Excited states of the neutron-rich niobium isotopes ${}_{\phantom{96,97,98,}41}{}^{96,97,98,99}\mathrm{Nb}$ have been populated in two experiments which used fusion-fission and multinucleon binary grazing reactions to populate high-spin yrast states. In the multinucleon-transfer experiment, a 530-MeV beam of ${}^{96}\mathrm{Zr}$ ions was incident on a thin ${}^{124}\mathrm{Sn}$ target; projectile-like ejectiles were detected and identified using the PRISMA magnetic spectrometer and the associated $\gamma$ rays were detected using the CLARA array of Ge detectors. In the second experiment, the GASP array of escape-suppressed Ge detectors was used to detect $\gamma$ rays from fusion-fission products formed following the interaction of a 230-MeV beam of ${}^{36}\mathrm{S}$ ions with a thick target of ${}^{176}\mathrm{Yb}$. Level schemes of ${}^{96,97,99}\mathrm{Nb}$ were established up to excitation energies of 4545, 5409, and 3814 keV, respectively; states with proposed spin values up to about 15 $\hslash$ were populated. Gamma-ray photopeaks corresponding to transitions in ${}^{98}\mathrm{Nb}$ were also observed in the PRISMA-CLARA experiment; however, it was not possible, in this case, to produce a level scheme based on $\gamma$-ray coincidence data from the GASP experiment. For ${}^{96}\mathrm{Nb}$ and ${}^{97}\mathrm{Nb}$, the level schemes are in agreement with the results of earlier publications. Two new decay sequences have been populated in ${}^{99}\mathrm{Nb}$; tentative $J^{\pi }$ values of the hitherto unobserved states have been assigned through comparisons with $J^{\pi }$ values of neighboring nuclei. In contrast with earlier published studies of the high-spin spectroscopy of ${}^{96}\mathrm{Nb}$ and ${}^{97}\mathrm{Nb}$, the present work provides an unambiguous association of the observed $\gamma$ rays with the $A$ and $Z$ of the excited nucleus. The structure of the yrast states of ${}^{96,97,99}\mathrm{Nb}$ is discussed within the context of shell-model calculations. The experimental results, supported by model calculations, indicate the first observation of shape coexistence at low spin and low excitation energy in the $N=58$ nucleus ${}^{99}\mathrm{Nb}$. The results of TRS calculations indicate that the $9/2^{+}$ ground state is triaxial, tending to oblate shapes with a transition to a more deformed prolate shape beyond the $17/2^{+}$ member of the decay sequence; here the sequence has been observed to ($29/2^{+}$). On the other hand, the previously unobserved decay sequence based on the $5/2^{-}$ state at 631 keV exhibits the characteristics of a rotational sequence and has been assigned Nilsson quantum numbers $5/2^{-}\left[303\right]$. TRS calculations indicate that the $5/2^{-}\left[303\right]$ band is gamma soft and this is consistent with the inability of the particle-rotor model to reproduce the observed behavior of the signature-splitting function.

Background: Microscopic determination of alpha-decay half-lives requires structure and reaction calculations. The structure part is given by the microscopic distribution of the constituent nucleons, while the relative motion of the product's decay provides the reaction part.

Purpose: This paper studies the clusterization of the $0^{+}$ excited states of ${}^{44}\mathrm{Ti}$ arising from the nucleonic degrees of freedom.

Methods: The continuum spectra of proton and neutron are incorporated through the Gamow shell-model formalism. The alpha-like wave function is calculated in the weak-coupling approximation. Gaussian effective interaction in each pair of nucleons is included.

Results: The $0^{+}$ ground and excited states are compared with experiment and shell-model calculations. The wave-function amplitudes are obtained and discriminated by their resonant and nonresonant contributions. The influence of a four-body truncated basis is analyzed.

Conclusions: Inclusion of the continuum spectra produces a gain in the excited states of a few hundred keV of energy. One candidate for alpha decay was identified near the experimental unresolved state ${(0,2)}^{+}$ of 6.8 MeV excitation energy, with a lower limit for the half-life of $\approx 0.8$ ns.

