The cross sections of the ${}^{59}\mathrm{Co}\left(d,p\right){}^{60m,g}\mathrm{Co},{}^{51}\mathrm{V}\left(d,p\right){}^{52}\mathrm{V}$, and ${}^{\mathrm{nat}}\mathrm{V}{\left(d,xn\right)}^{51}\mathrm{Cr}$ reactions were accurately measured at the Soreq Applied Research Accelerator Facility in the energy range 2.7–5.4 MeV. The obtained results together with other data, available in the same region of the nuclear chart, were used for verifying the theoretical models. The consistent theoretical model calculation successfully reproduces the experimental results.

Two-particle number and transverse momentum differential correlation functions are powerful tools for unveiling the detailed dynamics and particle production mechanisms involved in relativistic heavy-ion collisions. Measurements of transverse momentum correlators $P_2$ and $G_2$, in particular, provide added information not readily accessible with better known number correlation functions $R_2$. However, it is found that the $R_2$ and $G_2$ correlators are somewhat sensitive to the details of the experimental procedure used to measure them. They exhibit, in particular, a dependence on the collision centrality bin width, which may have a rather detrimental impact on their physical interpretation. A technique to correct these correlators for collision centrality bin-width averaging is presented. The technique is based on the hypothesis that the shape of single- and pair-probability densities vary slower with collision centrality than the corresponding integrated yields. The technique is tested with Pb-Pb simulations based on the HIJING and ultrarelativistic quantum molecular dynamics models and shown to enable a precision better than 1% for particles in the kinematic range $0.2\le p_{\mathrm{T}}\le 2.0$ GeV/$c$.

Experimental data on ${}^{96}\mathrm{Zr}$ indicate coexisting spherical and deformed structures with small mixing amplitudes. Although a possible geometrical description of such a shape coexistence is implied in the contemporary discussion, it does not exist yet for ${}^{96}\mathrm{Zr}$. The observed properties of the low-lying collective states of ${}^{96}\mathrm{Zr}$ based on the geometrical collective model are investigated. The quadrupole-collective Bohr Hamiltonian with the potential having two minima, spherical and deformed, is applied. Good agreement with the experimental data on the excitation energies, $B\left(E2\right)$, and $B\left(M1\right)$ reduced transition probabilities is obtained. It is shown that the low-energy structure of ${}^{96}\mathrm{Zr}$ can be described in a satisfactory way within the geometrical collective model with a potential function supporting shape coexistence without other restrictions of its shape. However, the excitation energy of the $2_2^{+}$ state can be reproduced only if the rotation inertia coefficient is taken to be 5 times smaller than the vibrational one in the region of the deformed well. It is shown also that shell effects are important for the description of $B(M1;2_2^{+}\to 2_1^{+})$. An indication of the influence of the pairing vibrational mode on the $0_2^{+}\to 0_1^{+}$ transition is obtained.

Spectroscopic properties of low-lying states and cluster structures in ${}^{12}\mathrm{C}$ are analyzed in a beyond mean-field framework based on global energy density functionals (EDFs). To build symmetry-conserving collective states, axially symmetric and reflection-asymmetric solutions of the relativistic Hartree-Bogoliubov equations are first projected onto good values of angular momentum, particle number, and parity. Configuration mixing is implemented using the generator coordinate method formalism. It is shown that such a global microscopic approach, based on a relativistic EDF, can account for the main spectroscopic features of ${}^{12}\mathrm{C}$, including the ground-state and linear-chain bands as well as, to a certain approximation, the excitation energy of the Hoyle state. The calculated form factors reproduce reasonably well the available experimental values, and display an accuracy comparable to that of dedicated microscopic cluster models.

