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To accurately predict the synthesis cross-sections of superheavy elements, identifying the optimal projectile-target combinations and the evaporation channels at specific collision energies, we have attempted to utilize high-quality microscopic nuclear masses (HQMNM) within the dinuclear system (DNS) model, which are obtained by fitting experimental data with the Skyrme energy density functional theory (DFT), as published in Phys. Lett. B 851 (2024) 138578. The atomic nuclear mass serves as a crucial input for the DNS model, as the Q-values and separation energies it generates directly influence the calculated fusion and survival probabilities. Our calculations have reproduced the experimental data for hot fusion and have been compared with results based on the finite-range droplet model (FRDM12) mass calculations. Compared to the FRDM12 mass results, we have found that the HQMNM provides a better fit to the experimental outcomes. For the specific reaction of \(^{48}\rm{Ca} + ^{243}\rm{Am} \rightarrow ^{291}\rm{Mc}^*\), we have conducted a detailed calculation of capture, fusion, and survival based on the HQMNM model and compared these with calculations based on other mass models. Based on these findings, we have systematically calculated available projectile target combinations for the synthesis of elements 119 and 120, and identified the optimal combinations. We provided the synthesis cross-sections, collision energies, and evaporation channels, offering a reference for conducting experiments on the synthesis of superheavy elements., Comment: 8 pages, 5 figures

To assess the potential of cold-fusion for synthesizing superheavy nuclei (SHN) with proton numbers 104-113, we systematically calculated 145 naturally occurring projectile-target combinations within the DNS model. Reactions predominantly show maximum cross-sections in the 1n to 2n channels, peaking near the Coulomb barrier with a sum of barrier and Q-value within 30 MeV. The maximum cross-section occurs below the Bass barrier, suggesting either the Bass model's limitation or significant deformation reducing the effective Coulomb barrier. Our calculations align well with experimental data, revealing that more neutron-rich projectiles slightly enhance fusion, though the effect is minor. For fixed targets (Pb, Bi), evaporation residue cross-sections decrease linearly with increasing projectile proton number, attributed to reduced fusion probability and lower fission barriers in heavier SHN. The touching potential $V_{\rm in}$ shows a linear trend with the product of projectile-target proton numbers, with neutron-rich systems exhibiting lower $V_{\rm in}$. Some reactions with $V_{\rm in} < V_{\rm S}$ may involve nucleon transfer before capture. Based on the DNS model, we identified optimal combinations and collision energies for synthesizing SHN with significant cross-sections. Collectively, our findings indicate that cold fusion is a promising avenue for creating proton-rich SHN around the drip line in the Z=104-113 region, offering distinct advantages over alternative mechanisms., Comment: 10 pages, 6 figures

Employing the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, the 1 GeV/nucleon deformed uranium-uranium ultra-central collisions are simulated. Based on sensitive observables, mean square collective flow and pion meson multiplicity, the impacts of high-momentum tails caused by short-range correlations and the symmetry energy in high-density regions on geometric effects are discussed under different reaction orientations. Finally, the neural network model for identifying reaction orientations is also developed.

Within the framework of the dinuclear system model, this study delves into the impact of various nuclear mass models on evaluating the fusion probability of superheavy nuclei. Nuclear mass models, as crucial inputs to the DNS model, exhibit slight variations in binding energy, quadrupole deformation, and extrapolation ability; these subtle differences can significantly influence the model's outcomes. Specifically, the study finds that nuclear mass plays a pivotal role in determining fusion probability, and Q-value. By numerically solving a set of master equations, the study examines how binding energies from different mass models affect the fusion probability of colliding nuclei, taking the example of $^{48}$Ca + $^{243}$Am $\rightarrow$ $^{291}$Mc. A careful analysis of the potential energy surface (PES) reveals that the inner fusion barriers lead to variations in fusion probabilities. Importantly, the study demonstrates that the synthesis cross sections of superheavy nuclei calculated using different nuclear mass models align well with experimental data, falling within an error range of one order of magnitude. This finding underscores the reliability of our model predictions. Looking ahead, the study utilizes five distinct nuclear mass models to predict the synthesis cross sections of superheavy elements 119 and 120, along with their associated uncertainties. These predictions offer valuable insights into the feasibility of synthesizing these elusive elements and pave the way for future experimental explorations.

Through ensemble learning with multitasking and complex connection neural networks, we aggregated nuclear properties, including ground state charge radii, binding energies, and single-particle state information obtained from the Kohn-Sham auxiliary single-particle systems. Compared to traditional density functional theory, our model can more accurately characterize nuclear ground state information. Aiming at binding energy, the root mean square error is reduced to 450 keV. Although the complexity involving the nuclear interaction is skipped, the model has not completely devolved into a black box. Leveraging the correlation between densities and binding energies, we calculate the neutron skin thickness of $^{208}$Pb to be 0.223 fm. This model will advance our understanding of nuclear properties and accelerate the integration of machine learning into modern nuclear physics.

