In two recent articles we have formulated nuclear mean-field theory predictions of existence of a new form of magic numbers, referred to as fourfold magic numbers. These predictions stipulate the presence of strong shell closures at the neutron numbers $N=136$ (actinide region) and $N=196$ (superheavy region) simultaneously at nonvanishing all four octupole deformations ${\alpha }_{3\mu =0,1,2,3}\ne 0$. In contrast to the traditional notion of magic numbers, the new notion refers to simultaneous nonspherical configurations (${\alpha }_{3\mu }\ne 0, {\alpha }_{2\mu }=0$). In this article we study the nuclear equilibrium deformations with ${\alpha }_{33}\ne 0$ combined with nonvanishing quadrupole deformation, ${\alpha }_{20}\ne 0$. One easily shows that such geometrical shapes have a threefold symmetry axis and are invariant under the symmetry operations of the ${\mathrm{D}}_{3h}$ point group. We employ a realistic phenomenological mean-field approach with the so-called universal deformed Woods-Saxon potential and its recently optimized parametrization based on actualized experimental data with the help of the inverse problem theory methods. The presence of parametric correlations among 4 of 12 parameters in total was detected and removed employing Monte Carlo approach leading to stabilization of the modeling predictions. Our calculations predict the presence of three nonoverlapping groups of nuclei with ${\mathrm{D}}_{3h}$ symmetry, referred to as islands on the nuclear ($Z,N$) plane (mass table). These islands lie in the rectangle $110\le Z\le 138$ and $166\le N\le 206$. The “repetitive” structures with the ${\mathrm{D}}_{3h}$ symmetry minima are grouped in three zones of oblate quadrupole deformation, approximately, at ${\alpha }_{20}\in [-0.10,-0.20]$ (oblate normal deformed), around ${\alpha }_{20}\approx -0.5$ (oblate superdeformed) and ${\alpha }_{20}\approx -0.85$ (oblate hyperdeformed). Importantly, the energies of those latter exotic deformation minima are predicted to be very close to the ground-state energies. We illustrate, compare, and discuss the evolution of the underlying shell structures. Nuclear surfaces parametrized as usual with the help of real deformation parameters, $\{{\alpha }_{\lambda \mu }^{}={\alpha }_{\lambda \mu }^{*}\}$, are invariant under ${\mathcal{O}}_{xz}$-plane reflection, the symmetry also referred to as $y$ simplex (${\widehat{S}}_y$). For the shapes with odd-multipolarity ($\lambda \to {\lambda }_{\mathrm{odd}}=3,5,7,...$) it follows that $E(-{\alpha }_{{\lambda }_{\mathrm{odd}},\mu })=E(+{\alpha }_{{\lambda }_{\mathrm{odd}},\mu })$. It turns out that the predicted equilibrium deformations generate symmetric double (or “twin”) minima separated by potential barriers, whose heights vary with the nucleon numbers, possibly inducing the presence of parity-doublets in the spectra. To facilitate possible experimental identification of such structures, we examine the appearance of such doublets solving the collective Schrödinger equation. Implied suggestions are illustrated and discussed.

The level structure of ${}^{158}\mathrm{Er}$ has been studied using the Gammasphere spectrometer via the ${}^{114}\mathrm{Cd}({}^{48}\mathrm{Ca},4n)$ reaction at 215 MeV with both thin (self-supporting) and thick (backed) targets. The level scheme has been considerably extended with more than 200 new transitions and six new rotational structures, including two strongly coupled high-$K$ bands. Configuration assignments for the new structures are based on their observed alignments, $B\left(M1\right)/B\left(E2\right)$ ratios of reduced transition probabilities, excitation energies, and comparisons with neighboring nuclei and theoretical calculations. With increasing angular momentum, this nucleus exhibits Coriolis-induced alignments of both neutrons and protons before it then undergoes a rotation-induced transition from near-prolate collective rotation to a noncollective oblate configuration. This transition occurs via the mechanism of band termination around spin $45\hslash$ in three rotational structures. Two distinct lifetime branches, consistent with the crossing of a collective “fast” rotational structure by an energetically favored “slow” terminating sequence, are confirmed for the positive-parity states, and similar behavior is established in the negative-parity states. Weak-intensity, high-energy transitions are observed to feed into the terminating states. At the highest spins, three collective bands with high dynamic moments of inertia and large quadrupole moments were identified. These bands are interpreted as triaxial strongly deformed structures and mark a return to collectivity at ultrahigh spin.

