We calculate the electric dipole moment (EDM) of the nuclei ${}^7\mathrm{Li}$ and ${}^{11}\mathrm{B}$ in the cluster model with $\alpha$ (${}^4\mathrm{He}$) and triton (${}^3\mathrm{H}$) clusters as degrees of freedom. The ${}^7\mathrm{Li}$ and ${}^{11}\mathrm{B}$ nuclei are treated in the two- and three-body problem, respectively, using the Gaussian expansion method, assuming the one-meson exchange P, $CP$-odd nuclear forces. We find that ${}^7\mathrm{Li}$ and ${}^{11}\mathrm{B}$ have larger sensitivity to the $CP$ violation than the deuteron. It is also suggested that the EDMs of ${}^7\mathrm{Li}$ and ${}^{11}\mathrm{B}$, together with those of ${}^6\mathrm{Li}, {}^9\mathrm{Be}$ and the $1/2_1^{+}$ excited state of ${}^{13}\mathrm{C}$, obey an approximate counting rule accounting for the EDM of the cluster and the $\alpha -N$ polarization. We show their sensitivity on the hadronic level $CP$ violation in terms of the chiral effective-field theory and discuss their role in probing new physics beyond the standard model.

Background: ${}^{58}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ is the first case where the influence of positive $Q$-value transfer channels on subbarrier fusion was evinced, in a very well known experiment by Beckerman et al. [Phys. Rev. Lett. 45, 1472 (1980)], by comparing with the two systems ${}^{58}\mathrm{Ni}+{}^{58}\mathrm{Ni}$ and ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$. Subsequent measurements on ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ showed that fusion hindrance is clearly present in this case. On the other hand, no indication of hindrance can be observed for ${}^{58}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ down to the measured level of 0.1 mb.

Purpose: Measuring deep subbarrier fusion cross sections for ${}^{58}\mathrm{Ni}+{}^{64}\mathrm{Ni}$, where the influence of positive $Q$-value transfer channels on near-barrier fusion was evidenced previously, in order to investigate whether hindrance shows up.

Methods: 167–200 MeV ${}^{58}\mathrm{Ni}$ beams from the XTU Tandem Accelerator of INFN-Laboratori Nazionali di Legnaro were used, bombarding thin metallic ${}^{64}\mathrm{Ni}\left(50\mu \mathrm{g}/{\mathrm{cm}}^2\right)$ enriched to $99.6\%$ in mass 64. An electrostatic beam deflector allowed fusion evaporation residues to be detected at very forward angles in a detector telescope.

Results: The excitation function has been extended by two orders of magnitude downward. The cross sections for ${}^{58}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ continue decreasing very smoothly below the barrier, down to $\simeq 1\mu \mathrm{b}$. The logarithmic slope of the excitation function increases slowly, showing a tendency to saturate at the lowest energies. No maximum of the astrophysical $S$ factor is observed. Coupled-channel (CC) calculations using a Woods-Saxon potential and including inelastic excitations only underestimate the subbarrier cross sections by a large amount. Good agreement is found by adding two-nucleon transfer couplings to a schematical level. This behavior is quite different from what already observed for ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ (no positive $Q$-value transfer channels available), where a clear low-energy maximum of the $S$ factor appears, and whose excitation function is overestimated by a standard Woods-Saxon CC calculation.

Conclusions: No hindrance effect is observed in ${}^{58}\mathrm{Ni}+{}^{64}\mathrm{Ni}$ in the measured energy range. This trend at deep subbarrier energies reinforces the recent suggestion that the availability of several states following transfer with $Q>0$ effectively counterbalances the Pauli repulsion that, in general, is predicted to reduce tunneling probability inside the Coulomb barrier.

