In most nuclear many-body methods, observables are calculated using many-body wave functions explicitly. The variational two-particle reduced density matrix method is one of the few exceptions to the rule. Ground-state energies of both closed-shell and open-shell nuclear systems can indeed be evaluated by minimizing a constrained linear functional of the two-particle reduced density matrix. However, it has virtually never been used in nuclear theory, because nuclear ground states were found to be well overbound, contrary to those of atoms and molecules. Consequently, we introduced new constraints in the nuclear variational two-particle reduced density matrix method, developed recently for atomic and molecular systems. Our calculations then show that this approach can provide a proper description of nuclear systems where only valence neutrons are included. For the nuclear systems where both neutrons and protons are active, however, the energies obtained with the variational two-particle reduced density matrix method are still overbound. The possible reasons for the noticed discrepancies and solutions to this problem will be discussed.

In the present work, we report a comprehensive theoretical study of the $logft$ values for the allowed and forbidden ${\beta }^{-}$ decay transitions of ${}^{46}\mathrm{K}$ and ${}^{47}\mathrm{K}$ corresponding to recently available experimental data from the GRIFFIN spectrometer at TRIUMF-ISAC [Phys. Rev. C 100, 054327 (2019); Phys. Rev. C 102, 054314 (2020)]. We perform the nuclear shell-model calculation in $sdpf$-valence space, with the SDPF-MU interaction, to calculate low-lying energy spectra of ${}^{46,47}\mathrm{K}$ and ${}^{46,47}\mathrm{Ca}$. For further investigation, we also calculate spectroscopic properties of ${}^{46,47}\mathrm{K}$ and ${}^{46,47}\mathrm{Ca}$ and compare the results with the experimental data. We suggest the spin-parity of several levels, which was previously tentative, in both the calcium isotopes. Based on the energy and $logft$ values, we conclude that the state at 3.984 MeV in ${}^{46}\mathrm{Ca}$ could be either $3^{-}$ or $2^{+}$ and a state at 4.432 MeV might be $3^{-}$. The spin-parity of the states at 2.875, 3.951, and 4.453 MeV are predicted to be $1/2^{-}, 3/2^{-}$, and $1/2^{-}$ or $1/2^{+}$, respectively, in ${}^{47}\mathrm{Ca}$. We also give the confirmation to the spin-parity of 2.850, 3.889, and 4.606 MeV states for ${}^{47}\mathrm{Ca}$. Our results of level schemes of ${}^{46,47}\mathrm{K}$ are in reasonable agreement with the experimental data, while the agreement of calculated $logft$ values for the ${\beta }^{-}$ decay with the experimental data is limited.

We present nonlinear (NL) and higher-twist (HT) corrections to the color dipole model bounds at low values of $x$ and $Q^2$ using the parametrization method. Consistency between the bounds at this region describe that a transition from the linear to the nonlinear behavior is dependence on the behavior of the gluon distribution function. The parameters in the color dipole model are comparable with the color dipole bounds at low values of $Q^2$. Consequently, the obtained reduced cross sections at low- and moderate-$Q^2$ values due to the NL $+$ HT effects show good agreement with the H1 Collaboration data.