A convolutional neural network-based classifier is elaborated to retrace the initial orientation of deformed nucleus-nucleus collisions by integrating multiple typical experimental observables. The isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model is employed to generate data for random orientations of ultra-central uranium-uranium collisions at $E_\text{beam} = 1\, \text{GeV/nucleon}$. Statistically, the data-driven polarization scheme is essentially accomplished via the classifier, whose distinct categories filter out specific orientation-biased collision events. This will advance the deformed nucleus-based studies on nuclear symmetry energy, neutron skin, etc.

This study employs the isospin-dependent Boltzmann-Uehling-Uhlenbeck model to simulate intermediate-energy heavy-ion collisions between prolate nuclei $^{24}$Mg. The emphasis is on investigating the influence of centrality and orientation in several collision scenarios. The final-state particle multiplicities and anisotropic flows are primarily determined by the eccentricity and the area of the initial overlap. This not only provides feedback on the collision systems, but also, to some extent, provides a means to explore the fine structure inside deformed nuclei. Additionally, non-polarized collisions have been further discussed. These results contribute to the understanding of the geometric effects in nuclear reactions, and aid in the exploration of other information on reaction systems, such as the equation of state and nuclear high-momentum tail.

A Kohn-Sham scheme based multi-task neural network is elaborated for the supervised learning of nuclear shell evolution. The training set is composed of the single-particle wave functions and occupation probabilities of 320 nuclei, calculated by the Skyrme density functional theory. It is found that the deduced density distributions, momentum distributions, and charge radii are in good agreements with the benchmarking results for the untrained nuclei. In particular, accomplishing shell evolution leads to a remarkable improvement in the extrapolation of nuclear density. After a further charge-radius-based calibration, the network evolves a stronger predictive capability. This opens the possibility to infer correlations among observables by combining experimental data for nuclear complex systems.

In the framework of the dinuclear system model, the synthesis mechanism of the superheavy nuclides with atomic number $Z=112, 114, 115$ in the reactions of projectiles $^{40,48}$Ca bombarding on targets $^{238}$U, $^{242}$Pu, and $^{243}$Am at a wide incident energies (excitation energy from 0-100 MeV) have been investigated systematically. Based on the available experimental excitation functions, the dependence of calculated synthesis cross sections on collision orientations has been studied thoroughly. The TKEs of these collisions with the fixed collision orientation show its orientation dependence which can be used to predict the tendency of kinetic energy diffusion. The TKEs are dependent on incident energies which have been discussed. The method of Coulomb barrier distribution function has been applied in our calculations which could treat all of the collision orientations from the tip-tip to side-side approximately. The calculations of excitation functions of $^{48}$Ca + $^{238}$U, $^{48}$Ca + $^{242}$Pu, and $^{48}$Ca + $^{243}$Am have a nice agreement with the available experimental data. The isospin effect of projectiles on production cross sections of moscovium isotopes and the influence of entrance channel effect on the synthesis cross sections of superheavy nuclei have been discussed. The synthesis cross section of new moscovium isotopes $^{278-286}$Mc have been predicted as large as hundreds pb, in the fusion-evaporation reactions of $^{35,37}$Cl + $^{248}$Cf, $^{38,40}$Ar + $^{247}$Bk, $^{39,41}$K + $^{247}$Cm, $^{40,42,44,46}$Ca + $^{238}$Am, $^{45}$Sc + $^{242}$Pu, and $^{46,48,50}$Ti + $^{243}$Np, $^{51}$V + $^{238}$U at the excitation energy interval of 0-100 MeV., Comment: 15 pages, 8 figures, 1 table

We adapt the local density approximation to add the high-momentum tails (HMTs) to finite nuclei's Slater-determinant momentum distributions. The HMTs are extracted by the extended Brueckner-Hartree-Fock (EBHF) method or by the lowest order cluster approximation. With a correction factor being added to EBHF, it is sufficiently in agreement with the experimental benchmark, i.e., the high-momentum $N/Z$ ratios approximately equal to $1$, and the low-momentum $N/Z$ ratios approximately equal to $N/Z$ of the systems. It is also found that the tensor force makes the nucleon-nucleon correlations appear more easily on the nuclear surface region and the percentage of high-momentum ($p > 300$ MeV/c) nucleons, around $17\%$--$18\%$, independent of isospin asymmetry.

