A systematic nucleus-nucleus potential for the ${}^9\mathrm{Be}$ projectile is derived by analyzing its elastic scattering on target nuclei from ${}^{16}\mathrm{O}$ to ${}^{209}\mathrm{Bi}$ with incident energies ranging from 12 to 202 MeV. The analysis is performed by using a single-folding model based on the Bruyères Jeukenne-Lejeune-Mahaux model nucleon-nucleus potentials. In combination with the previous systematic potential reported by Xu and Pang [Phys. Rev. C 87, 044605 (2013)], which was obtained by analyzing the elastic-scattering data of ${}^6\mathrm{Li}$ and ${}^7\mathrm{Li}$ at incident energies above 10 MeV/nucleon, we arrive at an updated systematic nucleus-nucleus potential which covers a range of incident energies from around the Coulomb barrier to about 100 MeV/nucleon. This updated potential is found to satisfy the dispersion relations better than the previous one.

In the current work, we present the influence of finite volume and magnetic field on the thermodynamic properties of isospin asymmetric quark matter using the Polyakov loop extended chiral SU(3) quark mean field (PCQMF) model at finite chemical potential and temperature. Within the PCQMF model, we use the scalar and vector field values in mean-field approximation to obtain the thermodynamic properties: pressure density, entropy density, and energy density. The susceptibilities of conserved charges for strongly interacting matter for different system sizes as well as for different values of the magnetic field have been studied. A sizable shift in phase boundary towards the higher values of quark chemical potential (${\mu }_q$) and temperature ($T$) has been observed for decreasing values of system volume as well as an opposite shift towards lower temperature and quark chemical potential for increasing magnetic field. We observe an enhancement in fluctuations of conserved charges in the regime of the transition temperature. These studies may have a significant role in understanding the thermodynamic observables extracted from heavy-ion collisions data.

The last five years have seen remarkable progress in our quest to determine the equation of state of neutron rich matter. Recent advances across the theoretical, experimental, and observational landscape have been incorporated in a Bayesian framework to refine existing covariant energy density functionals previously calibrated by the properties of finite nuclei. In particular, constraints on the maximum neutron star mass from pulsar timing, on stellar radii from the NICER mission, on tidal deformabilities from the LIGO-Virgo collaboration, and on the dynamics of pure neutron matter as predicted from chiral effective field theories have resulted in significant refinements to the models, particularly to those predicting a stiff symmetry energy. Still, even after these improvements, we find it challenging to reproduce simultaneously the neutron skin thickness of both ${}^{208}\mathrm{Pb}$ and ${}^{48}\mathrm{Ca}$ recently reported by the PREX/CREX collaboration.

For the first time, differential cross sections and photon beam asymmetries were measured for the reaction $\gamma p\to f_0\left(980\right)p\to {\pi }^0{\pi }^{0}p$ by using a linearly polarized photon beam up to $2.4\mathrm{GeV}$ and a liquid hydrogen target. The $f_0$(980) photoproduction signal was clearly observed owing to the absence of contributions from vector-meson photoproduction. The results indicate the $t$-channel exchange of vector mesons as a mechanism of the $f_0\left(980\right)$ photoproduction at $E_{\gamma }\approx 2.1\mathrm{GeV}$, putting constraints on the nature of $f_0\left(980\right)$.

We study two-neutrino ($2\nu \beta \beta$) and neutrinoless double-$\beta$ ($0\nu \beta \beta$) decays in the nuclear shell model and proton-neutron quasiparticle random-phase approximation (pnQRPA) frameworks. Calculating the decay half-life of several dozens of nuclei ranging from calcium to xenon with the shell model, and of $\beta \beta$ emitters with a wide range of proton-neutron pairing strengths in the pnQRPA, we observe good linear correlations between $2\nu \beta \beta$- and $0\nu \beta \beta$-decay nuclear matrix elements for both methods. We then combine the correlations with measured $2\nu \beta \beta$-decay half-lives to predict $0\nu \beta \beta$-decay matrix elements with theoretical uncertainties based on our systematic calculations. Our results include two-body currents and the short-range $0\nu \beta \beta$-decay operator.

