The spin-polarized ferromagnetic state of a cold Fermi gas is investigated for interacting and noninteracting charge-neutral and $\beta$-equilibrated gases. The standard minimal couplings between the magnetic field and the fermions' charges and magnetic dipole moments define the fermions' interaction with the magnetic field. Assuming a variable coupling strength between the magnetic field and the fermion (baryon) dipole moments, it is shown that a ferromagnetized state can be achieved that corresponds to a lower energy spin-polarized state with a magnetic field entirely due to the gas's magnetic response. We find that, depending on the density, a very large increase in the baryon dipole moments is needed to achieve this ferromagnetized state. While the required increase seems unlikely, the induced magnetic field is of the order $\approx {10}^{17}$ gauss. Furthermore, while externally magnetized Fermi gases have an anisotropic pressure, the pressure of the ferromagnetized gas is completely isotropic and in the thermodynamically preferred magnetized state.

A feed-forward neural network model is trained to calculate the nuclear charge radii. The model is trained with the input data set of proton and neutron number $Z,N$, the electric quadrupole transition strength $B\left(E2\right)$ from the first excited $2^{+}$ state to the ground state, together with the symmetry energy. The model reproduces well not only the isotope dependence of charge radii, but also the kinks of charge radii at the neutron magic numbers $N=82$ for Sn and Sm isotopes, and also $N=126$ for Pb isotopes. The important role of the $B\left(E2\right)$ value is pointed out to reproduce the kink of the isotope dependence of charge radii in these nuclei. Moreover, with the inclusion of the symmetry energy term in the inputs, the charge radii of Ca isotopes are well reproduced. This result suggests a new correlation between the symmetry energy and charge radii of Ca isotopes. The Skyrme Hartree-Fock-Bogoliubov calculation is performed to confirm the existence of this correlation in a microscopic model.

Since its inception, the so-called surrogate-reaction method (SRM) has motivated the development and improvement of theories in connection to direct reactions. This paper reassesses some of the developments carried out in previous decades to deal with the representation of direct reaction probability data. It is believed that the experimental probabilities assimilation in the neutron cross section evaluation process can be better estimated using tools resulting from the efforts made over the years. This paper provides a new perspective on this issue both in terms of fission and $\gamma$-ray emission probabilities. In addition to the “natural” assimilation path that considers analyzing probabilities jointly with cross sections to extract nuclei structural properties, this article puts forward a prescription to convert, with a good level of confidence, measured direct-reaction induced probabilities to pseudoexperimental neutron-induced cross sections. This approach is named after the SRM as extended SRM (ESRM).

The measurements of the (anti)deuteron elliptic flow ($v_2$) and the first measurements of triangular flow ($v_3$) in Pb-Pb collisions at a center-of-mass energy per nucleon-nucleon collision $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV are presented. A mass ordering at low transverse momentum ($p_{\mathrm{T}}$) is observed when comparing these measurements with those of other identified hadrons, as expected from relativistic hydrodynamics. The measured (anti)deuteron $v_2$ lies between the predictions from the simple coalescence and blast-wave models, which provide a good description of the data only for more peripheral and for more central collisions, respectively. The mass number scaling, which is violated for $v_2$, is approximately valid for the (anti)deuterons $v_3$. The measured $v_2$ and $v_3$ are also compared with the predictions from a coalescence approach with phase-space distributions of nucleons generated by iebe-vishnu with ampt initial conditions coupled with urqmd, and from a dynamical model based on relativistic hydrodynamics coupled to the hadronic afterburner smash. The model predictions are consistent with the data within the uncertainties in midcentral collisions, while a deviation is observed in the most central collisions.

