The change in the configuration of valence protons between the initial and final states in the neutrinoless double-$\beta$ decay of ${}^{130}\text{Te}\to {}^{130}\text{Xe}$ and of ${}^{136}\text{Xe}\to {}^{136}\text{Ba}$ has been determined by measuring the cross sections of the $\left(d,{}^3\text{He}\right)$ reaction with 101-MeV deuterons. Together with our recent determination of the relevant neutron configurations involved in the process, a quantitative comparison with the latest shell-model and interacting-boson-model calculations reveals significant discrepancies. These are the same calculations used to determine the nuclear matrix elements governing the rate of neutrinoless double-$\beta$ decay in these systems.

The ground and first excited $0^{+}$ states of the ${}^{156–172}\text{Er}$ isotopes are analyzed in the framework of the generator coordinate method. The shape parameter $\beta$ is used to generate wave functions with different deformations which together with the two-quasiparticle states built on them provide a set of states. An angular momentum and particle number projection of the latter spawn the basis states of the generator coordinate method. With this ansatz and using the separable pairing plus quadrupole interaction we obtain a good agreement with the experimental spectra and $E2$ transition rates up to moderate spin values. The structure of the wave functions suggests that the first excited $0^{+}$ states in the soft Er isotopes are dominated by shape fluctuations, while in the well deformed Er isotopes the two-quasiparticle states are more relevant. In between, both degrees of freedom are necessary.

We perform simultaneous analysis of (1) matter radii, (2) $B(E2;0^{+}\to 2^{+})$ transition probabilities, and (3) excitation energies, $E\left(2^{+}\right)$ and $E\left(4^{+}\right)$, for ${}^{24\text{–}40}\mathrm{Mg}$ by using the beyond-mean-field (BMF) framework with angular-momentum-projected configuration mixing with respect to the axially symmetric ${\beta }_2$ deformation with infinitesimal cranking. The BMF calculations successfully reproduce all of the data for $r_{\mathrm{m}},B\left(E2\right)$, and $E\left(2^{+}\right)$ and $E\left(4^{+}\right)$, indicating that it is quite useful for data analysis; particularly for low-lying states. We also discuss the absolute value of the deformation parameter ${\beta }_2$ deduced from measured values of $B\left(E2\right)$ and $r_{\mathrm{m}}$. This framework makes it possible to investigate the effects of ${\beta }_2$ deformation, the change in ${\beta }_2$ due to restoration of rotational symmetry, ${\beta }_2$ configuration mixing, and the inclusion of time-odd components by infinitesimal cranking. Under the assumption of axial deformation and parity conservation, we clarify which effect is important for each of the three measurements and propose the kinds of BMF calculations that are practical for each of the three kinds of observables.

High-spin states in the ${}^{129}\mathrm{Xe}$ nucleus are studied with the reaction ${}^{124}\mathrm{Sn}\left({}^9\mathrm{Be},4n\right)$ at a beam energy of 36 MeV. The level scheme is extended significantly. For the positive-parity band, the $\alpha =+1/2$ and the $\alpha =-1/2$ signature components are combined to form a complete band structure based on the $3/2^{+}$ state with spin and parity up to $21/2^{+}$. For the negative-parity band based on the $11/2^{-}$ state, the $\alpha =+1/2$ signature component is newly established and both the $\alpha =+1/2$ and the $\alpha =-1/2$ signature components also form a complete band structure up to the $35/2^{-}$ state. The positive- and negative-parity bands are proposed to originate from $\nu d_{3/2}3/2^{+}\left[402\right]$ and $\nu h_{11/2}11/2^{-}\left[505\right]$ Nilsson configurations, respectively. A backbending is observed in the negative-parity band, which originates from the alignments of two $h_{11/2}$ protons according to crank shell model calculations. Based on the total Routhian surface and quasiparticle triaxial rotor model calculations, the negative-parity band is interpreted as a triaxially deformed shape with $\gamma \approx -{30}^{\circ }$, while the positive-parity band is associated with $\gamma$ softness, in accordance with previous studies. In the high-spin states, three decoupled bands and one oblate band with $\gamma \approx -{60}^{\circ }$ are newly identified. The systematics and other characteristics of these bands are discussed.

We describe the evolution of the compact system formed by the touching of two colliding ions in reactions ${}^{58}\text{Fe}+{}^{248}\text{Cm}\to {}^{306-x}122+xn,{}^{64}\text{Ni}+{}^{244}\text{Pu}\to {}^{308-x}122+xn$, and ${}^{90}\text{Zr}+{}^{208}\text{Pb}\to {}^{298-x}122+xn$. The description is carried out within the dynamical multidimensional stochastic approach, based on Langevin equations for the shape degrees of freedom of colliding ions and the compact system. For the approach stage we take into account the shell structure of colliding ions, their orientation in the space, and the effect of tunneling of ions through the Coulomb barrier. By describing the evolution of the compact system formed after the touching of incident ions, the shell structure of the compact system is also taken into account. Within this approach we have calculated the compound nucleus and evaporation residue formation cross sections. These can be compared with the experimental data. We have also clarified the impact of the tunneling effect in the entrance channel on the fusion and evaporation residue cross sections.