We present an inference of the nuclear symmetry energy magnitude $J$, the slope $L$, and the curvature $K_{\mathrm{sym}}$ from combining neutron skin data on calcium, lead and tin isotopes, and our best theoretical information about pure neutron matter. A Bayesian framework is used to consistently incorporate prior knowledge of the pure neutron matter equation of state from chiral effective field theory calculations. Neutron skins are modeled in a fully quantum Skyrme-Hartree-Fock approach using an extended Skyrme energy-density functional which allows for independent variation of $J$, $L$, and $K_{\mathrm{sym}}$ without affecting the symmetric nuclear matter equation of state. The effect of using neutron skin data obtained with different physical probes is quantified. We argue that, given the existing data, combining the errors in quadrature is the more appropriate way to obtain unified errors for each nuclide, and in doing so we obtain 95% credible values of $J=31.3\begin{array}{c}+4.2\\ -5.9\end{array}\mathrm{MeV}$, $L=40\begin{array}{c}+34\\ -26\end{array}\mathrm{MeV}$, and $K_{\tau }=L-6K_{\mathrm{sym}}=-444\begin{array}{c}+100\\ -84\end{array}\mathrm{MeV}$ using uninformative priors in $J$, $L$, and $K_{\mathrm{sym}}$, and $J=31.9\begin{array}{c}+1.3\\ -1.3\end{array}\mathrm{MeV}$, $L=37\begin{array}{c}+9\\ -8\end{array}\mathrm{MeV}$, and $K_{\tau }=-480\begin{array}{c}+25\\ -26\end{array}\mathrm{MeV}$ using pure neutron matter (PNM) priors. We also show that the nonpositive correlation between $J$ and $L$ induced by neutron skin data is consistent with the nuclear droplet model. Neutron skin data alone are shown to place limits on the symmetry energy parameters as stringent as those obtained from chiral effective field theory alone, and when combined the 95% credible intervals are reduced by a factor of 4–5. It is also shown that the majority of nuclear interactions used in the literature have subsaturation density dependencies that are inconsistent with the combination of PNM priors and neutron skin data. We show measurements of lead and calcium neutron skins from upcoming parity-violating electron scattering experiments at Jefferson Lab and Mainz Superconducting Accelerator should obtain total error ranges $\mathrm{\Delta }L\approx 50\mathrm{MeV}$ and $\mathrm{\Delta }{K}_{\tau }\approx 240\mathrm{MeV}$ for uninformative priors and $\mathrm{\Delta }L\approx 30\mathrm{MeV}$ and $\mathrm{\Delta }{K}_{\tau }\approx 100\mathrm{MeV}$ for PNM priors at 67% credible bounds. Ahead of those experiments, we make predictions based on existing data on neutron skins of tin alone for the neutron skins of calcium and lead of $0.166\pm 0.008$ fm and $0.169\pm 0.014$ fm, respectively, using uninformative priors and $0.167\pm 0.008$ fm and $0.172\pm 0.015$ fm, respectively, using PNM priors.

Background: One-neutron removal reactions are used to study the single-particle structure of unstable nuclei, and in particular the exotic halo nuclei. The eikonal reaction theory (ERT) has been developed by Yahiro, Ogata, and Minomo [Prog. Theor. Phys. 126, 167 (2011)] to include dynamical effects, which are missing in the usual eikonal description of these reactions. Encouraging results have been obtained for total breakup cross sections in comparison to more elaborate reaction models.

Purpose: We extend these comparisons to more differential breakup cross sections expressed as functions of the relative energy or parallel momentum between the core and halo neutron.

Method: ERT predictions of these cross sections are compared to state-of-the-art calculations.

Results: The hypotheses upon which the ERT is based are confirmed and their range of validity is made clearer. The actual ordering of the evolution operators affects ERT differential cross sections and a specific choice leads to excellent agreement with the reference calculation. Dynamical effects in the treatment of the neutron-target interaction can be significant in the parallel-momentum observable.

Conclusions: The role of the different interactions in the dynamics of breakup reactions of one-neutron halo nuclei are better understood and improvements to the ERT are suggested.

We examine the properties of the isospin-asymmetry expansion of the nuclear equation of state from chiral two- and three-body forces. We focus on extracting the high-order symmetry energy coefficients that consist of both normal terms (occurring with even powers of the isospin asymmetry) as well as terms involving the logarithm of the isospin asymmetry that are formally nonanalytic around the expansion point of isospin-symmetric nuclear matter. These coefficients are extracted from numerically precise perturbation theory calculations of the equation of state coupled with a new set of finite difference formulas that achieve stability by explicitly removing the effects of higher-order terms in the expansion. We consider contributions to the symmetry energy coefficients from both two- and three-body interactions. It is found that the coefficients of the logarithmic terms are generically larger in magnitude than those of the normal terms from second-order perturbation theory diagrams, but overall the normal terms give larger contributions to the ground state energy. The high-order isospin-asymmetry terms are especially relevant at large densities where they affect the proton fraction in $\beta$-equilibrium matter, and in particular we find that at twice saturation density they can reduce the proton fraction by up to 0.02.

Background: The multiconfigurational dynamical symmetry (MUSY) is the common intersection of the shell, collective, and cluster models for the multi-major-shell problem. It is able to describe the spectra of different configurations in different energy windows in a unified way. It is based on some heuristic arguments, related to the connection of the wave functions, and energy eigenvalues. The detailed mathematical background has been worked out so far only for the simplest case of the two binary cluster configurations.

Purpose: I intend to construct the exact algebraic framework for the general case of the MUSY, i.e., for any number of configurations and any number of clusters or nucleons. As an illustrative example, the spectrum of different configurations of the ${}^{44}\mathrm{Ti}$ nucleus is described by a simple Hamiltonian.