We study the fermionic Matsubara Green functions in medium-mass nuclei at finite temperature. The single-fermion Dyson equation with the dynamical kernel of the particle-vibration-coupling (PVC) origin is formulated and solved in the basis of Dirac spinors, which minimize the grand canonical potential with the meson-nucleon covariant energy density functional. The PVC correlations beyond mean field are taken into account in the leading approximation for the energy-dependent self-energy, and the full solution of the finite-temperature Dyson equation is obtained for the fermionic propagators. Within this approach, we investigate the fragmentation of the single-particle states and its evolution with temperature for the nuclear systems ${}^{56,68}\mathrm{Ni}$ and ${}^{56}\mathrm{Fe}$ relevant for the core-collapse supernova. The energy-dependent, or dynamical, nucleon effective mass is extracted from the PVC self-energy at various temperatures.

Lifetimes of low- and high-spin states in the odd-$A$ nucleus ${}^{177}\mathrm{Hf}$ were measured during the EXILL&FATIMA campaign using a spectrometer equipped with eight HPGe-Clover detectors and 16 fast-timing ${\mathrm{LaBr}}_3\left(\mathrm{Ce}\right)$ detectors. For the determination of lifetimes in the pico- to nanosecond regime, the well-established generalized centroid difference method was used. Lifetimes of the $9/2^{-}$, $9/2^{+}$, $11/2^{-}$, $11/2^{+}$ states were remeasured, the lifetimes of the $13/2^{-}$, $17/2^{-}$, $13/2^{+}$, $15/2^{+}$, and $17/2^{+}$ states were determined for the first time and an upper limit for the $19/2^{+}$ state has been established. From these lifetimes absolute reduced transition probabilities were extracted and compared to particle-rotor-model calculations and quasiparticle-phonon-model calculations showing the importance of including multipole-multipole interactions in the description of odd-$A$ nuclei in the rare earth region.

Employing the covariant baryon chiral perturbation theory, we calculate the leading and next-to-leading order two-pion exchange (TPE) contributions to $NN$ interaction up to order $O\left(p^3\right)$. We compare the so-obtained $NN$ phase shifts with $2\le L\le 6$ and mixing angles with $2\le J\le 6$ with those obtained in the nonrelativistic baryon chiral perturbation theory, which allows us to check the relativistic corrections to the medium-range part of $NN$ interactions. We show that the contributions of relativistic TPE are more moderate than those of the nonrelativistic TPE. The relativistic corrections play an important role in $F$ waves especially the ${}^3{F}_2$ partial wave. Moreover, the relativistic results seem to converge faster than the nonrelativistic results in almost all the partial waves studied in the present work, consistent with the studies performed in the one-baryon sector.

The production of strange particles ${\mathrm{\Xi }}_c^{+},K^{-}$ is simulated in $pp$ collisions at $\sqrt{s}=7$ TeV at mid-rapidity with $0.2\le p_T\le 6$ $\mathrm{GeV}/c$ using the paciae model. The results are consistent with LHCb experimental data on ${\mathrm{\Xi }}_c^{+}$ and $K^{-}$ yield. Then, a dynamically constrained phase-space coalescence model plus paciae model was used to produce the ${\mathrm{\Xi }}_c^{+}{K}^{-}$ bound states and study the narrow excited ${\mathrm{\Omega }}_c^0$ states through ${\mathrm{\Omega }}_c^0\to {\mathrm{\Xi }}_c^{+}{K}^{-}$ in $pp$ collisions at $\sqrt{s}=7$ and 13 TeV. The yield, transverse momentum distribution, and rapidity distribution of the five new excited ${\mathrm{\Omega }}_c^0$ states of ${\mathrm{\Omega }}_c{\left(3000\right)}^0$, ${\mathrm{\Omega }}_c{\left(3050\right)}^0$, ${\mathrm{\Omega }}_c{\left(3066\right)}^0$, ${\mathrm{\Omega }}_c{\left(3090\right)}^0$, and ${\mathrm{\Omega }}_c{\left(3119\right)}^0$ were predicted.

