A complete solution to the inverse problem of Kohn-Sham (KS) density functional theory is proposed. Our method consists of two steps. First, the effective KS potential is determined from the ground-state density of a given system. Then, the knowledge of the potentials along a path in the space of densities is exploited in a line integration formula to determine numerically the KS energy of that system. A possible choice for the density path is proposed. A benchmark in the case of a simplified yet realistic nuclear system is shown to be successful, so the method seems promising for future applications.

Quasielastic scattering and breakup angular distributions for the neutron halo nucleus ${}^{11}\mathrm{Be}$ on a ${}^{208}\mathrm{Pb}$ target at the laboratory energy of 210 MeV, which corresponds to 5.2 times the Coulomb barrier, were measured at HIRFL-RIBLL (Heavy-Ion Research Facility in Lanzhou and Radioactive Ion Beam Line in Lanzhou). The quasielastic scattering angular distribution of ${}^{11}\mathrm{Be}$ shows an obvious suppression of the Coulomb nuclear interference peak (CNIP) even at such a high incident energy. Theoretical results with the continuum discretized coupled channels (CDCC) method are in correspondence with the experimental data. The measured angular distribution of the ${}^{10}\mathrm{Be}$ fragments is well reproduced considering elastic breakup contribution with the CDCC calculations plus nonelastic breakup contribution with the model of Ichimura, Austern and Vincent [Phys. Rev. C 32, 431 (1985)]. The reduced reaction cross section of the ${}^{11}\mathrm{Be}+{}^{208}\mathrm{Pb}$ system was compared with those of other reaction systems including tightly and weakly bound projectiles impinging on medium and heavy mass targets, where the former shows a significant enhancement. Systematical comparisons between the experimental data and theoretical calculations suggest that elastic scattering with heavy targets (such as ${}^{208}\mathrm{Pb}$) at relatively high incident energies is still sensitive to the structure of neutron-rich nuclei.

Collective inertial mass coefficients with respect to translational, relative, and rotational motions are microscopically calculated, along the collective reaction path self-consistently determined, based on the adiabatic self-consistent collective coordinate (ASCC) method. The impact of the time-odd component of the mean-field potential on the inertial masses are investigated. The results are compared with those calculated with the cranking formulas. The inertial masses based on the ASCC method reproduce the exact total nuclear mass for the translational motion as well as the exact reduced masses as the asymptotic values for the relative and rotational motions. In contrast, the cranking formulas fail to do so. This is due to the fact that the (local) Galilean invariance is properly restored in the ASCC method but violated in the cranking formulas. A model Hamiltonian for low-energy nuclear reaction is constructed with the microscopically derived potentials and inertial masses. The astrophysical $S$ factors are calculated, which indicates the importance of microscopic calculation of proper inertial masses.

One of the dynamical investigations foran understanding of the fission process is the analysis through Langevin trajectories in the nuclear deformation space. The main motivation of this analysis is to elucidate the characteristic nuclear-shape oscillation induced by a random force in the Langevin equation and its impact on the fission process. The characteristic random oscillation originates from the requirement of an overdamped condition. The properties of the friction tensor in the equation reveal that the directional nuclear shape fluctuations originate in the subspace of nuclear deformation. Our calculations exhibit a good agreement with the fission data for fermium isotopes, where the fission-fragment mass distribution changes dramatically from the asymmetric shape to the sharp symmetric shape as the masses of the fissioning Fm isotopes increase.

Background: In earlier studies, spherical and quadrupole deformed nuclei with closed shells were found to be the most probable fission fragments in the decay of heavy-mass compound nuclei at low excitation energies. Recently, the disintegration of heavy-mass actinides gave evidence of pear-shaped fission fragments, in the mass-asymmetric region, due to extra stability provided by the shell-stabilized octupole deformed ${}^{144}\mathrm{Ba}$ $(Z=56)$ nucleus.

Purpose: In our theoretical work, we have done an exercise to analyze the possibility of octupole deformed fragments in the decay of light- and heavy-mass isotopes of thorium, i.e., ${}^{222,224,226,228,230}\mathrm{Th}^{*}$.

Method: To carry forward the above idea, the mass and charge dispersions of chosen Th isotopes have been analyzed by including deformations (up to ${\beta }_3$) and related cold optimum orientations within the dynamical cluster-decay model (DCM), which is based on the collective clusterization approach of quantum mechanical fragmentation theory. The above analysis is worked out at low excitation energy, which corresponds to the cold synthesis criteria.