Background: Ground-state octupole deformations are suggested in nuclei located in the north-east neighbor of the doubly magic nuclei on the nuclear chart $(N,Z)$, such as those in Ba and Ra-Th regions. This systematics has been attributed to the parity mixing of the approximately degenerate $\mathrm{\Delta }l=3$ pair of single-particle levels near the Fermi surface.

Purpose: Nuclear deformations are governed in most cases by the gross shell structures of the single-particle spectra. I will consider the systematics in octupole deformation from the view point of the gross shell structure and investigate the mechanism of its manifestation using the semiclassical periodic-orbit theory (POT), which describes the quantum shell effect by means of the periodic orbits (POs) in the corresponding classical system.

Methods: To focus on the role of deformation, simplified infinite-well (cavity) and radial power-law potential models are employed taking account of quadrupole and octupole shape degrees of freedom. Nuclear ground-state deformations are investigated over the nuclear chart, and the properties of the deformed shell structures are analyzed by means of the semiclassical POT.

Results and conclusions: The systematics in nuclear ground-state octupole deformations are reproduced in simplified mean-field potential models either with or without parity mixing between $\mathrm{\Delta }l=3$ pair of levels. The strong octupole deformed shell effect at above the spherical shell closures are explained simply and clearly using the semiclassical periodic-orbit theory. They are associated with the local restoration of dynamical symmetry, which enhance the contribution of classical POs to the gross shell effect.

The meaningful correlations between the zero-sound modes and the stiffness of the nuclear equation of state (EOS) are uncovered in nuclear matter with the relativistic mean-field theory. It is demonstrated that the high-density zero-sound modes merely exist in models with the stiff EOS. While the stiff EOS can be softened by including $\omega$-meson self-interactions (the ${\omega }^4$ term), the weakened coupling of the $\omega$-meson self-interactions reignites the zero sound at high density. These results suggest that the high-density zero-sound modes can be used to probe the stiffness of the EOS at supra-normal densities. The implications and effects of zero sounds are also discussed in heavy ion collisions and neutron stars.

The present article reports new data on the ${}^{48}\mathrm{Ti}({}^{18}\mathrm{O},{}^{17}\mathrm{O}){}^{49}\mathrm{Ti}$ reaction at 275 MeV incident energy as part of the systematic research pursued within the NUMEN (NUclear Matrix Elements for Neutrinoless double $\beta$ decay) project. Supplementary measurements of the same reaction on ${}^{16}\mathrm{O}$ and ${}^{27}\mathrm{Al}$ targets were also performed in order to estimate the background arising from the use of a composite target (${\mathrm{TiO}}_2+{}^{27}\mathrm{Al}$). These data were analyzed under the same theoretical framework as those obtained with the titanium target in order to reinforce the conclusions of our analysis. Differential cross-section angular distribution measurements for the ${}^{17}\mathrm{O}^{8+}$ ejectiles were performed in a wide angular range by using the MAGNEX large acceptance magnetic spectrometer. The experimental results were analyzed within the distorted-wave and coupled-channels Born approximation frameworks. The optical potentials at the entrance and exit channels were calculated in a double folding approach adopting the São Paulo potential, and the spectroscopic amplitudes for the projectile and target overlaps were obtained from large-scale shell model calculations. The differential cross sections are well described by the theoretical calculations, where a weak coupling to collective excitations of projectile and target is inferred. The sensitivity of transfer cross sections on different model spaces adopted in nuclear structure calculations is also discussed.

In this article, we report a study of ejectile distributions of multinucleon transfer channels from the reaction of ${}^{70}\mathrm{Zn}$ with ${}^{64}\mathrm{Ni}$ at 15 MeV/nucleon. The measurements were performed with the MAGNEX large acceptance spectrometer in a wide angular range around the grazing angle and provided high-resolution characterization of the ejectiles in terms of the atomic number $Z$, the mass number $A$, the momentum-per-nucleon $p/A$, and the reaction angle ${\theta }_{\mathrm{lab}}$. The momentum distributions, angular distributions, and the production cross sections of several multinucleon transfer channels were extracted and studied in detail. Concerning the production of neutron-rich nuclides, that was one of the main motivations of this work, apart from proton-removal products, neutron-pickup isotopes (with up to three neutrons picked up from the target) were observed. The experimental distributions were compared with two dynamical models, the deep-inelastic transfer (DIT) model and the constrained molecular dynamics (CoMD) model, followed by the deexcitation code GEMINI. The DIT model, designed to describe the sequential exchange of nucleons, offered an overall fair description of the processes involving nucleon exchange, but was unable to describe the quasielastic part of the momentum distributions of several channels, suggesting the presence of direct reaction processes. The microscopic CoMD model gave an overall similar, but less accurate (with respect to DIT) description of the data, indicating that further development is needed. The present work outlines an experimental approach to investigate peripheral collisions of medium-mass heavy ions below the Fermi energy to extract information on the reaction mechanisms and provide guidance for the production of exotic neutron-rich nuclei.