We introduce a new relativistic energy density functional constrained by the ground state properties of atomic nuclei along with the isoscalar giant monopole resonance energy and dipole polarizability in ${}^{208}\mathrm{Pb}$. A unified framework of the relativistic Hartree-Bogoliubov model and random phase approximation based on the relativistic density-dependent point coupling interaction is established in order to determine the DD-PCX parametrization by ${\chi }^2$ minimization. This procedure is supplemented with the covariance analysis in order to estimate statistical uncertainties in the model parameters and observables. The effective interaction DD-PCX accurately describes the nuclear ground state properties including the neutron-skin thickness, as well as the isoscalar giant monopole resonance excitation energies and dipole polarizabilities. The implementation of the experimental data on nuclear excitations allows constraining the symmetry energy close to the saturation density, and the incompressibility of nuclear matter by using genuine observables on finite nuclei in the ${\chi }^2$ minimization protocol, rather than using pseudo-observables on the nuclear matter, or by relying on the ground state properties only, as it has been customary in the previous studies.

In a recent paper it has been shown that a number of rare-earth elements have a definite deviation from axial symmetry, with the triaxiality angle $\gamma \ge 8$ degrees and the ratios of the components of the inertia tensor in qualitative agreement with the irrotational model. Such results have been extracted from experimental data within the J-2 subspace, but scissors-mode resonances, which are most sensitive to the nuclear shape, were not included in the analysis. The irrotational and rigid inertia tensors have an opposite dependence on the triaxiality angle $\gamma$ and this affects in a striking way the fine structure of scissors-mode resonances.

Background: The computational resources needed to generate the ab initio solution of the nuclear many-body problem for increasing mass number and/or accuracy necessitates innovative developments to improve upon (i) the storage of many-body operators and (ii) the scaling of many-body methods used to evaluate nuclear observables. The storing and efficient handling of many-body operators with high particle ranks is currently one of the major bottlenecks limiting the applicability range of ab initio studies with respect to mass number and accuracy. Recently, the application of tensor decomposition techniques to many-body tensors has proven highly beneficial to reduce the computational cost of ab initio calculations in quantum chemistry and solid-state physics.

Purpose: The impact of applying state-of-the-art tensor factorization techniques to modern nuclear Hamiltonians derived from chiral effective field theory is investigated. Subsequently, the error induced by the tensor decomposition of the input Hamiltonian on ground-state energies of closed-shell nuclei calculated via second-order many-body perturbation theory is benchmarked.

Methods: The first proof-of-principles application of tensor-decomposition techniques to the nuclear Hamiltonian is performed. Two different tensor formats are investigated by systematically benchmarking the approximation error on matrix elements stored in various bases of interest. The analysis is achieved while including normal-ordered three-nucleon interactions that are nowadays used as input to the most advanced ab initio calculations in medium-mass nuclei. With the aid of the factorized Hamiltonian, the second-order perturbative correction to ground-state energies is decomposed and the scaling properties of the underlying tensor network are discussed.

Results: The employed tensor formats are found to lead to an efficient data compression of two-body matrix elements of the nuclear Hamiltonian. In particular, the sophisticated tensor hypercontraction scheme yields low tensor ranks with respect to both harmonic-oscillator and Hartree-Fock single-particle bases. It is found that the tensor rank depends on the two-body total angular momentum $J$ for which one performs the decomposition, which is itself directly related to the sparsity of the corresponding tensor. Furthermore, including normal-ordered two-body contributions originating from three-body interactions does not compromise the efficient data compression. Ultimately, the use of factorized matrix elements authorizes controlled approximations of the exact second-order ground-state energy corrections. In particular, a small enough error is obtained from low-rank factorizations in ${}^4\mathrm{He},{}^{16}\mathrm{O}$, and ${}^{40}\mathrm{Ca}$.

Conclusions: It is presently demonstrated that tensor-decomposition techniques can be efficiently applied to systematically approximate the nuclear many-body Hamiltonian in terms of lower-rank tensors. Beyond the input Hamiltonian, tensor-decomposition techniques can be envisioned to scale down the cost of state-of-the-art nonperturbative many-body methods in order to extend ab initio studies to (i) higher precisions, (ii) larger masses, and (iii) nuclei of doubly open-shell character.

