多任务神经网络对原子核低激发谱的研究

原子核低激发谱对深入理解原子核结构具有重要作用。采用多任务反向传播(Back Propagation,BP)的神经网络方法系统研究了原子核$ {2}_{1}^{+} $和$ {4}_{1}^{+} $的激发能量。除了质子数和中子数外,通过在网络输入层增加一个有关原子核集体性的物理量,BP神经网络在0.1 MeV到数MeV的能量范围内很好地拟合了原子核的低激发能。相比五维集体哈密顿量(Five-Dimensional Collective Hamiltonian,5DCH)方法,BP神经网络更好地再现了原子核低激发能的同位素趋势,以及由壳效应导致的幻数原子核低激发能的突然增大,并且将$ {2}_{1}^{+} $和$ {4}_{1}^{+} $激发能的预言精度分别提高了约80%和75%,该预言精度与单任务神经网络基本一致,但是改进了对轻核区与缺中子核区低激发谱的学习能力,这说明多任务神经网络可以实现多种激发能量的统一精确计算。     

原子核质量的测量和评估

质量是原子核的基本性质之一,在核物理和核天体物理中都有重要的应用。原子核质量测量是目前核物理研究的一个前沿热点课题,国际上各个核物理实验室积极发展新设备和新技术,在短寿命放射性核素测量和超高精度质量测量方面取得了重要进展,本文对此进行了总结评述。在兰州重离子加速器冷却储存环（HIRFL-CSR）上利用等时性质量谱仪测量了一些原子核的质量,本文对其在测量精度、核态最短寿命等前沿进展做了简要介绍,并介绍了正在发展的双飞行时间质量谱仪。原子质量评估收集所有与原子核质量相关的实验数据,经过评估后推荐出质量值及相应误差。原子质量评估AME2016于2017年3月发表,为科技工作者提供基准数据。Mass is a fundamental property of the atomic nucleus. Nuclear mass data play an important role in nuclear physics and nuclear astrophysics. Thanks to the developments of novel mass spectrometers and radioactive nuclear beam facilities, the experimental knowledge of nuclear masses has been continuously expanding along two main directions, including:measurements aimed at high-precision mass values and at the most exotic nuclei far from the stability. The latest progress are reviewed in the paper. In the past few years, mass measurements of short-lived nuclides were performed using isochronous mass spectrometry based on the Cooler Storage Ring at the Heavy Ion Research Facility in Lanzhou(HIRFL-CSR). The progresses on the frontiers of short half-life and high precision are introduced. The Atomic Mass Evaluation (AME) is the most reliable source for the comprehensive information related to the atomic (nuclear) masses. The latest version of the AME, i.e., AME2016, was published in March, 2017, serving the research community with the benchmark data.     

Examination of n-T_9 conditions required by N=50,82,126 waiting points in r-process

We examined the conditions of neutron density(n) and temperature(T_9) required for the N = 50, 82,and 126 isotopes to be waiting points(WP) in the r-process. The nuclear mass based on experimental data presented in the AME2020 database(AME and AME ±Δ) and that predicted using FRDM,WS4, DZ10, and KTUY models were employed in our estimations. We found that the conditions required by the N = 50 WP significantly overlap with those required by the N = 82 ones, except for the WS4 model. In addition, the upper(or lower) bounds of the n-T_9 conditions based on the models are different from each other due to the deviations in the two-neutron separation energies.The standard deviations in the nuclear mass of 108 isotopes in the three N = 50, 82, and 126 groups are about rms = 0.192 and 0.434 Me V for the pairs of KTUY-AME and WS4-KTUY models,respectively. We found that these mass uncertainties result in a large discrepancy in the nn-T_9 conditions, leading to significant differences in the conditions for simultaneously appearing all the three peaks in the r-process abundance. The newly updated FRDM and WS4 calculations can give the overall conditions for the appearance of all the peaks but vice versa for their old versions in a previous study. The change in the final r-process isotopic abundance due to the mass uncertainty is from a few factors to three orders of magnitude. Therefore, accurate nuclear masses of the r-process key nuclei, especially for ~(76) Fe,~(81)Cu,~(127)Rh,~(132)Cd,~(192)Dy, and ~(197)Tm, are highly recommended to be measured in radioactive-ion beam facilities for a better understanding of the r-process evolution.     

