The Buck-Perez analysis of mirror nuclei magnetic moments has been applied on an updated set of data for $T=1/2,3/2$ mirror pairs and attempted for the first time for $T=5/2$ nuclei. The spin expectation value for mirror nuclei up to mass $A=63$ has been reexamined. The main purpose is to test Buck-Perez analysis effectiveness as a prediction and—more importantly—an evaluation tool of magnetic moments in mirror nuclei. In this scheme, ambiguous signs of magnetic moments are resolved, evaluations of moments with multiple existing measurements have been performed, and a set of predicted values for missing moments, especially for several neutron-deficient nuclei is produced. A resolution for the case of the ${}^{57}\mathrm{Cu}$ ground-state magnetic moment is proposed. Overall, the method seems to be promising for future evaluations and planning future measurements.

A new method is suggested to extract pure transfer probabilities from the experimental data. For the ${}^{40}\text{Ca}+{}^{96}\text{Zr}$ reaction at sub-barrier energies, the one- and two-neutron transfer probabilities at backward angle are extracted from the experimental capture (fusion) and transfer excitation functions. The pure one- and two-neutron transfer probabilities are shown to be close at the barrier.

Neutron evaporation spectra have been measured from ${}^4\mathrm{He}+{}^{208}\mathrm{Pb}$ and ${}^4\mathrm{He}+{}^{209}\mathrm{Bi}$ reactions by using ${}^4\mathrm{He}$-ion beams of several bombarding energies. Excitation-energy dependence of the level density parameter has been studied for the two systems in the excitation energy range of $\sim 18$–50 MeV. For both the reactions an overall reduction of the asymptotic level density parameter with increasing excitation energy (temperature) is observed. The trend of the data was compared with the Thomas–Fermi model predictions and found to be in reasonable agreement. The value of the shell damping parameter has been extracted from the lowest-energy data in the case of ${}^{210,211}\mathrm{Po}$ and ${}^{211,212}\mathrm{At}$ nuclei close to the $Z=82$ and $N=126$ shell closure, and it was found to be consistent with the recent measurement in the vicinity of doubly magic ${}^{208}\mathrm{Pb}$ nucleus.

Two-particle correlation measurements and analysis are an important component of the relativistic heavy-ion physics program. In particular, particle pair-number correlations on two-dimensional transverse momentum ($p_t$) allow unique access to soft, semihard, and hard scattering processes in these collisions. Precise measurements of this type of correlation are essential for understanding the dynamics in heavy-ion collisions. However, transverse momentum correlation measurements are especially vulnerable to statistical and systematic biases. In this paper the origins of these large bias effects are explained and mathematical correlation forms are derived from mean-$p_t$ fluctuation quantities in the literature. Monte Carlo simulations are then used to determine the conditions, e.g., multiplicity and collision centrality bin widths, where each correlation form is minimally biased. The ranges of applicability for each correlation quantity are compared. Several are found to reproduce the assumed input correlations with reasonable fidelity over a wide range of conditions encountered in practical analysis of data.

The structure of the two-neutron halo ${}^{22}\mathrm{C}$ is investigated by means of a renormalized zero-range three-body model, with interactions in the $s$-wave channel, and a finite-range model with two- and three-body forces provided by the hyperspherical adiabatic expansion method. In both models the halo wave function in configuration space is obtained by using as inputs the two-body scattering lengths and the two-neutron separation energy. The halo-matter density is computed for ${}^{22}\mathrm{C}$ with different three-body forces and low-energy parameters, with two-neutron separation energy within the range $50\text{keV}\le S_{2n}\le 1000$ keV. The halo-neutron density depends weakly on the neutron-${}^{20}\mathrm{C}$ scattering length as long as its absolute value is larger than the neutron-neutron one. The halo-neutron density is then analyzed by means of the root-mean-square radius, the probability density, and also the geometry, taking into account the angle between the two Jacobi coordinates. The results of finite-range and zero-range two-neutron-core models are compared. The effects in the halo structure of short-range and long-range three-body forces are studied, and the emergent universal behavior of the halo-neutron density and its geometry is pointed out.