Semi-inclusive $\mathrm{CC}\nu$ cross sections based on factorized cross sections are studied for a selection of spectral function models with the objective of facilitating the choice of models for use as input into event generators. The basic formalism for such cross sections is presented along with an introduction to constructing spectral functions for simple models based on the independent-particle shell model, the relativistic Fermi gas model (RFG), and a local density approximation (LDA) based on the RFG. Spectral functions for these models are shown for ${}^{16}\mathrm{O}$ along with a more sophisticated model which includes nucleon-nucleon interactions [Alvarez-Ruso et al., Prog. Part. Nucl. Phys. 100, 1 (2018)]. Inclusive and semi-inclusive cross sections are calculated for these models. Although the inclusive cross sections are all of similar size and shape, the semi-inclusive cross sections are substantially different depending upon whether the spectral functions contain some features associated with the nuclear shell model or are based on the RFG and LDA models. Calculations of average values and standard deviations of the initial neutrino energy using the semi-inclusive cross section for the various models are presented and indicate that there may be simple kinematical descriptions of the average neutrino energy which is common to all of these models.

Background: Several previous studies provided contradicting results for the four-neutron system, some claiming the existence of a $0^{+}$ near-threshold resonance, others denying presence of any observable resonant states.

Purpose: Since most of the studies employed enhanced two-neutron interactions to follow the evolution of an artificially bound state into a continuum one, we examine several enhancement schemes that produce a bound dineutron as well.

Methods: We study the four-neutron system by solving exact four-particle equations. By varying the interaction enhancement factor we calculate two-dineutron scattering phase shifts and cross sections.

Results: When the same enhancement factor is used in all partial waves, a bound tetraneutron emerges together with a strongly bound dineutron. Furthermore, such a $0^{+}$ tetraneutron evolves not into a resonance but into a virtual state. Weak enhancement of $S$ waves together with strongly enhanced higher waves is needed for the emergence of the resonant state. Anyhow the resonant behavior disappears well before reaching the physical interaction strength.

Conclusions: The interaction enhancement scheme using the same factor for all waves, employed in several previous works, is misleading for the search of $0^{+}$ resonance as only a virtual state can emerge. Evolution of a bound tetraneutron into a resonance via an intermediate virtual state is possible with strong enhancement of higher two-neutron waves.

An analysis technique has been developed in order to mitigate energy summing due to sequential short-lived $\alpha$ decays from nuclei implanted into a silicon detector. Using this technique, $\alpha$-decay spectroscopy of the $N=130$ isotones ${}^{218}\mathrm{Ra}$ ($Z=88$) and ${}^{220}\mathrm{Th}$ ($Z=90$) has been performed. The energies of the $\alpha$ particles emitted in the ${}^{218}\mathrm{Ra}\to {}^{214}\mathrm{Rn}$ and ${}^{220}\mathrm{Th}\to {}^{216}\mathrm{Ra}$ ground-state-to-ground-state decays have been measured to be 8381(4) keV and 8818(13) keV, respectively. The half-lives of the ground states of ${}^{218}\mathrm{Ra}$ and ${}^{220}\mathrm{Th}$ have been measured to be 25.99(10) $\mu \mathrm{s}$ and 10.4(4) $\mu \mathrm{s}$, respectively. The half-lives of the ground states of the $\alpha$-decay daughters, ${}^{214}\mathrm{Rn}$ and ${}^{216}\mathrm{Ra}$, have been measured to be 259(3) ns and 161(11) ns, respectively. Fine structure in the $\alpha$ decay of ${}^{218}\mathrm{Ra}$ has been observed for the first time, populating the 695-keV $2_1^{+}$ state in ${}^{214}\mathrm{Rn}$. The fine-structure $\alpha$ decay has an $\alpha$-particle energy of 7715(40) keV and branching ratio $b_{\alpha }=0.123\left(11\right)\%$.