The effective polarization of the residual nucleus in the proton-induced $\alpha$ knockout reaction is investigated within the distorted wave impulse approximation framework. The strong absorption of the emitted $\alpha$ particle results in strong selectivity on the reaction position depending on the third component of the single-particle orbital angular momentum of the $\alpha$ particle inside a nucleus, hence on the spin direction of the reaction residue. This is caused by a mechanism that is similar to the Maris effect, the effective polarization in the proton-induced proton knockout reactions. However, as a distinct feature of the effective polarization in the $\alpha$ knockout process, the spin degrees of freedom of the reacting particles play no role. The $\alpha$ knockout process with complete kinematics can be a useful polarization technique for the residual nucleus, without actively controlling the spin of the proton.

Yrast and near-yrast states above the known $25/2^{+}$ isomer in ${}^{207}\mathrm{At}$ are established for the first time. The level scheme is extended up to $47/2\hslash$ and 6.5 MeV with the addition of about 60 new $\gamma$-ray transitions. The half-life of the $25/2^{+}$ isomer is revisited and a value of $T_{1/2}=107.5\left(9\right)$ ns is deduced. Evidence of a hitherto unobserved $29/2^{+}$ isomer in ${}^{207}\mathrm{At}$ is presented. A systematic study of $B\left(E3\right)$ values for the transitions deexciting the $29/2^{+}$ isomer in the neighboring odd-$A$ At isotopes suggests a half-life in the $2–4.5\mu \mathrm{s}$ range for this state in ${}^{207}\mathrm{At}$. The experimental results are compared with large-scale shell-model calculations performed using the KHM3Y effective interaction in the $Z=50–126$, $N=82–184$ model space and an overall good agreement is noted between the theory and the experiment. A qualitative comparison of the excited states and the isomers with analogous states in neighboring nuclei provides further insight into the structure of ${}^{207}\mathrm{At}$.

A neutron-energy dependent angular distribution was measured for individual $\gamma$ rays from the 3.2 eV $p$-wave resonance of ${}^{131}\mathrm{Xe}+n$, that shows enhanced parity violation owing to a mixing between $s$- and $p$-wave amplitudes. The $\gamma$-ray transitions from the $p$-wave resonance were identified, and the angular distribution with respect to the neutron momentum was evaluated as a function of the neutron energy for 7132 keV $\gamma$ rays, which correspond to a transition to the 1807 keV excited state of ${}^{132}\mathrm{Xe}$. The angular distribution is considered to originate from the interference between $s$- and $p$-wave amplitudes, and will provide a basis for a quantitative understanding of the enhancement mechanism of the fundamental parity violation in compound nuclei.

The production of ${\mathrm{K}}^{*}{\left(892\right)}^0$and $\varphi \left(1020\right)$resonances has been measured in $p$-Pb collisions at $\sqrt{s_{NN}}$ = 8.16 TeV using the ALICE detector. Resonances are reconstructed via their hadronic decay channels in the rapidity interval $-$0.5 $<$ $y$ $<$ 0 and the transverse momentum spectra are measured for various multiplicity classes up to $p_{\mathrm{T}}$ = 20 $\mathrm{GeV}/\mathrm{c}$ for ${\mathrm{K}}^{*}{\left(892\right)}^0$and $p_{\mathrm{T}}$ = 16 $\mathrm{GeV}/\mathrm{c}$ for $\varphi \left(1020\right)$. The $p_{\mathrm{T}}$-integrated yields and mean transverse momenta are reported and compared with previous results in pp, $p$-Pb and Pb-Pb collisions. The $x_{\mathrm{T}}$ scaling for ${\mathrm{K}}^{*}{\left(892\right)}^0$and $\varphi \left(1020\right)$resonance production is newly tested in $p$-Pb collisions and found to hold in the high-$p_{\mathrm{T}}$ region at Large Hadron Collider energies. The nuclear modification factors ($R_{\mathit{p}\mathrm{Pb}}$) as a function of $p_{\mathrm{T}}$ for ${\mathrm{K}}^{*0}$ and $\varphi$ at $\sqrt{s_{NN}}$ = 8.16 TeV are presented along with the new $R_{\mathit{p}\mathrm{Pb}}$ measurements of ${\mathrm{K}}^{*0}$, $\varphi$, $\mathrm{\Xi }$, and $\mathrm{\Omega }$ at $\sqrt{s_{NN}}$ = 5.02 TeV. At intermediate $p_{\mathrm{T}}$ (2–8 $\mathrm{GeV}/\mathrm{c}$), $R_{\mathit{p}\mathrm{Pb}}$ of $\mathrm{\Xi }$, $\mathrm{\Omega }$ show a Cronin-like enhancement, while ${\mathrm{K}}^{*0}$ and $\varphi$ show no or little nuclear modification. At high $p_{\mathrm{T}}$ ($>$8 $\mathrm{GeV}/\mathrm{c}$), the $R_{\mathit{p}\mathrm{Pb}}$ values of all hadrons are consistent with unity within uncertainties. The $R_{\mathit{p}\mathrm{Pb}}$ of ${\mathrm{K}}^{*}{\left(892\right)}^0$and $\varphi \left(1020\right)$at $\sqrt{s_{NN}}$ = 8.16 and 5.02 TeV show no significant energy dependence.