An attempt has been made to provide crucial information about the dependence of incomplete-fusion dynamics on various entrance channel parameters below 8 MeV/nucleon energy. The forward recoil range distributions of several evaporation residues produced in the ${}^{13}\mathrm{C}+{}^{175}\mathrm{Lu}$ system have been measured at $\approx 88$-MeV energy and examined in the framework of the code SRIM. Owing to the fractional linear momentum transfer from the projectile to the target nucleus, incomplete-fusion (ICF) products are observed to be trapped at lower cumulative thickness than that of complete fusion products. In order to study the incomplete-fusion behavior with various entrance channel parameters, the incomplete-fusion fraction ($F_{\mathrm{ICF}}$) has also been deduced and compared with those obtained for the systems available in the literature. The reinvestigation of the Coulomb factor $\left(Z_P{Z}_T\right)$ dependence of incomplete fusion indicates that it is somehow projectile structure dependent. No systematic trend is observed with the target deformation parameter $\left({\beta }_2\right)$ dependent study of ICF. A systematic linear growth in the incomplete-fusion probability function ($F_{\mathrm{ICF}}$) is observed with increasing the parameters $Z_P{Z}_T{\beta }_2$ and $Z_P{Z}_T/(1-{\beta }_2)$, but separately for $\alpha$- and non-$\alpha$-cluster structured projectiles with different targets. The present findings explore the role of Coulomb interaction on ICF dynamics more effectively. Moreover, the projectile $\alpha -Q$ value is found to be a suitable parameter which explains effectively the observed trend in the study of ICF with the above-mentioned parameters. The incomplete-fusion existence below critical angular momentum (${\ell }_{\mathrm{crit}}$), i.e., $\ell \le {\ell }_{\mathrm{crit}}$, is also observed for the present ${}^{13}\mathrm{C}+{}^{175}\mathrm{Lu}$ system.

Symmetry energy behavior of scalar mesons interactions is analyzed within the framework of the standard relativistic mean-field model. Whereas the presence of the $\delta$ meson itself makes the symmetry energy stiffer, the crossing term $\delta \text{−}\sigma$ allows its slope to decrease to the suggested experimental value. Moreover, such controlling of the symmetry energy does not significantly affect the stiffness of the equation of state and acceptable neutron star masses result. Interestingly, for the most plausible value of the symmetry energy slope, the phase transition occurs in the neutron star core.

Effects of pairing with isospin $T=0$ and $T=1$ are systematically studied in a model, which is based on a realistic nucleon-nucleon interaction and allows us to describe the transition from infinite nuclear matter to finite nuclei. Special attention is paid to the development of the spin-orbit term in the mean field of nucleons in finite nuclei. The spin-orbit term yields a drastic suppression of $T=0$ proton-neutron pairing but does not lead to a complete disappearance in finite nuclei. Arguments are presented as to why no clear evidence of $T=0$ pairing can be observed in the binding energies of finite nuclei.

The properties of hyperheavy nuclei and the extension of nuclear landscape to hyperheavy nuclei are extensively studied within covariant density functional theory. Axial reflection symmetric and reflection asymmetric relativistic Hartree-Bogoliubov (RHB) calculations are carried out. The role of triaxiality is studied within triaxial RHB and triaxial relativistic mean field + BCS frameworks. With increasing proton number beyond $Z\approx 130$ the transition from ellipsoidal-like nuclear shapes to toroidal ones takes place. The description of latter shapes requires the basis which is typically significantly larger than the one employed for the description of ellipsoidal-like shapes. Many hyperheavy nuclei with toroidal shapes are expected to be unstable toward multifragmentation. However, three islands of stability of spherical hyperheavy nuclei have been predicted for the first time in Afanasjev et al. [Phys. Lett. B 782, 533 (2018)]. Proton and neutron densities, charge radii, neutron skins, and underlying shell structure of the nuclei located in the centers of these islands have been investigated in detail. Large neutron shell gaps at $N=228,308,$ and 406 define approximate centers of these islands in neutron number. On the contrary, large proton gap appear only at $Z=154$ in the $(Z\approx 156,N\approx 310)$ island. As a result, this is the largest island of stability of spherical hyperheavy nuclei found in the calculations. The calculations indicate the stability of the nuclei in these islands with respect to octupole and triaxial distortions. The shape evolution of toroidal shapes along the fission path and the stability of such shapes with respect to fission have been studied. Fission barriers in neutron-rich superheavy nuclei are studied in triaxial RHB framework; the impact of triaxiality on the heights of fission barriers is substantial in some parts of this region. Based on the results obtained in the present work, the extension of nuclear landscape to hyperheavy nuclei is provided.