Released energy formula for proton radioactivity based on the liquid-drop model

In this work, based on the liquid-drop model and considering the shell correction, we propose a simple formula to calculate the released energy of proton radioactivity(Q_p). The parameters of this formula are obtained by fitting the experimental data of 29 nuclei with proton radioactivity from ground state. The standard deviation between the theoretical values and experimental ones is only 0.157 Me V. In addition, we extend this formula to calculate 51 proton radioactivity candidates in region 51≤Z≤83 taken from the latest evaluated atomic mass table AME2016 and compared with the Q_p calculated by WS4 and HFB-29. The calculated results indicate that the evaluation ability of this formula for Q_p is inferior to WS4 while better than HFB-29.     

The AME 2020 atomic mass evaluation (I). Evaluation of input data,and adjustment procedures

This is the first of two articles(Part I and Part II)that presents the results of the new atomic mass evaluation,Ame2020.It includes complete information on the experimental input data that were used to derive the tables of recommended values which are given in Part II.This article describes the evaluation philosophy and procedures that were implemented in the selection of specific nuclear reaction,decay and mass-spectrometric data which were used in a least-squares fit adjustment in order to determine the recommended mass values and their uncertainties.All input data,including both the accepted and rejected ones,are tabulated and compared with the adjusted values obtained from the least-squares fit analysis.Differences with the previous Ame2016 evaluation are discussed and specific examples are presented for several nuclides that may be of interest to Ame users.     

基于Weizsäcker-Skyrme核质量公式研究原子核基态性质

基于一个半经验的原子核宏观 微观质量公式——Weizsäcker-Skyrme质量公式, 研究了原子核的形变、 滴线、 壳能隙和超重核α衰变能等相关性质, 发现该模型能较好地再现实验结果。与此同时, 探索了原子核对称能系数对原子核质量公式的影响和超重稳定岛的可能位置。     

SYSTEMATICAL ANALYSES OF PROTON-NUCLEI SCATTERING WITH RELATIVISTIC MICROSCOPIC OPTICAL POTENTIAL

Relativistic microscopic optical potential of a nucleon above the fermi sea based on Walecka's model is used to systematically analyze the proton elastic scattering from nuclei at energies below 300MeV.It is shown that the experimental data of differential cross sections,analyzing powers and spin rotation functions are reproduced satisfactorily except for large angles.This simple model might be used in the nuclear transport theory and heavy ion collision to take account of both nuclear medium and relativistic effects.     

Absolute residue cross sections for 46–50Ti + 13C reactions at 36, 46 and 56 MeV

Absolute cross sections for nuclei produced in the reactions ^46–50Ti + ¹³C at 36, 46 and 56 MeV (lab) were measured. Complete identification in mass and atomic number for the evaporation residues was obtained by means of in-beam γ-ray spectroscopy techniques. In the entire energy range, an overall satisfactory account of the observed product nuclei is given by the predictions of the fusion-evaporation model. Direct channels like inelastic scattering and n-transfer appear to be noticeable and contribute ~ 15 % to the total cross section.     

Effective atomic number,electron density and kerma of gamma radiation for oxides of lanthanides

An attempt has been made to estimate the effective atomic number, electron density (0.001 to 10⁵ MeV) and kerma (0.001 to 20 MeV) of gamma radiation for a wide range of oxides of lanthanides using mass attenuation coefficient from WinXCom and mass energy absorption coefficient from Hubbell and Seltzer. The values of these parameters have been found to change with energy for different oxides of lanthanides. The lanthanide oxides find remarkable applications in the field of medicine, biology, nuclear engineering and space technology. Nano-oxides of lanthanide find applications in display and lighting industry.     

深度学习在核物理中的应用

深度学习是目前最好的模式识别工具，预期会在核物理领域帮助科学家从大量复杂数据中寻找与某些物理最相关的特征。本文综述了深度学习技术的分类，不同数据结构对应的最优神经网络架构，黑盒模型的可解释性与预测结果的不确定性。介绍了深度学习在核物质状态方程、核结构、原子核质量、衰变与裂变方面的应用，并展示如何训练神经网络预测原子核质量。结果发现使用实验数据训练的神经网络模型对未参与训练的实验数据拥有良好的预测能力。基于已有的实验数据外推，神经网络对丰中子的轻原子核质量预测结果与宏观微观液滴模型有较大偏离。此区域可能存在未被宏观微观液滴模型包含的新物理，需要进一步的实验数据验证。     