We report on the measurement of $J/\psi$ production in the dielectron channel at midrapidity $\left(\left|y\right|<1\right)$ in $p+p$ and $d+\mathrm{Au}$ collisions at $\sqrt{s_{NN}}=200\mathrm{GeV}$ from the STAR experiment at the Relativistic Heavy Ion Collider. The transverse momentum $p_T$ spectra in $p+p$ for $p_T<4\mathrm{GeV}/c$ and $d+\mathrm{Au}$ collisions for $p_T<3\mathrm{GeV}/c$ are presented. These measurements extend the STAR coverage for $J/\psi$ production in $p+p$ collisions to low $p_T$. The $\langle p_T^2\rangle$ from the measured $J/\psi$ invariant cross section in $p+p$ and $d+\mathrm{Au}$ collisions are evaluated and compared to similar measurements at other collision energies. The nuclear modification factor for $J/\psi$ is extracted as a function of $p_T$ and collision centrality in $d+\mathrm{Au}$ and compared to model calculations using the modified nuclear parton distribution function and a final-state $J/\psi$ nuclear absorption cross section.

Time reversal invariance violating parity conserving (TVPC) effects are calculated for elastic proton-deuteron scattering with proton energies up to 2 MeV. The distorted-wave Born approximation is employed to estimate TVPC matrix elements, based on hadronic wave functions, obtained by solving three-body Faddeev-Merkuriev equations in configuration space with realistic potentials.

The $f_1\left(1285\right)$ meson with mass $1281.0\pm 0.8$ MeV/$c^2$ and width $18.4\pm 1.4$ MeV (full width at half maximum) was measured for the first time in photoproduction from a proton target using CLAS at Jefferson Lab. Differential cross sections were obtained via the $\eta {\pi }^{+}{\pi }^{-},K^{+}{\overline{K}}^0{\pi }^{-}$, and $K^{-}{K}^0{\pi }^{+}$ decay channels from threshold up to a center-of-mass energy of 2.8 GeV. The mass, width, and an amplitude analysis of the $\eta {\pi }^{+}{\pi }^{-}$ final-state Dalitz distribution are consistent with the axial-vector $J^P=1^{+} f_1\left(1285\right)$ identity, rather than the pseudoscalar $0^{-} \eta \left(1295\right)$. The production mechanism is more consistent with $s$-channel decay of a high-mass $N^{*}$ state and not with $t$-channel meson exchange. Decays to $\eta \pi \pi$ go dominantly via the intermediate $a_0^{\pm }\left(980\right){\pi }^{\mp }$ states, with the branching ratio $\mathrm{\Gamma }\left[a_0\pi \text{(no}\overline{K}K\text{)}\right]/\mathrm{\Gamma }\left[\eta \pi \pi \text{(all)}\right]=0.74\pm 0.09$. The branching ratios $\mathrm{\Gamma }\left(K\overline{K}\pi \right)/\mathrm{\Gamma }\left(\eta \pi \pi \right)=0.216\pm 0.033$ and $\mathrm{\Gamma }\left(\gamma {\rho }^0\right)/\mathrm{\Gamma }\left(\eta \pi \pi \right)=0.047\pm 0.018$ were also obtained. The first is in agreement with previous data for the $f_1\left(1285\right)$, while the latter is lower than the world average.

The structure of ${}^{210}\mathrm{Fr}$ has been established up to an excitation energy of $\sim 5.5$ MeV and spins of $\sim 25\hslash$, via time-correlated $\gamma$-ray spectroscopy and using the ${}^{197}\mathrm{Au}$(${}^{18}\mathrm{O},5n$)${}^{210}\mathrm{Fr}$ reaction with pulsed beams at an energy of 97 MeV. A significantly different level scheme has been obtained compared to previous publications. Several isomers are reported here, including a $J^{\pi }={\left(23\right)}^{+},\tau =686\left(9\right)$-ns state at 4417 keV and a ${10}^{-}$, 29.8(11)-ns state at 1113 keV. The former isomer has been associated with the $\pi \left(h_{9/2}^3{i}_{13/2}^2\right)\nu \left(p_{1/2}^{-2}{f}_{5/2}^{-1}\right)$ configuration and decays via proposed $E3$ transitions with strengths of 8.4(3) and 21.2(8) W.u. There are only very few known cases of a high-spin isomer decaying via two parallel $E3$ transitions. Indeed, this is not seen in other Fr nuclei, and consequently these strengths differ from related decays in the neighboring isotopes. However, by examining the systematics of $E3$ transitions in trans-lead nuclei, we suggest that the weaker of the two transitions decays to a mixed ${20}^{-}$ state. Systematics of the ${10}^{-}$ isomer are also discussed. Comparisons are made between the observed spectrum of states and those predicted from semiempirical shell-model calculations.

