In the random-phase-approximation–amended (RPA-amended) Nilsson–Strutinskij method of calculating nuclear binding energies, the conventional shell correction terms derived from the independent-nucleon model and the Bardeen–Cooper–Schrieffer pairing theory are supplemented by a term which accounts for the pair-vibrational correlation energy. This term is derived by means of the RPA from a pairing Hamiltonian which includes a neutron-proton pairing interaction. The method was used previously in studies of the pattern of binding energies of nuclei with approximately equal numbers $N$ and $Z$ of neutrons and protons and even mass number $A=N+Z$. Here it is applied to odd-$A$ nuclei. Three sets of such nuclei are considered: (i) the sequence of nuclei with $Z=N-1$ and $25\le A\le 99$; (ii) the odd-$A$ isotopes of In, Sn, and Sb with $46\le N\le 92$; (iii) the odd-$A$ isotopes of Sr, Y, Zr, Nb, and Mo with $60\le N\le 64$. The RPA correction is found to contribute significantly to the calculated odd-even mass differences, particularly in the light nuclei. In the upper $sd$ shell this correction accounts for almost the entire odd-even mass difference for odd $Z$ and about half of it for odd $N$. The size and sign of the RPA contribution varies, which is explained qualitatively in terms of a closed expression for a smooth RPA counter term.

To study exotic odd nuclear systems, the self-consistent continuum Skyrme-Hartree-Fock-Bogoliubov theory formulated with Green's function technique is extended to include blocking effects with the equal filling approximation. Detailed formulas are presented. By comparing with box-discretized calculations, the great advantages of the Green's function method in describing the extended density distributions, resonant states, and the couplings with the continuum in exotic nuclei are shown. Taking the neutron-rich odd nucleus ${}^{159}\mathrm{Sn}$ as an example, the halo structure is investigated by blocking the lowest quasiparticle state. We find that it is mainly the weakly bound states near the Fermi surface that contribute a lot to the extended density distributions at large coordinate space. Finally, taking the neutron-rich Sn isotopes with mass numbers $A=122\text{–}178$ as examples, the halo structures are studied systematically. The small two-neutron separation energy and the low Fermi energy in a long mass range after the shell $N=82$ offer a good environment for the emergence of the halo structure. The neutron rms radius in ${}^{133}\mathrm{Sn}$ and the heavier isotopes display a steep increase with $A$ and deviate from the traditional rule of $r\propto A^{1/3}$. Correspondingly, the densities for those nuclei are very extended. Besides, the odd-even staggering of neutron radius $r_{\mathrm{rms}}$ is observed in the mass region $A=151\text{–}165$, due to the occupations of the odd neutrons on the low $p$ orbits.

Hyperfine-structure parameters and isotope shifts for the 795-nm atomic transitions in ${}^{217,218,219}\mathrm{At}$ have been measured at CERN-ISOLDE, using the in-source resonance-ionization spectroscopy technique. Magnetic dipole and electric quadrupole moments, and changes in the nuclear mean-square charge radii, have been deduced. A large inverse odd-even staggering in radii, which may be associated with the presence of octupole collectivity, has been observed. Namely, the radius of the odd-odd isotope ${}^{218}\mathrm{At}$ has been found to be larger than the average of its even-$N$ neighbors, ${}^{217,219}\mathrm{At}$. The discrepancy between the additivity-rule prediction and experimental data for the magnetic moment of ${}^{218}\mathrm{At}$ also supports the possible presence of octupole collectivity in the considered nuclei.

Low-energy positive and negative parity collective states in the equilibrium minimum, and the dynamics of induced fission of actinide nuclei are investigated in a unified theoretical framework based on the generator coordinate method (GCM) with the Gaussian overlap approximation (GOA). The collective potential and inertia tensor, both at zero and finite temperature, are computed using the self-consistent multidimensionally constrained relativistic mean field model, based on the energy density functional DD-PC1. Pairing correlations are treated in the Bardeen-Cooper-Schrieffer approximation with a separable pairing force of finite range. A collective quadrupole-octupole Hamiltonian characterized by zero-temperature axially symmetric deformation energy surface and perturbative cranking inertia tensor, is used to model the low-lying excitation spectrum. The fission fragment charge distributions are obtained by propagating the initial collective states in time with the time-dependent GCM+GOA that uses the same quadrupole-octupole Hamiltonian, but with the collective potential and inertia tensor computed at finite temperature. The illustrative charge yields of ${}^{228}\mathrm{Th}$, ${}^{234}\mathrm{U}$, ${}^{240}\mathrm{Pu}$, ${}^{244}\mathrm{Cm}$, and ${}^{250}\mathrm{Cf}$ are in very good agreement with experiment, and the predicted mass asymmetry is consistent with the result of a recent microscopic study that has attributed the distribution (peak) of the heavier-fragment nuclei to shell-stabilized octupole deformations.

