In this paper we present the results of large-scale shell-model calculations of muon-to-electron lepton-flavor-violating transitions for the case of the target nucleus ${}^{27}\mathrm{Al}$. We extend the previous shell-model calculations, done in the $sd$ model space, by including also the $p$ orbitals in order to see whether the negative-parity states produce any significant effect in the conversion rate. The analysis of the results shows the dominance of coherent transitions mediated by isovector operators and going by the ground state of the target, with practically null influence of excited positive- or negative-parity states.

We examine the importance of conserving the vector current in calculating low-energy neutrino-nucleus interactions by implicitly invoking Siegert's theorem in describing the vector transverse electric current. We find that at low neutrino energies ($E_{\nu }<50$ MeV), Siegert's theorem can change neutrino cross sections for normal-parity non-spin-flip excitations by about a factor of two. The same is true of muon capture rates. At higher neutrino energies the effect of Siegert's theorem diminishes, and by about 100 MeV the effect is very small.

Rapid shape evolutions near $A=100$ are now the focus of much attention in nuclear science. Much of the recent work has been centered on isotopes with $Z\le 40$, where the shapes are observed to transition between near-spherical to highly deformed with only a single pair of neutrons added. At higher $Z$, the shape transitions become more gradual as triaxiality sets in, yet the coexistence of varying shapes continues to play an important role in the low-energy nuclear structure, particularly in the odd-$Z$ isotopes. This work aims to characterize competing shapes in the triaxial region between Zr and Sn isotopes using ultrafast timing techniques to measure lifetimes of excited states in the neutron-rich nucleus ${}^{109}\mathrm{Rh}$. The measurements confirm the persistence at higher $Z$ of similarly large deformations observed near $Z=40$. Moreover, we show that new self-consistent mean-field calculations, with proper treatment of the odd nucleon, are able to reproduce the coexisting triaxial and highly deformed configurations revealing, for the first time, the important contribution of the unpaired nucleon to these different shapes based on the blocking of specific single-particle orbitals.

We have made a thorough study of the low-energy behavior of the $\gamma$-ray strength function within the framework of the shell model. We have performed large-scale calculations spanning isotopic and isotonic chains over several mass regions, considering 283 nuclei in total, with the purpose of studying the systematic behavior of the low-energy enhancement (LEE) for $M1$ transitions. There are clear trends in the calculations: From being nearly absent in the lowest mass region, the LEE becomes steeper and more pronounced as the mass number increases, and for a given mass region it further increases toward shell closures. Moreover, the LEE is found to be steeper in regions near doubly magic nuclei where proton particles couple to neutron holes. These trends enable us to consolidate several previous works on the LEE into a single, consistent concept. We compare the inferred trends to the available experimental data from the Oslo method and find support for the systematic behavior. Lastly, we have compared the calculations to strength functions compiled from discrete, experimental lifetimes and find excellent agreement; the discrete data are consistent with an LEE and indicate that the slope varies as function of mass number.

Anomalous viscous fluid dynamics model calculations for ${}_{44}{}^{96}\mathrm{Ru}+{}_{44}{}^{96}\mathrm{Ru}$ and ${}_{40}{}^{96}\mathrm{Zr}+{}_{40}{}^{96}\mathrm{Zr}$ collisions ($\sqrt{s_{NN}}=200$ GeV) are used in concert with a charge-sensitive correlator to test its ability to detect and characterize the charge separation difference expected from the chiral magnetic effect (CME) in these isobaric collisions. The tests indicate a larger charge separation for ${}_{44}{}^{96}\mathrm{Ru}+{}_{44}{}^{96}\mathrm{Ru}$ than for ${}_{40}{}^{96}\mathrm{Zr}+{}_{40}{}^{96}\mathrm{Zr}$ collisions and a discernible CME-driven difference of $\sim 10\%$ in the presence of realistic non-CME backgrounds. They also indicate a strategy for evaluating the relative influence of the background correlations, present for each isobar. These results suggest that charge-separation measurements for these isobaric species could serve to further constrain unambiguous identification and characterization of the CME in upcoming measurements at the Relativistic Heavy Ion Collider.