Background: The response of hadrons, the bound states of the strong force (QCD), to external probes can be described in two different, complementary frameworks: as direct interactions with their fundamental constituents, quarks and gluons, or alternatively as elastic or inelastic coherent scattering that leaves the hadrons in their ground state or in one of their excited (resonance) states. The former picture emerges most clearly in hard processes with high momentum transfer, where the hadron response can be described by the perturbative expansion of QCD, while at lower energy and momentum transfers, the resonant excitations of the hadrons dominate the cross section. The overlap region between these two pictures, where both yield similar predictions, is referred to as quark-hadron duality and has been extensively studied in reactions involving unpolarized hadrons. Some limited information on this phenomenon also exists for polarized protons, deuterons, and ${}^3\mathrm{He}$ nuclei, but not yet for neutrons.

Purpose: In this paper, we present comprehensive and detailed results on the correspondence between the extrapolated deep inelastic structure function $g_1$ of both the proton and the neutron with the same quantity measured in the nucleon resonance region. Thanks to the fine binning and high precision of our data, and using a well-controlled perturbative QCD (pQCD) fit for the partonic prediction, we can make quantitative statements about the kinematic range of applicability of both local duality and global duality.

Method: We use the most updated QCD global analysis results at high $x$ from the Jefferson Lab Angular Momentum Collaboration to extrapolate the spin structure function $g_1$ into the nucleon resonance region and then integrate over various intervals in the scaling variable $x$. We compare the results with the large data set collected in the quark-hadron transition region by the CLAS Collaboration, including, for the first time, deconvoluted neutron data, integrated over the same intervals. We present this comparison as a function of the momentum transfer $Q^2$.

Results: We find that, depending on the integration interval and the minimum momentum transfer chosen, a clear transition to quark-hadron duality can be observed in both nucleon species. Furthermore, we show, for the first time, the approach to scaling behavior for $g_1$ measured in the resonance region at sufficiently high momentum transfer.

Conclusions: Our results can be used to quantify the deviations from the applicability of pQCD for data taken at moderate energies and can help with extraction of quark distribution functions from such data.

In this work, I present new extractions of the positron-proton to electron-proton elastic scattering cross-sections ratio $R_{e^{+}{e}^{-}}(\varepsilon ,Q^2)$ at high $Q^2$ covering the range 5.994 $\le Q^2\le 15.721{(\mathrm{GeV}/c)}^2$ following two approaches. I also present an estimate of the size of the hard-TPE correction to ${\sigma }_R$ at high $Q^2$, along with the uncertainties associated with the model dependence of the extractions. My results on $R_{e^{+}{e}^{-}}$, based on the two approaches used, are in generally very good quantitative agreement with each other. Because world data on the ratio $R_{e^{+}{e}^{-}}$ are only available for $Q^2<2.1{(\mathrm{GeV}/c)}^2$, below where the discrepancy on the proton's form factors ratio ${\mu }_p{R}_p={\mu }_p{G}_E/G_M$ is significant, my results provide new predictions for $R_{e^{+}{e}^{-}}(\varepsilon ,Q^2)$ at such a high-$Q^2$ range, which is yet to be measured.

Nuclear mass is responsible for many key processes in both nuclear physics and astrophysics. While the theoretical accuracy of masses has reached a quite astonishing level, the extrapolations among various predictions have been conflicting due to several possible reasons, such as the missing physics and overfitting problems in current formulas. Instead of the single target of binding energies, we make use of both the $\alpha$ decay energy and the Garvey-Kelson relations as multiple physical constraints on mass models to address the above issues to some extent. By means of the multiobjective optimization, the Bethe-Weizsäcker–type and the Duflo-Zucker (DZ) mass models are carried out to perform such a study as specific examples. Thanks to very recent measured neutron-rich nuclei beyond the AME20, we further test the predictive power on two DZ-type formulas as accompanied by the impressive accuracy. The discrepancies between the predicted values of the DZ10 and the DZ33 can be significantly reduced, which implies the therapy of the overfitting phenomenon in some degree. This leads to lower uncertainties of extrapolations for the models themselves.