Based on the isospin-dependent quantum molecular dynamics model, finite-size scaling effects on nuclear liquid-gas phase transition probes are investigated by studying the de-excitation processes of six thermal sources of different sizes with the same initial density and similar $N/Z$. Using several probes including the total multiplicity derivative ($d{M}_{\text{tot}}/dT$), second moment parameter ($M_2$), intermediate mass fragment (IMF) multiplicity ($N_{\text{IMF}}$), Fisher's power-law exponent ($\tau$), and Ma's nuclear Zipf's law exponent ($\xi$), the relationship between the phase transition temperature and the source size has been established. It is observed that the phase transition temperatures obtained from the IMF multiplicity, Fisher's exponent, and Ma's nuclear Zipf's law exponent have a strong correlation with the source size. Moreover, by employing the finite-size scaling law, the critical temperature $T_c$ and the critical exponent $\nu$ were obtained for infinite nuclear matter.

Background: The “proton radius puzzle” refers to an 8-year-old problem that highlights major inconsistencies in the extraction of the charge radius of the proton from muonic Lamb-shift experiments as compared against experiments using elastic electron scattering. For the latter approach, the determination of the charge radius involves an extrapolation of the experimental form factor to zero momentum transfer.

Purpose: To estimate the proton radius, a novel and powerful nonparametric method based on a constrained Gaussian process is introduced. The constrained Gaussian process models the electric form factor as a function of the momentum transfer.

Methods: Within a Bayesian paradigm, we develop a model flexible enough to fit the data without any parametric assumptions on the form factor. The Bayesian estimation is guided by imposing only two physical constraints on the form factor: (a) its value at zero momentum transfer (normalization) and (b) its overall shape, assumed to be a monotonically decreasing function of the momentum transfer. Variants of these assumptions are explored to assess their impact.

Results: By adopting both constraints and incorporating the whole range of experimental data available we extracted a charge radius of $r_p=0.845\pm 0.001\mathrm{fm}$, consistent with the muonic experiment. Nevertheless, we show that within our model the extracted radius depends on both the assumed constraints and the range of experimental data used to fit the Gaussian process. For example, if only low-momentum-transfer data are used, relaxing the normalization constraint provides a value compatible with the larger electronic value.

Conclusions: We have presented a novel technique to estimate the proton radius from electron-scattering data based on a constrained Gaussian process. We demonstrated that the impact of imposing sensible physical constraints on the form factor is substantial. Also critical is the range of the experimental data used in the extrapolation. We are hopeful that as the technique gets refined, together with the anticipated new results from the PRad experiment, we will get closer to a resolution of the puzzle.

The parity-violating neutron spin rotation in ${}^4\mathrm{He}$ is studied at vanishing incident neutron energy limit. Calculations have been realized by solving five-body Faddeev-Yakubovsky equations in configuration space employing modern strong-interaction Hamiltonian based on chiral perturbation theory including three-nucleon force. Parity-violating nucleon-nucleon interaction of the Desplanques, Donoghue, and Holstein model is employed. An implication of the recent theoretical large-$N_c$ estimation of weak couplings [Phillips et al., Phys. Rev. Lett. 114, 062301 (2015)] is also discussed.

