Precise nuclear charge radii provide stringent constraints on nuclear structure and few-body nuclear calculations. Their extraction from isotope-shift measurements relies critically on an accurate evaluation of the atomic field-shift factors. In this work, we present high-precision calculations of the field-shift factors for the helium isotopes ^3 He and ^4 He, including second-order relativistic perturbative corrections. For the 2 ^3S-2 ^3P transition, we achieve ppm-level accuracy and obtain field-shift factors of -1212.291(1) kHz/fm^2 for ^3 He and -1212.455(1) kHz/fm^2 for ^4 He. Using these improved values, we re-evaluate the difference of the squared nuclear charge radii to Δ R^2=1.0736(21) fm^2 based on the latest electronic-helium isotope-shift measurement. The resulting value is currently limited mainly by experimental uncertainty and shows a 2.7σ tension with the determination from muonic-helium spectroscopy. Our results provide an improved nuclear-size benchmark for helium isotopes and highlight the importance of further high-precision nuclear and atomic studies to achieve a consistent determination of nuclear charge radii across different probes.

The particle-hole nuclei ^134-136 Xe are studied using large-scale shell-model calculations with an extended pairing-plus-multipole interaction and monopole corrections. The negative-parity states 2^- to 8^- in ^136 Xe are predicted at 3.4–3.9 MeV. The quantitative analysis reveals that the monopole effects provide the dominant contribution to reproducing the spectroscopic structure of ^135 Xe. The monopole effects between the π g_7/2 and ν h_11/2 orbits substantially improve the shell-model precision in these particle-hole nuclei ^134-136 Xe near the doubly magic nucleus ^132 Sn.

Nuclear mass is an important property in both nuclear and astrophysics. In this study, we explore an improved mass model that incorporates a higher-order term of symmetry energy using algorithms. The sequential least squares programming (SLSQP) algorithm augments the precision of this multinomial mass model by reducing the error from 1.863 MeV to 1.631 MeV. These algorithms were further examined using 200 sample mass formulae derived from the δ E term of the E_isospin mass model. The SLSQP method exhibited superior performance compared to the other algorithms in terms of errors and convergence speed. This algorithm is advantageous for handling large-scale multiparameter optimization tasks in nuclear physics.

The nuclear mass model has significant applications in nuclear physics, astrophysics, and nuclear engineering. The accurate prediction of binding energy is crucial for studying nuclear structure, reactions, and decay. However, traditional mass models exhibit significant errors in double magic number region and heavy nuclear region. These models are difficult to effectively describe shell effect and parity effect in the nuclear structure, and also fail to capture the subtle differences observed in experimental results. This study demonstrates the powerful modeling capabilities of MLP neural networks, which optimize the parameters of the nuclear mass model, and reduce prediction errors in key regions and globally. In the neural network, neutron number, proton number, and binding energy are used as training feature values, and the mass-model coefficient is regarded as training label value. The training set is composed of the multiple sets of calculated nuclear mass model coefficients. Through extensive experiments, the optimal parameters are determined to ensure the convergence speed and stability of the model. The Adam optimizer is used to adjust the weight and bias of the network to reduce the mean squared error loss during training. Based on the AME2020 dataset, the trained neural network model with the minimum loss is used to predict the optimal coefficients of the nuclear mass model. The optimized BW2 model significantly reduces root-mean-square errors in double magic number and heavy nuclear regions. Specifically, the optimized model reduces the root-mean-square error by about 28%, 12%, and 18% near Z = 50 and N = 50; Z(N) = 50 and N = 82; Z = 82 and N = 126, respectively. In the heavy nuclear region, the error is reduced by 48%. The BW3 model combines higher-order symmetry energy terms, and after parameter optimization using the neural network, reduces the global root-mean-square error from 1.86 MeV to 1.63 MeV. This work reveals that the model with newly optimized coefficients not only exhibit significant error reduction near double magic numbers, but also shows the improvements in binding energy predictions for both neutron-rich and neutron-deficient nuclei. Furthermore, the model shows good improvements in describing parity effects, accurately capturing the differences related to parity in isotopic chains with different proton numbers. This study demonstrates the tremendous potential of MLP neural networks in optimizing the parameters of nuclear mass model and provides a novel method for optimizing parameters in more complex nuclear mass models. In addition, the proposed method is applicable to the nuclear mass models with implicit or nonlinear relationships, providing a new perspective for further developing the nuclear mass models.

