292}\mathrm{Fl}^{*}$, and ${}_{116}{}^{296}\mathrm{Lv}^{*}$ superheavy nuclei formed in ${}^{48}\mathrm{Ca}+{}^{238}\mathrm{U},{}^{244}\mathrm{Pu},{}^{248}\mathrm{Cm}$ reactions. The dynamics of ${}^{48}\mathrm{Ca}$-induced reactions is investigated by including GSkI and SSk forces for the hot-optimum configurations of decay fragments. The neutron evaporation $(3n \mathrm{and} 4n)$, compound nucleus fission (CN fission) and quasifission (QF) cross sections are calculated with the application of both forces, but the GSkI force seems to be appropriate only for the neutron evaporation channels. However, by including SSk force various decay processes can be handled by including the only parameter of the model, called the neck length parameter $\left(\mathrm{\Delta }R\right)$. The fragment mass distribution of $Z=112$–116 nuclei shows considerable modifications in the fission, symmetric quasifission $\left({\mathrm{QF}}_{\mathrm{sym}.}\right)$ and asymmetric quasifission $\left({\mathrm{QF}}_{\mathrm{asym}.}\right)$ regions with the inclusion of the SSk force as compared to analysis based on the density independent potentials. In addition to this, the role of ${\beta }_2$ deformations and magic shell effects (around the Pb isotope) is scrutinized through the fragmentation behavior and preformation probability of ${}_{112}{}^{286}\mathrm{Cn}^{*}$, ${}_{114}{}^{292}\mathrm{Fl}^{*}$, and ${}_{116}{}^{296}\mathrm{Lv}^{*}$ nuclei. Finally, the distribution of the average total kinetic energy of fragments is calculated with the density dependent SSk force and compared with experimental data and earlier work based on the proximity potential.

We develop a “hybrid” model of the proton inelastic structure functions applicable in a wide region of invariant mass of produced states $W$ and invariant momentum transfer $Q$ including deep inelastic scattering (DIS), nucleon resonance production, as well as the region close to inelastic threshold. DIS is described in terms of the parton distributions together with higher-twist corrections from an available global QCD fit. The resonant part is addressed in terms of the Breit-Wiegner contributions from five states including the $\mathrm{\Delta }\left(1232\right)$ resonance, the $N\left(1440\right)$ Roper resonance, and three effective resonances describing the second and third resonance regions. The couplings of the nucleon resonances to photon are described in terms of helicity amplitudes. The nonresonant background is addressed in terms of DIS structure functions smoothly extrapolated to low-$W$ and low-$Q$ values with the proper behavior at the real photon limit $Q^2=0$ as well as near the inelastic threshold. We independently treat the transverse $F_T$ and the longitudinal $F_L$ structure function and fix the model parameters from a global analysis of the world hydrogen electroproduction and photoproduction cross-section data. We demonstrate a very good performance of the model by comparing our predictions with data on differential cross sections and the structure functions $F_2$ and $R=F_L/F_T$.

Background: In the solid crust of neutron stars, a variety of crystalline structures may exist. Recently the band theory of solids was applied to the inner crust of neutron stars, and the significance of the entrainment between dripped neutrons and the solid crust was advocated. Since it influences interpretations of various phenomena of neutron stars, it is desirable to develop deeper understanding of the underlying microphysics.

Purpose: The purpose of the present article is to propose a fully self-consistent microscopic framework for describing time-dependent dynamics of neutron star matter, which allows us to explore diverse properties of nuclear matter, including the entrainment effect.

Methods: A fully self-consistent nuclear band theory is employed with the Skyrme SLy4 energy density functional. A time-dependent extension of the microscopic band theory is developed based on the time-dependent density functional theory (TDDFT). An intuitive real-time method is proposed for extracting the collective mass of a nuclear cluster immersed in a sea of dripped neutrons, taking into account the band structure effects.

Results: As the first application of the time-dependent self-consistent band theory for nuclear systems, we investigate the slab phase of nuclear matter with various proton fractions. From a dynamic response of the system to an external force, we extract the collective mass of a slab, associated with entrained neutrons (due to the Bragg scattering of dripped neutrons off the periodic potential) as well as bound nucleons. We find that the extracted collective mass is smaller than a naive estimation based on a potential profile and single-particle energies. We show that the reduction is mainly caused by “counterflow” of dripped neutrons towards the direction opposite to the motion of the slabs. We interpret it as an “anti-entrainment” effect. As a result, the number of effectively bound neutrons is reduced, indicating an enhancement of the number density of conduction neutrons. We demonstrate that those findings are consistent with a static treatment in the band theory of solids.

Conclusions: The proposed approach offers a new research possibility of investigating nonlinear many-body dynamics of nuclear matter microscopically, taking full account of the periodic structure in neutron star crusts. The fully self-consistent band theory calculations, in both static and dynamic formalisms, suggest that the mobility of dripped neutrons is larger than expected without band structure effects, at least for the slab phase of nuclear matter.