We have measured for the first time the charge-changing cross sections $\left({\sigma }_{\text{CC}}\right)$ of ${}^{12\text{–}16}\mathrm{C}$ on a ${}^{12}\mathrm{C}$ target at energies below $100A$ MeV. To analyze these low-energy data, we have developed a finite-range Glauber model with a global parameter set within the optical-limit approximation which is applicable to reaction cross section $\left({\sigma }_{\text{R}}\right)$ and ${\sigma }_{\text{CC}}$ measurements at incident energies from $10A$ to $2100A$ MeV. Adopting the proton-density distribution of ${}^{12}\mathrm{C}$ known from the electron-scattering data, as well as the bare total nucleon-nucleon cross sections and the real-to-imaginary-part ratios of the forward proton-proton elastic scattering amplitude available in the literatures, we determine the energy-dependent slope parameter ${\beta }_{pn}$ of the proton-neutron elastic differential cross section so as to reproduce the existing ${\sigma }_{\text{R}}$ and interaction cross-section data for ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ over a wide range of incident energies. The Glauber model thus formulated is applied to calculate the ${\sigma }_{\text{R}}$'s of ${}^{12}\mathrm{C}$ on a ${}^9\mathrm{Be}$ and ${}^{27}\mathrm{Al}$ targets at various incident energies. Our calculations show excellent agreement with the experimental data. Applying our model to the ${\sigma }_{\text{R}}$ and ${\sigma }_{\text{CC}}$ for the so-called neutron-skin ${}^{16}\mathrm{C}$ nucleus, we reconfirm the importance of measurements at incident energies below $100A$ MeV. The proton root-mean-square radii of ${}^{12\text{–}16}\mathrm{C}$ are extracted using the measured ${\sigma }_{\text{CC}}$'s and the existing ${\sigma }_{\text{R}}$ data. The results for ${}^{12\text{–}14}\mathrm{C}$ are consistent with the values from the electron scatterings, demonstrating the feasibility, usefulness of the ${\sigma }_{\text{CC}}$ measurement, and the present Glauber model.

The Tamura coupling model [Rev. Mod. Phys. 37, 679 (1965)] has been extended to consider the coupling of additional low-lying rotational bands to the ground-state band. Rotational bands are built on vibrational bandheads (even-even targets) or single-particle bandheads (odd-$A$ targets) including both axial and nonaxial deformations. These additional excitations are introduced as a perturbation to the underlying axially symmetric rigid-rotor structure of the ground-state rotational band. Coupling matrix elements of the generalized optical model are derived for extended multiband transitions in even-even and odd-$A$ nuclei. Isospin symmetric formulation of the optical model is employed. A coupled-channels optical-model potential (OMP) containing a dispersive contribution is used to fit simultaneously all available optical experimental databases including neutron strength functions for nucleon scattering on ${}^{232}\mathrm{Th},{}^{233,235,238}\mathrm{U}$, and ${}^{239}\mathrm{Pu}$ nuclei. Quasielastic $\left(p,n\right)$ scattering data on ${}^{232}\mathrm{Th}$ and ${}^{238}\mathrm{U}$ to the isobaric analog states of the target nucleus are also used to constrain the isovector part of the optical potential. Lane consistent OMP is derived for all actinides if corresponding multiband coupling schemes are defined. For even-even (odd-$A$) actinides almost all low-lying collective levels below 1 MeV (0.5 MeV) of excitation energy are coupled. OMP parameters show a smooth energy dependence and energy-independent geometry. A phenomenological optical-model potential that couples multiple bands in odd-$A$ actinides is published for a first time. Calculations using the derived OMP potential reproduce measured total cross-section differences between several actinide pairs within experimental uncertainty for incident neutron energies from 50 keV up to 150 MeV. The importance of extended coupling is studied. Multiband coupling is stronger in even-even targets owing to the collective nature of the coupling; the impact of extended coupling on predicted compound-nucleus formation cross section reaches 5% below 3 MeV of incident neutron energy. Excitation of multiple bands in odd-$A$ targets is weaker owing to the single-particle nature of the coupling. Coupling of ground-state rotational band levels in odd-$A$ nuclei is sufficient for a good description of the compound-nucleus formation cross sections as long as the coupling is saturated (a minimum of seven coupled levels are typically needed).

The outer crust of a cold nonaccreting neutron star has been generally assumed to be stratified into different layers, each of which consists of a pure body-centered cubic ionic crystal in a charge compensating background of highly degenerate electrons. The validity of this assumption is examined by analyzing the stability of multinary ionic compounds in dense stellar matter. It is thus shown that their stability against phase separation is uniquely determined by their structure and their composition irrespective of the stellar conditions. However, equilibrium with respect to weak and strong nuclear processes imposes very stringent constraints on the composition of multinary compounds, and thereby on their formation. By examining different cubic and noncubic lattices, it is found that substitutional compounds having the same structure as cesium chloride are the most likely to exist in the outer crust of a nonaccreting neutron star. The presence of ternary compounds is also investigated. Very accurate analytical expressions are obtained for the threshold pressure, as well as for the densities of the different phases irrespective of the degree of relativity of the electron gas. Finally, numerical calculations of the ground-state structure and of the equation of state of the outer crust of a cold nonaccreting neutron star are carried out using recent experimental and microscopic nuclear mass tables.