Cross sections for radiative neutron capture have been measured for the formation of 25-d ${}^{179}\mathrm{Hf}^{m_2}$ ($J^{\pi }=25/2^{+}$) using targets of enriched ${}^{178}\mathrm{Hf}$. Based on irradiations using pure epithermal neutrons as well as mixed thermal + epithermal neutrons, the thermal cross section has been determined to be $\sigma =6\left(5\right)\mu \mathrm{b}$ and the resonance integral $I=1.63\left(5\right)\mathrm{mb}$. To enhance the determination of the cross sections, the energies and intensities of the $\gamma$ rays from the decay of ${}^{179}\mathrm{Hf}^{m_2}$ have been re-determined with improved precision. The half-life of ${}^{179}\mathrm{Hf}^{m_2}$ has been measured to be 24.91(27) d, in agreement with the previously accepted value. The analysis of the ${}^{179}\mathrm{Hf}^{m_2}$ decay required more precise spectrometry on competing $\gamma$ rays from the decay of ${}^{181}\mathrm{Hf}$, whose results are presented (along with that of the decay of ${}^{175}\mathrm{Hf}$) from irradiation of a source of natural Hf. The measured cross sections are compared with those of other high-spin neutron captures.

The excited states of ${}^{197}\mathrm{Tl}$ have been studied via ${}^{197}\mathrm{Au}({}^4\mathrm{He}$, $4\mathrm{n}){}^{197}\mathrm{Tl}$ reaction at a beam energy of 50 MeV from the K-130 cyclotron at the Variable Energy Cyclotron Centre (VECC). The $\gamma$ rays were detected using the VECC array for Nuclear Spectroscopy (VENUS) with six Compton-suppressed clover HPGe detectors. An improved level scheme of ${}^{197}\mathrm{Tl}$ has been proposed from this work, which has been extended to 5.1 MeV of excitation energy and 39/2 $\hslash$ of spin from the placement of 28 new $\gamma$-ray transitions. Band crossings in the known one- and three-quasiparticle (qp) bands have been identified for the first time in this work. Two new bands, based on 3-qp and 5-qp configurations, have been observed for the first time in this nucleus; both of which are identified as the magnetic rotational (MR) in nature. The excitation energies of these bands are similar to that of the doubly degenerate bands observed for the similar 3-qp and 5-qp configurations in ${}^{195}\mathrm{Tl}$. These indicate a transition from an aplanar geometry of the neutron, proton, and the core angular momentum vectors to a planar one for neutron number $N\ge 116$ in Tl isotopes. The total Routhian surface calculations suggest a change in shape from oblate for the 1-qp configuration to a near-spherical one for the 3- and 5-qp configurations. This is consistent with the observed MR nature of the bands with multi-qp configuration. The MR bands are well reproduced by a model calculations in the frame work of the shears mechanism with the principal axis cranking.

Background: Selenium and germanium nuclei are associated with both triaxiality and shape coexistence. The relative influence of these deformation effects on the low-lying nuclear structure remains the subject of much discussion with additional attention drawn to ${}^{76}\mathrm{Se}$ and ${}^{76}\mathrm{Ge}$ due to the potential for the observation of neutrinoless double-$\beta$ decay.

Purpose: Experimental observables related to the deformation of ${}^{76}\mathrm{Se}$ are lacking in precision. The purpose of the present paper is to provide electric quadrupole matrix elements with improved precision in order to determine the deformation of low-lying states in a model-independent manner.

Methods: Sub-barrier Coulomb excitation was employed at the reaccelerated beam facility of the National Superconducting Cyclotron Laboratory using the JANUS setup. Using this method nineteen $E2$ matrix elements were extracted.

Results: Extracted matrix elements agree within uncertainties with those in the literature but with improved precision. Through both a comparison with geometric models and a model-independent evaluation of $E2$ matrix elements using rotational invariants, the ground state of ${}^{76}\mathrm{Se}$ is best described as having a significant triaxial component, but is not maximally triaxially deformed.

Conclusions: Selenium-76 exhibits a significant degree of triaxiality in its ground state. A detailed comparison with configuration-interaction calculations indicates that this can be well reproduced theoretically.

We perform time-dependent Hartree-Fock (TDHF) calculations, employing Skyrme functionals, to investigate the small amplitude dipole response of selected neutron-rich nuclei and Sn isotopes. A detailed comparison with the dipole strength predicted by random-phase approximation calculations is presented for the first time. TDHF results are also confronted to Vlasov calculations, to explore up to which extent a semiclassical picture can explain the properties of the nuclear response. The focus is on the low-energy response, below the giant dipole resonance region, where different modes of nonnegligible strength are identified. We show that the relative weight of these excitations evolves with nuclear global features, such as density profile and neutron skin, which in turn reflect important properties of the nuclear effective interaction. A thorough analysis of the associated transition densities turns out to be quite useful to better characterize the mixed isoscalar (IS)-isovector (IV) nature of the different modes and their surface/volume components. In particular, we show that the dipole response in the so-called pygmy dipole resonance region corresponds to isoscalarlike surface oscillations, of larger strength in nuclei with a more diffuse surface. The ratio between the IV and IS energy-weighted sum rule fractions exhausted in this region is shown to almost linearly increase with the neutron skin thickness in Sn isotopes.