Background: Complete fusion cross sections in collisions of light weakly bound nuclei and high-$Z$ targets show suppression of complete fusion at above-barrier energies. This has been interpreted as resulting from the breakup of the weakly bound nucleus prior to reaching the fusion barrier, reducing the probability of complete charge capture. Below-barrier studies of reactions of ${}^9\mathrm{Be}$ have found that the breakup of ${}^8\mathrm{Be}$ formed by neutron stripping dominates over direct breakup and that transfer-triggered breakup may account for the observed suppression of complete fusion.

Purpose: This paper investigates how the above conclusions are affected by lifetimes of the resonant states that are populated prior to breakup. If the mean life of a populated resonance (above the breakup threshold) is much longer than the fusion time scale, then its breakup (decay) cannot suppress complete fusion. For short-lived resonances, the situation is more complex. This work explicitly includes the mean life of the short-lived $2^{+}$ resonance in ${}^8\mathrm{Be}$ in classical dynamical model calculations to determine its effect on energy and angular correlations of the breakup fragments and on model predictions of suppression of cross sections for complete fusion at above-barrier energies.

Method: Previously performed coincidence measurements of breakup fragments produced in reactions of ${}^9\mathrm{Be}$ with ${}^{144}\mathrm{Sm}, {}^{168}\mathrm{Er}, {}^{186}\mathrm{W}, {}^{196}\mathrm{Pt}, {}^{208}\mathrm{Pb}$, and ${}^{209}\mathrm{Bi}$ at energies below the barrier have been reanalyzed using an improved efficiency determination of the BALiN detector array. Predictions of breakup observables and of complete and incomplete fusion at energies above the fusion barrier are then made using the classical dynamical simulation code platypus, modified to include the effect of lifetimes of resonant states.

Results: The agreement of the breakup observables is much improved when lifetime effects are included explicitly. Sensitivity to subzeptosecond lifetime is observed. The predicted suppression of complete fusion owing to breakup is nearly independent of $Z$ and has an average value of $\sim 9\%$. This is below the experimentally determined fusion suppression, which is typically $\sim 30\%$ in these systems.

Conclusions: Inclusion of resonance lifetimes is essential to correctly reproduce breakup observables. This results in a larger fraction of nuclei remaining intact at the fusion-barrier radius compared with calculations that do not explicitly include lifetime effects. The more realistic treatment of breakup followed in this work leads to the conclusion that the suppression of complete fusion cannot be fully explained by breakup prior to reaching the fusion barrier. Only one-third of the observed fusion suppression can be attributed to the competing process of breakup. Other mechanisms that can suppress complete fusion must therefore be investigated. One of the possible candidates is cluster transfer that produces the same heavy targetlike nuclei as those formed by incomplete fusion.

The half-lives of deformed cluster emission have been calculated by using the proximity potential Christensen-Winther potential form (1976) and compared to the experimental data and theoretical results of the liquid drop model. Also the calculated results have been compared to the results obtained by a universal form of the proximity potential for spherical cluster emission. The results show reasonable agreement with the experimental data.

Background: Measurements of polarization observables for the reactions $\vec{\gamma }p\to K^{+}\mathrm{\Lambda }$ and $\vec{\gamma }p\to K^{+}{\mathrm{\Sigma }}^0$ have been performed. This is part of a program of measurements designed to study the spectrum of baryon resonances in particular, and nonperturbative QCD in general.

Purpose: The accurate measurement of several polarization observables provides tight constraints for phenomenological fits, which allow the study of strangeness in nucleon and nuclear systems. Beam-recoil observables for the $\vec{\gamma }p\to K^{+}{\mathrm{\Sigma }}^0$ reaction have not been reported before now.

Method: The measurements were carried out using linearly polarized photon beams incident on a liquid hydrogen target, and the CLAS detector at the Thomas Jefferson National Accelerator Facility. The energy range of the results is $1.71<W<2.19\mathrm{GeV}$, with an angular range $-0.75<cos{\theta }_K^{\star }<+0.85$.

Results: The observables extracted for both reactions are beam asymmetry $\mathrm{\Sigma }$, target asymmetry $T$, and the beam-recoil double polarization observables $O_x$ and $O_z$.

Conclusions: Comparison with theoretical fits indicates that, in the regions where no previous data existed, the new data contain significant new information, and strengthen the evidence for the set of resonances used in the latest Bonn-Gatchina fit.