Neutron matter, through its connection to neutron stars as well as systems such as cold atom gases, is one of the most interesting yet computationally accessible systems in nuclear physics. The configuration-interaction Monte Carlo (CIMC) method is a stochastic many-body technique allowing us to tackle strongly coupled systems. In contrast to other quantum Monte Carlo methods employed in nuclear physics, the CIMC method can be formulated directly in momentum space allowing for an efficient use of nonlocal interactions. In this work we extend CIMC method to include three-nucleon interactions through the normal-ordered two-body approximation. We present results for the equation of state of neutron matter in line with other many-body calculations that employ low-resolution chiral interactions, and provide predictions for the momentum distribution and the static structure factor.

In the ${}^{12}\mathrm{C}$ nucleus, the Hoyle state $\left(0_2^{+}\right)$ is considered to be an $\alpha$-condensed state, and the $0_3^{+}$ state is considered to be its breathing mode. We investigated whether the $\alpha$ condensation in ${}^{12}\mathrm{C}$ is realized using a microscopic $3\alpha$ cluster model with short-range correlation induced by nucleon-nucleon interactions, where we used the Argonne $v_4^{\prime }$ potential having a short-range repulsion constructed from the realistic Argonne $v_{18}$ potential. Short-range correlation was treated using the unitary correlation operator method, and the Bloch–Brink wave function was adopted as a variational wave function where the $\alpha$ cluster motions were treated by generator coordinates. We obtained four $0^{+}$ states, including short-range correlation, and analyzed them in terms of the Tohsaki–Horiuchi–Schuck–Röpke (THSR) wave function. In addition to the ordinary THSR wave function, we defined a second-order TSHR wave function to describe the $2\hslash \omega$ excitation of the $\alpha$-condensed state. The $0_2^{+}$ state (the Hoyle state) is an $\alpha$-condensed state mainly comprising the ${}^8\mathrm{Be}\left(0^{+}\right)+\alpha (0S$-wave) configuration, and the $0_3^{+}$ state mainly comprises the ${}^8\mathrm{Be}\left(0^{+}\right)+\alpha (2S$-wave) configuration, which is regarded as the breathing mode of the $\alpha$ condensation excited from the Hoyle state.

The $\alpha$ decays of even-even Ra, Th, U, and Pu isotopes to ground and excited states of daughter nuclei with neutron numbers of $N=130–140$ are investigated. These nuclei show some enhanced $\alpha$-branching ratios to negative-parity states $(1^{-},$ $3^{-})$, compared with the decays to positive-parity states $\left(4^{+}\right)$ of comparable energy. This enhancement correlates with appearance of static octupole deformation, rather than spherical nuclear shapes or dynamic asymmetric vibrational states. The highly enhanced branching ratios occur for $\alpha$ decays to the $1^{-}$ and $3^{-}$ states of the Ra isotopes with $N=134, 136, 138$, then to $1^{-}$ state in Th $(N=134–140)$ and to the $3^{-}$ state in Rn $(N=132–136)$ isotopes.

Reaction dynamics and effective in-medium nucleon-nucleon $\left(NN\right)$ cross section are studied, using the antisymmetrized molecular dynamics (AMD) model with one of the simplest heavy ion collisions, ${}^{12}\mathrm{C}+{}^1\mathrm{H}$. The roles of different stochastic processes are studied, which are installed in the original AMD. One is the diffusion process as a part of the quantum fluctuation originated from the Fermi motion during the time evolution of the wave packets in the mean field (AMD/D). The second is a coalescence treatment for light clusters with $A\le 8$ (AMD/D-COALS). The third is the collision process, installed in AMD with different form of the in-medium $NN$ cross sections. These different processes are examined, using the experimental angular distributions and energy spectra of light charged particles and intermediate mass fragments. The effective in-medium $NN$ cross sections are evaluated from the simulated AMD events and compared with the experimentally extracted values. A good agreement is obtained between the AMD values from the ${}^{12}\mathrm{C}$ $+$ ${}^1\mathrm{H}$ reaction at 95 MeV/nucleon and the experimental results for nuclear matter.