A comprehensive systematic study is made for the collective $\beta$ and $\gamma$ bands in even-even isotopes with neutron numbers $N=88$ to 92 and proton numbers $Z=62\left(\mathrm{Sm}\right)$ to 70 (Yb). Data, including excitation energies, $B\left(E0\right)$ and $B\left(E2\right)$ values, and branching ratios from previously published experiments are collated with new data presented for the first time in this study. The experimental data are compared to calculations using a five-dimensional collective Hamiltonian (5DCH) based on the covariant density functional theory (CDFT). A realistic potential in the quadrupole shape parameters $V(\beta ,\gamma$) is determined from potential energy surfaces (PES) calculated using the CDFT. The parameters of the 5DCH are fixed and contained within the CDFT. Overall, a satisfactory agreement is found between the data and the calculations. In line with the energy staggering $S\left(I\right)$ of the levels in the ${2_{\gamma }}^{+}$ bands, the potential energy surfaces of the CDFT calculations indicate $\gamma$-soft shapes in the $N=88$ nuclides, which become $\gamma$ rigid for $N=90$ and $N=92$. The nature of the ${0_2}^{+}$ bands changes with atomic number. In the isotopes of Sm to Dy, they can be understood as $\beta$ vibrations, but in the Er and Yb isotopes the ${0_2}^{+}$ bands have wave functions with large components in a triaxial superdeformed minimum. In the vicinity of ${}^{152}\mathrm{Sm}$, the present calculations predict a soft potential in the $\beta$ direction but do not find two coexisting minima. This is reminiscent of ${}^{152}\mathrm{Sm}$ exhibiting an $X\left(5\right)$ behavior. The model also predicts that the ${0_3}^{+}$ bands are of two-phonon nature, having an energy twice that of the ${0_2}^{+}$ band. This is in contradiction with the data and implies that other excitation modes must be invoked to explain their origin.

Background: Simulations by transport codes are indispensable for extracting valuable physical information from heavy-ion collisions. Pion observables such as the ${\pi }^{-}/{\pi }^{+}$ yield ratio are expected to be sensitive to the symmetry energy at high densities.

Purpose: To evaluate, understand, and reduce the uncertainties in transport-code results originating from different approximations in handling the production of $\mathrm{\Delta }$ resonances and pions.

Methods: We compare ten transport codes under controlled conditions for a system confined in a box, with periodic boundary conditions, and initialized with nucleons at saturation density and at a temperature of 60 MeV. The reactions $NN\leftrightarrow N\mathrm{\Delta }$ and $\mathrm{\Delta }\leftrightarrow N\pi$ are implemented, but the Pauli blocking and the mean-field potential are deactivated in the present comparison. Thus, these are cascade calculations including pions and $\mathrm{\Delta }$ resonances. Results are compared to those from the two reference cases of a chemically equilibrated ideal gas mixture and of the rate equation.

Results: For the numbers of $\mathrm{\Delta }$ and $\pi$, deviations from the reference values are observed in many codes, and they depend significantly on the size of the time step. These deviations are tied to different ways in ordering the sequence of reactions, such as collisions and decays, that take place in the same time step. Better agreements with the reference values are seen in the reaction rates and the number ratios among the isospin species of $\mathrm{\Delta }$ and $\pi$. Both the reaction rates and the number ratios are, however, affected by the correlations between particle positions, which are absent in the Boltzmann equation, but are induced by the way particle scatterings are treated in many of the transport calculations. The uncertainty in the transport-code predictions of the ${\pi }^{-}/{\pi }^{+}$ ratio, after letting the existing $\mathrm{\Delta }$ resonances decay, is found to be within a few percent for the system initialized at $n/p=1.5$.

Conclusions: The uncertainty in the final ${\pi }^{-}/{\pi }^{+}$ ratio in this simplified case of particles in a box is sufficiently small so that it does not strongly impact constraining the high-density symmetry energy from heavy-ion collisions. Most of the sources of uncertainties have been understood, and individual codes may be further improved in future applications. This investigation will be extended in the future to heavy-ion collisions to ensure the problems identified here remain under control.

In this study, the α-decay half-life of 160 superheavy nuclei (SHN) with $105\le Z\le 120$ has been calculated using six empirical formulas: the scaling law of Brown (SLB), the modified scaling law Brown formula (MSLB), the Yibin et al. formula (YQZR), the modified Yibin et al. formula (MYQZR), the Viola-Seaborg formula (VS), and the modified Viola-Seaborg formula (MVS). The formulas were readjusted with new coefficients using the experimental α-decay half-life data of 356 nuclei. The six models were tested for their accuracy by comparing with the experimental results, and the MYQZR reveals best agreement. Later on the calculations have been extended to cover the specified range of SHN isotopes. The obtained results from MYQZR can be adopted to predict acceptable α-decay half-lives for the studied SHN nuclei.