Direct reaction experiments provide a powerful tool to probe the structure of neutron-rich nuclei like beryllium-11. We use halo effective field theory to calculate the cross section of the deuteron-induced neutron transfer reaction ${}^{10}\mathrm{Be}(d,p){}^{11}\mathrm{Be}$. The effective theory contains dynamical fields for the beryllium-10 core, the neutron, and the proton. In contrast, the deuteron and the beryllium-11 halo nucleus are generated dynamically from contact interactions using experimental and ab initio input. Breakup contributions are then included by construction. The reaction amplitude is constructed up to next-to-leading order in an expansion in the ratio of the length scales characterizing the core and the halo. The Coulomb repulsion between core and proton is treated perturbatively. Finally, we compare our results to cross-section data and other calculations.

The reactions of ${}^{40}\mathrm{Ar}+{}^{45}\mathrm{Sc}$ are studied using the quantum molecular dynamics (QMD) model at various incident energies. The phase space generated using the QMD model is coupled with various clusterization algorithms to identify fragments. The obtained charge yield of intermediate mass fragments ($3\le Z_f\le 12$) is fitted with power law $[Y\left(Z_f\right)\propto Z_f^{-\tau }]$ and exponential fits $[Y\left(Z_f\right)\propto e^{-\lambda Z_f}]$ in search of critical behavior. We also analyzed other critical parameters based on the moments and the charge of the second largest fragment. Our detailed study indicates that the extraction of the critical point of the liquid-gas phase transition is nearly insensitive towards different spatial-based clusterization algorithms, freeze-out time, as well as towards different binding energies at microlevels.

We present a detailed comparison of coalescence and thermal-statistical models for the production of (anti-) (hyper-)nuclei in high-energy collisions. For the first time, such a study is carried out as a function of the size of the object relative to the size of the particle emitting source. Our study reveals large differences between the two scenarios for the production of objects with extended wave functions. While both models give similar predictions and show similar agreement with experimental data for (anti-)deuterons and (anti-)${}^3\mathrm{He}$ nuclei, they largely differ in their description of (anti-)hypertriton production. We propose to address experimentally the comparison of the production models by measuring the coalescence parameter systematically for different (anti-)(hyper-)nuclei in different collision systems and differentially in multiplicity. Such measurements are feasible with the current and upgraded Large Hadron Collider experiments. Our findings highlight the unique potential of ultrarelativistic heavy-ion collisions as a laboratory to clarify the internal structure of exotic QCD objects and can serve as a basis for more refined calculations in the future.

Ab initio approaches in nuclear theory, such as the no-core shell model (NCSM), have been developed for approximately solving finite nuclei with realistic strong interactions. The NCSM and other approaches require an extrapolation of the results obtained in a finite basis space to the infinite basis space limit and assessment of the uncertainty of those extrapolations. Each observable requires a separate extrapolation and many observables have no proven extrapolation method. We propose a feed-forward artificial neural network (ANN) method as an extrapolation tool to obtain the ground-state energy and the ground-state point-proton root-mean-square (rms) radius along with their extrapolation uncertainties. The designed ANNs are sufficient to produce results for these two very different observables in ${}^6\mathrm{Li}$ from the ab initio NCSM results in small basis spaces that satisfy the following theoretical physics condition: independence of basis space parameters in the limit of extremely large matrices. Comparisons of the ANN results with other extrapolation methods are also provided.

