In this work, the Langevin approach within the two-center shell model incorporated with the statistical evaporation model is applied to consistently describe the fission dynamics and the deexcitation process of primary fragments. The charge distribution and the ratio of the average neutron number to proton number of fission fragments, the preneutron and postneutron mass distributions, the total kinetic energy (TKE) distribution and the TKE-mass correlation of fragments, as well as the multiplicity and energy spectrum of prompt neutron in 235U fission induced by thermal and 14 MeV neutron are calculated with the present approach. The calculation results are overall in good agreement with available experimental data and GEF calculations. In addition, the excitation energy distribution of the fission fragments and the correlation between the neutron multiplicity and the TKE are studied within the present model and are highly reasonable. It is straightforward to extend the present approach to study the fission observables for high-energy neutron induced fission on actinides, where multichance fission plays a more important role.

In this study, Langevin approach incorporated with the statistical model is adopted to investigate independent fission yields for a large quantity of fission products and the dependence of prompt fission observables on the incident neutron energy in U-235(n, f). The neutron evaporation from the fission process is considered by coupling the Weisskopf statistical model to Langevin dynamical simulation, where the potential energy surface of the respective fissioning nucleus from each fission chance is calculated using the macroscopic-microscopic model within the two-center shell model. The partitions of the charge and total excitation energy between the two complementary fragments are evaluated such that the prompt neutron emissions from fission fragments can be described based on the characteristics of primary fragments. With the present model, the calculated independent fission yields of the isotopes from Z = 30-61 in 14 MeV n+U-235 fission are in good agreement with the evaluated data from ENDF/B-VIII.0. Moreover, the evolution of the independent mass yields and the cumulative yields for select isotopes with the incident neutron energy, as well as the tendency of both the average TKE and prompt neutron multiplicity with the increase in the incident neutron energy, are consistent with the experimental data. The present model can aid in reproducing prompt fission observables across a range of incident neutron energies for major actinides.

The predictive power of the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) with density functional PC-PK1 is demonstrated for superheavy region (101 <= Z <= 120) by comparing with available experimental and evaluated data from AME2020. The DRHBc theory predicts 93 bound nuclei beyond the drip line N = 258 in the region of 106 <= Z <= 112, which form a stability peninsula. The odd-even differences between odd-N and even-N nuclei are remarkable in the peninsula; the one-neutron separation energy of an odd-N nucleus is smaller than those of its neighboring even-N nuclei due to the blocking effect, and as a result the number of bound odd-N nuclei is less than that of bound even-N nuclei. The deformation effect is indispensable for the re-entrant stability beyond the drip line by significantly affecting the structure of single-particle levels around the Fermi energy. The interplay between deformation and pairing influences the location of the first bound odd-N nucleus in the peninsula. By examining the deformation effect at different orders, it is found that quadrupole deformation beta(2) contributes predominantly to the appearance of stability peninsula, and the effects of higher-order deformations beta(4) and beta(6) are non-negligible.

The mass table in the deformed relativistic Hartree–Bogoliubov theory in continuum (DRHBc) with the PC-PK1 density functional has been established for even-Z nuclei with 8≤Z≤120, extended from the previous work for even–even nuclei (Zhang et al. (DRHBc mass table collaboration), At. Data Nucl. Data Tables 144, 101488 (2022)). The calculated binding energies, two-nucleon and one-neutron separation energies, root-mean-square (rms) radii of neutron, proton, matter, and charge distributions, quadrupole deformations, and neutron and proton Fermi surfaces are tabulated and compared with available experimental data. A total of 4829 even-Z nuclei are predicted to be bound, with an rms deviation of 1.433 MeV from the 1244 mass data. Good agreement with the available experimental odd–even mass differences, α decay energies, and charge radii is also achieved. The description accuracy for nuclear masses and nucleon separation energies as well as the prediction for drip lines is compared with the results obtained from other relativistic and nonrelativistic density functional. The comparison shows that the DRHBc theory with PC-PK1 provides an excellent microscopic description for the masses of even-Z nuclei. The systematics of the nucleon separation energies, odd–even mass differences, pairing energies, two-nucleon gaps, α decay energies, rms radii, quadrupole deformations, potential energy curves, neutron density distributions, and neutron mean-field potentials are discussed.