Using the Remler formalism for the creation of composed particles, we study charmonium production both in thermalized and thermalizing boxes, which contain charm and anticharm quarks. The thermalizing box studies include the lowering of the box temperature, the spatial diffusion of charm and anticharm quarks, which are initially confined in the central region, as well as the combination of both, what imitates heavy-ion collisions. Comparing numerical and analytical results we demonstrate that the rate of the original Remler formalism has to be supplemented by two rates to obtain, for $t\to \infty$, results which are consistent with the statistical model predictions: i) a rate, which takes into account the temperature dependence of the Wigner density of the quarkonium during the expansion and, in the case that a heavy quark potential is not implemented in the Monte Carlo approach, ii) a rate which comes from the change of the relative distance between the heavy quark and antiquark. These results provide the basis for future applications of the Remler formalism to heavy-ion collisions.

Background: Mass and angle distribution measurements have illuminated many aspects of the physical variables controlling quasifission. However, mapping from detection angle to reaction time is clouded by the wide range of contributing angular momenta $L\hslash$, ranging from $0\hslash$ to the maximum of the reaction ($⪆100\hslash$), which complicates the mapping, and thus limits our understanding of the reaction dynamics.

Purpose: To investigate the angular momentum dependence of the reaction dynamics in quasifission and determine the fission fragment mass evolutions in the reaction.

Method: The mass and angular distributions of products of the reactions ${}^{52}\mathrm{Cr}+{}^{198}\mathrm{Pt}$ and ${}^{54}\mathrm{Cr}+{}^{196}\mathrm{Pt}$ were measured. The distributions were compared with quasifission simulation results.

Results: Mass angle distributions are reproduced by utilizing a new quasifission mass evolution model, and including a mass-symmetric component associated with low $L$. The latter increases in yield at higher beam energy.

Conclusions: The symmetric component represents the total of slow quasifission and fusion-fission. The increase in contribution with energy above the Coulomb barrier suggests that an extra-push energy is required to achieve fusion.

Quarkonium production has been studied extensively in relativistic heavy-ion collision experiments to understand the properties of the quark-gluon plasma. The experimental results on the yield modification in heavy-ion collisions relative to that in $p+p$ collisions can be described by several models considering dissociation and regeneration effects. A yield modification beyond initial-state effects has also been observed in small collision systems such as $p+\mathrm{Au}$ and $p+\mathrm{Pb}$ collisions, but it is still premature to claim any hot medium effect. A model study in various small collision systems such as $p+p$, $p+\mathrm{Pb}$, $p+\mathrm{O}$, and $\mathrm{O}+\mathrm{O}$ collisions will help quantitatively the understanding of nuclear effects on the $\mathrm{{\rm Y}}\left(nS\right)$ production. A theoretical calculation considering the gluo-dissociation and inelastic parton scattering for dissociation, and their inverse reaction for regeneration, reasonably describes the modification of $\mathrm{{\rm Y}}\left(1S\right)$ in $\mathrm{Pb}+\mathrm{Pb}$ collisions. Based on this calculation, a Monte Carlo simulation considering the dissociation effect is developed to more realistically incorporate the medium produced in heavy-ion collisions with event-by-event initial collision geometry and hydrodynamic evolution. We extend this framework to small systems to study the medium effects. In this work, we quantify the nuclear modification factor of $\mathrm{{\rm Y}}\left(nS\right)$ as a function of charged particle multiplicity ($d{N}_{ch}/d\eta$) and transverse momentum. We also calculate the elliptic flow of $\mathrm{{\rm Y}}\left(nS\right)$ in small collision systems.