An efficient solution of the Dirac Hamiltonian flow equations has been proposed through a novel expansion with the inverse of the Dirac effective mass. The efficiency and accuracy of this new expansion have been demonstrated by reducing a radial Dirac Hamiltonian with large scalar and vector potentials to two nonrelativistic Hamiltonians corresponding to particles and antiparticles, respectively. By solving the two nonrelativistic Hamiltonians, it is found that the exact solutions of the Dirac equation, for both particles and antiparticles, can be reproduced with a high accuracy up to only a few lowest order terms in the expansion. This could help compare and bridge the relativistic and nonrelativistic nuclear energy density functional theories in the future.

In the nuclear fission process, the excitation energy sharing mechanism between the fission fragments, the fragment angular momentum generation process and the interdependence between the two are still poorly known. The study of the neutron and $\gamma$ emission characteristics as a function of fragment and compound nucleus properties brings valuable information on these mechanisms since they decrease respectively the fragment excitation energy and angular momentum. In the 1980s, Naqvi and Müller experimentally highlighted, with ${}^{237}\mathrm{Np}(n,f)$ direct fission reactions, that only the prompt neutron multiplicity for the heavy fragment increases with the incident neutron energy. This means that the additional excitation energy goes into the heavy fragment. This data set allows one to test the different energy sharing models. This paper investigates, using the fifrelin fission fragment deexcitation code, the impact of the models used to assign the fragment initial state on fission observables. It focuses on the impact of a constant or an energy dependent spin cutoff model, whose parameters define the initial total angular momentum distribution, coupled with an energy sharing model based on an empirical temperature ratio law $R_T\left(A\right)$ in which fission fragments are considered to behave as a Fermi gas. It shows that both spin cutoff models succeed in reproducing the experimental neutron multiplicities which are mainly driven by the $R_T\left(A\right)$ law. However, they predict different $\gamma$ observables and neutron-$\gamma$ multiplicity correlations. Therefore, to infer about the validity of the two models, it is necessary to measure neutron and $\gamma$ observables in correlation in order to have a deeper understanding of the fission mechanism.

Fission of atomic nuclei often produces mass asymmetric fragments. However, the origin of this asymmetry was believed to be different in actinides and in the sub-lead region [Andreyev et al., Phys. Rev. Lett. 105, 252502 (2010)]. It has recently been argued that quantum shell effects stabilizing pear shapes of the fission fragments could explain the observed asymmetries in fission of actinides [Scamps and Simenel, Nature 564, 382 (2018)]. This interpretation is tested in the sub-lead region using microscopic mean-field calculations of fission based on the Hartree-Fock approach with BCS pairing correlations. The evolution of the number of protons and neutrons in asymmetric fragments of mercury isotope fissions is interpreted in terms of deformed shell gaps in the fragments. A new method is proposed to investigate the dominant shell effects in the prefragments at scission. We conclude that the mechanisms responsible for asymmetric fissions in the sub-lead region are the same as in the actinide region, which is a strong indication of their universality.

Three-nucleon ($3N$) short-range correlations (SRCs) are some of the most elusive structures in nuclei. Their observation and the subsequent study of their internal makeup will have a significant impact on our understanding of the dynamics of the superdense nuclear matter which exists at the cores of neutron stars. We discuss the kinematic conditions and observables that are most favorable for probing $3N$ SRCs in inclusive electronuclear processes and make a prediction for a quadratic dependence of the probabilities of finding a nucleon in $2N$ and $3N$ SRCs. We demonstrate that this prediction is consistent with the limited high-energy experimental data available, suggesting that we have observed, for the first time, $3N$ SRCs in electronuclear processes. Our analysis enables us to extract $a_3(A,Z)$, the probability of finding $3N$ SRCs in nuclei relative to the $A=3$ system.

