Theoretical investigation of the Gamow-Teller transition across N=40 shell

The Gamow-Teller transitions for pf shell nuclei with proton number less than 40 and neutron number larger than 40 were believed to be blocked, due to the full filling of the neutron orbit. However, recent experimental research shows that the Gamow-Teller transitions for these kinds of nuclei are not blocked. In this paper, we systematically calculate the GT transition of pf shell nuclei ⁷⁶Se in different truncations, and the results are compared with experimental results. It is shown that, due to correlations, the believed blocked GT transition occurs, and the shell model calculations reproduce the experimental GT strength. In addition, the electron capture rates in a stellar environment are calculated and discussed.     

利用改进的pn-QRPA模型研究等待点原子核的β衰变性质

r-过程等待点原子核的β衰变半衰期对研究宇宙中重元素起源有重要意义。质子-中子准粒子无规相位近似(pn-QRPA)是研究原子核β衰变的重要理论模型。本工作提出了一个改进的 pn-QRPA 模型,系统研究了满壳附近原子核的 β 衰变性质。与之前的工作相比,改进的模型采用了中子数和质子数依赖的新粒子-粒子和粒子-空穴相互作用形式。本工作首先计算了满壳附近一些已知原子核的 β衰变半衰期和 Gamow-Teller 强度分布,发现理论结果与实验数据符合较好,检验了新模型的可靠性。随后,理论预测了 $N=50$, $N=82$ 和 $N=126$附近未知的等待点原子核的 β衰变半衰期,如124Mo, 126Ru, 128Pd, 186Nd, 188Sm, 192Dy, 194Er, 196Yb, 198Hf等,预测结果与之前的模型相近。这些结果对未来满壳层附近的r-过程物理研究有参考价值。     

Properties of isovector 1+ states in A=28 nuclei and nuclear muon capture

A method is proposed for taking into account, in a calculation of partial rates of muon capture by nuclei, experimental information about strength functions for Gamow-Teller and isovector M1 transitions. The method, which amounts to choosing an orthogonal transformation that acts in the subspace of wave functions for excited states, requires neither modifying transition operators nor introducing effective charges. The matrix of the above transformation is constructed as a product of the matrices of reflection in a plane. All calculations are performed on the basis of the multiparticle shell model. Numerical results are obtained for isovector states in A=28 nuclei. Strength functions for Gamow-Teller and isovector M1 transitions in ²⁸Si are considered, and the lifetimes of 1⁺ states in ²⁸Al and the branching fractions for gamma decays of this state are calculated. Owing to taking into account experimental information about the properties of isovector states, the branching fractions for the γ decays of the 1⁺ state at 2.201 MeV in ²⁸Al are successfully described for the first time. The above transformation of the wave functions changes substantially the distribution of partial rates of allowed muon capture by a ²⁸Si nucleus among the 1⁺ states of the final nucleus ²⁸Al in relation to the results of the calculations with the eigenfunctions of the Hamiltonian of the multiparticle shell model. The muon-capture rates calculated with the transformed functions agree well with experimental data.     

Shell effects for isovector <Emphasis Type="Italic">l</Emphasis>-forbidden <Emphasis Type="Italic">M</Emphasis>1 transitions in odd nuclei

It is inferred from the analysis of the experimental data that the reduced probabilities of isovector l-forbidden M1 transitions achieve maximum values in nuclei with a magic core. The minimum values are related to γ transitions in nuclei belonging to the region of stable deformation with A ≈ 25. Isovector l-forbidden M1 transitions in mirror nuclei are explored. The ratio of the reduced probabilities for proton and neutron transitions shows the maximum deviation from the theoretical evaluations for the pair of nuclei ⁴¹Ca-⁴¹Sc consisting of the even-even magic core ⁴⁰Ca and one nucleon outside the closed 1d2s shell.     

Theoretical half-lives for the heaviest nuclei

Spontaneous-fission and alpha-decay half-lives are calculated for even-even nuclei with the atomic numberZ=104–110. The results reproduce rather well the existing experimental data for these nuclei and predict rather large total lifetimes for nuclei even heavier than observed up to now. The latter is mainly due to a deformed shell at the neutron numberN=162–164, obtained in calculations.     