We investigate the implications of parity-violating electron scattering experiment on neutron skin thickness of ${}^{48}\mathrm{Ca}$ [calcium radius experiment (CREX)] and ${}^{208}\mathrm{Pb}$ [lead radius experiment (PREX-II)] data on the bulk properties of finite nuclei, nuclear matter, and neutron stars. The neutron skin thickness from the CREX and PREX-II data is employed to constrain the parameters of relativistic mean-field models which includes different nonlinear, self- and cross-couplings among isoscalar-scalar $\sigma$, isoscalar-vector $\omega$, isovector-scalar $\delta$, and isovector-vector $\rho$ meson fields up to the quartic order. Three parametrizations of RMF model are proposed by fitting CREX, PREX-II, and both CREX as well as PREX-II data to assess their implications. A covariance analysis is performed to assess the theoretical uncertainties of model parameters and nuclear matter observables along with correlations among them. The RMF model parametrization obtained with the CREX data acquires much smaller value of symmetry energy ($J=28.97\pm 0.99$ MeV) and its slope parameter ($L=30.61\pm 6.74$ MeV) in comparison to those obtained with PREX-II data. The neutron star properties are studied by employing the equations of state composed of nucleons and leptons in $\beta$ equilibrium.

Background: Type I x-ray bursts provide an opportunity to constrain the equation of state of nuclear matter. Observations of the light curves from these bursts allow the compactness of neutron stars to be constrained. However, the behavior of these light curves also depends on a number of important thermonuclear reaction rates. One of these reactions, ${}^{18}\mathrm{Ne}(\alpha ,p){}^{21}\mathrm{Na}$, has been extensively studied but there is some tension between the rate calculated from spectroscopic information of states above the $\alpha$-particle threshold in ${}^{22}\mathrm{Mg}$ and the rate determined from time-reversed measurements of the cross section.

Purpose: The time-reversed measurement of the cross section is only sensitive to the ground state-to-ground state contribution. Therefore, corrections must be made to this reaction rate to account for the contribution of branches to excited states in ${}^{21}\mathrm{Na}$. At present this is done with statistical models which may not be applicable in such light nuclei. Basing the correction of the time-reversed cross section on experimental data is much more robust.

Method: The ${}^{24}\mathrm{Mg}(p,t){}^{22}\mathrm{Mg}$ reaction was used to populate states in ${}^{22}\mathrm{Mg}$. The reaction products from the reaction were analysed by the K600 magnetic spectrometer at iThemba Laboratories, South Africa. Protons decaying from excited states of ${}^{22}\mathrm{Mg}$ ($S_p=5502$ keV) were detected in an array of five double-sided silicon strip detectors placed at backward angles. The branching ratio for proton decays to the ground state of ${}^{21}\mathrm{Na}, B_{p_0}$, was determined by comparing the inclusive (triton-only focal-plane) and exclusive (focal-plane gated on a specific proton decay) spectra.

Results: The experimental proton decay branching ratio to the ground state of ${}^{21}\mathrm{Na}$ from excited states in ${}^{22}\mathrm{Mg}$ were found to be a factor of about two smaller than the ratios predicted by Hauser-Feshbach models. Using the experimental branchings for a recalculation of the ${}^{18}\mathrm{Ne}(\alpha ,p_0){}^{21}\mathrm{Na}$ cross section leads to a considerably improved agreement with previous reaction data. Updated information on the disputed number of levels around $E_x\approx 9$ MeV and on the possible ${}^{18}\mathrm{Ne}(\alpha ,2p){}^{20}\mathrm{Ne}$ cross section at astrophysical energies is also reported.