Nucleonic matter is described within an SU(2) extended Nambu–Jona-Lasinio (NJL) model. Several parametrizations with different nuclear matter saturation properties are proposed. At subsaturation, nuclear pasta phases are calculated within two methods: the coexistence-phases approximation and the compressible liquid drop model, with the surface tension coefficient determined using a geometrical approach at zero temperature. A unified equation of state of stellar matter for the inner crust, with the nuclear pasta phases, and the core is calculated. The mass and radius of neutron stars within this framework are obtained for several families of hadronic and hybrid stars. The quark phase of hybrid stars is described within the SU(3) NJL model including a vector term. Stellar macroscopic properties are in accordance with some of the recent results in the literature.

We perform a detailed analysis of the properties of the finite-range tensor term associated with the Gogny and M3Y effective interactions. In particular, by using a partial-wave decomposition of the equation of state of symmetric nuclear matter, we show how we can extract their tensor parameters directly from microscopic results based on bare nucleon-nucleon interactions. Furthermore, we show that the zero-range limit of both finite-range interactions has the form of the next-to-next-to-next-leading-order (N3LO) Skyrme pseudopotential, which thus constitutes a reliable approximation in the density range relevant for finite nuclei. Finally, we use Brueckner-Hartree-Fock results to fix the tensor parameters for the three effective interactions.

The particle-hole symmetry (equivalence) of the full shell-model Hilbert space is straightforward and routinely used in practical calculations. In this work I show that this symmetry is preserved in the subspace truncated up to a certain generalized seniority and give the explicit transformation between the states in the two types (particle and hole) of representations. Based on the results, I study particle-hole symmetry in popular theories that could be regarded as further truncations on top of the generalized seniority, including the microscopic interacting boson (fermion) model, the nucleon-pair approximation, and other models.

We have performed the ${}^{70}\mathrm{Zn}(d,{}^3\mathrm{He}){}^{69}\mathrm{Cu}$ proton pick-up reaction in direct kinematics using a deuteron beam at 27 MeV. The outgoing ${}^3\mathrm{He}$ particles were detected at the focal-plane detection system of an Enge split-pole spectrometer. The excitation-energy spectrum was reconstructed up to 7 MeV and spectroscopic factors were obtained after analysis of the angular distributions in the finite-range distorted-wave Born approximation. The results show three new angular distributions for which the $\pi f_{7/2}$ strength was measured and a lower limit of the centroid is established. State-of-the-art shell-model calculations are performed and predict a $\pi f_{7/2}$ strength that lies too high in energy in comparison to our experimental results.

We compute the isospin-asymmetry dependence of microscopic optical model potentials from realistic chiral two- and three-body interactions over a range of resolution scales $\mathrm{\Lambda }\simeq 400–500$ MeV. We show that at moderate projectile energies, $E=110–200$ MeV, the real isovector part of the optical potential changes sign, a phenomenon referred to as isospin inversion. We also extract the strength and energy dependence of the imaginary isovector optical potential and find no evidence for an analogous phenomenon over the range of energies, $E\le 200$ MeV, considered in the present work. Finally, we compute for the first time the leading (quadratic) corrections to the Lane parametrization for the isospin-asymmetry dependence of the optical potential and observe an enhanced importance at low scattering energies.

The ${}^{11}\mathrm{C}{(\alpha ,p)}^{14}\mathrm{N}$ reaction is an important $\alpha$-induced reaction competing with $\beta$-limited hydrogen-burning processes in high-temperature explosive stars. We directly measured its reaction cross sections both for the ground-state transition $(\alpha ,p_0)$ and the excited-state transitions $(\alpha ,p_1)$ and $(\alpha ,p_2)$ at relevant stellar energies 1.3–4.5 MeV by an extended thick-target method featuring time of flight for the first time. We revised the reaction rate by numerical integration including the $(\alpha ,p_1)$ and $(\alpha ,p_2)$ contributions and also low-lying resonances of $(\alpha ,p_0)$ using both the present and the previous experimental data which were totally neglected in the previous compilation works. The present total reaction rate lies between the previous $(\alpha ,p_0)$ rate and the total rate of the Hauser-Feshbach statistical model calculation, which is consistent with the relevant explosive hydrogen-burning scenarios such as the $\nu p$ process.

Using an array of high-purity Compton-suppressed germanium detectors, we performed an independent measurement of the $\beta$-decay branching ratio from ${}^{12}\mathrm{B}$ to the second-excited state, also known as the Hoyle state, in ${}^{12}\mathrm{C}$. Our result is $0.64\left(11\right)\%$, which is a factor $\sim 2$ smaller than the previously established literature value, but is in agreement with another recent measurement. This could indicate that the Hoyle state is more clustered than previously believed. The angular correlation of the Hoyle state $\gamma$ cascade has also been measured for the first time. It is consistent with theoretical predictions.