The dipole strength distribution of ${}^{206}\mathrm{Pb}$ was investigated via a nuclear resonance fluorescence experiment using bremsstrahlung produced with an electron beam at a kinetic energy of 10.5 MeV at the linear accelerator ELBE. We identified 88 states resonantly excited at energies from 3.7 to 8.2 MeV. The analysis of the measured $\gamma$-ray spectra includes the quasicontinuum of levels at high energy. Monte Carlo simulation of $\gamma$-ray cascades were performed to obtain the intensities of inelastic transitions and branching ratios of the ground-state transitions. The extracted photoabsorption cross section shows enhanced dipole strength at the excitation energies around 5.5 and 7 MeV, which may related to a pygmy dipole resonance. The present $(\gamma ,\gamma \prime )$ data combined with $(\gamma ,n)$ data from the literature were used for confining input parameters of the statistical calculation code CCONE to derive the neutron-capture cross section of the unstable ${}^{205}\mathrm{Pb}$ nucleus.

Shape evolution of Zr nuclei are investigated by the axial Hartree-Fock (HF) calculations using the semirealistic interaction M3Y-P6, with focusing on roles of the tensor force. Deformation at $N\approx 40$ is reproduced, which has not been easy to describe within the self-consistent mean-field calculations. The spherical shape is obtained in $46\le N\le 56$, and the prolate deformation is predicted in $58\le N\le 72$, while the shape switches to oblate at $N=74$. The sphericity returns at $N=80$ and 82. The deformation in $60\lesssim N\lesssim 70$ resolves the discrepancy in the previous magic-number prediction based on the spherical mean-field calculations [Prog. Theor. Exp. Phys. 2014, 033D02 (2014)]. It is found that the deformation at $N\approx 40$ takes place owing to the tensor force with a good balance. The tensor-force effects significantly depend on the configurations, and are conspicuous when the unique-parity orbit (e.g., $n0h_{11/2}$) is present near the Fermi energy, delaying deformation. These effects are crucial for the magicity at $N=56$ and for the predicted shape change at $N=74$ and 80.

We propose a particle number conserving formalism for the treatment of isovector-isoscalar pairing in nuclei with $N>Z$. The ground state of the pairing Hamiltonian is described by a quartet condensate to which is appended a pair condensate formed by the neutrons in excess. The quartets are built by two isovector pairs coupled to the total isospin $T=0$ and two collective isoscalar proton-neutron pairs. To probe this ansatz for the ground state we performed calculations for $N>Z$ nuclei with the valence nucleons moving above the cores ${}^{16}\mathrm{O}$, ${}^{40}\mathrm{Ca}$, and ${}^{100}\mathrm{Sn}$. The calculations are done with two pairing interactions, one state-independent and the other of zero range, which are supposed to scatter pairs in time-reversed orbits. It is proven that the ground-state correlation energies calculated within this approach are very close to the exact results provided by the diagonalization of the pairing Hamiltonian. Based on this formalism we have shown that moving away from the $N=Z$ line, both the isoscalar and the isovector proton-neutron pairing correlations remain significant and that they cannot be treated accurately by models based on a proton-neutron pair condensate.

Background: The physics of fission and the features of the fission fragment yields—symmetric or asymmetric shapes for different atomic nuclei and their energies of excitation or temperatures $T$-are among the “popular puzzles” of nuclear physics. Explanation of these features requires understanding both the nature of the interaction between the nucleons and the thermodynamics of nuclear matter transformations. The new statistical method for investigation of the ordering of the postscission ensemble of fission fragments is also essential.

Purpose: The goal of this article is to demonstrate the possibility of a new type of phase transition in nuclear fission within the fixed temperature range when there is a change in the shape of fission fragment yields from asymmetric to symmetric. The temperature dependence of the thermodynamic functions indicates a Schottky-like phase transition, known from solid-state physics.

Methods: We used the proposed statistical method based on the study of thermodynamic ordering for a postscission ensemble of fission fragments. This method allows us to investigate the temperature evolution of the yields (both mass and charge) and the features of the change of the thermodynamic functions of the ensemble of the fragments of fission. The isotope ${}^{235}\mathrm{U}$ for which the data of the fission fragment yields are well known was chosen for the numerical investigations.