A new method, namely the improved quantum molecular dynamics model incorporated with the microscopic potential energy surface, is proposed to simulate the dynamical evolution from saddle to scission point and to calculate the isotope yields of fission fragments in thermal neutron-induced fission of actinide nuclei near 236U. With this approach, the shell and pairing effects are introduced by the microscopic potential energy, while the isospin effect, the dynamical effects of fluctuations and correlations in fission process are automatically included in the improved quantum molecular dynamics model. These two aspects eventually influence the productions of fission fragments. The calculated both charge and mass distributions of fission fragments for a series of actinide nuclei are in overall agreement with the evaluated data from JEFF-3.3 and ENDF/B-VIII.0. The isotope distributions of fission fragments in the fission of 236U reproduce the data reasonable well, from which we extract the relationship between peak mass number of the isotope distributions and the charge number of fission fragments. We find that this relationship deviates linear relation slightly at certain cases, which indicates the isospin nonequilibrium effect. By tracking back to the fission process on the two dimension plane of elongation and mass asymmetry of prefragments, we find that the necked-in shape and the separation of two parts happen much faster for the 132Sn than 128,136Sn in the time evolution of the distance R between the centers of two parts of the fissioning system. The events producing 128,132,136Sn and 136,140,144Xe present two kinds of average fission paths with bypassing and going through the minimum-energy valley of the microscopic potential energy surface, respectively.

The threedimensional Langevin model was used to study the fragment mass distribution and total kinetic energy (TKE) distribution and the scission configuration in lowenergy nuclear fission, in which the potential energy surface was calculated by using the macroscopicmicroscopic model based on the twocenter shell model and the finite range liquid drop model, and the inertia tensor and the friction tensor were obtained within the WernerWheeler method and the wallandwindow model, respectively. Taking the case of 14 MeV n+235U fission as an example, the influence of the elongation deformation space on the fission fragment mass distribution and the TKE distribution was investigated, and the correlation between the elongation and the mass asymmetry at the scission point was also studied. It is found that the elongation deformation space has a significant influence on the symmetric fission channel, especially for the calculation of the TKE around the symmetric mass region, which is because that the symmetric channel corresponds to the super-long deformation for the light actinide nuclei such as U, Np, Pu and so on, so that the less elongation deformation space could block the larger elongated nuclear shapes along the Langevin trajectories. In addition, the influence of the shell damping parameter on the fission fragment mass distribution and TKE distribution and the scission configuration was studied. It is found that the shell damping parameter has a larger influence on the fragment mass distribution, and the ratio of the peak height and the valley increases with the larger shell damping parameter, due to the stronger shell effect. However, it has little influence on the TKE distribution which indicates that the strength of the shell effect has little influence on the nuclear elongation. In the last, the preneutron and postneutron fragment mass distributions for the 14 MeV n+233,235U fission were calculated, and the results agree well with the evaluated data from ENDF/BⅧ0, which shows that the present model has the power of calculating the fission fragment mass distribution quantitatively.

The influence of the neck parameter on the fission dynamics at low excitation energy is studied based on the three-dimensional Langevin approach in which the nuclear shape is described with the two-center shell model (TCSM) parametrization, and the elongation, the mass asymmetry and the fragment deformation are set to be the generalized coordinates of the Langevin equation. We first study the influence of the neck parameter on the scission configuration. We find that there is almost no obvious correlation between the neck parameter ε and the mass asymmetry η at the scission point indicating that the ε has no obvious impact on the fragment mass distribution. The elongation Z0/R0 and its correlation with the mass asymmetry η at the scission point are obviously influenced by the neck parameter ε, which has a strong effect on the total kinetic energy (TKE) distribution of fragments. The pre-neutron emission fragment mass distributions for 14 MeV n+^{233,235,238}U and ^{239}Pu are calculated and then based on these results the post-neutron emission fragment mass distributions are obtained by using the experimental data of prompt neutron emission. The calculated post-neutron emission fragment mass distributions can reproduce the experimental data well. The TKE distributions for 14 MeV n+^{235}U fission are calculated for ε=0.25,0.35,0.45, and the results show that the TKE distribution cannot be described very well for the three cases. However, the trend of the calculated TKE distribution with ε is just as that is expected from the scission configuration calculations and the results with ε=0.35 present a better agreement with the experiment data compared with the other two cases.

The impact of nuclear dissipation on the dynamics of nuclear fission at low excitation energy is studied with a three-dimensional Langevin approach in which the two-center shell model is adopted to describe the nuclear shape and the single-particle potential. With three types of formulas for the friction tensor, such as the wall formula, the wall-and-window formula with and without the term related to the mass asymmetry change, the fragment mass and the total kinetic energy (TKE) distributions in low-energy fission are calculated. The calculated fragment mass distributions are almost identical for both with the wall formula and with the wall-and-window model without the term related to the mass asymmetry change, and both the results are consistent with the evaluated mass yields and the calculated results with the GEF model. Our study found that the term related to the mass asymmetry change in the window formula leads to an unreasonable shift of the peak position of the mass distribution. The TKE values calculated with the wall model are slightly larger than those with the wall-and-window model due to the more compact configuration obtained with the pure wall model. Moreover, the influences of the strength of friction tensor on the fragment distribution, the scission configuration, and the fission time distribution are investigated. With the present model the fission fragment mass distributions of U, Np, Pu, and Am isotopes are well reproduced and the systematic dependence of the averaged TKE on the Coulomb parameter is also well reproduced.