In-source resonance ionization spectroscopy of the neutron-rich actinium isotopes ${}^{225-229}\mathrm{Ac}$ has been performed at the ISAC facility in TRIUMF, probing a ${}^{2}D_{3/2}\to {}^{4}P_{5/2}^{\circ }$ atomic transition. New data on the magnetic dipole moments and changes in mean-square charge radii $\delta \langle r^2\rangle$ of ${}^{226,228,229}\mathrm{Ac}$ have been obtained. The comparison of the measured isotope shifts and magnetic dipole coupling constants $a\left({}^{4}P_{5/2}^{\circ }\right)$ of ${}^{225,227}\mathrm{Ac}$ with a high-resolution data set is used to identify systematic uncertainties on the deduced $\delta {\langle r^2\rangle }^{A,215}$ and magnetic dipole moment values. The charge radii odd-even staggering is evaluated for the odd-$N$ isotopes, showing that ${}^{226}\mathrm{Ac}$ has an inverted odd-even staggering that might be linked with a reflection-asymmetric shape. Comparison of the magnetic dipole moments of ${}^{225,227,229}\mathrm{Ac}$ with Nilsson-model estimates supports the assumption of octupole deformation in isotopes ${}^{225,227}\mathrm{Ac}$ and its gradual decrease toward isotope ${}^{229}\mathrm{Ac}$. The changes in mean-square charge radii are compared to self-consistent calculations employing multiple modern energy density functionals: SLy5s1, BSk31, and DD-MEB1. For SLy5s1 in particular, self-consistent time-reversal breaking calculations of odd-odd nuclei incorporating finite octupole deformation are reported for the first time. For these calculations, the overall best agreement is obtained when the octupole degree of freedom is taken into account.

Background: Aside from being a one-neutron halo nucleus, ${}^{15}\mathrm{C}$ is interesting because it is involved in reactions of relevance for several nucleosynthesis scenarios.

Purpose: The aim of this work is to analyze various reactions involving ${}^{15}\mathrm{C}$, using a single structure model based on halo effective field theory (halo EFT) following the excellent results obtained in [P. Capel et al., Phys. Rev. C 98, 034610 (2018)].

Method: To develop a halo-EFT model of ${}^{15}\mathrm{C}$ at next to leading order (NLO), we first extract the asymptotic normalization coefficient (ANC) of its ground state by analyzing ${}^{14}\mathrm{C}(d,p){}^{15}\mathrm{C}$ transfer data at low energy using the method developed in [J. Yang and P. Capel, Phys. Rev. C 98, 054602 (2018)]. Using the halo-EFT description of ${}^{15}\mathrm{C}$ constrained with this ANC, we study the ${}^{15}\mathrm{C}$ Coulomb breakup at high (605 MeV/nucleon) and intermediate (68 MeV/nucleon) energies using eikonal-based models with a consistent treatment of nuclear and Coulomb interactions at all orders, and which take into account proper relativistic corrections. Finally, we study the ${}^{14}\mathrm{C}(n,\gamma ){}^{15}\mathrm{C}$ radiative capture.

Results: Our theoretical cross sections are in good agreement with experimental data for all reactions, thereby assessing the robustness of the halo-EFT model of this nucleus. Since a simple NLO description is enough to reproduce all data, the only nuclear-structure observables that matter are the ${}^{15}\mathrm{C}$ binding energy and its ANC, showing that all the reactions considered are purely peripheral. In particular, it confirms the value we have obtained for the ANC of the ${}^{15}\mathrm{C}$ ground state: ${\mathcal{C}}_{1/2^{+}}^2=1.59\pm 0.06{\mathrm{fm}}^{-1}$. Our model of ${}^{15}\mathrm{C}$ provides also a new estimate of the radiative-capture cross section at astrophysical energy: ${\sigma }_{n,\gamma }\left(23.3\mathrm{keV}\right)=4.66\pm 0.14\mu \mathrm{b}$.