Background: The variational Hartree-Fock-Bogoliubov (HFB) mean-field theory is the starting point of various (ab initio) many-body methods dedicated to superfluid systems. In this context, pairing correlations may be driven towards zero either on purpose via HFB calculations constrained on, e.g., the particle-number variance or simply because internucleon interactions cannot sustain pairing correlations in the first place in, e.g., closed-shell systems. While taking this limit constitutes a text-book problem when the system is of closed-shell character, it is typically, although wrongly, thought to be ill-defined whenever the naive filling of single-particle levels corresponds to an open-shell system.

Purpose: The present work demonstrates that the zero-pairing limit of an HFB state is well-defined independently of the average particle number $\mathrm{A}$ it is constrained to. Still, the nature of the limit state is shown to depend on the regime, i.e., on whether the nucleus characterizes as a closed-shell or an open-shell system when taking the limit. Finally, the consequences of the zero-pairing limit on Bogoliubov many-body perturbation theory (BMBPT) calculations performed on top of the HFB reference state are illustrated.

Methods: The zero-pairing limit of a HFB state constrained to carry an arbitrary (integer) number of particles $\mathrm{A}$ on average is worked out analytically and realized numerically using a two-nucleon interaction derived within the frame of chiral effective field theory.

Results: The zero-pairing limit of the HFB state is mathematically well-defined, independently of the closed- or open-shell character of the system in the limit. Still, the nature of the limit state strongly depends on the underlying shell structure and on the associated naive filling reached in the zero-pairing limit for the particle number $\mathrm{A}$ of interest. First, the textbook situation is recovered for closed-shell systems, i.e., the limit state is reached for a finite value of the pairing strength (the well-known BardeenCooperSchrieffer (BCS) collapse) and takes the form of a single Slater determinant displaying (i) zero pairing energy, (ii) nondegenerate elementary excitations, and (iii) zero particle-number variance. Contrarily, a nonstandard situation is obtained for open-shell systems, i.e., the limit state is only reached for a zero value of the pairing interaction (no BCS collapse) and takes the form of a specific finite linear combination of Slater determinants displaying (a) a nonzero pairing energy, (b) degenerate elementary excitations, and (c) a nonzero particle-number variance for which an analytical formula is derived. This nonzero particle-number variance acts as a lower bound that depends in a specific way on the number of valence nucleons and on the degeneracy of the valence shell. All these findings are confirmed and illustrated numerically. Last but not least, BMBPT calculations of closed-shell (open-shell) nuclei are shown to be well-defined (ill-defined) in the zero-pairing limit.

Conclusions: While HFB theory has been intensively scrutinized formally and numerically over the last decades, it still uncovers unknown and somewhat unexpected features. In the present paper, the zero-pairing limit of a HFB state carrying an arbitrary number of particles has been worked out and shown to lead to drastic differences and consequences depending on the closed-shell or open-shell nature of the system in that limit. From a general perspective, the present analysis demonstrates that HFB theory does not reduce to HF theory when the pairing field is driven to zero in the HFB Hamiltonian matrix.

Hanbury Brown–Twiss interferometry (HBT) provides crucial insights into both the space-time structure and the momentum-space evolution of ultrarelativistic nuclear collisions at freeze-out. In particular, the dependence of the HBT radii on the transverse pair momentum $K_T$ and the system charged multiplicity $d{N}_{\mathrm{ch}}/d\eta$ may reflect the mechanisms driving collective behavior in small systems. This paper argues that certain features observed in the multiplicity dependence of the HBT radii can be naturally understood if small systems evolve hydrodynamically at high multiplicity. This study thus establishes a baseline for the multiplicity dependence of HBT in hydrodynamics which may prove useful in discriminating between competing models of collectivity in nuclear collisions.

Background: In the “island of inversion,” ground states of neutron-rich $sd$-shell nuclei exhibit strong admixtures of intruder configurations from the $fp$ shell. The nucleus ${}^{30}\mathrm{Mg}$, located at the boundary of the island of inversion, serves as a cornerstone to track the structural evolution as one approaches this region.