The neutron emission in projectile fragmentation at relativistic energies was studied with the Large-Area-Neutron-Detector LAND coupled to the ALADIN forward spectrometer at the GSI Schwerionen-Synchrotron (SIS). Stable ${}^{124}\mathrm{Sn}$ and radioactive ${}^{107}\mathrm{Sn}$ and ${}^{124}\mathrm{La}$ beams with an incident energy of 600 MeV/nucleon were used to explore the $N/Z$ dependence of the identified neutron source. A cluster-recognition algorithm is applied for identifying individual particles within the hit distributions registered with LAND. The obtained momentum distributions are extrapolated over the full phase space occupied by the neutrons from the projectile-spectator source. The mean multiplicities of spectator neutrons reach values of up to about 11 and depend strongly on the isotopic composition of the projectile. An effective source temperature of $T\approx 2–5$ MeV, monotonically increasing with decreasing impact parameter, is deduced from the transverse momentum distributions. For the interpretation of the data, calculations with the statistical multifragmentation model were performed. The variety of excited projectile spectators assumed to decay statistically is represented by an ensemble of excited sources with parameters determined previously from the fragment production observed in the same experiments. The obtained agreement is very satisfactory for more peripheral collisions where, according to the model, neutrons are mainly emitted during the secondary decays of excited fragments. The neutron multiplicity in more central collisions is underestimated, indicating that other sources besides the modeled statistical breakup contribute to the observed neutron yield. The choice made for the symmetry-term coefficient of the liquid-drop description of produced fragments has a weak effect on the predicted neutron multiplicities.

In this work we extend a previously derived $n\text{−}{}^9\mathrm{Be}$ optical potential up to 500 MeV and apply it to the system $n\text{−}{}^{12}\mathrm{C}$, finding excellent results for the energy dependence of the total cross sections. Results obtained with a standard optical model calculation are compared to those from the eikonal formalism in order to asses the accuracy of the latter as a function of the nucleon incident energy. For comparison, single folded (s.f.) nucleon-target potentials are also obtained using ${}^{12}\mathrm{C}$ densities from different models. These potentials are sensitive to the density used and none of them reproduce the characteristics of the phenomenological potential nor the cross section results. We then calculate nucleus-nucleus ($NN$) potentials and total reaction cross sections for some “normal” and exotic projectile nuclei on ${}^{12}\mathrm{C}$ within the eikonal formalism. We find that single folded (S.F.) projectile-target imaginary potentials and double folded (D.F.) potentials can produce similar energy dependence of the reaction cross sections but the S.F. results agree better with experimental data provided the radius parameter of the phenomenological $n$-target potential is allowed to be energy dependent. We conclude that the results previously obtained for a ${}^9\mathrm{Be}$ target are quite general, at least for light systems, and that a S.F. $NN$ potential built on a phenomenological nN potential can constitute an interesting and useful alternative to D.F. potentials.

We consider the problem of including a finite number of scattering centers in dynamical energy loss and classical DGLV formalism. Previously, either one or an infinite number of scattering centers were considered in energy loss models, while efforts to relax such approximations require a more conclusive and complete treatment. In reality, however, the number of scattering centers is generally estimated to be 4–5 at the BNL Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC), making the above approximations (a priori) inadequate and this theoretical problem significant for QGP tomography. We derived explicit analytical expressions for dynamical energy loss and DGLV up to the fourth order in opacity, resulting in complex, highly oscillatory, mathematical expressions. These expressions were then implemented into an appropriately generalized DREENA framework to calculate the effects of higher orders in opacity on a wide range of high-$p_{\perp }$ light and heavy flavor predictions. Results of extensive numerical analysis and interpretations of nonintuitive results are presented. We find that, for both RHIC and the LHC, higher-order effects on high-$p_{\perp }$ observables are small, and the approximation of a single scattering center is adequate for dynamical energy loss and DGLV formalisms.