Methods: Classification schemes defined by different algebra chains need to be combined; in particular, those of the major shell scheme and of the particle index scheme.

Results: A class of Hamiltonians, which is invariant under the transformations from one configuration to the other, is determined. In case of the ${}^{44}\mathrm{Ti}$ low-lying shell-model spectrum, as well as ${}^{40}\mathrm{Ca}+{}^4\mathrm{He}$ and ${}^{28}\mathrm{Si}+{}^{16}\mathrm{O}$ cluster states are obtained in a unified way.

Conclusions: The MUSY is based on two pillars: (i) a unified multiplet structure for shell, collective, and cluster model states and (ii) a Hamiltonian which is invariant with respect to the transformations from one configuration to the other.

A systematic study on radioactive decay of various isotopes of superheavy element oganesson $(Z=118)$ with mass numbers varying from 288 to 296 via heavy cluster emission is considered. The half-life of an emitted cluster is computed using the modified generalized liquid drop model with the Q value dependent preformation factor, for all possible splitting of each Og isotope. The heavy clusters with half-lives comparable to or less than the alpha half-life are probable for emission. From calculations, it is evident that for each Og isotope, the cluster emission with half-life comparable to alpha decay are indium and cadmium, which have nearly a proton magic number $(Z=50)$ and also the cluster emission with minimum half-lives among all splitting are ${}^{136}\mathrm{Xe}$ and ${}^{138}\mathrm{Ba}$, both having a magic neutron number $N=82$. The role of the magic number in the stability of heavy cluster decay is evident. Modes of decay of each isotope of Og is identified by comparing $T_{1/2}^{\alpha }$ values with corresponding $T_{1/2}^{\mathrm{SF}}$ values computed using the new mass inertia $\left(I_{\mathrm{rigid}}\right)$ dependent formula. The experimental alpha decay half-life of ${}^{294}\mathrm{Og}$ is 0.89 ms and the theoretically predicted value using our model is 0.395 ms. We were able to reproduce experimental alpha decay half-lives and decay modes in the case of ${}^{294}\mathrm{Og}$, thereby proving the reliability of our model, hence we believe that the predictions made in the case of other isotopes of Og would serve as a guiding tool for future studies in this field.

Multinucleon transfer cross sections around targetlike fragments of the ${}^{58}\mathrm{Ni}+{}^{208}\mathrm{Pb}$ reaction and the ${}^{64}\mathrm{Ni}+{}^{207,208}\mathrm{Pb}$ reactions were calculated by the improved dinuclear system $\mathrm{model}+\mathrm{GEMINI}++$. One finds that the ${}^{64}\mathrm{Ni}+{}^{208}\mathrm{Pb}$ reaction is more favorable to obtain neutron-rich nuclei as compared to the ${}^{58}\mathrm{Ni}+{}^{208}\mathrm{Pb}$ and ${}^{64}\mathrm{Ni}+{}^{207}\mathrm{Pb}$ reactions. That is because the difference of injection point position on the potential energy surface has a significant influence on the transfer of protons and neutrons in multinucleon transfer reaction. The effect of the entrance channel on transfer cross sections was predicted and analyzed by ${}^{58,64,70}\mathrm{Ni}+{}^{198}\mathrm{Pt}$ and ${}^{86,91,102}\mathrm{Kr}+{}^{208}\mathrm{Pb}$ reactions.

The constituent counting ruling (CCR) has been found to hold for numerous hard, exclusive processes. It predicts the differential cross section at high energies and fixed $cos{\theta }_{\mathrm{c}.\mathrm{m}.}$ should follow $\frac{d\sigma }{dt}\sim \frac{1}{s^{n-2}}$, where $n$ is the minimal number of constituents involved in the reaction. Conversely, there are hard, exclusive processes for which it has been found that the CCR does not work. The exact reasons for these have not been clearly established. One such example, for which the analysis of CLAS data deviates from the prediction of the CCR, is the omega photoproduction reaction. Here, we provide an in-depth analysis of the reaction $\gamma p\to \omega p$ at ${\theta }_{\mathrm{c}.\mathrm{m}.}\approx {90}^{\circ }$ using CLAS data with an energy range of $s=5\text{–}8{\mathrm{GeV}}^2$, where the CCR has been shown to work in other reactions. We argue for a stringent method to select data to test the CCR. Naïvely, this reaction would have $n=9$ and we would expect a scaling of $s^{-7}$. Instead, a scaling of $s^{-(9.08\pm 0.11)}$ was observed. A careful analysis of conservation of angular momentum is proposed to explain the discrepancy, supporting the validity of the CCR when applied properly.