Incomplete fusion of the 16O + 27Al reaction

Velocity spectra of fusion-like residues produced in the reactions of 90 MeV and 150 MeV ¹⁶O with ²⁷Al were measured. At 90 MeV the velocity spectra were well reproduced by a statistical model calculation. At 150 MeV the observed centroids of the velocity spectra deviate from the statistical model predictions. The centroid shifts as a function of the atomic and mass numbers of evaporation residues were analyzed by two different model calculations based on the assumption that incomplete fusion is (a) a peripheral process, or (b) independent on the angular momentum of the entrance channel, respectively. The later assumption is in better agreement with the presented data.     

Evolution of the giant dipole resonance in excited 120Sn and 208Pb nuclei populated by inelastic alpha scattering

The evolution of the giant dipole resonance (GDR) in ¹²⁰Sn and ²⁰⁸Pb nuclei at excitation energies in the range of 30–130 MeV and 40–110 MeV, respectively, were studied by measuring high energy γ rays from the decay of the resonance. The excited states were populated by inelastic scattering of α particles at beam energies of 40 and 50 MeV/nucleon for ¹²⁰Sn and 40 MeV/nucleon for ²⁰⁸Pb. A systematic increase of the resonance width with increasing excitation energy was observed for both nuclei. The observed width evolution was compared to calculations employing a model that adiabatically couples the collective excitation to the nuclear shape, and to a model based on the collisional damping of nucleons. The adiabatic coupling model described the width evolution in both nuclei well, whereas the collisional damping calculation could describe the width evolution only in ²⁰⁸Pb. Light-particle inelastic scattering populates low angular momentum states in the target nucleus. The observed width increase is therefore interpreted to be predominantly due to fluctuations in the nuclear shape induced by temperature. This interpretation is consistent with the adiabatic model calculations and with recent angular momentum-gated measurements of the GDR in excited Sn isotopes.     

LASP软件3.0版本的最新进展：针对多元素的全局神经网络势函数以及长程相互作用描述符

基于神经网络势函数的大尺度原子模拟软件(LASP软件)是我们在2018年开发的软件平台(www.lasphub.com),主要用于针对复杂材料体系的原子模拟. 软件整合了基于机器学习的神经网络势函数计算与全局势能面搜索功能,可以广泛运用于各种材料的结构预测以及化学反应机理研究. 本文介绍了我们在最近发布的LASP软件3.0版本中的一些更新,主要聚焦在针对神经网络势函数的一些重要改进,包括为多元素体系设计的多重神经网络架构,以及为长程相互作用设计的S⁷和S⁸两个新的基于幂指数结构描述符. 这些新的改进一方面提高了势函数的计算精度,另一方面降低了基于神经网络势函数的大尺度原子模拟软件软件对多元素体系的训练代价. 本文利用Cu-C-H-O神经网络势函数以及Cu(111)表面催化甘油裂解反应这一非均相催化体系对新的功能进行测试,结果表明,通过使用已有的神经网络作为输入,多重神经网络架构可以将训练效率提高50%. 分子动力学模拟结果表明,基于双重网络,以及S⁷、S⁸结构描述符的CuCHO势函数具有良好的稳定性,且计算精度可以提高1倍.     

136Xe+198Pt多核子转移反应机制的理论研究

如何生成丰中子重核是目前原子核物理领域的热点问题之一,多核子转移反应是生成丰中子重核的一种可行途径。本工作采用时间相关的Hartree-Fock(TDHF)方法研究了136Xe+198Pt在E_c.m.=645 MeV的多核子转移反应。对动力学过程中的核子转移、能量耗散、形变核的朝向效应等进行了细致的分析,并结合统计衰变模型GEMINI++处理初级碎片的退激发过程,计算了类弹核的同位素生成截面,并与实验结果进行了对比。结果表明,对于少量核子转移的产物截面,TDHF方法可以给出较好的描述;而对于较多核子转移生成的远离弹靶的产物截面,理论计算与实验结果有较大的偏差。最后,对这些偏差产生的原因进行了讨论。     

New mass relations and two- and four-nucleon correlations

Periodic terms in the nuclear binding energies, such as the pairing energy, are investigated. To this end we introduce a new, general set of mass relations (indicators) sensitive to specific types of periodicities in the binding-energy surface. Based on experimental data, the analysis leads to an improved expression for the (average) pairing term in the mass formulas. No trace of α-clustering is found and an upper limit for the corresponding energy gain can be deduced to be 0.4 MeV per α-particle or 1.5% of the total α-binding energy. The Wigner term, especially important for light nuclei, is accurately determined. An extra binding in odd N = Z nuclei is observed above the average of all other odd-odd nuclei.     