For weakly bound quarkonia, we rederive the next-to-leading order cross sections of quarkonium dissociation by partons that include the hard thermal loop (HTL) resummation. Our results calculated with an effective vertex from the Bethe–Salpeter amplitude reduce to those obtained by potential nonrelativistic QCD (pNRQCD) in the relevant kinematical limit, and they can be used in a wide temperature range applicable to heavy-quark systems in heavy-ion collisions. Based on the lattice computation of the temperature-dependent binding energy, our numerical analysis on $\mathrm{{\rm Y}}\left(1S\right)$ indicates that at high temperature the dominant mechanism for quarkonium dissociation is inelastic parton scattering as expected in the quasifree approximation, while it is gluo-dissociation at low temperature. By comparing with the momentum diffusion coefficient of a heavy quark, we discuss possible $O\left(g\right)$ corrections to the next-to-leading-order thermal width.

Octupole deformation results in a strongly enhanced collective Schiff moment in ${}^{229}\mathrm{Th}$ nucleus. An additional enhancement of time-reversal (T) and parity- (P) violating effects (such as T,P-violating electric dipole moments) appears in the ground ${}^1\mathrm{\Sigma }$ state and in the metastable ${}^3\mathrm{\Delta }_1$ state of diatomic molecule ${}^{229}\mathrm{ThO}$. Similar enhancements exist in molecular ions ${}^{229}\mathrm{ThOH}^{+}$, ${}^{229}\mathrm{ThF}^{+}$, and ${}^{225,223}\mathrm{RaOH}^{+}$. Corresponding experiments may be used to test charge conjugation and parity (CP)-violation theories predicting T,P-violating nuclear forces and to search for axions.

Internal structure and macroscopic properties of neutron stars are strongly correlated with the equation of state (EOS) of dense matter, while the EOS remains exceedingly uncertain especially at high densities. The observed massive neutron star with gravitation mass of $\approx 2M_{\odot }$ have imposed strong constraints on the EOS of super-dense matter. The upper limit of the speed of sound, as a crucial quantity to characterize the stiffness of the EOS, has significant influence on the maximum mass of a neutron star. The main propose of this work is to probe the possible lower bound for the upper limit of the speed of sound, where being coincident with the observations for massive neutron stars is considered. By employing a set of heterogeneous EOSs and through a constructed EOS model to describe the high-density part of the employed EOSs, we conclude that the upper limit of the speed of sound can be as low as 0.5386 $c$ (where $c$ is the speed of light). Furthermore, to eliminate the effect of the model dependence for the EOSs, we adopt a set of parameterized and model-independent EOSs to investigate this problem. As a result, a lower bound 0.5749 $c$ of the upper limit of the speed of sound is obtained, which is very close to the free-quark-matter's speed of sound, $\frac{1}{\sqrt{3}}c$. In addition, we semiempirically analyze the characteristics of the profile of neutron star $M\text{−}R$ relations and find out that the profiles of $M\text{−}R$ relations mainly depend on the speed of sound of the central density of neutron star sequences in the mass range around $0.3\text{to}1M_{\odot }$. However, the $M\text{−}R$ profile also can be explained by the universal relation proposed by Lattimer et al. Astroph. J. 550, 426 (2001), where the case with extremely soft EOS in ${\rho }_0\text{to}2{\rho }_0$ should be excluded.

We study momentum distributions and short-range correlation probabilities in $A=2$ and $A=3$ systems. First, we show results with phenomenological and meson-theoretic two- and three-nucleon forces to verify consistency with previous similar studies. We then apply most recent high-quality chiral nucleon-nucleon potentials up to fifth order in the chiral expansion together with the leading chiral three-nucleon force. The focal points of our investigations are the model dependence of one- and two-body momentum distributions and the impact of three-body forces on them.

