While the ground state configuration is classically determined by the variational principle minimizing the binding energy of the system, we propose here a different procedure to identify the configuration of the ground state in odd-$A$ nuclei. This procedure is based on the Hartree-Fock-Bogolyubov (HFB) framework with a self-consistent blocking of the unpaired nucleon and identifies the ground state as the blocked quasiparticle configuration compatible with the observed spin and parity and, most importantly, the measured magnetic moment. The magnetic moments are calculated within the HFB framework for all odd Hg isotopes for which experimental data is available. To validate the method, a systematic comparison between the predicted and measured electric quadrupole moments and isotopic shifts is performed. For even-even isotopes, we show that the ground state deformation, and more particularly the competition between the prolate and oblate shapes, can hardly be determined through a comparison of the QRPA $\beta$-decay half-life with experiment, though this approach also calls for an observable similar to the one used for odd-$A$ isotopes, namely the spin-flip component of the isovector part of the magnetic moment operator. For even isotopes with shape coexistence, no adequate constraint could be identified, except though the charge radius. Assuming light even-even Hg isotopes to have an oblate shape, the resulting charge radii staggering observed in the Hg chain by laser spectroscopy can through this identification procedure be reproduced.

Background: Recent accumulation of experimental data is revealing nuclear deformation in vicinity of ${}^{42}\mathrm{Si}$. This demands systematic theoretical studies to clarify more specific aspects of nuclear deformation and its causes.

Purpose: The purpose of this study is to investigate the nature and mechanism of the nuclear deformations and its relation to the disappearance of the neutron magic number $N=28$.

Method: The framework of antisymmetrized molecular dynamics with Gogny D1S density functional has been applied. The model assumes no spatial symmetry and can describe triaxial deformation. It also incorporates with the configuration mixing by the generator coordinate method.

Results: We show that the shell effects and the loss of the magicity induce various nuclear deformations. In particular, the $N=26$ and $N=30$ isotones have triaxially deformed ground states. We also note that the erosion of the $N=28$ magicity gradually occurs and has no definite boundaries.

Conclusion: The present calculation predicts various nuclear deformations in vicinity of ${}^{42}\mathrm{Si}$, and suggests that the interband electric transitions are good measure for it. We also remark that the magicity is lost without the single-particle level inversion in the oblate deformed nuclei such as ${}^{42}\mathrm{Si}$.

In this paper, we present a method to determine the dipole polarizability of light exotic nuclei with a two-body deuteronlike cluster structure. Using the adiabatic approximation, we solve the Schrödinger equation for the internal motion of the exotic projectile incident on a heavy target nucleus and express the resulting Coulomb dynamical polarization potential (CDPP) in terms of regular and irregular Coulomb functions. We then obtain a new expression for the dipole polarizability (${\alpha }_0$) by equating the real part of this CDPP to the classical expression for the polarization potential. The ${\alpha }_0$ values for many weakly bound light nuclei are calculated and where values are available were found to be in good agreement with those obtained in previous studies using various other methods.

In this work $\mathit{n}$-transfer and incomplete fusion cross sections for the ${}^9\mathrm{Be}+{}^{197}\mathrm{Au}$ system are reported over a wide energy range, ${\mathrm{E}}_{\mathrm{c}.\mathrm{m}.}\approx 29\text{−}45$ MeV. The experiment was carried out using the activation technique and off-line $\gamma$ counting. The transfer process is found to be the dominant mode as compared to all other reaction channels. Detailed coupled reaction channel (CRC) calculations have been performed for $\mathit{n}$-transfer stripping and pickup cross sections. The measured $1\mathit{n}$-stripping cross sections are explained with CRC calculations by including the ground state and the $2^{+}$ resonance state ($E=3.03$ MeV) of ${}^8\mathrm{Be}$. The calculations for $1\mathit{n}$-pickup cross sections, including only the ground state of ${}^{10}\mathrm{Be}$ agrees reasonably well with the measured cross sections, while it overpredicts the data at subbarrier energies. For better insight into the role of the projectile structure in the transfer process, a comprehensive analysis of the $1\mathit{n}$-stripping reaction has been carried out for various weakly bound projectiles on a ${}^{197}\mathrm{Au}$ target nucleus. The transfer cross sections scaled with the square of the total radius of interacting nuclei show the expected $Q$-value dependence of the $1\mathit{n}$-stripping channel for weakly bound stable projectiles.