This paper explores low-density neutron matter and its behavior in proximity to the unitary limit. To that end, unitary nucleon-nucleon potentials, with infinite ${}^1\mathrm{S}_0$ neutron-neutron scattering lengths, are constructed and the Berstch parameter is discussed in relation to results from ultracold atomic gases. A focal point is unitarity as a constraint for neutron matter and the symmetry energy, a topic that has been discussed in the literature. I revisit some of those arguments and emphasize the relevance of keeping a firm link with low-energy nuclear physics for robust predictions of neutron-rich systems. The predictions are obtained from realistic few-nucleon forces based on chiral effective field theory at ${\mathrm{N}}^3\mathrm{LO}$.

In this paper we discuss the centrality and energy dependence of $K^{*0}$ resonance production using ultrarelativistic quantum molecular dynamics (UrQMD) and thermal models. The $K^{*0}/K$ ratios obtained from the UrQMD and thermal models are compared with measurements done by the STAR experiment in $\text{Au}+\text{Au}$ collisions at $\sqrt{s_{NN}}=7.7$, 11.5, 14.5, 19.6, 27, and 39 GeV. The $K^{*0}/K$ ratio from the thermal model is consistent with data in most-peripheral collisions, however it overpredicts the ratio in central $\text{Au}+\text{Au}$ collisions. This could be due to the fact that the thermal model does not have a hadronic rescattering phase, which is expected to be dominant in more central collisions. Furthermore, we have studied the $K^{*0}/K$ ratio from UrQMD by varying the hadron propagation time ($\tau$) within the range 5 to 50 fm/$c$. It was found that the $K^{*0}/K$ ratio decreases with increasing $\tau$. Comparison between data and UrQMD suggest one needs to consider $\tau \approx$ 10–50 fm/$c$ to explain data at $\sqrt{s_{NN}}=7.7$–39 GeV in $\text{Au}+\text{Au}$ collisions. We also predict the rapidity distribution of $K^{*0}$ from UrQMD, which could be measured in the STAR beam energy scan phase II (BES-II) program.

We incorporate the empirical low-density properties of isospin symmetric nuclear matter into the excluded-volume model for quarkyonic matter by including attractive mean field in the nucleonic sector and considering variations on the nucleon excluded volume mechanism. This corresponds to the quantum van der Waals equation for nucleons with the interaction parameters fixed to empirical ground state properties of nuclear matter. The resulting equation of state exhibits the nuclear liquid-gas transition at $n_B\le {\rho }_0$ and undergoes a transition to quarkyonic matter at densities $n_B\approx 1.5-2{\rho }_0$ that are reachable in intermediate energy heavy-ion collisions. The transition is accompanied by a peak in the sound velocity. The results depend only mildly on the chosen excluded volume mechanism but do require the introduction of an infrared regulator $\mathrm{\Lambda }$ to avoid an acausal sound velocity. We also consider the recently proposed baryquark matter scenario for the realization of the Pauli exclusion principle, which yields a similar equation of state and turns out to be energetically favored in all the considered setups.

Background: Globular clusters show strong correlations between different elements, such as the well-known sodium-oxygen anticorrelation. One of the main sources of uncertainty in this anticorrelation is the ${}^{22}\mathrm{Ne}(p,\gamma ){}^{23}\mathrm{Na}$ reaction rate, due to the possible influence of an unobserved resonance state at $E_x=8862$ keV ($E_{\mathrm{r},\mathrm{c}.\mathrm{m}.}=68$ keV). The influence of two higher-lying resonance states at $E_x=8894$ and 9000 keV has already been ruled out by direct ${}^{22}\mathrm{Ne}(p,\gamma ){}^{23}\mathrm{Na}$ measurements.

Purpose: The purpose of this paper is to study excited states in ${}^{23}\mathrm{Na}$ above the proton threshold to determine if the unconfirmed resonance states in ${}^{23}\mathrm{Na}$ exist.

