Statistical errors in Weizscker-Skyrme mass model

The statistical uncertainties of 13 model parameters in the Weizscker-Skyrme(WS*) mass model are investigated for the first time with an efficient approach,and the propagated errors in the predicted masses are estimated.The discrepancies between the predicted masses and the experimental data,including the new data in AME 2016,are almost all smaller than the model errors.For neutron-rich heavy nuclei,the model errors increase considerably,and go up to a few MeV when the nucleus approaches the neutron drip line.The most sensitive model parameter which causes the largest statistical error is analyzed for all bound nuclei.We find that the two coefficients of symmetry energy term significantly influence the mass predictions of extremely neutron-rich nuclei,and the deformation energy coefficients play a key role for well-deformed nuclei around the β-stability line.     

Ability of the radial basis function approach to extrapolate nuclear mass

The ability of the radial basis function(RBF) approach to extrapolate the masses of nuclei in neutron-rich and superheavy regions is investigated in combination with the Duflo-Zuker(DZ31), Hartree–Fock-Bogoliubov(HFB27), finite-range droplet model(FRDM12) and Weizs?cker-Skyrme(WS4) mass models. It is found that when the RBF approach is employed with a simple linear basis function, different mass models have different performances in extrapolating nuclear masses in the same region, and a single mass model may have different performances when it is used to extrapolate nuclear masses in different regions. The WS4 and FRDM12 models(two macroscopic–microscopic mass models), combined with the RBF approach, may perform better when extrapolating the nuclear mass in the neutron-rich and superheavy regions.     

哪些核适合被液滴模型描述:基于不确定度分解方法的统计研究（英文）

一个模型适合描述哪些物理量? 这个问题可以通过模型的物理来源来回答。比如,液滴模型适合描述重核和远离满壳核。这是因为液滴近似更适用于核子数多的核以及液滴模型不包含壳效应。这样的回答是定性的并需要清楚模型的物理来源。是否可能仅通过模型的数学形式和实验数据就能给出半定量的解答? 利用最近提出的不确定度分解方法尝试对液滴模型适合描述哪些核这一问题进行半定量的回答。并且不需已知液滴模型的物理来源,仅需其数学形式以及实验数据。通过不确定度分解方法,液滴模型与实验数据间的残差可以分解为系统不确定度和统计不确定度。两者分别代表了模型的缺陷和模型不精确的参数带来的不确定度。基于这一分解,核素图上的原子核可以按其对应的残差被半定量地划分为系统不确定度主导、统计不确定度主导、以及中间区域。液滴模型适合描述的核就是统计不确定度主导残差的核而不是像通常认为的是残差最小的核。从核素图上看,统计不确定度主导残差的核正是重核以及远离满壳核,与液滴模型物理来源一致,但得到这一结果的过程是半定量的且仅需液滴模型的数学形式以及实验数据。如果对由统计不确定度主导残差的核重新拟合液滴模型的参数,模型可以很好地描述这些核（标准差小于0.7 MeV）。Which data are well described by a theoretical model? Such questions can be answered through the physical origin of the model. For example, the liquid drop model (LDM) well describes the heavy and far from shell nuclei. Because the liquid-drop assumption is more suitable for nuclei with more nucleons and LDM does not include the shell effect. Such answer is qualitative and needs a clear view on the physical origin of the model. Is it possible to give an semi-quantitatively answer only from the mathematical form of the model and the observed data. In the present work, the recently suggested uncertainty decomposition method (UDM) is used to answer which nuclei are well described by LDM. The residues between LDM and the observed data can be decomposed through UDM to systematic and statistical uncertainties, which represent the uncertainty of the deficiency of the model and the indeterminate parameters, respectively. Based on UDM, the chart of nuclides are semi-quantitatively divided into three parts, areas dominated by the systematic and statistical uncertainties, and the cross area. Contrary to the common sense, the well described nuclei by LDM are not the nuclei with small residues, but actually the nuclei of which the residues are dominated by the statistical uncertainty. These nuclei are indeed the heavy and far from shell nuclei, which agrees with the physical consideration of LDM. But only the mathematical form of the model and the experimental data are needed during the use of UDM. The nuclides dominated by the statistical uncertainty can be well described by LDM (standard deviation less than 0.7 MeV) with parameters fitting to these nuclei.     

Exploring the uncertainties in theoretical predictions of nuclear β-decay half-lives

Nuclear β-decay half-lives are predicted based on an empirical formula and the mass predictions from various nuclear models.It is found that the empirical formula can reproduce the nuclearβ-decay half-lives well,especially for short-lived nuclei with T_1/2<1s.The theoretical half-life uncertainties fromβ-decay energies and the parameters of the empirical formula are further investigated.It is found that the uncertainties of the half-lives are relatively large for heavy nuclei and nuclei near the neutron-drip line.For nuclei on the r-process path,the uncertainties for those with N=126 are about one order of magnitude,which are much larger than the uncertainties for those with N=50 and 82.However,theoretical uncertainties from the parameters of the empirical formula are relatively small for the nuclei on the r-process path,which indicates that the empirical formula is very suitable for predicting theβ-decay half-lives in r-process simulations.     