Purpose: Spin-parity assignments for excited states in ${}^{30}\mathrm{Mg}$, especially negative-parity levels, have yet to be established. In the present work, the nuclear structure of ${}^{30}\mathrm{Mg}$ was investigated by in-beam $\gamma$-ray spectroscopy mainly focusing on firm spin-parity determinations.

Method: High-intensity rare-isotope beams of ${}^{31}\mathrm{Mg}$, ${}^{32}\mathrm{Mg}$, ${}^{34}\mathrm{Si}$, and ${}^{35}\mathrm{P}$ bombarded a Be target to induce nucleon removal reactions populating states in ${}^{30}\mathrm{Mg}$. $\gamma$ rays were detected by the state-of-the-art $\gamma$-ray tracking array GRETINA. For the direct one-neutron removal reaction, final-state exclusive cross sections and parallel momentum distributions were deduced. Multinucleon removal reactions from different projectiles were exploited to gain complementary information.

Results: With the aid of the parallel momentum distributions, an updated level scheme with revised spin-parity assignments was constructed. Spectroscopic factors associated with each state were also deduced.

Conclusions: Results were confronted with large-scale shell-model calculations using two different effective interactions, showing excellent agreement with the present level scheme. However, a marked difference in the spectroscopic factors indicates that the full delineation of the transition into the island of inversion remains a challenge for theoretical models.

We report on an isomer yield ratio study of biologically important ${}^{94}\mathrm{Tc}$ following the fusion of the ${}^9\mathrm{Be}+{}^{89}\mathrm{Y}$ system, carried out using the offline $\gamma$-ray spectroscopy in continuation to the online activation method. The incident beam energies considered are above the Coulomb barrier for the present paper. The platypus model in conjunction with a potential model calculation was employed to analyze the data. An agreement in the order of magnitude between the experimental data and the theoretical predictions has been achieved by applying a phenomenological approach. The approach was further tested with isomer yield ratios of ${}^{94}\mathrm{Tc}$ formed through ${}^3\mathrm{He}+{}^{93}\mathrm{Nb}$ reactions. Possible factors that relate to the isomer yield ratios are also presented.

The ${\beta }^{-}$ decay of ${}^{47}\mathrm{K}$ to ${}^{47}\mathrm{Ca}$ is an appropriate mechanism for benchmarking interactions spanning the $sd$ and $pf$ shells, but current knowledge of the ${\beta }^{-}$-decay scheme is limited. We have performed a high-resolution, high-efficiency study of the ${\beta }^{-}$ decay of ${}^{47}\mathrm{K}$ with the GRIFFIN spectrometer at TRIUMF-ISAC. The study revealed 48 new transitions, a more precise value for the ${}^{47}\mathrm{K}$ half-life [17.38(3) s], and new spin and parity assignments for 8 excited states. Levels placed for the first time here raise the highest state observed in ${\beta }^{-}$ decay to within 568(3) keV of the $Q$ value and confirm the previously measured large ${\beta }^{-}$-decay branching ratios to the low-lying states. Previously unobserved ${\beta }^{-}$ feeding to $3/2^{+}$ states between 4.5 and 6.1 MeV excitation energy was identified with a total ${\beta }^{-}$-feeding intensity of 1.29(2)%. The sum of the $B\left(GT\right)$ values for these states indicates that the $1s_{1/2}$ proton hole strength near this excitation energy is comparable to the previously known $1s_{1/2}$ proton and neutron hole strengths near 2.6 MeV.