Methods: The nonselective proton inelastic-scattering reaction at low energies was used to search for excited states in ${}^{23}\mathrm{Na}$ above the proton threshold. Protons scattered from various targets were momentum-analyzed in the Q3D magnetic spectrograph at the Maier-Leibnitz Laboratorium, Munich, Germany.

Results: The resonance states previously reported at $E_x=8862$, 8894, and 9000 keV in other experiments were not observed in the present experiment at any angle. This result, combined with other nonobservations of these resonance states in most other experiments, results in a strong presumption against the existence of these resonance states.

Conclusions: The previously reported resonance states at $E_x=8862$, 8894, and 9000 keV are unlikely to exist and should be omitted from future evaluations of the ${}^{22}\mathrm{Ne}(p,\gamma ){}^{23}\mathrm{Na}$ reaction rates. Indirect studies using low-energy proton inelastic scattering are a simple and yet exceptionally powerful tool in helping to constrain astrophysical reaction rates by providing nonselective information of the excited states of nuclei.

One of the current research focuses on ${}^{229}\mathrm{Th}$ is to search for efficient methods to excite the nucleus from the ground state to the low-lying isomeric state. While existing methods are either optical or electronic excitation, we propose herein to use Coulomb excitation by protons for producing the isomer. A theoretical framework is developed for the protonic Coulomb excitation process, and the isomeric excitation cross section is calculated to be over 10 mb with a typical proton energy of 10 MeV. Proton excitation is particularly advantageous for solid-state targets owing to its strong penetrability through materials, and its experimental implementation is relatively straightforward. An experimental scheme featuring ${}^{229}\mathrm{Th}$-doped crystals is envisaged, and an assessment of the expected excitation efficiency is provided.

The triaxial projected shell model (TPSM) approach is generalized to investigate the negative parity band structures in even-even systems. In the earlier version of the TPSM approach, the quasiparticle excitations were restricted to one major oscillator shell and it was possible to study only positive parity states in even-even systems. In the present extension, the excited quasiparticles are allowed to occupy two major oscillator shells, which makes it possible to generate the negative parity states. As a major application of this development, the extended approach is applied to elucidate the negative parity high-spin band structures in ${}^{102–112}\mathrm{Ru}$ and it is shown that energies obtained with neutron excitation are slightly lower than the energies calculated with proton excitation. However, the calculated aligned angular momentum $i_x$ clearly separates the two spectra with neutron $i_x$, in reasonable agreement with the empirically evaluated $i_x$ from the experimental data, whereas proton $i_x$ shows large deviations. Furthermore, we have also deduced the transition quadrupole moments from the TPSM wave functions along the negative parity yrast and yrare bands and it is shown that these quantities exhibit rapid changes in the band-crossing region.

Shell-model calculations of the electric dipole ($E1$) polarizability have been performed for the ground state of selected $p$- and $sd$-shell nuclei, substantially advancing previous knowledge. Our results are slightly larger compared with the somewhat more scattered photoabsorption cross-section data, albeit agreeing with ab initio calculations at shell closures and presenting a smooth trend that follows the leptodermous approximation provided by the finite-range droplet model (FRDM). The total $E1$ strengths also show an increasing trend proportional to the mass number which follows from the classical oscillator strength (TRK) sum rule for the $E1$ operator. The enhancement of the energy-weighted sum over $E1$ excitations with respect to the TRK sum rule arises from the use of experimental single-particle energies and the residual particle-hole interaction.

In this work, we develop an updated model for pion-nucleus scattering in the framework of the distorted wave impulse approximation in momentum space. We construct the second-order pion-nucleus potential, which involves analysis of pion-nucleus elastic scattering as a solution of the Lippmann-Schwinger equation. The potential is based on the individual pion-nucleon scattering amplitudes extracted from SAID, and its second-order correction is presented in detail. We estimate optimal energy-independent parameters of the potential by a multienergy fit of the pion-${}^{12}\mathrm{C}$ total, reaction, and differential elastic cross sections. We show the predictive power by applying it to pion elastic scattering on ${}^{16}\mathrm{O}, {}^{28}\mathrm{Si}$, and ${}^{40}\mathrm{Ca}$.