The experiment E94-107 in Hall A at Jefferson Lab started a systematic study of high-resolution hypernuclear spectroscopy in the $0p$-shell region of nuclei such as the hypernuclei produced in electroproduction on ${}^9\mathrm{Be},{}^{12}\mathrm{C}$, and ${}^{16}\mathrm{O}$ targets. In order to increase counting rates and provide unambiguous kaon identification, two superconducting septum magnets and a ring-imaging Cherenkov detector were added to the Hall A standard equipment. The high-quality beam, the good spectrometers, and the new experimental devices allowed us to obtain very good results. For the first time, measurable strength with sub-MeV energy resolution was observed for the core-excited states of ${}_{\mathrm{\Lambda }}{}^{12}\mathrm{B}$. A high-quality ${}_{\mathrm{\Lambda }}{}^{16}\mathrm{N}$ hypernuclear spectrum was likewise obtained. A first measurement of the $\mathrm{\Lambda }$ binding energy for ${}_{\mathrm{\Lambda }}{}^{16}\mathrm{N}$, calibrated against the elementary reaction on hydrogen, was obtained with high precision, $13.76\pm 0.16$ MeV. Similarly, the first ${}_{\mathrm{\Lambda }}{}^9\mathrm{Li}$ hypernuclear spectrum shows general agreement with theory (distorted-wave impulse approximation with the SLA and BS3 electroproduction models and shell-model wave functions). Some disagreement exists with respect to the relative strength of the states making up the first multiplet. A $\mathrm{\Lambda }$ separation energy of 8.36 MeV was obtained, in agreement with previous results. It has been shown that the electroproduction of hypernuclei can provide information complementary to that obtained with hadronic probes and the $\gamma$-ray spectroscopy technique.

We combine the framework of the inverse problem theory and the Monte Carlo approach to formulate exact mathematical models that enable estimates of the uncertainty distributions for modeling predictions. We illustrate and discuss in particular what we refer to as the “NO GO property.” When the uncertainties of data constituting the input to the parameter adjustment procedures exceed certain critical value(s), even an exact modeling looses its stochastic reliability; its further use may provide “acceptably looking” rms deviations in the fitting zone with very likely meaningless, because they are unstable, predictions outside of it. We examine confidence intervals for intraneous (inside of the adjustment zone) and extraneous (outside of the adjustment zone) predictions and we demonstrate that “satisfactory” rms deviations in the intraneous modeling regime offer generally null certitude about the quality of extraneous predictions. Even though not entirely unknown, this property requires strong emphasizing since ignoring it has lead to misleading conclusions and confusing messages in the literature. We generalize our considerations to the realistic nuclear mean-field simulations of the properties of the nucleonic mean-field energies in spherical nuclei. We predict quantitatively the deterioration with increasing mass of the nucleonic-energy confidence intervals in superheavy nuclei. We show a strong dependence of those confidence intervals on the quantum characteristic of nucleonic states and provide detailed illustrations. In particular we demonstrate that, in the realistic predictions for the superheavy nuclei with the phenomenological Woods-Saxon Hamiltonian for up to $Z\approx 114$ or so, one obtains relatively stable predictions of the single-particle spectra with $N\le 180$, while approaching the NO GO zone of this model for further increasing neutron numbers. Thus the main area of today's interest within the instrumental reach for the superheavy nuclei studies remains, according to these estimates for the Woods-Saxon modeling, within the stability zone.

Light and heavy clusters are calculated for asymmetric warm nuclear matter in a relativistic mean-field approach. In-medium effects, introduced via a universal cluster-meson coupling, and a binding energy shift contribution, calculated in a Thomas-Fermi approximation, were taken into account. This work considers, besides the standard lightest bound clusters ${}^4\mathrm{He},{}^3\mathrm{He},{}^3\mathrm{H}$, and ${}^2\mathrm{H}$, also stable and unstable clusters with higher number of nucleons, in the range $5\le A\le 12$, as it is natural that heavier clusters also form in core-collapse supernova matter, before the pasta phases set in. We show that these extra degrees of freedom contribute with non-negligible mass fractions to the composition of nuclear matter, and may prevail over deuterons and $\alpha$ particles at high density in strongly asymmetric matter, and not too high temperatures. The presence of the light clusters reduces the contribution of heavy clusters to a much smaller density range, and to a smaller mass fraction.

The cross section of the ${}^9\mathrm{Be}(n,\gamma ){}^{10}\mathrm{Be}$ reaction was calculated in the direct capture model. All parameters of the calculations were adjusted to properties of the ${}^9\mathrm{Be}+n$ system at thermal energies. The calculated cross section at thermonuclear energies shows the expected $1/v$ behavior of $s$-wave capture at low energies, but increases towards higher energies as typical $p$-wave capture. Excellent agreement between new experimental data in the astrophysically relevant energy region and the present calculation is found.