Searches for neutrinoless double-$\beta$ decay rates are crucial in addressing questions within fundamental symmetries and neutrino physics. The rates of these decays depend not only on unknown parameters associated with neutrinos, but also on nuclear properties. In order to reliably extract information about the neutrino, one needs an accurate treatment of the complex many-body dynamics of the nucleus. Neutrinoless double-$\beta$ decays take place at momentum transfers on the order of $100\mathrm{MeV}/c$ and require both nuclear electroweak vector and axial current matrix elements. Muon capture, a process in the same momentum transfer regime, has readily available experimental data to validate these currents. In this Letter, we present results of ab initio calculations of partial muon capture rates for ${}^3\mathrm{He}$ and ${}^6\mathrm{Li}$ nuclei using variational and Green's function Monte Carlo computational methods. We estimate the impact of the three-nucleon interactions, the cutoffs used to regularize two-nucleon $(2N)$ interactions, and the energy range of $2N$ scattering data used to fit these interactions.

States in ${}^{28}\mathrm{S}$ and ${}^{30}\mathrm{Cl}$ have been studied using one- and two-proton decay spectroscopies. In the first spectrometer setting, states in ${}^{28}\mathrm{S}$ were populated following one-neutron knockout from a fast ${}^{29}\mathrm{S}$ beam. Three new states are observed in ${}^{28}\mathrm{S}$ from one- and two-proton decays. For the two-proton case the nature of the decay was investigated and found to proceed via sequential two-proton emission. For the second setting, states in ${}^{30}\mathrm{Cl}$ were populated via one-proton knockout from a fast ${}^{31}\mathrm{Ar}$ beam. The decay energy of the ground and first excited state were measured with the ground-state decay energy found to be in disagreement with a previous measurement. The spin and parity of these two ${}^{30}\mathrm{Cl}$ states were inferred from shell-model calculations.

The fine structure of the scissors mode is investigated within the time dependent Hartree-Fock-Bogoliubov (TDHFB) approach. The solution of TDHFB equations by the Wigner function moments (WFM) method predicts a splitting of the scissors mode into three intermingled branches. Together with the conventional scissors mode two new modes arise due to spin degrees of freedom. They generate significant $M1$ strength below the conventional energy range. The results of calculations of scissors resonances in rare earths and actinides by WFM and quasiparticle-phonon nuclear model methods are compared with experimental data. A remarkable coherence of both methods together with experimental data is observed.

The mean spin polarization vector of spin 1/2 particles in a relativistic fluid at local thermal equilibrium (LTE) in different pseudogauges (PGs), i.e., with different choices for the decomposition of orbital and spin angular momentum, is obtained. The spin polarization obtained in the canonical PG differs from the one obtained in the Belinfante PG. It is found that this difference can not be written by replacing the thermal vorticity with the spin potential in the usual polarization formula. Other PG choices affect the contribution of thermal shear to the spin polarization. Therefore, the choice of a PG affects the predictions for the polarization measured in heavy-ion collisions. In general, it is shown that the Wigner function of a noninteracting Dirac field at LTE is affected by the PG transformations. Explicit expressions of the mean axial current are also calculated and it is found that even the axial vortical effect conductivity depends on the PG.

Background: The ${}^{30}\mathrm{P}(p,\gamma ){}^{31}\mathrm{S}$ reaction rate is one of the largest remaining sources of uncertainty in the final abundances of nuclei created in a classical nova involving a ONe white dwarf. The reaction rate directly influences silicon isotopic ratios, which are used as identifiers of presolar grains with nova origins. In addition, the uncertainty in the ${}^{30}\mathrm{P}(p,\gamma ){}^{31}\mathrm{S}$ reaction rate has been found to limit the use of nova nuclear thermometers based on observations of elemental ratios in nova ejecta.

Purpose: Reduce uncertainties in the nuclear data for proton-unbound states in ${}^{31}\mathrm{S}$, which act as resonances for the ${}^{30}\mathrm{P}(p,\gamma ){}^{31}\mathrm{S}$ reaction at classical nova temperatures, and develop a technique for high efficiency, high-resolution reaction-decay coincidence measurements.

Methods: The ${}^{32}\mathrm{S}(p,d){}^{31}\mathrm{S}$ reaction was used to populate the states of interest in ${}^{31}\mathrm{S}$. The experiment was performed at the Texas A&M Cyclotron Institute using the LLNL Hyperion array for the detection of charged particles and $\gamma$ rays. A downstream silicon telescope was used to select reaction deuterons, and a single upstream silicon detector was used to measure protons emitted in the decay of unbound ${}^{31}\mathrm{S}$ levels.

Results: Several states in ${}^{31}\mathrm{S}$ above the proton separation energy were observed to have been populated. Decay protons from the resonant states in ${}^{31}\mathrm{S}$ were identified as events in the upstream silicon detectors that came in coincidence with deuterons in the downstream telescope. Protons emitted from these states were measured and branching ratios extracted.

Conclusions: While no new reaction rate is derived, spin-parity assignments for several higher-lying proton unbound states have been confirmed. Measured $p_0$ branching ratios for these levels have been compared to previous measurements with good agreement, and in some cases provided a reduction in uncertainty. The previously identified $T=3/2$ state may have been incorrectly assigned a large $p_0$ branching ratio in a previous measurement. The technique of measuring reaction-decay coincidences with a particle-gamma setup appears promising.