The pairing model with configuration mixing has been applied to the odd-A 133 Cs nucleus to study band mixing. Then, a simple two-state mixing model has been utilized for the two lowest ground and excited bands. Unique solutions were identified for the 3/2+ and 5/2+ mixing in both bands, as well as for the E 2 matrix elements connecting the basis states. The excited band exhibited greater collectivity compared to the ground-state band. The use of a quasispin pairing operator with configuration mixing significantly improves the model's accuracy, especially in replicating experimental data for positive parity states and E 2 transition rates.

Understanding the properties of nuclei near the double magic nucleus 40Ca is crucial for both nuclear theory and experiments. In this study, Ca isotopes were investigated using an extended pairing-plus-quadrupole model with monopole corrections. The negative-parity states of 44Ca were coupled with the intruder orbital g_9/2 at 4 MeV. The values of E_4+ / E_2+ agree well with experimental trend from 42Ca to 50Ca, considering monopole effects between ν f_7/2 and ν p_3/2 ( ν f_5/2 ). This monopole effect, determined from data of 48Ca and 50Ca, supports the proposed new nuclear magic number N = 34 by predicting a high-energy 2^+ state in 54Ca.

This study analyzes the evolution of single-proton states within the odd-A isotopes of 117−133Sb. We identified the monopole force interaction between the πg7/2 and νh11/2 orbitals as the key driver of the ground-state inversion observed in 121Sb. Moreover, we provide an additional asset for this monopole force by investigating the negative-parity states in 132Sb and demonstrating its manifestation through a comparative assessment of πg-νh multiplets. Our results provide conclusive evidence, for the first time, explaining the ground-state inversion in 121Sb through observations in 132Sb. The increasing occupation and configurations of the orbit πd5/2 revealed that the single-proton property of state 5/2+ remained robust even in the neutron mid-shell region.

The level spectra of neutron-rich Sb isotopes have been investigated within a shell-model space containing cross-shell excitations and the intruder orbit i 13/2 .High-spin levels（27/2 - ） and（29/2 - ） in 135 Sb are taken over by the monopole effect induced by orbit i 13/2 .The ground state and excited levels in 136 Sb are well improved by considering the monopole correction between neutron orbits f 7/2 and h 9/2 .The energy shrinking of the first excited state 5/2 + in 135,137 Sb isotopes is explained by the πd 5/2 shift due to the attractive πd 5/2 vf 7/2 monopole interaction when increasingly more neutrons occupy orbit f 7/2 .The ground state of 139 Sb is predicted as 5/2+owing to the shrinking of the 5/2+states in Sb isotopes that causes ground state inversion when N=88.Further monopole effects extend the applicable range of the present Hamiltonian to nuclei with more neutrons above the N=82 shell.This Hamiltonian will be public,and researchers are encouraged to contact the authors.

The persistence of alpha-cluster states in light nuclei has aroused great interest in nuclear physics during the past several decades, and the cluster-core configuration is expected to play a key role in interpreting the spectroscopic properties of heavier nuclei. In this study, we have systematically investigated the energy spectra of alpha-cluster structures above the double shell closures within the binary cluster-core model (BCM), especially for rotational bands with negative parities. The reliability and integrity of BCM can be proved by the excellent reproduction of energy spectra. Analogously, this kind of picture is generalized to the case of heavier clusters above doubly magic core 208Pb by modifying the quantum condition for the number of nodes in the cluster-core wave function. The uncertainties of relevant parameters in the nuclear potential are determined by the nonparametric resampling strategy, leading to our statistical results on these states with negative parities. It is hoped that our present study can stimulate further insight into clustering phenomena of heavy and superheavy nuclei.