Conclusions: The proton decay branching of excited states in ${}^{22}\mathrm{Mg}$ to the ground state of ${}^{21}\mathrm{Na}$ have been measured using the K600 Q2D spectrometer at iThemba Laboratories coupled to the double-sided silicon-strip detector array CAKE. Using these experimental data, the modeling of the ${}^{18}\mathrm{Ne}(\alpha ,p_0){}^{21}\mathrm{Na}$ cross section has been improved. The result is not only in better agreement with previous cross section data but also consistent with a recent direct measurement of ${}^{18}\mathrm{Ne}(\alpha ,p){}^{21}\mathrm{Na}$. This strengthens the case for the application of statistical models for these reactions.

We calculated the energy spectra of the neutron-rich He $\mathrm{\Lambda }$ hypernuclei with $A$ = 6 to 9 within the framework of an $\alpha +\mathrm{\Lambda }+Xn$ ($X$ = 1–4) cluster model using the cluster orbital shell model. The employed constituent particles reproduce their observed properties. For resonant states of core nuclei such as ${}^5\mathrm{He}$, ${}^6\mathrm{He}$, and ${}^7\mathrm{He}$, the complex scaling method is employed to obtain energies and decay widths. The calculated ground states of ${}_{\mathrm{\Lambda }}{}^6\mathrm{He}$ and ${}_{\mathrm{\Lambda }}{}^7\mathrm{He}$ are in good agreement with published data. The energy levels of ${}_{\mathrm{\Lambda }}{}^8\mathrm{He}$ and ${}_{\mathrm{\Lambda }}{}^9\mathrm{He}$ are predicted. In ${}_{\mathrm{\Lambda }}{}^9\mathrm{He}$, we find one deeply bound state and two excited resonant states, which are proposed to be produced at the Japan proton accelerator research complex (J-PARC) by the double-charge-exchange reaction $({\pi }^{-},K^{+})$ using a ${}^9\mathrm{Be}$ target.

The increase in yields of light nuclei with charged particle multiplicity, as reported by the ALICE Collaboration at CERN in $p\text{−}p$ and $p$-Pb collisions at the Large Hadron Collider energy is investigated in the thermal hadron resonance gas model. The model is extended to account for exact baryon number conservation. The focus is on the production of protons, deuterons, ${}^3\mathrm{He}$, and ${}_{\mathrm{\Lambda }}{}^3\mathrm{H}$. A very good description of proton and deuteron yields is obtained as a function of charged particle multiplicity in the midrapidity region using the same fixed temperature as in central Pb-Pb collisions. The yields of light nuclei ${}^3\mathrm{He}$ and ${}_{\mathrm{\Lambda }}{}^3\mathrm{H}$, though qualitatively explained as a function of multiplicity, are lower than the model expectation. One of the possible reasons could be that for ${}^3\mathrm{He}$ and ${}_{\mathrm{\Lambda }}{}^3\mathrm{H}$, the chemical equilibrium is not yet reached at small multiplicities.

Femtoscopic correlations of nonidentical charged kaons ($K^{+}{K}^{-}$) are studied in Pb-Pb collisions at a center-of-mass energy per nucleon-nucleon collision $\sqrt{s_{NN}}=2.76$ TeV by ALICE at the CERN Large Hadron Collider. One-dimensional $K^{+}{K}^{-}$ correlation functions are analyzed in three centrality classes and eight intervals of particle-pair transverse momentum. The Lednický and Luboshitz interaction model used in the $K^{+}{K}^{-}$ analysis includes the final-state Coulomb interactions between kaons and the final-state interaction through $a_0\left(980\right)$ and $f_0\left(980\right)$ resonances. The mass of $f_0\left(980\right)$ and coupling were extracted from the fit to $K^{+}{K}^{-}$ correlation functions using the femtoscopic technique. The measured mass and width of the $f_0\left(980\right)$ resonance are consistent with other published measurements. The height of the $\varphi \left(1020\right)$ meson peak present in the $K^{+}{K}^{-}$ correlation function rapidly decreases with increasing source radius, qualitatively in agreement with an inverse volume dependence. A phenomenological fit to this trend suggests that the $\varphi \left(1020\right)$ meson yield is dominated by particles produced directly from the hadronization of the system. The small fraction subsequently produced by final-state interactions could not be precisely quantified with data presented in this paper and will be assessed in future work.