A decay spectroscopy experiment on proton-rich nuclei in the vicinity of the doubly magic ${}^{100}\mathrm{Sn}$ was carried out at RIKEN Nishina Center. More than 20 nuclei with $43\le Z\le 50$ and $N\le 51$, produced by fragmentation reactions were investigated via analyses of $\beta$-decay, $\beta p$-decay, and subsequent $\gamma$-ray data. Owing to higher statistics, the precision on the half-lives of many of the ground states and isomers was improved. $\beta$-decay endpoint energies of 11 states in 8 nuclei were measured for the first time, and the corresponding $Q_{\text{EC}}$ and excitation energies were generally consistent with various mass models. Many $\beta$-delayed proton emission branching ratios were measured either for the first time or with higher precision compared to literature values, and some of them differed by more than $2\sigma$. Many of the large discrepancies were associated with nuclei with long-lived isomeric states, highlighting large systematic uncertainties involved in these measurements. Twenty-five new $\gamma$ rays were observed, and ten new states are proposed with unambiguous excitation energies, spins, and parities. Most of the energies of the excited states were consistent within 300 keV or 20%, whichever was greater, compared to shell model predictions in the proton/neutron $(p_{1/2},g_{9/2})$ model space assuming a ${}^{76}\mathrm{Sr}$ core. A signature of a new $(1/2^{-})$ isomer in ${}^{97}\mathrm{Cd}$ with $T_{1/2}=0.73\left(7\right)$ s was found, in good agreement with shell model predictions.

With a half-life of 3.85(5) d, the fission product ${}^{127}\mathrm{Sb}$ is potentially useful for the characterization of fallout debris that would be collected for forensic analysis following a hypothetical nuclear event. The $\beta$ decay of ${}^{127}\mathrm{Sb}$ has many characteristic $\gamma$-ray lines, however, the majority of decay strength is concentrated in the three strongest lines near 686, 473, and 784 keV, based on low-precision spectroscopic measurements from decades ago. In a new measurement of ${}^{127}\mathrm{Sb}\beta$ decay, obtained from radiochemical separations of U photofission products, we show that the energies of the 686 and 784 lines are actually shifted lower by 0.8 and 1.1 keV, respectively. Such large discrepancies in the nuclear data inhibit accurate isotopic analyses and have important implications, for example, on the assessment of fission debris that might be collected in the days following a nuclear event. Therefore, a new evaluation of ${}^{127}\mathrm{Sb}\beta$ decay and appropriate revisions to the various nuclear databases are warranted. This paper reports a new set of $\gamma$-ray energies and relative intensities corresponding to ${}^{127}\mathrm{Sb}$ decay.

Background: In recent years, considerable interest has been focused on the study of the effect of neutron skin on the collective properties of vibrational nuclei. This can be best evidenced by exclusively determining neutron and proton transition matrix elements involved in a particular excitation by investigating the Coulomb-nuclear interference feature of inelastic scattering.

Purpose: Measurement of angular distributions of the inelastic scattering cross sections for excitations to low-lying $2_1^{+}$ and $3_1^{-}$ states in ${}^{112,116,118,120,122,124}\mathrm{Sn}$ using ${}^7\mathrm{Li}$ beam as probe at $E_{\mathrm{lab}}=28\mathrm{MeV}$ and determination of neutron and proton transition matrix elements involved in each excitation.

Methods: Projectilelike fragments were detected using six sets of Si-surface barrier detector telescopes to measure the cross sections for elastic and inelastic scattering channels. Optical model analysis of elastic scattering data, coupled reaction channels, and continuum discretized coupled channels calculations were performed to understand the measured differential cross sections. An attempt has been made to extract the microscopic mass and charge deformation lengths.

Results: For the $2_1^{+}$ state, experimental $B\left(E2\right)$ values are in good agreement with existing results obtained by electromagnetic methods. Charge and mass quadrupole vibrations are homogeneous. Significant differences are observed for excitation to the $3_1^{-}$ state across the Sn isotopic chain. Available structural information for collective octupole vibrations could not reproduce the present data for this excitation. Results show much lower values of octupole mass deformation parameters.

Conclusions: Isoscalar nature of surface vibrations for the $2_1^{+}$ state in Sn isotopes is verified, with $M_n/M_p\sim N/Z$. For the $3_1^{-}$ state, damped mass vibration is the primary observation. On comparison with existing estimates, a significant deviation from isoscalar nature is conjectured for this excitation, when probed with ${}^7\mathrm{Li}$.