Based on the back-propagation neural networks and density functional theory, a supervised learning is performed firstly to generate the nuclear charge density distributions. The charge density is further calibrated to the experimental charge radii by a composite loss function. It is found that, when the parity, pairing, and shell effects are taken into account, about $96\%$ of the nuclei in the validation set fall within two standard deviations of the predicted charge radii. The calibrated charge density is then mapped to the matter density, and further mapped to the binding energies according to the Hohenberg-Kohn theorem. It provides an improved description of some nuclei in both binding energies and charge radii. Moreover, the anomalous overbinding in $^{48}$Ca implies the existence of an indispensable beyond-mean-field effect.

Within the framework of the dinuclear system model, the reaction mechanisms for synthesizing target-like isotopes from Bk to compound nuclei Lv are thoroughly investigated in complete and incomplete fusion reaction of $^{48}$Ca +$^{248}$Cm around Coulomb barrier energies. Production cross-section of $^{292,293}$Lv as a function of excitation energy in fusion-evaporation reactions and target-like isotopic yields in multinucleon transfer reactions are evaluated, in which a statistical approach is used to describe the decay process of excited nuclei. The available experimental data can be reproduced well with the model reasonably. The products of all possible formed isotopes in the dynamical pre-equilibrium process for collision partners at incident energy $E_{\rm lab}$ = 5.5 MeV/nucleon are exported, systematically. It is found that the quasi-fission fragments are dominant in the yields. The optimal pathway from the target to compound nuclei shows up along the valley of potential surface energy. The effective impact parameter of two colliding partners leading to compound nuclei is selected from head-on collision to semi-central collision with $L$ = 52 $\rm \hbar$. The timescale boundary between complete fusion and multinucleon transfer reactions is about 5.7$\times 10^{-21}$ s with effective impact parameters. Synthesis cross-section of unknown neutron-rich actinides from Bk to Rf have been predicted around several nanobarns.

We investigate the density distributions of finite nuclei employing a well-designed deep neural network method. We calculate the target nucleon density distributions with Skyrme density functional theories, which are used to train the networks. We find that the training with only about $10\%$ nuclei ($300-400$) is sufficient to describe the nucleon density distributions of all the nuclear chart within 2\% relative error. The relative error comes to 5\% when about 200 proton(neutron) density distributions are used for training. We obtained very similar results for different Skyrme density functional theories. Therefore the ability to train networks is weakly dependent on the theoretical model. Moreover, in the process of machine learning, there is a turning point showing the transition from the Fermi-like distribution to the realistic Skyrme distribution, which provides significant properties of convergence process., Comment: 7 pages, 6 figures

We study a problem of $\pi$ production in heavy ion collisions in the context of the Isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model. We generated nucleon densities using two different models, the Skyrme-Hartree-Fock (SHF) model and configuration interaction shell model (SM). Indeed, inter-nucleon correlations are explicitly taken into account in SM, while they are averaged in the SHF model. As an application of our theoretical frameworks, we calculated the $\pi^{-}$ and $\pi^{+}$ yields in collisions of nuclei with $A = 30-40$ nucleons. We used different harmonic oscillator lengths $b_{HO}$ to generate the harmonic oscillator basis for SM in order to study both theoretical and experimental cases. It is found that SM framework with $b_{HO}$ = 2.5 fm and SHF can be distinguished by the yield of $\pi$ mesons, in this case the density distribution calculated by the shell model produces more $\pi$ in the collision. In comparison, SM with $b_{HO}$ = 2.0 fm is characterized from SHF by the double $\pi^{-}/\pi^{+}$ ratios with different large impact parameters, from which one can find the double $\pi^{-}/\pi^{+}$ ratios of SM change smoother and are less than those of SHF., Comment: 7 pages, 4 figures

Based on the Isospin-dependent transport model Boltzmann-Uehling-Uhlenbeck (IBUU), effects of the difference of the high momentum tails (HMTs) of nucleon momentum distribution in colliding nuclei on some isospin-sensitive observables are studied in the $^{197}\rm {Au}+^{197}\rm {Au}$ reactions at incident beam energy of 400 MeV/nucleon. It is found that the nucleon transverse and elliptic flows, the free neutron to proton ratio at low momenta are all less sensitive to the specific form of the HMT, while the free neutron to proton ratio at high momenta and the yields of $\pi^{-}$ and $\pi^{+}$ as well as the $\pi^{-}/\pi^{+}$ ratio around the Coulomb peak are sensitive to the specific form of the HMT. Combining the present studies with the experimental measurements at rare-isotope reaction facilities worldwide, one may get more insights into the nuclear short-range correlations in heavy nuclei or nuclear matter., Comment: 5 pages, 8 figures, accepted by PRC