中能重离子碰撞中同位旋相关核子-核子碰撞截面和同位旋相关平均场的探针

在最近几年我们通过使用同位旋相关的量子分子动力学模型（IQMD）系统的研究了同位旋相关的平均场和介质中核子－核子（N－N）碰撞截面对中能重离子碰撞（HIC）中碎裂和耗散的同位旋效应。我们发现原子核阻R和Qzz，中等质量碎片多重性Nimf和质子（中子）发射数Np(Nn）敏感的依赖于介质中N－N碰撞截面的同位旋效应，而弱的依赖于同位旋相关的平均场（对称势），这些物理量作为提取相对高能范围缺中子系统的同位旋相关介质中N－N碰撞截面的探针。我们也可以通过相对低能区到150MeV/u的前平衡核子发射中质比来提取关于对称势的知识和讨论它的同位旋依赖性。     

中能重离子碰撞中同位旋相关核子-核子碰撞截面和同位旋相关平均场的探针

在最近几年我们通过使用同位旋相关的量子分子动力学模型 (IQMD)系统的研究了同位旋相关的平均场和介质中核子 核子 (N N)碰撞截面对中能重离子碰撞 (HIC)中碎裂和耗散的同位旋效应。我们发现原子核阻止R和Qzz,中等质量碎片多重性Nimf和质子(中子 )发射数Np(Nn)敏感的依赖于介质中N N碰撞截面的同位旋效应 ,而弱的依赖于同位旋相关的平均场 (对称势 ) ,这些物理量作为提取相对高能范围缺中子系统的同位旋相关介质中N N碰撞截面的探针。我们也可以通过相对低能区到 1 5 0MeV/u的前平衡核子发射中质比来提取关于对称势的知识和讨论它的同位旋依赖性。     

Inclusive 2(3He,t) reaction at 2 GeV

The inclusive ²(³He,t) reaction has been studied at 2 GeV for energy transfers up to 500 MeV and scattering angles from 0.25⁰ up to 4⁰. Data are well reproduced by a model based on a coupled-channel approach for describing the NN and N( systems. The effect of final state interaction is important in the low energy part of the spectra. In the delta region, the cross-section is very sensitive to the effects of (-N interaction and (N M NN process. The latter has also a large influence well below the pion threshold. The calculation underestimates the experimental cross-section between the quasi-elastic and the delta peaks; this is possibly due to projectile excitation or purely mesonic exchange currents.     

Finite nuclei to nuclear matter: a leptodermous approach

The liquid drop model (LDM) expansions of energy and incompressibility of finite nuclei are studied in an analytical model using Skyrme-like effective interactions to examine, whether such expansions provide an unambiguous way to go from finite nuclei to nuclear matter, and thereby can yield the saturation properties of the latter, from nuclear masses. We show that the energy expansion is not unique in the sense that, its coefficients do not necessarily correspond to the ground state of nuclear matter and hence, the mass formulas based on it are not equipped to yield saturation properties. The defect is attributed to its use of liquid drop without any reference to particles as its basis, which is classical in nature. It does not possess an essential property of an interacting many-fermion system namely, the single particle property, in particular the Fermi state. It is shown that, the defect is repaired in the infinite nuclear matter model by the use of generalized Hugenholtz–Van Hove theorem of many-body theory. So this model uses infinite nuclear matter with well defined quantum mechanical attributes for its basis. The resulting expansion has the coefficients which are at the ground state of nuclear matter. Thus a well defined path from finite nuclei to nuclear matter is found out. Then using this model, the saturation density 0.1620 fm⁻³ and binding energy per nucleon of nuclear matter 16.108 MeV are determined from the masses of all known nuclei. The corresponding radius constant r₀ equal to 1.138 fm thus determined, agrees quite well with that obtained from electron scattering data, leading to the resolution of the so-called ‘r₀-paradox’. Finally a well defined and stable value of 288±20 MeV for the incompressibility of nuclear matter K_∞ is extracted from the same set of masses and a nuclear equation of state is thus obtained.