We perform statistically rigorous uncertainty quantification (UQ) for chiral effective field theory ($\chi \mathrm{EFT}$) applied to infinite nuclear matter up to twice nuclear saturation density. The equation of state (EOS) is based on high-order many-body perturbation theory calculations with nucleon-nucleon and three-nucleon interactions up to fourth order in the $\chi \mathrm{EFT}$ expansion. From these calculations our newly developed Bayesian machine-learning approach extracts the size and smoothness properties of the correlated EFT truncation error. We then propose a novel extension that uses multitask machine learning to reveal correlations between the EOS at different proton fractions. The inferred in-medium $\chi \mathrm{EFT}$ breakdown scale in pure neutron matter and symmetric nuclear matter is consistent with that from free-space nucleon-nucleon scattering. These significant advances allow us to provide posterior distributions for the nuclear saturation point and propagate theoretical uncertainties to derived quantities: the pressure and incompressibility of symmetric nuclear matter, the nuclear symmetry energy, and its derivative. Our results, which are validated by statistical diagnostics, demonstrate that an understanding of truncation-error correlations between different densities and different observables is crucial for reliable UQ. The methods developed here are publicly available as annotated Jupyter notebooks.

The neutron-rich ${}^{130–134}\mathrm{Te}$ isotopes are investigated by large-scale shell-model calculations with the extended pairing plus multipole-multipole force (EPQQM model). The orbits of $(0g_{7/2},1d_{5/2},1d_{3/2},2s_{1/2},0h_{11/2})$ are included for both proton and neutron model space, while two more neutron orbits $(1f_{7/2},2p_{3/2})$ above the $N=82$ shell gap are included to study neutron-core excitations. The higher core-excited states in ${}^{132,133}\mathrm{Te}$ are calculated for the first time in this region. The present work well describes both the low-lying and the high-energy states for ${}^{134}\mathrm{Te}$, ${}^{133}\mathrm{Te}$, and ${}^{132}\mathrm{Te}$, as well as the low-lying levels of ${}^{131}\mathrm{Te}$ and ${}^{130}\mathrm{Te}$. The several multiplets with clear boundary exist in ${}^{134,133}\mathrm{Te}$, while a new configuration lying between 4.8 and 6.0 MeV is found as a theoretical prediction in ${}^{134}\mathrm{Te}$. Finally, the transition probabilities in these nuclei are calculated and compared with available data. The predicted energy levels and electromagnetic transition will be useful for planning future experiments.

A microscopic method for calculating nuclear level density (NLD) is developed, based on the framework of energy density functionals. Intrinsic level densities are computed from single-quasiparticle spectra obtained in a finite-temperature self-consistent mean-field (SCMF) calculation that takes into account nuclear deformation, and is specified by the choice of the energy density functional (EDF) and pairing interaction. The total level density is calculated by convoluting the intrinsic density with the corresponding collective level density, determined by the eigenstates of a five-dimensional quadrupole or quadrupole plus octupole collective Hamiltonian. The parameters of the Hamiltonian (inertia parameters, collective potential) are consistently determined by deformation-constrained SCMF calculations using the same EDF and pairing interaction. The model is applied in the calculation of NLDs of ${}^{94,96,98}\mathrm{Mo}$, ${}^{106,108}\mathrm{Pd}$, ${}^{106,112}\mathrm{Cd}$, ${}^{160,162,164}\mathrm{Dy}$, ${}^{166}\mathrm{Er}$, and ${}^{170,172}\mathrm{Yb}$, in comparison with available data. It is shown that the collective enhancement of the intrinsic level density, consistently computed from the eigenstates of the corresponding collective Hamiltonian, leads to total NLDs that are in very good agreement with data over the entire energy range of measured values.