Background: One-nucleon knockout reactions provide insightful information on the single-particle structure of nuclei. When applied to one-neutron halo nuclei, they are purely peripheral, suggesting that they could be properly modeled by describing the projectile within a halo effective field theory (halo-EFT).

Purpose: We reanalyze the one-neutron knockout measurements of ${}^{11}\mathrm{Be}$ and ${}^{15}\mathrm{C}$—both one-neutron halo nuclei—on beryllium at about 60 MeV/nucleon. We consider halo-EFT descriptions of these nuclei which already provide excellent agreement with breakup and transfer data.

Method: We include a halo-EFT description of the projectile within an eikonal-based model of the reaction and compare its outcome to existing data.

Results: Excellent agreement with experiment is found for both nuclei. The asymptotic normalization coefficients inferred from this comparison confirm predictions from ab initio nuclear-structure calculations and values deduced from transfer data.

Conclusions: Halo-EFT can be reliably used to analyze one-neutron knockout reactions measured for halo nuclei and test predictions from state-of-the-art nuclear structure models on these experimental data.

Neutron-rich Pm ($Z=61$) isotopes were studied by delayed $\gamma$-ray spectroscopy at RIBF, RIKEN Nishina Center using the in-flight fission of a 345 MeV/nucleon ${}^{238}\mathrm{U}$ beam. A cluster-type Ge detector array, EURICA, was used to measure the delayed $\gamma$ rays from stopped ions. Isomeric $\gamma$ decays were observed in ${}^{159}\mathrm{Pm}$ and ${}^{161}\mathrm{Pm}$ with half-lives of 4.97(12) $\mu \mathrm{s}$ and 0.79(4) $\mu \mathrm{s}$, respectively. Level schemes for ${}^{159}\mathrm{Pm}$ and ${}^{161}\mathrm{Pm}$ were constructed in this study. The isomeric states of ${}^{159}\mathrm{Pm}$ and ${}^{161}\mathrm{Pm}$ could be interpreted as two quasiparticle excitations of neutrons with the configurations of $\nu (7/2[633]\otimes 5/2[523\left]\right)$ and $\nu (7/2[633]\otimes 1/2[521\left]\right)$, respectively. They are analogous to the isomers that have been observed systematically in other even-mass $N=98$ and $N=100$ isotones in this region. A projected shell model calculation was performed and it reproduced the order of three-quasiparticle states only if new Nilsson parameters with an $N$-dependent spin-orbit interaction were used. This work demonstrates that the strength of spin-orbit interactions in standard Nilsson parameters needs to be modified to study the properties of neutron-rich rare-earth nuclei around $A=165$, and provides new evidence supporting the existence of the deformed $N=98$ subshell gap in odd-mass nuclei for the first time.

Normal ordering provides an approach to approximate three-body forces as effective two-body operators and it is therefore an important tool in many-body calculations with realistic nuclear interactions. The corresponding neglect of certain three-body terms in the normal-ordered Hamiltonian is known to influence translational invariance, although the magnitude of this effect has not yet been systematically quantified. In this paper we study in particular the normal-ordering two-body approximation applied to a single harmonic-oscillator reference state. We explicate the breaking of translational invariance and demonstrate the magnitude of the approximation error as a function of model space parameters for ${}^4\mathrm{He}$ and ${}^{16}\mathrm{O}$ by performing full no-core shell-model calculations with and without three-nucleon forces. We combine two different diagnostics to better monitor the breaking of translational invariance. While the center-of-mass effect is shown to become potentially very large for ${}^4\mathrm{He}$, it is also shown to be much smaller for ${}^{16}\mathrm{O}$ although full convergence is not reached. These tools can be easily implemented in studies using other many-body frameworks and bases.