Based on the relativistic calculations of the nuclear masses in the transfermium region from No（Z = 102） to Ds（Z = 110） using the deformed relativistic Hartree-Bogoliubov theory in continuum（DRHBc）, the possible existence of bound nuclei beyond the neutron drip lines is studied. The two-neutron and multi-neutron emission bound nuclei beyond the primary neutron drip line of N = 258 are predicted in Z = 106, 108, and 110 isotopes.A detailed microscopic mechanism investigation reveals that nuclear deformation plays a vital role in the existence of bound nuclei beyond the drip line. Furthermore, not only the quadrupole deformation β 2 but also the higher orders of deformation are indispensable in the reliable description of the phenomenon of reentrant binding.

In this study, 218Ac and 221Th nuclides were produced via the heavy-ion induced fusion evaporation reaction 40Ar + 186W. Their decay properties were studied with the help of the gas-filled recoil spectrometer SHANS and a digital data acquisition system. The cross section ratio between 222Pa and 218Ac was extracted experimentally, with measured value 0.69(9). Two new possible α decay branches to 221Th are suggested. The valence neutron configurations for the daughter 217Ra are discussed in terms of the hindrance factors.

Following publication of the original article, Formula (2) is missing and Fig. 11, Fig. 9 are identical.

The effects of neutron skin on the multiplicity (Nch) and eccentricity (ϵ2) in relativistic 4496Ru+4496Ru and 4096Zr+4096Zr collisions at sNN=200 GeV are investigated with the Trento model. It is found that the Ru+Ru/Zr+Zr ratios of the Nch distributions and ϵ2 in mid-central collisions are exquisitely sensitive to the neutron skin type (skin vs. halo). The state-of-the-art calculations by energy density functional theory (DFT) favor the halo-type neutron skin and can soon be confronted by experimental data. It is demonstrated that the halo-type density can serve as a good surrogate for the DFT density, and thus can be efficiently employed to probe nuclear deformities by using elliptic flow data in central collisions. We provide hereby a proof-of-principle venue to simultaneously determine the neutron skin type, thickness, and nuclear deformity.

以互联网+网络平台为基础,以建构主义理论为指导,结合翻转课堂构建地方高校大学物理4A(Anyone|Anytime| Anywhere| Anyway)式教学模式,并以大学物理课程"电磁感应定律"教学设计为例,探索4A式教学模式的应用与实践途径,从而为大学物理教学提供一种新的改革思路,也为其他课程教学创新提供新的启示.

A new framework is proposed for the study of collisions between very heavy ions which lead to the synthesis of Super-Heavy Elements (SHE), to address the fusion hindrance phenomenon. The dynamics of the reaction is studied in terms of collective degrees of freedom undergoing relaxation processes with different time scales. The Nakajima–Zwanzig projection operator method is employed to eliminate fast variables and derive a dynamical equation for the reduced system with only slow variables. There, the time evolution operator is renormalised and an inhomogeneous term appears, which represents a propagation of the given initial distribution. The term results in a slip to the initial values of the slow variables. We expect that gives a dynamical origin for the so-called “injection point $s$” introduced by Swiatecki et al. in order to reproduce absolute values of measured cross sections for SHE. A formula for the slip is given in terms of physical parameters of the system, which confirms the results recently obtained with a Langevin equation, and permits us to compare various incident channels.

The masses of $$\sim$$ 2500 nuclei have been measured experimentally; however, >7000 isotopes are predicted to exist in the nuclear landscape from H ( $$Z=1$$ ) to Og ( $$Z=118$$ ) based on various theoretical calculations. Exploring the mass of the remaining isotopes is a popular topic in nuclear physics. Machine learning has served as a powerful tool for learning complex representations of big data in many fields. We use Light Gradient Boosting Machine (LightGBM), which is a highly efficient machine learning algorithm, to predict the masses of unknown nuclei and to explore the nuclear landscape on the neutron-rich side from learning the measured nuclear masses. Several characteristic quantities (e.g., mass number and proton number) are fed into the LightGBM algorithm to mimic the patterns of the residual $$\delta (Z,A)$$ between the experimental binding energy and the theoretical one given by the liquid-drop model (LDM), Duflo–Zucker (DZ, also dubbed DZ28) mass model, finite-range droplet model (FRDM, also dubbed FRDM2012), as well as the Weizsäcker–Skyrme (WS4) model to refine these mass models. By using the experimental data of 80 $$\%$$ of known nuclei as the training dataset, the root mean square deviations (RMSDs) between the predicted and the experimental binding energy of the remaining 20% are approximately $$0.234\pm 0.022$$ , $$0.213\pm 0.018$$ , $$0.170\pm 0.011$$ , and $$0.222\pm 0.016$$ MeV for the LightGBM-refined LDM, DZ model, WS4 model, and FRDM, respectively. These values are approximately 90%, 65%, 40%, and 60% smaller than those of the corresponding origin mass models. The RMSD for 66 newly measured nuclei that appeared in AME2020 was also significantly improved. The one-neutron and two-neutron separation energies predicted by these refined models are consistent with several theoretical predictions based on various physical models. In addition, the two-neutron separation energies of several newly measured nuclei (e.g., some isotopes of Ca, Ti, Pm, and Sm) predicted with LightGBM-refined mass models are also in good agreement with the latest experimental data. LightGBM can be used to refine theoretical nuclear mass models and predict the binding energy of unknown nuclei. Moreover, the correlation between the input characteristic quantities and the output can be interpreted by SHapley additive exPlanations (a popular explainable artificial intelligence tool), which may provide new insights for developing theoretical nuclear mass models.