Neutron ${}^{3}P_2$ superfluids consisting of neutron pairs with the total angular momentum $J=2$, spin-triplet, and $P$ wave are believed to be realized in neutron star cores. Within the Ginzburg-Landau theory it was previously found that a singly quantized vortex is split into two half-quantized non-Abelian vortices connected by one (or three) soliton(s) forming a vortex molecule with the soliton bond(s), in the absence (presence) of a magnetic field parallel to them. In this paper, we investigate proximity effects of two vortex molecules by exhausting all possible two vortex molecule states consisting of four half-quantized vortices and determine the phase diagram spanned by the magnetic field and rotation speed. As the rotation speed is increased, the distance between the two vortex molecules becomes shorter. In the magnetic field below the critical value, we find that as the rotation speed is increased, the two separated vortex molecules transit to a dimerized vortex molecule, where the two vortex molecules are bridged by two solitons that we call “covalent bonds” in analogy with chemical molecules. We also find that the orders of the constituent half-quantized vortex cores transit from a ferromagnetic order to a cyclic order as the vortex molecules come closer. On the other hand, no dimerization occurs in the magnetic field above the critical value. Instead, we find a transition for the polarization direction of the vortex molecules from a configuration parallel to the separation to one perpendicular to the separation as they come closer. We also show some examples of three, four, and many vortex molecule states.

I extend the previous results on solving the inverse problem of quantum scattering theory (Marchenko theory, fixed-$l$ inversion). In particular, a set of isosceles triangular-pulse functions is applied to expand the Marchenko equation input kernel in a separable form. The separable form enables a reduction of the Marchenko equation to a system of linear equations for the output kernel expansion coefficients. In the general case of a single partial wave, a linear expression of the input kernel is obtained in terms of the Fourier series coefficients of $q^{1-m}(1-S\left(q\right))$ functions in the finite range of the momentum $0\le q\le \pi /h$ [$S\left(q\right)$ is the scattering matrix; $m=0,1,\cdots ,2l$; $l$ is the angular orbital momentum]. Thus, I show that the partial $S$ matrix on the finite interval determines the potential function of the corresponding radial Schrödinger equation with $h$-step accuracy. A numerical algorithm was developed to implement the method. The developed procedure was applied to the partial-wave analysis data of $NN$ elastic scattering up to 3 GeV. Calculated energy-independent complex partial potentials describe these data for single $P$ waves.

Nuclei in the vicinity of ${}^{78}\mathrm{Ni}$ are important benchmarks for nuclear structure, which can reveal changes in the shell structure far from stability. Spectroscopy of the odd-odd isotope ${}^{78}\mathrm{Cu}$ was performed for the first time in an experiment with the EURICA setup at the Radioactive Isotope Beam Factory at RIKEN Nishina Center. Excited states in the neutron-rich isotope were populated following the $\beta$ decay of ${}^{78}\mathrm{Ni}$ produced by in-flight fission and separated by the BigRIPS separator. A level scheme based on the analysis of $\gamma \text{−}\gamma$ coincidences is presented. Tentative spin and parity assignments were made when possible based on the $\beta$-decay feeding intensities and $\gamma$-decay properties of the excited states. Time correlations between $\beta$ and $\gamma$ decay show clear indications of an isomeric state with a half-life of 3.8(4) ms. Large-scale Monte Carlo shell-model calculations were performed using the A3DA-m interaction and a valence space comprising the full $fp$ shell and the $1g_{9/2}$ and $2d_{5/2}$ orbitals for both protons and neutrons. The comparison of the experimental results with the shell-model calculations allows interpreting the excited states in terms of spin multiplets arising from the proton-neutron interaction. The results provide further insight into the evolution of the proton single-particle orbitals as a function of neutron number, and quantitative information about the proton-neutron interaction outside the doubly magic ${}^{78}\mathrm{Ni}$ core.