Excited states in ${}^{13}\mathrm{O}$ were investigated using inelastic scattering of an $E/A=69.5$ MeV ${}^{13}\mathrm{O}$ beam off of a ${}^9\mathrm{Be}$ target. The excited states were identified in the invariant-mass spectra of the decay products. Both single-proton and sequential two-proton decays of the excited states were examined. For a number of the excited states, the protons were emitted with strong anisotropy where emissions transverse to the beam axis are favored. The measured proton-decay angular distributions were compared to predictions from distorted-wave Born-approximation calculations of the spin alignment which was shown to be largely independent of the excitation mechanism. The deduced ${}^{13}\mathrm{O}$ level scheme is compared to ab initio no-core shell model with continuum predictions. The lowest-energy excited states decay isotropically consistent with predictions of strong proton $1s_{1/2}$ structure. Above these states in the level scheme, we observed a number of higher-spin states not predicted within the model. Possibly these are associated with rotational bands built on deformed cluster configurations predicted by antisymmetrized molecular dynamics calculations. The spin alignment mechanism is shown to be useful for making spin assignments and may have widespread use.

A study of the laser-ionized and mass-separated neutron-deficient isotopes ${}^{176,177,179}\mathrm{Au}$ was performed using the Resonance Ionization Laser Ion Source and the Windmill detection setup at ISOLDE, CERN. New and improved data on complex fine-structure $\alpha$ decays of the three isotopes were deduced, providing insight into the low-lying levels in the daughter nuclei ${}^{172,173,175}\mathrm{Ir}$. New information on the properties of $\beta$-decay daughter products ${}^{177,179}\mathrm{Pt}$ was also obtained. From the first in-source laser spectroscopy measurements of the hyperfine structure in the atomic 267.6-nm transition of ${}^{176}\mathrm{Au}$, the nuclear magnetic moments for both high- and low-spin $\alpha$-decaying states were deduced. Together with the values determined from the additivity relations, they were used to propose the most probable spins and configurations for both states. The $\alpha$-decay branching ratios were determined as $b_{\alpha }\left({}^{176}\mathrm{Au}^{\text{ls}}\right)=58\left(5\right)\%$ and $b_{\alpha }\left({}^{176}\mathrm{Au}^{\text{hs}}\right)=29\left(5\right)\%$.

It has been proposed that one can look for the QCD critical point (CP) by the Beam Energy Scan accurately monitoring event-by-event fluctuations. This experimental program is under way at the BNL RHIC collider. Separately, it has been studied how clustering of nucleons at freeze out affects proton multiplicity distribution and light nuclei production. It was found that even a minor increase of the range of nuclear forces dramatically increases clustering, while large correlation length $\xi$ near CP makes attraction due to binary forces unrealistically large. In this paper we show that repulsive many-body forces near CP should overcome the binary ones and effectively suppress clustering. We also discuss current experimental data and point out locations at which a certain drop in clustering may already be observed.

A formula of the $D\text{−}D$ correlation function is derived. The deuterons are treated either as elementary particles or as neutron-proton bound states. In the first case the deuterons are directly emitted from a source and in the second case the deuteron formation is a final-state process simultaneous with a generation of $D\text{−}D$ correlation. The source radius of deuterons formed due to final-state interactions is bigger by the factor of $\sqrt{2}$ than that of directly emitted deuterons. To check how sizable is the effect we compute the $D\text{−}D$ correlation function taking into the Bose-Einstein statistics of deuterons, the $s$-wave scattering due to the strong interaction and Coulomb repulsion. The correlation function is shown to be sensitive to the source radius for sources which are sufficiently small with rms radii smaller than 3.5 fm. Otherwise, the correlation function is dominated by the Coulomb repulsion and weakly depends on the source radius. Measurements which can make use of our finding are discussed.