Results: We have found anomalies of the thermodynamic functions of the ensemble of fragments of fission of ${}^{235}\mathrm{U}$ in the temperature range when the shape of the yields of fragment fission changes from asymmetric to symmetric. In particular, the peaklike form of the heat capacity $C\left(T\right)$ indicates a Schottky-like phase transition. We also point out the experimental possibility of observing such a phase transition within the nuclear temperature range of 1–2 MeV.

Conclusions: This article shows that a new Schottky-like phase transition can be observed under nuclear fission. It differs from known phase-type transformations under nuclear fission, which have been intensively investigated lately and may be due to fundamental factors such as loss of statistical nonequivalence or the identity of nucleons in different fission fragments.

We demonstrate that the intricate energy spectrum of neutron-rich helium isotopes can be straightforwardly described by taking advantage of the low-energy properties of neutron-neutron interaction and the scale separation that is present in diluted drip-line systems. By using arguments based on the halo effective field theory, we carry out a parameter reduction of the complex-energy configuration interaction framework in the $spd$ space, including resonant and scattering states. By constraining the core potential to $\alpha \text{−}n$ scattering phase shifts and adjusting the strength of the spin-singlet central neutron-neutron interaction, we reproduce experimental energies and widths of ${}^{5–8}\mathrm{He}$ within tens of keV precision. We predict a parity inversion of narrow resonances in ${}^9\mathrm{He}$ and show that the ground state of ${}^{10}\mathrm{He}$ is an $s$-wave-dominated configuration that could decay through two-neutron emission. This threshold state can be viewed as a “double-halo” structure in an analogy to the atomic ${}^3\mathrm{He}{}^4{\mathrm{He}}_2$ trimer.

Using an energy density functional (EDF) based on the thermodynamic Gibbs-Duhem relation, found equivalent to the standard Skyrme EDF for infinite nuclear matter, it is demonstrated that the parameters of this EDF are not uniquely determined from the fit of the empirical and theoretical data related to nuclear matter. This prevents an unambiguous determination of the nucleon effective mass $\left(\frac{m_0^{*}}{m}\right)$ and its isovector splitting $\left(\mathrm{\Delta }{m}_0^{*}\right)$. Complementary information from dipole polarizability of atomic nuclei helps in removing this ambiguity and plausible values of $\frac{m_0^{*}}{m}$ and $\mathrm{\Delta }{m}_0^{*}$ can be arrived at. Presently considered fit data on infinite nuclear matter and dipole polarizability of finite nuclei yield $\frac{m_0^{*}}{m}=0.68\pm 0.04$ and $\mathrm{\Delta }{m}_0^{*}=(-0.20\pm 0.09)\delta$. This EDF is consistent with the constraint on the maximum mass of the neutron star.

Using a covariant quark coalescence model combined with a blast-wave-like analytical parametrization for (anti-)strange-quark phase-space freeze-out configuration, we extract information on strange-quark freeze-out dynamics in $\text{Pb}+\text{Pb}$ collisions at $\sqrt{s_{NN}}=2.76$ TeV by fitting the measured transverse momentum spectra and elliptic flows ($v_2$) of $\varphi$ mesons and $\mathrm{\Omega }$ baryons. We find that, although both the measured and calculated $v_2$ of $\varphi$ and $\mathrm{\Omega }$ satisfy the number-of-constituent-quark (NCQ) scaling, the NCQ-scaled $v_2$ is significantly smaller than the $v_2$ of strange quarks, implying that the NCQ-scaled $v_2$ of $\varphi$ and $\mathrm{\Omega }$ cannot be simply identified as the $v_2$ of strange quarks at hadronization. Meanwhile, our results indicate that the covariant quark coalescence model can nicely describe the spectra and elliptic flows of $\varphi$ and $\mathrm{\Omega }$ simultaneously, suggesting the coalescence mechanism is still valid for $\varphi$ and $\mathrm{\Omega }$ production in $\text{Pb}+\text{Pb}$ collisions at energies typical of the CERN Large Hadron Collider.