A new anchor-based optimization method of defining energy density functionals (EDFs) is proposed. In this approach, the optimization of the parameters of EDFs is carried out for a selected set of spherical anchor nuclei, the physical observables of which are modified by the correction function, which takes into account the global performance of EDFs. It is shown that the use of this approach leads to a substantial improvement in the global description of binding energies for several classes of covariant EDFs. The computational cost of defining a new functional within this approach is drastically lower as compared with the one for the optimization which includes the global experimental data on spherical, transitional, and deformed nuclei in the fitting protocol.

Difference in the charge radii of mirror nuclei $\mathrm{\Delta }{R}_{\text{ch}}$ was proposed as a probe to the slope parameter of symmetry energy $L$. However, it has not been studied systematically by different models with pairing effects. In this work, we study the linear correlations between $\mathrm{\Delta }{R}_{\text{ch}}$ and $L$ using 36 functionals including Skyrme and covariant models for 16 pairs of spherical or nearly spherical mirror nuclei, while the pairing effects are considered by Bogoliubov transformation. With the consideration of more models, the linear correlations between $\mathrm{\Delta }{R}_{\text{ch}}$ and $L$ are weakened. The pairing effects further decrease the correlation. Besides the slope parameter, the curvature of symmetry energy $K_{\text{sym}}$ and symmetry energy at nucleon density $0.1{\mathrm{fm}}^{-3}{E}_{\text{sym}}\left(0.1\right)$ also play a role in determining $\mathrm{\Delta }{R}_{\text{ch}}$. We find $\mathrm{\Delta }{R}_{\text{ch}}$ in ${}^{14}\mathrm{O}\text{−}{}^{14}\mathrm{C},$ ${}^{22}\mathrm{Si}\text{−}{}^{22}\mathrm{O},$ ${}^{36}\mathrm{Ca}\text{−}{}^{36}\mathrm{S},$ ${}^{38}\mathrm{Ca}\text{−}{}^{38}\mathrm{Ar},$ ${}^{54}\mathrm{Ni}\text{−}{}^{54}\mathrm{Fe},$ ${}^{58}\mathrm{Zn}\text{−}{}^{58}\mathrm{Ni},$ ${}^{60}\mathrm{Ge}\text{−}{}^{60}\mathrm{Ni},$ ${}^{22}\mathrm{Mg}\text{−}{}^{22}\mathrm{Ne},$ and ${}^{34}\mathrm{Ar}\text{−}{}^{34}\mathrm{S}$ are not suitable to be taken as a probe to study $L$. Taking ${}^{54}\mathrm{Ni}\text{−}{}^{54}\mathrm{Fe}$ as an example, we find it seems hard to constrain $L$ even with a high experimental accuracy of $\mathrm{\Delta }{R}_{\text{ch}}$. However, there is a possibility to provide an upper or lower limit of $L$ from $\mathrm{\Delta }{R}_{\text{ch}}$ of mirror pairs ${}^{44}\mathrm{Cr}\text{−}{}^{44}\mathrm{Ca}$ and ${}^{46}\mathrm{Fe}\text{−}{}^{46}\mathrm{Ca}$.

Predicting the structure of quantum many-body systems from the first principles of quantum mechanics is a common challenge in physics, chemistry, and material science. Deep machine learning has proven to be a powerful tool for solving condensed matter and chemistry problems, while for atomic nuclei it is still quite challenging because of the complicated nucleon-nucleon interactions, which strongly couple the spatial, spin, and isospin degrees of freedom. By combining essential physics of the nuclear wave functions and the strong expressive power of artificial neural networks, we develop FeynmanNet, a deep-learning variational quantum Monte Carlo approach for ab initio nuclear structure. We show that FeynmanNet can provide very accurate solutions of ground-state energies and wave functions for ${}^4\mathrm{He}, {}^6\mathrm{Li}$, and even up to ${}^{16}\mathrm{O}$ as emerging from the leading-order and next-to-leading-order Hamiltonians of pionless effective field theory. Compared to the conventional diffusion Monte Carlo approaches, which suffer from the severe inherent fermion-sign problem, FeynmanNet reaches such a high accuracy in a variational way and scales polynomially with the number of nucleons. Therefore, it paves the way to a highly accurate and efficient ab initio method for predicting nuclear properties based on the realistic interactions between nucleons.