Predictive power of the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) for nuclear mass is examined in the superheavy region 102 ≤ Z ≤ 120. The accuracy to predict the 10 (56) measured (measured and empirical) masses is 0.635 (0.642) MeV, which is in comparison with 0.515 (1.360) MeV by WS4 and 0.910 (2.831) MeV by FRDM. Possible stability against multineutron emission beyond the two-neutron drip line is explored by the DRHBc theory, which takes into account simultaneously the deformation effects, the pairing correlations, and the continuum effects. Nuclei stable against twoand multi-neutron emissions beyond the two-neutron drip line are predicted in 106Sg, 108Hs, 110Ds, and 112Cn isotopic chains, forming a peninsula of stability adjacent to the nuclear mainland. This stability is mainly due to the deformation which significantly affects the shell structure around the Fermi surface. The pairing correlations and continuum influence the stability peninsula in a self-consistent way. ∗Electronic address: mengj@pku.edu.cn

The aim of this work is to extend the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc) based on the point-coupling density functionals to odd-A and odd-odd nuclei and examine its applicability by taking odd-A Nd isotopes as examples. In the DRHBc theory, the densities and potentials with axial deformation are expanded in terms of Legendre polynomials, and the relativistic Hartree-Bogoliubov equations are solved in a Dirac Woods-Saxon basis to include the continuum effects. For an odd-A or odd-odd nucleus, the blocking effect of unpaired nucleon(s) is taken into account with the equal filling approximation. To determine its ground state, an automatic blocking procedure is adopted, in which the orbital with the lowest quasiparticle energy is blocked during the iteration. This procedure is justified by comparing with the results from the orbital-fixed blocking calculations, in which the blocked orbital near the Fermi surface is fixed during the iteration. The ground states for both light and heavy nuclei can be provided by the automatic blocking procedure as the orbital-fixed blocking procedure, but with considerably reduced computational cost. The numerical details for even-even nuclei are found to be valid for odd-A and odd-odd nuclei as well. Taking Nd isotopes including both even-even and odd-A ones as examples, the calculated ground-state properties with PC-PK1 are in good agreement with the available experimental data. This work paves the way to construct the DRHBc mass table including all even-even, odd-A and odd-odd nuclei in the nuclear chart.

Based on the Skyrme energy density functional, the self-consistent HF calculations have been performed for 16O, and the results show that the double point group tetrahedral symmetry TdD may play an important role in the configuration of many-body fermion system in the ground state of 16O. The corresponding total density distribution in the ground state, calculated by using the HF wave functions, presents the distinct 4α cluster-like tetrahedral structure with the Td symmetry. Among others, the necessary restoration of the rotational and parity symmetry, plays a crucial role for the occurrence of the tetrahedral symmetry in 16O.

The three-dimensional Langevin model plus a constraint on the heavy fragment deformation is used to study the fission dynamics for uranium and plutonium isotopes at low excitation energies. The potential energy surface is calculated with the macroscopic-microscopic model based on the two-center shell model. The Werner-Wheeler approximation is used to calculate the inertia tensor and the wall-and-window model is applied to calculate the friction tensor. In this work, the influence of the model parameters on the fission fragment mass distribution is investigated. The fission fragment mass distributions for U-234,U-236,U-239 and Pu-240 at low excitation energies are calculated and compared with the results of GEF code as well as the evaluated data of ENDF/B-VIII.0. A nice agreement is found in the comparison, in which the incorporation of the constraint on the heavy fragment deformation plays an important role. In addition, the dependence of the mass distribution on the excitation energies for n + U-235 fission is also studied within the model. Furthermore, the correlation between the elongation and mass asymmetry at the scission point and the correlations of the fission time with both the elongation and mass asymmetry are studied. This study may shed light on understanding the dynamics of the superlong channel for symmetric fission and the standard channels for asymmetric fission in the GEF model and other phenomenological fission models.