In 2017, the STAR collaboration at the BNL Relativistic Heavy Ion Collider measured finite global angular momentum in heavy-ion collisions through a spin polarization measurement of $\mathrm{\Lambda }$ hyperons. This measurement revealed a high angular momentum of the heavy ions and provided experimental evidence for vorticity in the quark-gluon plasma for the first time. In order to investigate the underlying mechanisms, a dynamic description of the transfer of angular momentum is required. In this work, the microscopic nonequilibrium transport approach SMASH (simulating many accelerated strongly interacting hadrons) is applied to study the generation of global angular momentum by the interaction of two nuclei. As SMASH provides access to the whole phase-space evolution of every particle at any given time, it allows to assess the fraction of angular momentum generated in the fireball by all participants. We confirm the previous modeling by Becattini et al., [Phys. Rev. C 77, 024906 (2008)] within a geometric Glauber model approach, which found that the angular momentum transfer reaches a unique maximum in mid-central collisions during time evolution. The corresponding impact parameter is around $b=4\text{–}6$ fm for all beam energies from $\sqrt{s_{NN}}=2.41\text{–}200$ GeV. Even though angular momentum is not conserved locally in the transport approach a priori, we identify the contributions to the conservation violation and propose optimal setups for different energy regimes that recover conservation, based upon the test particle method and the treatment of Fermi motion. Furthermore, the system size and centrality dependence are investigated.

Background: As a Borromean system, ${}^9\mathrm{Be}$ is weakly bound, while its mirror partner ${}^9\mathrm{B}$ is an unbound system. Such weakly bound and unbound nuclei are usually accompanied with exotic structures and decay modes which attract a lot of experimental and theoretical attentions.

Purpose: Due to the mirror symmetry, ${}^9\mathrm{B}$ and ${}^9\mathrm{Be}$ share many similar properties, but experience different continuum effect mainly caused by Coulomb interaction. In this work, we try to gain more insight into the cluster structures of ${}^9\mathrm{B}$ and ${}^9\mathrm{Be}$, and analyze the Thomas-Ehrman effect therein. Meanwhile, another purpose of this work is to study the decay dynamics and mechanisms of ${}^9\mathrm{Be}$ and ${}^9\mathrm{B}$, and explore the possible three-body decay in their low-lying states.

Methods: The three-body Gamow coupled-channel method has been used to calculate the structures of ${}^9\mathrm{Be}$ and ${}^9\mathrm{B}$ mirror systems. The corresponding wave functions have been propagated to analyze the decay dynamics.

Results: According to the calculated spectra and density distributions of ${}^9\mathrm{Be}$ and ${}^9\mathrm{B}$, the Thomas-Ehrman effect is found in those states with small orbital-angular momenta. By comparing the wave functions in two- and three-body frameworks, the nature of the $1/2^{+}$ state of ${}^9\mathrm{Be}$ has been discussed. Moreover, the low-lying states with possibly different decay mechanisms have been discussed based on the results of the density evolution and asymptotic correlations.

Conclusions: Consequently, it has been found that the behavior of the two-body virtual state can leave an imprint in a many-body system, but its characteristics might be diluted by the configuration mixing especially for the nuclei with two subsystems unbound. As to the decay properties, it has been demonstrated that ${}^9\mathrm{Be}(5/2_1^{+}), {}^9\mathrm{Be}(1/2_1^{+})$, and ${}^9\mathrm{B}(5/2_1^{-})$ are likely to correspond to the sequential, “democratic”, and three-body decay mechanisms, respectively.

The recently proposed Bayesian neural network (BNN) model was adopted to investigate the systematic behaviors of fragments cross sections produced in projectile fragmentation reactions. Mainly two phenomena are studied, i.e., (1) The scaling behavior in the difference between mass excess of mirror nuclei based on the binding energies of proton-rich fragments determined using the BNN-predicted cross sections for the $345A\mathrm{MeV}{}^{78}\mathrm{Kr}+{}^9\mathrm{Be}$ reaction, which shows that the scaling phenomenon exists up to neutron excess $\left|I\right|=|N-Z|$ of 5; (2) the isobaric yield ratio distributions for mirror fragments [IYR(m)] produced in a series of projectile fragmentation reactions with projectiles of isotopes, isobars, and those that have the same neutron-skin thickness at different levels. The IYR(m) distributions predicted by the BNN model reflect the systematic evolution with neutron-skin thickness of projectile nuclei.