The main goal of this work is the determination of spins and parities of excited states in ${}^{97}\mathrm{Zr}$, among others the 2264.3-keV level, which had previously been tentatively reported as the $11/2^{-}$ excitation corresponding to the $h_{11/2}$ neutron orbital. Low-spin excited states in ${}^{97}\mathrm{Zr}$ were populated via the cold-neutron capture reaction. The $\gamma$ rays emitted following the reaction were measured using the highly efficient array of high-purity germanium detectors, EXILL, at the Institut-Laue-Langevin (ILL), Grenoble. The primary $\gamma$ rays deexciting the capture state in ${}^{97}\mathrm{Zr}$ were identified for the first time. The new, precise neutron binding energy in ${}^{97}\mathrm{Zr}$ of 5569.15(4) keV differs significantly from the value reported in the literature. The previously reported level scheme has been amended by several new low-spin levels. The ($n,\gamma$) data were complemented by a measurement of the ${\beta }^{-}$ decay of ${}^{97}\mathrm{Y}$ at the Lohengrin fission-fragment separator of the ILL, and the observation of the ${\beta }^{-}$ decay of ${}^{97}\mathrm{Y}$ populated in neutron-induced fission of ${}^{235}\mathrm{U}$ and measured using the EXILL Ge array. The combined data allowed unique spin-parity assignments for many levels in ${}^{97}\mathrm{Zr}$. The 2264.3-keV level, with a new spin-parity assignment of $9/2^{+}$, may correspond to the $\nu g_{9/2}$ extruder orbital.

In this paper, we study charged-current deep-inelastic scattering of muon neutrinos off ${}^{56}\mathrm{Fe}$ nuclei by using the Hirai, Kumano, and Saito model. The LHA parton distribution functions (PDFs) - CT10 are used to describe the partonic content of hadrons. Modification of PDFs inside the nuclei is done by using EPPS16 parametrization at next-to-leading order. Target mass correction has also been incorporated in the calculations. We calculate the structure functions $[F_2(x,Q^2)$ and $x{F}_3(x,Q^2)]$, the ratios $[R_2(x,Q^2)=F_2^{{}^{56}\mathrm{Fe}}/F_2^{\text{Nucleon}}$ and $R_3(x,Q^2)=F_3^{{}^{56}\mathrm{Fe}}/F_3^{\text{Nucleon}}]$, and the differential cross sections of ${\nu }_{\mu }$ deep-inelastic scattering off nucleons and ${}^{56}\mathrm{Fe}$ nuclei. We compare the results obtained with measured experimental data. The present theoretical approach gives a good description of data.

The Coulomb excitation of the neutron-rich nucleus ${}^{70}\mathrm{Ni}$ was measured in inverse kinematics at $260A\mathrm{MeV}$ bombarding energy and with a ${}^{197}\mathrm{Au}$ target. The beam energy allowed us to study the dipole response around the neutron separation energy (up to about 12 MeV). The experiment was performed at the RIKEN Radioactive Isotope Beam Factory (RIBF). The $\gamma$ decay from the scattered ${}^{70}\mathrm{Ni}$ ions at around zero degree was measured with a scintillator detection system composed of large volume ${\mathrm{LaBr}}_3$:Ce detectors (${\mathrm{HECTOR}}^{+}$ array) and NaI(Tl) detectors (DALI2 array). Results were obtained for the $E1$ strength in the region where the dipole response is characterized by the presence of the pygmy dipole resonance. The measured $E1$ strength is found to be larger as compared with that of ${}^{68}\mathrm{Ni}$ below the neutron binding energy. The measured $E1$ strength as a function of energy is compared with available predictions based on relativistic and nonrelativistic approaches, and only in some cases does theory give a reasonable account of the data.

Inspired by the newly discovered isomeric states in the rare-earth neutron-rich nuclei, high-$K$ isomeric states in neutron-rich samarium and gadolinium isotopes are investigated within the framework of the cranked shell model (CSM) with pairing correlation treated by a particle-number-conserving (PNC) method. The experimental multiparticle state energies and moments of inertia are reproduced quite well by the PNC-CSM calculations. A remarkable effect from the high-order deformation ${\varepsilon }_6$ is demonstrated. Based on the occupation probabilities, the configurations are assigned to the observed high-$K$ isomeric states. The lower $5^{-}$ isomeric state in ${}^{158}\mathrm{Sm}$ is preferred as the two-proton state with configuration $\pi {\frac{5}{2}}^{+}\left[413\right]\otimes \pi {\frac{5}{2}}^{-}\left[532\right]$. More low-lying two-particle states are predicted. The systematics of the electric quadrupole transition probabilities $B\left(E2\right)$ among the neodymium, samarium, gadolinium, and dysprosium isotopes and $N=96,98,100,102$ isotones is investigated to reveal the midshell collectivities.