Nuclear mass is a fundamental property of nuclear physics and a necessary input in nuclear astrophysics.Owing to the com-plexity of atomic nuclei and nonperturbative strong interactions,conventional physical models cannot completely describe nuclear binding energies.In this study,the mass formula was improved by considering an additional term from the Fermi gas model.All nuclear masses in the Atomic Mass Evaluation Database were reproduced with a root-mean-square deviation(RMSD)of～1.86 MeV(1.92 MeV).The new mass formula exhibits good performance in the neutron-rich nuclear region.The RMSD decreases to 0.393 MeV when the ratio of the neutron number to the proton number is ≥1.6.

The neutron-rich nuclei near doubly magic Sn-132 have attracted considerable interest in both nuclear physics and nuclear astrophysics. For the particle-hole nuclei in this region, the low-lying and high core excitations have been well described by shell model calculations using the extended pairing plus multipole-multipole force model. However, there is a significant difference between experiment and theory in the high-spin level 17(+) of Te-132. We intend to illustrate this difference through monopole interactions. For this purpose, the monopole corrections between pi(v) 0(g7/2) v1(d5/2) and pi(v)0h(11/2) are investigated in Te132-134, Sb131-133, and Sn-130. Some theoretical levels are connected to the (17(+)) state of (132) Te with the monopole correction (Mc) of Mc (vd5/2, vh11/2) and the quadruple-quadruple force between the proton and neutron, i.e., levels 3(-) (8(-)) in Sn-130, level 14(-) in Te-132, and level 23/2(-) in Sb-131. Their observations at lower energies can confirm the datum of level (17(+)) in Te-132 with an illustration of monopole effects and quadruple-quadruple force.

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-Weizsacker-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.

超新星是人们能看到的宇宙中最为绚丽的烟花，其爆发时释放的能量约为太阳光度的100亿倍，可以帮助科学家们看得更远。Ia超新星作为标准烛光，人们可以借助它来测量宇宙中星系间的距离。超新星爆炸也会把产生的大量重元素抛射到星际空间，成为星系化学演化的主要驱动力。此外，超新星还对银河系元素的起源、太阳系结构形成和地球生命演化至关重要。对超新星的研究有助于丰富人们对宇宙的认识，帮助我们破解宇宙膨胀、重元素产生和生命起源之谜。当前，科学家们预测下一个超新星将随时爆发，研究人员正为观测即将爆发的超新星做充分准备。

This study utilizes large-scale shell model calculations with the extended pairing and multipole–multipole force model (EPQQM) to investigate low-lying states in the nuclei of 42 Ca, ^42 Sc, and ^42-44 Ti. The model space in this study includes the fp shell as well as the intruder g_9/2 orbit, which accurately reproduces the positive parity levels observed in the aforementioned nuclei and predicts high energy states with negative parity coupled with the intruder g_9/2 . The study further predicts two different configurations in ^43 Ti at around 6 MeV, specifically π f^2_7/2ν g_9/2 and π f_7/2g_9/2ν f_7/2 , both of which involve the intruder orbit g_9/2 . The levels coupled with the intruder g_9/2 in ^44 Ti are predicted to lie between 7 and 11 MeV. The inclusion of the intruder orbit g_9/2 is crucial for the exploration of high energy states in the northeast region of the doubly magic nucleus 40 Ca.