Conclusions: Including a halo-EFT description of ${}^{15}\mathrm{C}$ within precise models of reactions is confirmed to be an excellent way to relate the reaction cross sections and the structure of the nucleus. Its systematic expansion enables us to establish how the reaction process is affected by that structure and deduce which nuclear-structure observables are actually probed in the collision. From this, we can infer valuable information on both the structure of ${}^{15}\mathrm{C}$ and its synthesis through the ${}^{14}\mathrm{C}(n,\gamma ){}^{15}\mathrm{C}$ radiative capture at astrophysical energies.

The spectroscopy of ${}^{79}\mathrm{Se}$ is studied via the ${}^{82}\mathrm{Se}(\alpha$, $\alpha 3n$)${}^{79}\mathrm{Se}$ fusion-evaporation reaction. A negative-parity magnetic dipole band in ${}^{79}\mathrm{Se}$ is established for the first time. Based on the calculations by the self-consistent tilted axis cranking covariant density functional theory, this new dipole band can be classified as a “stapler” band, which has a relatively stable symmetric prolate deformation as a function of rotational frequency. Hence, it is demonstrated that the stapler bands exist not only in the oblate and triaxial nuclei, but also in prolate nuclei. By examining the angular momentum coupling, it is found that the five valence nucleons in the high-$j$ orbitals play a major role in the closing of the stapler.

Background: Predictions of spectroscopic properties of low-lying states are critical for nuclear structure studies. Theoretical methods can be particularly involved for odd-mass nuclei because of the interplay between the unpaired nucleon and collective degrees of freedom. Only a few models have been developed for systems in which octupole collective degrees of freedom play a role.

Purpose: We aim to predict spectroscopic properties of odd-mass nuclei characterized by octupole shape deformation, employing a model that describes single-particle and collective degrees of freedom within the same microscopic framework.

Method: A microscopic core-quasiparticle coupling (CQC) model based on the covariant density functional theory is developed, which includes collective excitations of even-mass core nuclei and single-particle states of the odd nucleon, calculated using a quadrupole-octupole collective Hamiltonian combined with a constrained reflection-asymmetric relativistic Hartree-Bogoliubov model.

Results: Model predictions for low-energy excitation spectra and transition rates of odd-mass radium isotopes ${}^{223,225,227}\mathrm{Ra}$ are shown to be in good agreement with available data.

Conclusions: A microscopic CQC model based on covariant density functional theory has been developed for odd-mass nuclei characterized by both quadrupole and octupole shape deformations. Theoretical results reproduce data in odd-mass Ra isotopes and provide useful predictions for future studies of octupole correlations in nuclei and related phenomena.

The paper is devoted to the description and prediction of various bulk observables in the $\mathrm{Pb}+\mathrm{Pb}$ collisions at the Large Hadron Collider energy $\sqrt{s_{NN}}=5.02\mathrm{TeV}$ within the integrated hydrokinetic model (iHKM). Sensitivity of the results to the choice of the appropriate model parameter values is also investigated. It is found that changing of the relaxation time and the rate of thermalization, which characterize the prethermal stage of the matter evolution, as well as switching to another equation of state at the hydrodynamic stage and the corresponding hadronization temperature, does not destroy the results if simultaneously one provides an appropriate adjusting of the initial time for the superdense matter formation and related maximal initial energy density.

Results are presented from the first neutron-transfer measurement on ${}^{80}\mathrm{Ge}$ using an exotic beam from the Holifield Radioactive Ion Beam Facility at Oak Ridge National Laboratory. Newly measured spins and spectroscopic factors of low-lying states of ${}^{81}\mathrm{Ge}$ are determined, and the neutron capture cross section on ${}^{80}\mathrm{Ge}$ was calculated in a direct-semidirect model to provide a more realistic ($n,\gamma$) reaction rate for $r$-process simulations. Furthermore, a region of shape coexistence around $N\approx 50$ is confirmed and implications for the magic nature of ${}^{78}\mathrm{Ni}$ are discussed.