Quantum phase transitions between competing ground-state shapes of atomic nuclei with an odd number of protons or neutrons are investigated in a microscopic framework based on nuclear energy density functional theory and the particle-plus-boson-core coupling scheme. The boson-core Hamiltonian, as well as the single-particle energies and occupation probabilities of the unpaired nucleon, are completely determined by constrained self-consistent mean-field calculations for a specific choice of the energy density functional and paring interaction, and only the strength parameters of the particle-core coupling are adjusted to reproduce selected spectroscopic properties of the odd-mass system. We apply this method to odd-$A$ Eu and Sm isotopes with neutron number $N\approx 90$, and explore the influence of the single unpaired fermion on the occurrence of a shape phase transition. Collective wave functions of low-energy states are used to compute quantities that can be related to quantum order parameters: deformations, excitation energies, $E2$ transition rates, and separation energies, and their evolution with the control parameter (neutron number) is analyzed.

We study the effect of strong magnetic fields, of the order of ${10}^{15}–{10}^{17}$ G, on the extension of the crust of magnetized neutron stars. The dynamical instability region of neutron-proton-electron $\left(npe\right)$ matter at subsaturation densities and the mode with the largest growth rate are determined within a relativistic mean-field model. It is shown that the effect of a strong magnetic field on the instability region is very sensitive to the density dependence of the symmetry energy, and that it is at the origin of an increase of the extension of the crust and of the charge content of clusters.

Neutron skins in coordinate space and proton skins in momentum space are predicted to coexist in heavy nuclei, and their correlation is governed by Liouville's theorem and Heisenberg's uncertainty principle. An analysis of their correlation within a further extended Thomas-Fermi approximation incorporating effects of nucleon short-range correlations reveals generally that protons move faster than neutrons in neutron skins of heavy nuclei.

Background: A characteristic observable of nuclear collective motion is the relative $B\left(E2\right)$ values from the $\gamma$ band to the ground band in even-even deformed nuclei. The Alaga rules provide an idealized set of benchmarks for these observables. However, deviations from the Alaga rules are universally observed and have been traditionally and successfully interpreted in terms of parameterized $\gamma$-band–ground-band bandmixing. An alternate approach, partial dynamical symmetries, has no bandmixing whatsoever and is parameter free, yet mimics closely the effects of bandmixing, due solely to the effects of finite valence nucleon number.

Purpose: To investigate the relation between these two seemingly contradictory approaches to understand how they can produce such similar results.

Method: To derive approximate relations between the two formalisms.

Results: A consistent relationship is found linking bandmixing to finite valence nucleon number effects on interband $\gamma$ to ground-band $B\left(E2\right)$ values.

Conclusions: Two disparate approaches to one of the iconic characteristics of deformed nuclei are shown to be intimately related. Moreover, a systematic difference in their predictions also emerges naturally from the derivation. The qualitative linkage of valence nucleon number and the separation of vibrational and rotational degrees of freedom has long been assumed but never before explicitly demonstrated through complementary models.

‘‘Subthreshold pions” and so-called “hard photons” are two important channels for producing less than 1 GeV $\gamma$ rays and $e^{\pm }$ pairs from nuclear collisions with energy per nucleon below the $\pi$-meson production threshold. I use publicly available experimental data to parametrize these two channels’ $\gamma$-ray and $e^{\pm }$ production cross sections and extend the pion contribution to these particles spectra at higher energies using their corresponding spectra from $pp$ interactions. These parametrizations are valid for collision energy $T_p\le 100A$ GeV and agree reasonably well with the available experimental data. The new parametrizations allow, for the first time, accurate studies of astrophysical $\gamma$ rays below 1 GeV.

The PHENIX experiment at the BNL Relativistic Heavy Ion Collider has measured second- and third-order Fourier coefficients of the azimuthal distributions of direct photons emitted at midrapidity in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{s_{{}_{NN}}}=200$ GeV for various collision centralities. Combining two different analysis techniques, results were obtained in the transverse momentum range of $0.4<p_T<4.0 \text{GeV}/c$. At low $p_T$ the second-order coefficients, $v_2$, are similar to the ones observed in hadrons. Third-order coefficients, $v_3$, are nonzero and almost independent of centrality. These new results on $v_2$ and $v_3$, combined with previously published results on yields, are compared to model calculations that provide yields and asymmetries in the same framework. Those models are challenged to explain simultaneously the observed large yield and large azimuthal anisotropies.