The Hamiltonian including core excitations and the intruder orbit i13/2 is used to investigate spectroscopic factors and level spectra in neutron-rich Sn isotopes. The state 13/2+ of 131Sn is predicted with a relative small value of spectroscopic factor, since the competition driven by pair cross-shell excitations weakens the single particle properties of this high-lying state near 5 MeV. The level 11/2- of 133Sn is predicted at 3.6 MeV coupled by cross-shell configuration vh-1 11/2f 2 7/2. In 135Sn,the state 3/2+ is predicted at 2.66 MeV with a main cross-shell configuration vd-1 3/2 f 47/2, and the state 13/2+ at about 2.5 MeV is predicted as a good isomer coupled by intruder orbit i13/2. The level 3- of 134Sn(136Sn) is predicted as a good isomer, due to the & gamma; decay blocked by the spin-trap structures. The level 13/2+ of 137Sn is predicted at about 2.1 MeV with 49% of configuration vf47/2i13/2. The ground state of 137Sn is predicted as 7/2- level with a main configuration v f 57/2. This work emphasizes the importance of the intruder orbit i13/2 to explain level spectra of neutron-rich Sn isotopes, and these predictions would provide useful guidance for further experiments in this nuclei region.

A new Hamiltonian is established for the particle nuclei near 132Sn by including both core excitations and neutron intruder orbit i13/2. In this Hamiltonian, the two-body force strengths and monopole terms are determined by the data in 133Sn, 134Sn, 133Sb, 134Sb, 134Te, 135Te, and 135I. According to this interaction, the level spectra and electromagnetic transitions are described well in the model space including six proton orbits (0g9/2, 0g7/2, 1d5/2, 1d3/2, 2s1/2, 0h11/2), and eight neutron orbits (1d3/2, 0h11/2, 1 f7/2, 2p3/2, 2p1/2, 0h9/2, 1 f5/2, 0i13/2). This work shows that the neutron intruder orbit i13/2 is necessary to describe particle nuclei near 132Sn. The configuration including orbit i13/2 forms a spin-trap structure and wins the competition of the lowest states at level 13/2+ in 137,139Te. Spin-trap structures are also existed in levels 2- and 9-in 136,138Te. Due to the decay block by spin-trap structures, these states are predicted as good isomers.

The p-nuclei are supposed to be produced in different astrophysical processes, such as rapid-proton capture, photonuclear reaction, and neutrino-induced reaction. To date, their abundance cannot be reasonably explained. In the present work, the cross sections of the 74 Ge ( ν e , e − ) 74 As reaction are calculated with the theoretical and experimental B (GT) values, respectively. The abundance ratios between 74 Se and 74 Ge produced from the neutrino process ( ν -process) are estimated based on the simple hypothesis for core-collapse supernova explosions. The results show that the upper limit of the 74 Se and 74 Ge abundance ratio resulting from the ν -process is about 36% of the value in the solar system.

In this work, we propose to search for the doublet vectorlike B quark (VLQ-B) based on a model-independent framework, where the VLQ-B only couples with the third generation of Standard Model quarks. We investigate the observability for single electroweak production process pp→Bb¯j with the subsequent decay mode of B→bZ and Z→ℓ+ℓ−(ℓ=e,μ) at the future high-luminosity Large Hadron Collider (HL-LHC). After a fast simulation of signal and background events, the 95% confidence level excluded regions and the 5σ discovery reach in the parameter plane of κB−mB, are respectively obtained in the narrow width case. The projected sensitivity in terms of the production cross section times branching fraction is also predicted with 10% systematic uncertainty.

The high-spin levels and β− decay in neutron-rich hole nuclei of A=128 are studied by large-scale shell-model calculations with the extended pairing plus multipole-multipole force model. The excited energy and logft values of β− decay are predicted in the final states of 128Ag, 128Cd, and 128In by the cascaded decays calculated in A=128 hole nuclei. The 16+ level of 128Cd is predicted as a spin-trap isomer feeding the existing high-spin 16+ of 128In by β− decay. The monopole effects are investigated carefully in the β− decay process from the ground state 0+ of 128Cd to the 1+ levels of 128In, while the half-life is affected by monopole corrections acting on the configuration of final states.