The low-lying excited states in the neutron-deficient $N=Z+1$ nucleus ${}_{43}{}^{87}\mathrm{Tc}_{44}$ have been studied via the fusion-evaporation reaction ${}^{54}\mathrm{Fe}({}^{36}\mathrm{Ar}, 2n1p){}^{87}\mathrm{Tc}$ at the Grand Accélérateur National d'Ions Lourds (GANIL), France. The AGATA spectrometer was used in conjunction with the auxiliary NEDA, Neutron Wall, and DIAMANT detector arrays to measure coincident prompt $\gamma$ rays, neutrons, and charged particles emitted in the reaction. A level scheme of ${}^{87}\mathrm{Tc}$ from the ($9/2_{\mathrm{g}.\mathrm{s}.}^{+}$) state to the ($33/2_1^{+}$) state was established based on six mutually coincident $\gamma$-ray transitions. The constructed level structure exhibits a rotational behavior with a sharp backbending at $\hslash \omega \approx 0.50$ MeV. A decrease in alignment frequency and increase in alignment sharpness in the odd-mass isotonic chains around $N=44$ is proposed as an effect of the enhanced isoscalar neutron-proton interactions in odd-mass nuclei when approaching the $N=Z$ line.

The effect of coupling between pairing and quadrupole triaxial shape vibrations on the low-energy collective states of $\gamma$-soft nuclei is investigated using a model based on the framework of nuclear energy density functionals (EDFs). Employing a constrained self-consistent mean-field (SCMF) method that uses universal EDFs and pairing interactions, potential energy surfaces of characteristic $\gamma$-soft Os and Pt nuclei with $A\approx 190$ are calculated as functions of the pairing and triaxial quadrupole deformations. Collective spectroscopic properties are computed using a number-nonconserving interacting boson model (IBM) Hamiltonian, with parameters determined by mapping the SCMF energy surface onto the expectation value of the Hamiltonian in the boson condensate state. It is shown that, by simultaneously considering both the shape and pairing collective degrees of freedom, the EDF-based IBM successfully reproduces data on collective structures based on low-energy $0^{+}$ states, as well as $\gamma$-vibrational bands.

Exclusive dimuon production in ultraperipheral collisions (UPC), resulting from photon-photon interactions in the strong electromagnetic fields of colliding high-energy lead nuclei, $\mathrm{PbPb}\left(\gamma \gamma \right)\to {\mu }^{+}{\mu }^{-}\left({\mathrm{Pb}}^{\left(★\right)}{\mathrm{Pb}}^{\left(★\right)}\right)$, is studied using ${\mathcal{L}}_{\mathrm{int}}=0.48{\mathrm{nb}}^{-1}$ of $\sqrt{s_{NN}}=5.02\text{TeV}$ lead-lead collision data at the LHC with the ATLAS detector. Dimuon pairs are measured in the fiducial region $p_{\mathrm{T},\mu }>4$ $\text{GeV}$, $|{\eta }_{\mu }|<2.4$, invariant mass $m_{\mu \mu }>10$ $\text{GeV}$, and $p_{\mathrm{T},\mu \mu }<2$ $\text{GeV}$. The primary background from single-dissociative processes is extracted from the data using a template fitting technique. Differential cross sections are presented as a function of $m_{\mu \mu }$, absolute pair rapidity ($|y_{\mu \mu }|$), scattering angle in the dimuon rest frame ($|cos{\vartheta }_{\mu \mu }^{★}|$), and the colliding photon energies. The total cross section of the UPC $\gamma \gamma \to {\mu }^{+}{\mu }^{-}$ process in the fiducial volume is measured to be ${\sigma }_{\mathrm{fid}}^{\mu \mu }=34.1\pm 0.3(\mathrm{stat}.)\pm 0.7(\mathrm{syst}.)$ $\mu \mathrm{b}$. Generally good agreement is found with calculations from STARlight, which incorporate the leading-order Breit-Wheeler process with no final-state effects, albeit differences between the measurements and theoretical expectations are observed. In particular, the measured cross sections at larger $|y_{\mu \mu }|$ are found to be about 10–20% larger in data than in the calculations, suggesting the presence of larger fluxes of photons in the initial state. Modification of the dimuon cross sections in the presence of forward and/or backward neutron production is also studied and is found to be associated with a harder incoming photon spectrum, consistent with expectations.