The invariant-mass method is used to study the structure of a number of light proton-rich isotopes utilizing fast beams. Reactions where the projectile picks up a proton have been used to study $d$-wave resonances in ${}^{14}\mathrm{F}, {}^{16}\mathrm{F}$, and ${}^{18}\mathrm{Na}$. While the ${}^{16}\mathrm{F}$ and ${}^{18}\mathrm{Na}$ results are consistent with previous studies, the ${}^{14}\mathrm{F}$ results are not consistent with the only previous work. We have tentatively identified the $4^{+}$ member of a rotational band in ${}^{10}\mathrm{B}$, which is the analog of well-known states with strong $\alpha$-cluster structure in ${}^{10}\mathrm{Be}$ and ${}^{10}\mathrm{C}$. Finally, spin and parities of newly observed states in ${}^{11}\mathrm{C}$ which decay sequentially into three-body exit channels have been determined or restricted.

Parton energy-momentum exchange with the quark gluon plasma (QGP) is a multiscale problem. In this work, we calculate the interaction of charm quarks with the QGP within the higher twist formalism at high virtuality and high energy using the Modular All Twist Transverse-scattering Elastic-drag and Radiation (MATTER) model, while the low-virtuality and high-energy portion is treated via a linearized Boltzmann transport formalism. Coherence effect that reduces the medium-induced emission rate in the MATTER model is also taken into account through a virtuality-dependent $\widehat{q}$, leaving the simultaneous dependence of $\widehat{q}$ on heavy quark mass and virtuality for future studies. The interplay between these two formalisms is studied phenomenologically and used to produce a first description of the D-meson and charged hadron nuclear modification factor $R_{AA}$ across multiple centralities. All calculations were carried out utilizing the Jet Energy-loss Tomography with a Statistically and Computationally Advanced Program Envelope framework.

A configuration-interaction model is presented for the barrier region of induced fission. The configuration space is composed of seniority-zero configurations constructed from self-consistent mean-field wave functions. The Hamiltonian matrix elements between configurations include diabatic and pairing interactions between particles. Other aspects of the Hamiltonian are treated statistically, guided by phenomenological input of compound-nucleus transmission coefficients. In this exploratory study the configuration space is restricted to neutron excitations only. A key observable calculated in the model is the fission-to-capture branching ratio. We find that both pairing and diabatic interactions are important for achieving large branching to the fission channels. In accordance with the transition-state theory of fission, the calculated branching ratio is found to be quite insensitive to the fission decay widths of the pre-scission configurations. However, the barrier-top dynamics appear to be quite different from transition-state theory in that the transport is distributed over many excited configurations at the barrier top.

The neutron-induced fission cross sections of ${}^{232}\mathrm{Th}$ and ${}^{233}\mathrm{U}$ were measured relative to ${}^{235}\mathrm{U}$ in a wide neutron energy range up to 1 GeV (and from fission threshold in the case of ${}^{232}\mathrm{Th}$, and from 0.7 eV in case of ${}^{233}\mathrm{U}$), using the white-spectrum neutron source at the CERN Neutron Time-of-Flight (n_TOF) facility. Parallel plate avalanche counters (PPACs) were used, installed at the Experimental Area 1 (EAR1), which is located at 185 m from the neutron spallation target. The anisotropic emission of fission fragments were taken into account in the detection efficiency by using, in the case of ${}^{233}\mathrm{U}$, previous results available in EXFOR, whereas in the case of ${}^{232}\mathrm{Th}$ these data were obtained from our measurement, using PPACs and targets tilted ${45}^{\circ }$ with respect to the neutron beam direction. Finally, the obtained results are compared with past measurements and major evaluated nuclear data libraries. Calculations using the high-energy reaction models INCL$++$ and ABLA07 were performed and some of their parameters were modified to reproduce the experimental results. At high energies, where no other neutron data exist, our results are compared with experimental data on proton-induced fission. Moreover, the dependence of the fission cross section at 1 GeV with the fissility parameter of the target nucleus is studied by combining those $(p,f)$ data with our $(n,f)$ data on ${}^{232}\mathrm{Th}$ and ${}^{233}\mathrm{U}$ and on other isotopes studied earlier at n_TOF using the same experimental setup.