Results: In the decay of considered Th isotopes, the minima of fragmentation potential and peaks of preformation probability appear in two regions, near symmetric and asymmetric, respectively due to the presence of quadrupole (${\beta }_2$) and octupole deformations (${\beta }_3$) of decay fragments. However, the emission of ${\beta }_3$-deformed fission fragments is prominent in the heavier isotopes of Th, i.e., ${}^{226,228,230}\mathrm{Th}^{*}$. The above result is in agreement with the experimentally obtained mass and charge distributions.

Conclusions: The disintegration of thorium isotopes into octupole deformed fragments in the asymmetric region signifies their relative stability, which is enhanced for ${}^{144}\mathrm{Ba}$ ($Z=56$) or in its vicinity.

The simultaneous emission of two protons is an exotic and complex three-body process. It is very important for experimental groups investigating the nuclear stability on the proton drip line to have a simple rule predicting the two-proton decay widths with a reasonable accuracy for transitions between ground as well as excited states in terms of relevant physical variables. In spite of its complexity, we show that the two-proton emission process obeys similar rules as for binary emission processes like proton, $\alpha$, and heavy cluster decays. It turns out that the logarithm of the decay width, corrected by the centrifugal barrier, linearly depends upon the Coulomb parameter within one order of magnitude. On the other hand, the universal linear dependence with a negative slope between the logarithm of the reduced width and the fragmentation potential, valid for any kind of binary decay process, is also fulfilled for the two-proton emission with a relative good accuracy. As a consequence of pairing correlations the two protons are simultaneously emitted from a spin singlet paired state. We evidence that indeed one obtains a linear dependence between the logarithm of the reduced width and pairing gap within a factor of two, giving a good predictive power to this law. It turns out that the two-proton and alpha-cluster formation probabilities have similar patterns versus the pairing gap, while in the one-proton case one has a quasiconstant behavior.

Three new isomers have been identified in the transitional odd-odd ${}^{216}\mathrm{Fr}$ nucleus. The properties of the $\left({11}^{+}\right)$ isomer with $T_{1/2}$ = 9.6(14) ns are compared with those of the similar isomeric states in neighboring doubly-odd nuclei. The experimental results are compared with predictions of shell-model calculations and a fair agreement is observed between the experimental and calculated excitation energies of the $\left({11}^{+}\right)$ isomeric state and the states to which it decays. The deviation between the measured and calculated reduced transition probabilities suggests contribution from effects other than the single-particle degrees of freedom in these states. Evidence of two high-spin $[J^{\pi }>\left({18}^{+}\right)]$ isomers above 2.2 MeV excitation energy with $T_{1/2}=7.8\left(14\right)$ and 89(9) ns is also presented. These isomers at high excitation energies reflect a pronounced change in the structure above the previously established level scheme, where moderate quadrupole collectivity and octupole correlations were evident.

We calculate $J/\psi$ triangular flow in high energy nuclear collisions. The charmonium motion in medium is controlled by a transport equation with loss and gain terms, and the evolution of the hot medium is governed by a single-shot hydrodynamic equation with a triangularly deformed initial condition. In comparison with the elliptic flow $v_2$, the triangular flow $v_3$ comes almost completely from the charmonium regeneration in the quark gluon plasma and therefore is more sensitive to the medium properties.

We study the dynamics of identified, strange, and multistrange particle production in Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV using the recently developed Angantyr model, incorporated within pythia8. We show the interplay between multiparton interactions (MPIs) and color reconnection (CR) on the experimentally measured quantities. We also investigate the role of string shoving within the rope hadronization framework and its impact in particle production. The charged-particle multiplicity ($N_{\mathrm{ch}}$) and mean transverse momentum ($\langle p_{\mathrm{T}}\rangle$) distributions are well explained by pythia8 Angantyr with proper tuning, as presented in this paper. Predictions of $p_{\mathrm{T}}$ spectra, $\langle p_{\mathrm{T}}\rangle$, and $p_{\mathrm{T}}$ integrated yields of the identified, strange, and multistrange particles are studied. To provide insight into the collective nature of the produced particles, we look into the ratio of particle yields to pions and kaons. pythia8 Angantyr with MPI$+$CR and hadronization via string shoving is seen to mimic signs of collectivity due to different implementations in string interactions.