Background: Abundance calculations of a certain class of proton-rich isotopes, known as $p$ nuclei, require knowledge of the cross sections of thousands of nuclear reactions entering a reaction network. As a result, the solution of the latter relies on the predictions of the Hauser-Feshbach (HF) theory and, hence, on the reliability of the models describing the nuclear parameters entering the HF calculations, notably the optical model potential (OMP), the nuclear level density (NLD) and the $\gamma$-ray strength function ($\gamma \mathrm{SF}$).

Purpose: The present work reports on a systematic study of proton capture reactions on Sr isotopes at energies relevant to the $p$ process which is responsible for the production of the $p$ nuclei at explosive stellar sites. The purpose of the work reported here is to perform a validity test of the different OMP, NLD, and $\gamma \mathrm{SF}$ models through extensive and detailed comparisons between HF calculations and experimental cross section data. This test is necessary to understand the origin of discrepancies between the $p$-nuclei abundances observed in the solar system and those predicted by the different astrophysical models, known as $p$-process models, aiming at describing the nucleosynthesis of the $p$ isotopes.

Method: Cross sections were determined from $\gamma$-angular distribution measurements and from angle-integrated $\gamma$ spectra taken with the $4\pi \gamma$-summing technique. Cross-section data and the resulting astrophysical $S$ factors were compared with Hauser-Feshbach calculations obtained with the latest version 1.95 of the nuclear reaction code talys using combinations of global semi-microscopic and phenomenological models of optical potentials (OMPs), nuclear level densities (NLDs), and $\gamma$-ray strength functions ($\gamma \mathrm{SFs}$).

Results: Total cross sections as well as cross sections to the ground and metastable states were determined for the reactions ${}^{86}\mathrm{Sr}(p,\gamma ){}^{87}\mathrm{Y}$, ${}^{87}\mathrm{Sr}(p,\gamma ){}^{88}\mathrm{Y}$, and ${}^{88}\mathrm{Sr}(p,\gamma ){}^{89}\mathrm{Y}$ at incident proton-beam energies from 2.5 to 3.6, 2 to 5, and 1.5 to 5 MeV, respectively.

Conclusions: The experimental data reported in the present work are in very good agreement with the talys 1.95 calculations obtained with the default combination of OMP, NLD, and $\gamma \mathrm{SF}$ models. This combination is based on purely phenomenological models. A semimicroscopic proton-nucleus optical model potential was optimized at low energies leading to an equally good agreement between experimental data and theoretical calculations based solely on combinations of fully semimicroscopic models of OMP, NLD, and $\gamma \mathrm{SF}$. Our results highlight the need for a continued effort on the systematic study of proton-capture reactions to reduce the range of uncertainties arising from global nuclear models for as wide a range of relevant nuclei as possible. In this regard, new ($p,\gamma$) data at the lowest possible energies below the opening of the neutron channel are of key importance to improve global proton-nucleus optical model potentials.