$\alpha$-clustered structures in light nuclei could be studied through “snapshots” taken by relativistic heavy-ion collisions. A multiphase transport model is employed to simulate the initial structure of collision nuclei and the proceeding collisions at center of mass energy $\sqrt{s_{NN}}=6.37$ TeV. This initial structure can finally be reflected in the subsequent observations, such as elliptic flow ($v_2$), triangular flow ($v_3$), and quadrangular flow ($v_4$). Three sets of the collision systems are chosen to illustrate that the system scan is a good way to identify the exotic $\alpha$-clustered nuclear structure: case I, ${}^{16}\mathrm{O}$ nucleus (with or without $\alpha$-cluster) $+$ ordinary nuclei (always in Woods-Saxon distribution) in most central collisions; case II, ${}^{16}\mathrm{O}$ nucleus (with or without $\alpha$-cluster) $+$ ${}^{197}\mathrm{Au}$ nucleus collisions for centrality dependence; and case III, symmetric collision systems [namely, ${}^{10}\mathrm{B}$ $+$ ${}^{10}\mathrm{B}$, ${}^{12}\mathrm{C}$ $+$ ${}^{12}\mathrm{C}$, ${}^{16}\mathrm{O}$ $+$ ${}^{16}\mathrm{O}$ (with or without $\alpha$-cluster), ${}^{20}\mathrm{Ne}$ $+$ ${}^{20}\mathrm{Ne}$, and ${}^{40}\mathrm{Ca}$ $+$ ${}^{40}\mathrm{Ca}]$ in most central collisions. Our calculations propose that relativistic heavy-ion collision experiments at $\sqrt{s_{NN}}=6.37$ TeV are promised to distinguish the tetrahedral structure of ${}^{16}\mathrm{O}$ from the Woods-Saxon one and shed light on the system scan projects in experiments.

The observation of long range ridge-like structure in the near-side region of the two particle $\mathrm{\Delta }\eta -\mathrm{\Delta }\varphi$ correlations as measured by CERN Large Hadron Collider experiments in high multiplicity $p\text{−}p$ collisions indicated towards the presence of collective effects which are similar to that observed in $p\text{−}A$(nucleon-nucleus) and $A\text{−}A$ (nucleus-nucleus) collisions. The two particle correlation between the charged particles in $\mathrm{\Delta }\eta -\mathrm{\Delta }\varphi$ for $p\text{−}p$ collisions at $\sqrt{s}=7$ TeV and 13 TeV is studied using the pythia 8 event generator within the framework of final-state partonic color reconnection effects as well as the microscopic rope hadronization model. The rope hadronization relies on the formation of ropes due to overlapping of strings in high multiplicity events followed by string shoving. A near side ridge-like structure which is qualitatively similar to the observed ridge in data was observed for high-multiplicity events when the mechanism of rope hadronization (with shoving) was enabled.

The astrophysical ${}^6\mathrm{Li}(p,\gamma ){}^7\mathrm{Be}$ reaction occurs during Big Bang nucleosynthesis and the pre-main sequence and main sequence phases of stellar evolution. The low-energy trend of its cross section remains uncertain, since different measurements have provided conflicting results. A recent experiment reported a resonancelike structure at center-of-mass energy 195 keV, associated to a positive-parity state of ${}^7\mathrm{Be}$. The existence of such resonance is still a matter of debate. We report a new measurement of the ${}^6\mathrm{Li}(p,\gamma ){}^7\mathrm{Be}$ cross section performed at the Laboratory for Underground Nuclear Astrophysics, covering the center-of-mass energy range $E=60$–350 keV. Our results rule out the existence of low-energy resonances. The astrophysical $S$-factor varies smoothly with energy, in agreement with theoretical models.

We propose a method to incorporate the coupling between shape and pairing collective degrees of freedom in the framework of the interacting boson model (IBM), based on the nuclear density functional theory. To account for pairing vibrations, a boson-number nonconserving IBM Hamiltonian is introduced. The Hamiltonian is constructed by using solutions of self-consistent mean-field calculations based on a universal energy density functional and pairing force, with constraints on the axially symmetric quadrupole and pairing intrinsic deformations. By mapping the resulting quadrupole-pairing potential energy surface onto the expectation value of the bosonic Hamiltonian in the boson condensate state, the strength parameters of the boson Hamiltonian are determined. An illustrative calculation is performed for ${}^{122}\mathrm{Xe}$, and the method is further explored in a more systematic study of rare-earth $N=92$ isotones. The inclusion of the dynamical pairing degree of freedom significantly lowers the energies of bands based on excited $0^{+}$ states. The results are in quantitative agreement with spectroscopic data, and are consistent with those obtained using the collective Hamiltonian approach.