The capture cross section of ${}^{209}\mathrm{Bi}(n,\gamma ){}^{210g}\mathrm{Bi}$ was measured at different astrophysically relevant energies including thermal capture cross section (25 meV), resonance integral, and the Maxwellian averaged cross section at a thermal energy of $kT=30$ keV. The partial capture cross section $\left({\sigma }_g\right)$ was determined using the activation technique and by measuring the ${}^{210}\mathrm{Po}$ activity. The newly developed and tested NICE detector setup was used to measure the $\alpha$ activity of the ${}^{210}\mathrm{Po}$. Using this setup the thermal and resonance integral cross sections were determined to be $16.2\pm 0.97$ mb and $89.81\pm 8.0$ mb, respectively. And the Maxwellian average cross section was measured to be $2.01\pm 0.38$ mb.

The direct $\gamma$ decays of the giant dipole resonance (GDR) and the giant quadrupole resonance (GQR) of ${}^{208}\mathrm{Pb}$ to low-lying states are investigated by means of a microscopic self-consistent model. The model considers effects beyond the linear response approximation. The experimental $\gamma$-decay widths from GQR to the first $3^{-}$ state and the low-lying dipole states are well reproduced with the Skyrme interaction SkP. The strong sensitivity of $\gamma$ decay to the isospin of the involved states is proven. By comparing the decay widths between GDR to $2_1^{+}$ and GQR to $3_1^{-}$, a much larger weight of the $3_1^{-}$ component in the GQR wave function of ${}^{208}\mathrm{Pb}$ is deduced, with respect to the weight of the $2_1^{+}$ component in the GDR wave function. Thus, we have shown that $\gamma$ decay is a unique probe of the resonance wave functions, and a test ground for nuclear structure models.

In the present work, I discuss the effect of the Coulomb interaction on the dynamics of two-particle systems bound in various traps. The strategy of including the Coulomb interaction into the quantization condition of a trapped system is discussed in a general and nonperturbative manner. In most cases, Coulomb corrections to the quantization condition largely rely on a numerical approach or on perturbation expansion. Only for some special cases, such as the spherical hard wall trap, a closed form of the quantization condition with all orders of Coulomb corrections can be obtained.

We study the momentum dependence of the production of light nuclei in high-energy collisions in the nucleon coalescence mechanism. We derive formulas of the momentum distributions of deuterons $d$ and helions ${}^3\mathrm{He}$. We obtain the analytic expressions of the coalescence factor $B_A$ ($B_2$ for $d$ and $B_3$ for ${}^3\mathrm{He}$) as functions of the collision system size and the momentum. We apply the deduced results to $p-p$, $p$-Pb and Pb-Pb collisions to explain naturally the interesting behavior of $B_A$ observed in experiments at the CERN Large Hadron Collider.

Based on an improved multiphase transport (AMPT) model, which gives a good description of proton production with a smooth quark matter to hadronic matter transition in relativistic heavy ion collisions, we study deuteron and triton productions from the coalescence of nucleons at the kinetic freezeout of these collisions. For central $\mathrm{Au}+\mathrm{Au}$ collisions at center-of-mass energies $\sqrt{s_{\text{NN}}}$ from 7.7 GeV to 200 GeV available at the Relativistic Heavy Ion Collider (RHIC), we find that the yield ratio $N_{\text{t}}{N}_{\text{p}}/N_{\text{d}}^2$ of proton, deuteron, and triton is a monotonic function of collision energy. Our study confirms the results from similar studies based on different dynamic model, which have either no phase transition or a crossover transition between the quark-gluon plasma and the hadronic matter, that this yield ratio does not show any nonmonotonic behavior in its collision-energy dependence.

The even- and odd-spin two-quasiparticle yrast bands in ${}^{136}\mathrm{Nd}$ are investigated with the triaxial projected shell model, focusing on the possible interpretation as transverse wobbling. With the experimental observables reproduced reasonably, the conditions under which the wobbling approximation is valid are examined via the angular momentum geometry and the configuration components extracted from the microscopic wave functions. The impact of the rotational alignment of the quasiparticles on the scenario of transverse wobbling is emphasized. It turns out that the $n=0$ band of the wobbling candidate is more affected than the $n=1$ one, which tends to go against the decreasing trend of the wobbling energy expected in the transverse case.