The nuclear symmetry energy plays an important role in the description of the properties of finite nuclei as well as neutron stars. Especially, for low values of baryon density, the accurate description of the crust-core interface strongly depends on the symmetry energy. Usually, the well known parabolic approximation is employed for the definition of the symmetry energy without avoiding some drawbacks. In the present paper, a class of nuclear models, suitable for the description of the inner and outer core of neutron stars, is applied in studying the effect of higher orders of the expansion of the energy on the location of the crust-core transition. The thermodynamical and dynamical methods are used for the determination of the transition density $n_{\mathrm{t}}$ and pressure $P_{\mathrm{t}}$. The corresponding energy density functional is applied for the study of some relevant properties of both nonrotating and slowly rotating neutron stars. We found that the larger the value of the slope parameter $L$, the slower the convergence of the expansion. In addition, a universal relation is presented between $n_{\mathrm{t}}$ and $L$, by employing the full expression and dynamical approach. The crustal moment of inertia is very sensitive to the location of the transition while the effects are moderated concerning the critical angular velocity of the $r$-mode instability and minimum mass configuration. The effect on the tidal deformability is less but not negligible. In any case, the use of the parabolic approximation leads to the overestimation of $n_{\mathrm{t}}$ and $P_{\mathrm{t}}$ and, consequently, on inaccurate predictions. Moreover, in some cases, even the matching process at the interface may affect considerably the predictions, introducing errors of the same order with the one due to the employed method.

We analyze various flow coefficients of anisotropic momentum distribution of final state particles in mid-central ($b=5\text{–}9\mathrm{fm}$) $\mathrm{Au}+\mathrm{Au}$ collisions in the beam energy range $E_{\mathrm{Lab}}=1A\text{–}158A$ GeV. Different variants of the ultrarelativistic quantum molecular dynamics (UrQMD) model, namely the pure transport (cascade) mode and the hybrid mode, are employed for this investigation. In the hybrid UrQMD model, the ideal hydrodynamical evolution is integrated with the pure transport calculation for description of the evolution of the fireball. We opt for the different available equations of state (EoS) replicating the hadronic as well as partonic degrees of freedom together with possible phase transitions, viz., hadron gas, chiral $+$ deconfinement EoS, and bag model EoS, to investigate their effect on the properties of the final state particles. We also attempt to gain insights about the dynamics of the medium by studying different features of particle production such as particle ratios and net-proton rapidity distribution. The results and conclusions drawn here would be useful to understand the response of various observables to the underlying physics of the model as well as to make comparisons with the upcoming measurements of the future experiments at the Facility for Antiproton and Ion Research (FAIR) and the Nuclotron-based Ion Collider fAcility (NICA).

This paper concerns the theory of direct $A(d,p)B$ reactions and how practical three-body models of them are related to the optical model potentials describing the interaction of the deuterons constituents and the target $A$. A new definition of the nucleon optical potential is introduced which necessitates a careful examination of the boundary conditions involved in the associated coupled-channel formalism. The new definition turns out to be very convenient for making a connection with the theory of the $A(d,p)B$ reaction. The analysis is carried out within an antisymmetrized, translationally invariant formalism and provides a firm basis from a many-body point of view for the three-body force effects calculated in [Phys. Rev. C 99, 064612 (2019)].

I investigate the ${}^{11}\mathrm{Li}(p,t){}^9\mathrm{Li}$ two-neutron transfer reaction at $E_{\mathrm{lab}}=33$ MeV within the distorted wave Born approximation (DWBA). The ${}^{11}\mathrm{Li}$ and ${}^3\mathrm{H}$ nuclei are described in the hyperspherical formalism, as ${}^9\mathrm{Li}+n+n$ and $p+n+n$ configurations, respectively. The calculation of the cross section is shown to be much more complicated than in one-neutron transfer reactions, owing to the three-body structure of ${}^{11}\mathrm{Li}$. The ${}^{11}\mathrm{Li}+p$ and ${}^9\mathrm{Li}+t$ scattering wave functions are determined with the continuum discretized coupled channel (CDCC) method. Approximations derived from equivalent local potentials are used to compute the transfer cross section at the DWBA. The model reproduces experimental data reasonably well, considering that there is no adjustable parameter. I show that the cross section is fairly sensitive to the long-range part of the ${}^{11}\mathrm{Li}$ wave function, and therefore to its halo structure.