Background: The tensor interaction is known to play an important role in the nuclear structure studies of exotic nuclei. However, most microscopic studies of low-energy nuclear reactions neglect the tensor force, resulting in a lack of knowledge concerning the effect of the tensor force on heavy-ion collisions. An accurate description of the heavy-ion interaction potential is crucial for understanding the microscopic mechanisms of heavy-ion fusion dynamics. Furthermore, the building blocks of the heavy-ion interaction potential in terms of the ingredients of the effective nucleon-nucleon interaction provides the physical underpinnings for connecting the theoretical results with experiment. The tensor force has never been incorporated for calculating the nucleus-nucleus interaction potential.

Purpose: The theoretical study of the influence of the tensor force on heavy-ion interaction potentials is required to further our understanding of the microscopic mechanisms entailed in fusion dynamics.

Method: The full Skyrme tensor force is implemented into the static Hartree-Fock and dynamic density-constrained time-dependent Hartree-Fock (DC-TDHF) theory to calculate both static (frozen density) and dynamic microscopic interaction potentials for reactions involving exotic and stable nuclei.

Results: The static potentials are found to be systematically higher than the dynamical results, which are attributed to the microscopic dynamical effects included in TDHF. We also show that the dynamical potential barriers vary more significantly by the inclusion of tensor force than the static barriers. The influence of isoscalar and isovector tensor terms is also investigated with the $\mathrm{T}IJ$ set of forces. For light systems, the tensor force is found to have an imperceptible effect on the nucleus-nucleus potential. However, for medium and heavy spin-unsaturated reactions, the potentials may change from a fraction of an MeV to almost 2 MeV by the inclusion of tensor force, indicating a strong impact of the tensor force on subbarrier fusion.

Conclusions: The tensor force could indeed play a large role in the fusion of nuclei, with spin-unsaturated systems seeing a systematic increase in ion-ion barrier height and width. This fusion hindrance is partly due to static, ground-state effects from the inclusion of the tensor force, though additional hindrance appears when studying nuclear dynamics.

We construct parameter sets of the relativistic mean-field model fitted to the recent constraints on the asymmetry energy $J$ and the slope parameter $L$ for pure neutron matter. We find cases of unphysical behavior, i.e., the appearance of negative pressures, for stiff parameter sets with low values of the effective mass $m^{*}/m$. In some cases the equation of state of pure neutron matter turns out to be outside the allowed band given by chiral effective field theory. The mass-radius relations of neutron stars for all acceptable parameter sets shows a maximum mass in excess of $2M_{\odot }$ being compatible with pulsar mass measurements. Given the constraints on the model in the low-density regime coming from chiral effective theory, we find that the radius of a $1.4M_{\odot }$ neutron star is nearly independent of the value of $L$. This is in contrast to some previous claims for a strong connection of the slope parameter with the radius of a neutron star. In fact, the mass-radius relation turns out to depend only on the isoscalar parameters of symmetric matter. The constraints of GW170817 on the tidal deformability and on the radius are also discussed.

We have studied nuclear matter with a new M3Y-type effective nucleon-nucleon interaction based on the lowest order constrained variational approach (LOCV) as the principal investigating tool. The chosen interaction, called B3Y-Fetal, has been used in its DDM3Y1, BDM3Y0, BDM3Y1, BDM3Y2, and BDM3Y3 density-dependent versions to reproduce the saturation properties of cold nuclear matter at the saturation density, $\rho =0.17{\mathrm{fm}}^{-3}$. Such properties as the binding energy per nucleon, also called the equation of state (EOS), and the incompressibility of symmetric nuclear matter have been computed, with results proving to be acceptably in agreement with previous work done with the M3Y-Paris and M3Y-Reid interactions by other researchers. Insightful information on symmetric nuclear matter obtained from the folding analysis in this work has shown it to be possibly governed by a soft EOS.