A novel machine learning approach is used to provide further insight into atomic nuclei and to detect orderly patterns amid a vast data of large-scale calculations. The method utilizes a neural network that is trained on ab initio results from the symmetry-adapted no-core shell model (SA-NCSM) for light nuclei. We show that the SA-NCSM, which expands ab initio applications up to medium-mass nuclei by using dominant symmetries of nuclear dynamics, can reach heavier nuclei when coupled with the machine learning approach. In particular, we find that a neural network trained on probability amplitudes for $s$- and $p$-shell nuclear wave functions not only predicts dominant configurations for heavier nuclei but in addition, when tested for the ${}^{20}\mathrm{Ne}$ ground state, accurately reproduces the probability distribution. The non-negligible configurations predicted by the network provide an important input to the SA-NCSM for reducing ultralarge model spaces to manageable sizes that can be, in turn, utilized in SA-NCSM calculations to obtain accurate observables. The neural network is capable of describing nuclear deformation and is used to track the shape evolution along the ${}^{20-42}\mathrm{Mg}$ isotopic chain, suggesting a shape coexistence that is more pronounced toward the very neutron-rich isotopes. We provide first descriptions of the structure and deformation of ${}^{24}\mathrm{Si}$ and ${}^{40}\mathrm{Mg}$ of interest to x-ray burst nucleosynthesis, and even of the extremely heavy nuclei such as ${}^{166,168}\mathrm{Er}$ and ${}^{236}\mathrm{U}$, that build on first-principles considerations.

The level scheme of ${}^{215}\mathrm{Fr}$ is extended up to 55/2 $\hslash$ and 4.8 MeV excitation energy with the addition of 52 new $\gamma$-ray transitions. Previously established isomers and their half-lives, except for the ${\mathrm{47/2}}^{+}$ state, are revisited. The discrepancy in the half-life of the ${\mathrm{39/2}}^{-}$ state is resolved, and its half-life is revised to 11.4(14) ns. An overall good agreement is observed between the experimental results and the shell-model calculations performed using the CD-Bonn $NN$ interaction derived from the $V_{\text{low-}k}$ renormalization approach. A weak coupling of the odd proton to the even-even core is observed to account for the level structure at lower energies, which strongly resembles a decoupled nonrotational band. A new positive-parity sequence is also established which is observed to originate from the coupling of the $i_{13/2}$ proton at low excitation energy.

We report on the measurement of spin density matrix elements of the $\mathrm{\Lambda }\left(1520\right)$ in the photoproduction reaction $\gamma p\to \mathrm{\Lambda }\left(1520\right)K^{+}$, via its subsequent decay to $K^{-}p$. The measurement was performed as part of the GlueX experimental program in Hall D at Jefferson Laboratory using a linearly polarized photon beam with $E_{\gamma }=8.2\mathrm{GeV}\text{–}8.8\mathrm{GeV}$. These are the first such measurements in this photon energy range. Results are presented in bins of momentum transfer squared, $-(t-t_{\text{0}})$. We compare the results with a Reggeon exchange model and determine that natural exchange amplitudes are dominant in $\mathrm{\Lambda }\left(1520\right)$ photoproduction.

The photoproduction of $J/\psi$ mesons at low transverse momentum is studied in peripheral lead-lead collisions collected by the LHCb Collaboration at a center-of-mass energy per nucleon pair of $5\mathrm{TeV}$, corresponding to an integrated luminosity of 210 $\mu {\mathrm{b}}^{-1}$. The $J/\psi$ candidates are reconstructed through the prompt decay into two muons of opposite charge in the rapidity region of $2.0<y<4.5$. The results significantly improve previous measurements and are compared to the latest theoretical prediction.

The nature of two high-spin bands in ${}^{136}\mathrm{Nd}$ built on the two-quasiparticle configuration $\pi h_{11/2}^2$, predicted by the triaxial projected shell model as good candidates of transverse wobbling bands, are investigated experimentally. The mixing ratio of one $\mathrm{\Delta }I=1$ transition connecting the one-phonon and the zero-phonon wobbling bands is established from a high-statistics JuroGam II $\gamma$-ray spectroscopy experiment by using the combined angular correlation and linear polarization method. The resulting wobbling excitation energy and ratios of reduced electromagnetic transition probabilities are in good agreement with results of a new particle-rotor model which rigidly couples the total angular momentum of two quasiparticles to a triaxial core in an orthogonal geometry, confirming thus the transverse wobbling nature of the bands.