We have studied the ${}^{26}\mathrm{Mg}(t,p){}^{28}\mathrm{Mg}$ reaction. The nucleus ${}^{28}\mathrm{Mg}$ lies between ${}^{24}\mathrm{Mg}$ and ${}^{32}\mathrm{Mg}$, the latter of which is central to the “island of inversion” characterized by low-lying neutron $fp$-shell configurations. The present results show that the second-excited $0^{+}$ state in ${}^{28}\mathrm{Mg}$ contains large $fp$-shell occupation for the neutrons. The experiment was performed in inverse kinematics using the HELIcal Orbit Spectrometer (HELIOS) at Argonne National Laboratory. Shell-model calculations using the SDPF-MU interaction yielded level energies and two-neutron transfer amplitudes that were used in one-step distorted-wave Born approximation calculations to provide theoretical predictions of the proton angular distributions. In many, but not all cases, the data were in good agreement with theoretical predictions.

We present systematic measurements of azimuthal anisotropy for strange and multistrange hadrons ($K_s^0, \mathrm{\Lambda }, \mathrm{\Xi }$, and $\mathrm{\Omega }$) and $\varphi$ mesons at midrapidity ($\left|y\right|<$ 1.0) in collisions of $\mathrm{U}+\mathrm{U}$ nuclei at $\sqrt{s_{NN}}=193$ GeV, recorded by the STAR detector at the Relativistic Heavy Ion Collider. Transverse momentum ($p_T$) dependence of flow coefficients ($v_2, v_3$, and $v_4$) is presented for minimum bias collisions and three different centrality intervals. Number of constituent quark scaling of the measured flow coefficients in $\mathrm{U}+\mathrm{U}$ collisions is discussed. We also present the ratio of $v_n$ scaled by the participant eccentricity (${\varepsilon }_n\left\{2\right\}$) to explore system size dependence and collectivity in $\mathrm{U}+\mathrm{U}$ collisions. The magnitude of $v_2/{\varepsilon }_2$ is found to be smaller in $\mathrm{U}+\mathrm{U}$ collisions than that in central $\mathrm{Au}+\mathrm{Au}$ collisions contradicting naive eccentricity scaling. Furthermore, the ratios between various flow harmonics ($v_3/v_2^{3/2}, v_4/v_2^{4/2}$) are studied and compared with hydrodynamic and transport model calculations.

We report the results of a study aimed at inferring direct information on the repulsive three-nucleon potential $V_{ijk}^R$—driving the stiffness of the nuclear matter equation of state at supranuclear densities—from astrophysical observations. Using a Bayesian approach, we exploit the measurements of masses, radii, and tidal deformabalities performed by the NICER satellite and the LIGO/Virgo Collaborations as well as the mass of the heaviest observed pulsar to constrain the strength of $V_{ijk}^R$. The baseline of our analysis is the widely employed nuclear Hamiltonian comprising the Argonne $v_{18}$ nucleon-nucleon potential and the Urbana IX model of the three-nucleon potential. The numerical results, largely determined by the bound on the maximum mass, suggest that existing and future facilities have the potential to provide valuable new insight into microscopic nuclear dynamics at supranuclear densities.

We study the beam-normal single-spin asymmetry (BNSSA) in high-energy elastic electron scattering from several spin-0 nuclei. Existing theoretical approaches work in the plane-wave formalism and predict the BNSSA to scale as $\sim A/Z$ with the atomic number $Z$ and nuclear mass number $A$. While this prediction holds for light and intermediate nuclei, a striking disagreement in both the sign and the magnitude of BNSSA was observed by the PREX collaboration for ${}^{208}\mathrm{Pb}$, coined the “PREX puzzle.” To shed light on this disagreement, we go beyond the plane-wave approach which neglects Coulomb distortions known to be significant for heavy nuclei. We explicitly investigate the dependence of BNSSA on $A$ and $Z$ by (i) including inelastic intermediate states' contributions into the Coulomb problem in the form of an optical potential, (ii) by accounting for the experimental information on the $A$-dependence of the Compton slope parameter, and (iii) giving a thorough account of the uncertainties of the calculation. Despite of these improvements, the PREX puzzle remains unexplained. We discuss further strategies to resolve this riddle.