Systematic description of nuclear electric quadrupole moments

The nuclear electric quadrupole moment(NQM) is one of the fundamental bulk properties of the nucleus with which nuclear deformations can be investigated. The number of measured NQMs is significantly less than that of known masses, and there is still no global NQM formula for all bound nuclei. In this paper, we propose an analytical formula, which includes the shell corrections and which is the function of the charge number, mass number, spin,charge radius, and nuclear deformation, for calculating the NQMs of all bound nuclei. Our calculated NQMs of 524 nuclei in their ground states are reasonable compared to the experimental data based on the nuclear deformation parameters derived from the Weizs¨acker-Skyrme(WS) nuclear mass models. Smaller rms deviations between the calculated NQMs and experimental data indicate that the deformation parameters predicted from the WS mass models are reasonable. In addition, 161 unmeasured NQMs with known spins are also predicted with the proposed formula.     

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.     

夸克平均场模型研究有限核及超核

采用组分夸克模型描述重子,首先由自由核子及超子的性质定出模型参数,进一步考虑核介质中重子性质的变化,核介质中的介子平均场直接与重子内部的组分夸克相互作用.夸克平均场模型已被用于研究有限核及超核的性质,能够给出令人满意的有限核及超核的性质,该模型也预言了核介质中核子体积的膨胀及核子有效质量的降低. The quark mean field model, which describes the baryon by using the constituent quark model, is applied to study the properties of finite nuclei and hypernuclei. The meson mean fields couple directly with the quarks and change the properties of baryons in nuclear medium. The quark mean field model provides satisfactory results on the properties of spherical nuclei and hypernuclei. It also predicts an increasing size of the nucleon as well as a reduction of the effective mass in the nuclear environment.     

Shell Evolution Study for New Magic Number N =32 via Isochronous Mass Spectrometry

Recent results and progress of mass measurements of neutron-rich nuclei utilizing Isochronous Mass Spectrometry (IMS) based on the HIRFL-CSR complex at Lanzhou are reported. The nuclei of interest were produced through projectile fragmentation of primary 86Kr ions at a realistic energy of 460.65 MeV/u. After in-flight separation by the fragment separator RIBLL2, the fragments were injected and stored in the experimental storage ring CSRe, and their masses were determined from measurements of their revolution times. The re-determined masses were compared and evaluated with other mass measurements, and the impact of these evaluated masses on the shell evolution study is discussed.     

Two-proton radioactivity of exotic nuclei beyond proton drip-line

To search for new candidates of the true and simultaneous two-proton(2 p) radioactivity, the 2 p decay energies(Q2 p) are extracted by the Weizs?cker–Skyrme-4(WS4) model, the finite-range droplet model(FRDM), the Koura–Tachibana–Uno–Yamada(KTUY) model and the Hartree–Fock–Bogoliubov mean-field model with the BSk29 Skyrme interaction(HFB29). Then, the 2 p radioactivity half-lives are calculated within the generalized liquid drop model by inputting the four types of Q2 pvalues. By the energy and half-life constraints, it is found that the probable 2 p decay candidates are the nuclei beyond the proton-drip line in the region of Z≤50 based on the WS4 and KTUY mass models. For the FRDM mass model, the probable 2 p decay candidates are found in the region of Z≤44. However, the 2p-decaying candidates are predicted in the region of Z≤58 by the HFB29 mass model. It means that the probable 2 p decay candidates of Z50 are only predicted by the HFB29 mass model. Finally, the competition between the true 2p radioactivity and α-decay for the nuclei above the N=Z=50 shell closures is discussed. It is shown that ~(101)Te,~(111)Ba and ~(114)Ce prefer to 2p radioactivity and the dominant decay mode of ~(107)Xe and ~(116)Ce is α-decay.     

Numerical tests of the electroweak phase transition and thermodynamics of the electroweak plasma

The finite temperature phase transition in the SU(2) Higgs model at a Higgs boson mass M_H ≅ 34 GeV is studied in numerical simulations on four-dimensional lattices with time-like extensions up to L_t = 5. The effects of the finite volume and finite lattice spacing on masses and couplings are studied in detail. The errors due to uncertainties in the critical hopping parameter are estimated. The thermodynamics of the electroweak plasma near the phase transition is investigated by determining the relation between energy density and pressure.     

Study of excited Ds mesons

The spectrum of D s mesons is systematically studied in a semi-classic mass loaded flux tube model.D s in D-wave multiplets is predicted to have lower masses in comparison with most theoretical predictions.D sJ (2632) +,D s1 (2700) ±,D sJ (2860) + and D sJ (3040) + are interpreted in the constituent quark model.     

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.     

Extending the nuclear chart by continuum: From oxygen to titanium

Nuclear masses ranging from O to Ti isotopes are systematically investigated with relativistic continuum Hartree-Bogoliubov (RCHB) theory, which can provide a proper treatment of pairing correlations in the presence of the continuum. From O to Ti isotopes, there are 402 nuclei predicted to be bound by the density functional PC-PK1. For the 234 nuclei with mass measured, the root mean square (rms) deviation is 2.23 MeV. It is found that the proton drip-lines predicted with various mass models are roughly the same and basically agree with the observation. The neutron drip-lines predicted, however, are quite different. Due to the continuum couplings, the neutron drip-line nuclei predicted are extended further neutron-rich than other mass models. By comparison with finite-range droplet model (FRDM), the neutron drip-line nucleus predicted by RCHB theory has respectively 2(O), 10(Ne), 10(Na), 6(Mg), 8(Al), 6(Si), 8(P), 6(S), 14(K), 10(Ca), 10(Sc), and 12(Ti) more neutrons.