Low-lying states in the odd-$Z$ isotopes ${}_{89}{}^{221}\mathrm{Ac}_{132}$ and ${}_{91}{}^{225}\mathrm{Pa}_{134}$ have been studied using $\alpha$-particle and $\alpha \gamma$-coincidence spectroscopy in the ${}^{225}\mathrm{Pa}\to {}^{221}\mathrm{Ac}\to {}^{217}\mathrm{Fr}$ decay chain. Ground-state spin and parity assignments of $I^{\pi }$ = ${\mathrm{5/2}}^{-}$ are proposed for both ${}^{221}\mathrm{Ac}$ and ${}^{225}\mathrm{Pa}$, with the odd proton occupying the $\mathrm{\Omega }$ = 5/2 orbital of the quadrupole-octupole deformed shell model in both nuclei. In ${}^{221}\mathrm{Ac}$, excited states in the bands based on the $\mathrm{\Omega }$ = 5/2 and $\mathrm{\Omega }$ = 3/2 orbitals have been identified, including proposed parity-doublet states. The results suggest that reflection-asymmetric deformation of the ground state persists in the odd-$A$ members of the isotope chains down to $N$ = 132 for Ac and $N$ = 134 for Pa, before reaching the transitional region at $N$ = 130.

Background: Despite its age, the nuclear liquid drop (LD) model, plus the microscopic corrections, still plays an important role in nuclear mass studies. Especially, the LD model readily correlate the finite nucleus and the nuclear matter through the symmetry energy term.

Purpose: To systematically analyze the model uncertainty of the LD mass formula and check the corresponding symmetry energy coefficients.

Method: The Monte Carlo bootstrap approach, based on the nonparametric sampling, is applied to determine the statistical uncertainties of the parameter set in two popular LD formulas. The dependence between these parameters is also quantified via the correlation coefficients.

Results: The least required proportion of the experimental mass data is fixed for the fitting process of the LD formula. After the statistical deviation is determined for each parameter in the LD formula, the model uncertainty is evaluated as illustrated for one heavy isotopic chain. The Pearson coefficients between each two parameters involved in the LD mass formula are tabulated and figured plus the detailed discussions on the surface and volume symmetry energy coefficients.

Conclusion: The uncertainties of the fitted parameters and the LD model itself are smooth, leading to a relatively stable extrapolation. It is necessary to include the Wigner energy term in the LD model when yielding the reasonable symmetry energy coefficients.

The correlation between neutron skin-thickness of a nucleus with neutron excess and density slope parameter of symmetry energy is assessed as a function of density using relativistic mean-field models containing nonlinear couplings among different mesons. Models with larger skin were found to probe the density slope parameter even at suprasaturation densities, whereas models with smaller skin were observed to be sensitive only at specific subsaturation density, connected to the average density of nuclei. Possible reasons behind this density dependence are explored systematically. These results might be model specific, which need to be reassessed in other types of interactions existing in the literature. Nevertheless, extrapolating the predictions at high densities from models, which are optimized by data at saturation or subsaturation densities, needs to be handled with care.

We study the origin of the directed flow of charged particles produced in relativistic heavy-ion collisions. Three different initial conditions, $\mathrm{Boz}\dot{\text{e}}\mathrm{k}$-Wyskiel, CCNU, and Shen-Alzhrani, of energy density distributions are coupled to the $(3+1)$-dimensional viscous hydrodynamic model CLVisc, and their effects on the development of the anisotropic medium geometry, pressure gradient, and radial flow are systematically compared. By comparison to experimental data at both the Relativistic Heavy-Ion Collider and the Large Hadron Collider, we find that the directed flow provides a unique constraint on the tilt of the initial medium profile in the plane spanned by the impact parameter and space-time rapidity. Within midrapidity, the counterclockwise tilt is shown to be a crucial source of the positive-negative force by the pressure gradient along the impact parameter $\left(x\right)$ direction at backward-forward rapidity, which drives a negative slope of the $x$ component of the medium flow velocity with respect to rapidity, and in the end the same feature of the charged particle directed flow.

The nucleus ${}^{29}\mathrm{Ne}$ is situated at the border of the island of inversion. Despite significant efforts, no bound low-lying intruder $f_{7/2}$ state, which would place ${}^{29}\mathrm{Ne}$ firmly inside the island of inversion, has yet been observed. Here, the first investigation of unbound states of ${}^{29}\mathrm{Ne}$ is reported. The states were populated in ${}^{30}\mathrm{Ne}(p,pn)$ and ${}^{30}\mathrm{Na}(p,2p)$ reactions at a beam energy of around 230 MeV/nucleon, and analyzed in terms of their resonance properties, partial cross sections, and momentum distributions. The momentum distributions are compared to calculations using the eikonal, direct reaction model, allowing $\ell$ assignments for the observed states. The lowest-lying resonance at an excitation energy of 1.48(4) MeV shows clear signs of a significant $\ell =3$ component, giving first evidence for $f_{7/2}$ single particle strength in ${}^{29}\mathrm{Ne}$. The excitation energies and strengths of the observed states are compared to shell-model calculations using the sdpf-u-mix interaction.