The structure of ${}^{29}\mathrm{Al}$ and ${}^{27}\mathrm{Mg}$ was investigated using the reactions ${}^{18}\mathrm{O}$(${}^{14}\mathrm{C},p2n$) and ${}^{18}\mathrm{O}$(${}^{14}\mathrm{C},\alpha n$) at 40 MeV. The charged particles were detected and identified with a $\mathrm{\Delta }E-E$ telescope in coincidence with $\gamma$ radiation detected in the Florida State University Compton suppressed $\gamma$ detector array. The level and decay schemes of both nuclei have been expanded at higher spins and excitation energies. The positive-parity states up to 3.5–4.5 MeV agree well with shell model calculations using the USDA interaction. The negative-parity states in ${}^{27}\mathrm{Mg}$ are reproduced relatively well by one-particle–one-hole calculations with the WBP-a interaction. Three ${}^{27}\mathrm{Mg}$ states unbound by 0.4–1.4 MeV to neutron decay were observed to decay radiatively. One of these states had been previously observed to $\gamma$ decay in a ($d,p\gamma$) experiment along with a surprising 16 other neutron unbound states. The competition between neutron and $\gamma$ decay in these states is discussed in terms of angular momentum barriers and spectroscopic factors.

We have calculated the spectroscopic factor strengths for the one-proton and one-neutron pick-up reactions ${}^{27}\mathrm{Al}$($d,{}^3\mathrm{He}$)${}^{26}\mathrm{Mg}$ and ${}^{27}\mathrm{Al}$($d,t$)${}^{26}\mathrm{Al}$ within the framework of the shell model. We employed two different ab initio approaches: an in-medium similarity renormalization targeted for a particular nucleus, and the coupled-cluster effective interaction. We also compared our results with recently determined experimental spectroscopic factors.

New results for matter radii of C nuclei have prompted an update on the experimental and theoretical research on this topic. Newest results for ${}^{22}\mathrm{C}$ suggest a major change may be needed in our understanding of the separation energy of that nucleus.

For suggested cluster states beginning at about 10 MeV in ${}^{12}\mathrm{Be}$, absolute energy and relative energy spacings agree well with calculations for the ${}^8\mathrm{Be}\times {\left(sd\right)}^4$ configuration. Comparison indicates that the proposed $\left(8^{+}\right)$ state at 20.9 MeV is probably $6^{+}$. A similar calculation for ${}^{14}\mathrm{Be}$ predicts that the lowest ${\left(sd\right)}^2$ and ${\left(sd\right)}^4$ states are rather close together in that nucleus.

The structure of ${}^{133}\text{La}$ has been investigated using the ${}^{116}\text{Cd}({}^{22}\text{Ne},4pn)$ reaction and the Gammasphere array. Three new bands of quadrupole transitions and one band of dipole transitions are identified and the previously reported level scheme is revised and extended to higher spins. The observed structures are discussed using the cranked Nilsson-Strutinsky formalism, covariant density functional theory, and the particle-rotor model. Triaxial configurations are assigned to all observed bands. For the high-spin bands it is found that rotations around different axes can occur, depending on the configuration. The orientation of the angular momenta of the core and of the active particles is investigated, suggesting chiral rotation for two nearly degenerate dipole bands and magnetic rotation for one dipole band. It is shown that the $h_{11/2}$ neutron holes present in the configuration of the nearly degenerate dipole bands have significant angular momentum components not only along the long axis but also along the short axis, contributing to the balance of the angular momentum components along the short and long axes and thus giving rise to a chiral geometry.

Dynamical calculations based on a four-dimensional stochastic Langevin approach are used to study fission in the Businaro-Gallone region. The use of such a model to map the Businaro-Gallone transition is proposed for the first time, exploiting recent theoretical developments and computing resources. The significance of the approach is supported by a systematic comparison with measurements for a set of systems. Experimental observations on fission-fragment charge distributions, which remained unexplained within a unified framework so far, are described by the dynamical model in a consistent manner. A detailed analysis reveals the interplay of dynamical effects, going beyond statistical-models interpretation and suggesting to revisit the commonly admitted idea about the prevalence of static effects in the Businaro-Gallone region.