Interplay of direct and spin-flip contributions in Gamow-Teller decay to odd-odd N = Z nuclei

Strengths of Gamow-Teller decays of T_z = ±1 nuclei to T_z = 0 odd-odd nuclei have been calculated by using spherical shell model and deformed Nilsson wave functions. The role and competition of the microscopic direct and spin-flip mechanisms generating Gamow-Teller transitions are analyzed. Analytical expressions derived for the B(GT) values give useful insight into the regularities of B(GT) values along the N = Z line. The crucial role of configuration mixing is discussed.     

丰中子锰同位素的壳模型计算

利用球形壳模型和投影壳模型两种方法对Z≤28,N=40附近pf壳的丰中子核素的结构进行了一系列的研究。以丰中子的锰同位素为例讨论了对奇奇核58,60Mn的两种壳模型计算结果。结果显示,两种理论方法都很好地再现了58,60Mn实验上观测到的从低激发到高自旋态的能级。在对这两个同位素由中子g_9/2轨道闯入所产生的负宇称转动带进行描述时,两种理论计算也得到了一致的结果。通过对比,阐明了两种壳模型方法及其采用的有效相互作用在该丰中子核区的适用性,特别强调了中子g_9/2轨道的激发对于pf壳Z≤28丰中子核素结构的重要性。Recently,we have carried out a series of studies on the structures of pf shell neutron-rich nuclei around N=40 using the spherical shell model and the projected shell model respectively.As an example,these two types of shell model calculations for the neutron-rich odd-odd isotopes 58,60Mn are discussed in this paper.The results show that both the calculations reproduce the observed experimental energy levels from the lowexcitation states to the high-spin ones in 58,60Mn.Consistent results are also obtained by these two theoretical calculations when describing the negative-parity rotational band derived from the intruder neutron g_9/2 orbital in both isotopes.Through comparison,we show the applicability of these two shell model methods and the adopted effective interactions in the present neutron-rich mass region.The significance of the excitations from neutron g_9/2 orbital to the structures of the neutron-rich nuclei in pf shell with Z≤28 are especially emphasized in this paper.     

Properties and structure of N=Z nuclei within relativistic mean field theory

The axially deformed relativistic mean field theory with the force NLSH has been performed in the blocked BCS approximation to investigate the properties and structure of N=Z nuclei from Z=20 to Z=48.Some ground state quantities such as binding energies, quadrupole deformations, one/two-nucleon separation energies, root-mean-square (rms) radii of charge and neutron, and shell gaps have been calculated.The results suggest that large deformations can be found in medium-heavy nuclei with N=Z=38-42.The charge and neutron rms radii increase rapidly beyond the magic number N=Z=28 until Z=42 with increasing nucleon number, which is similar to isotope shift, yet beyond Z=42, they decrease dramatically as the structure changes greatly from Z=42 to Z=43.The evolution of shell gaps with proton number Z can be clearly observed.Besides the appearance of possible new shell closures, some conventional shell closures have been found to disappear in some region.In addition, we found that the Coulomb interaction is not strong enough to breakdown the shell structure of protons in the current region.     

High spin states in48Cr

The self-consistent finite Fermi-system theory with three different parameter sets is used to calculate decay energies and Gamow-Teller strength distributions of neutronrich short-lived nuclides near shell closures Z=50, N=82. Among the parameters, the role of a strong surface neutron-proton attraction and an isovector spin-orbit force is discussed. The obtainedβ-decay half-lives are compared with large-scale calculation results and with available experimental data. Some predictions for the ground state properties of other unstable closed-shell nuclei are presented.     

Mass differences and neutron pairing in Ca,Sn and Pb isotopes

Various estimates of the even-odd effect of the mass shell of atomic nuclei are considered.Based on the experimental mass values of the Ca,Sn,and Pb isotopes,the dependence of the energy gap on the neutron number is traced and the relationship of this characteristic to the properties of external neutron subshells is shown.In nuclei with closed proton shells,effects directly related to neutron pairing and effects of nucleon shells are discussed.     

超新星的前身星阶段fp壳层的电子俘获

基于核的壳层模型，本文讨论了大质量恒星的超新星前身星阶段核的fp壳层电子俘获，分析中引入了一高斯函数来表征Gamow-Teller跃迁强度分布，结果表明，由于这一修正，在高密度下，电子俘获率较前人给出的结果有较大幅度的增加。     

Renormalization of the axial-vector coupling constant in nuclear β-decay (II)

A systematic comparison is made between the experimental strengths of accurately measured allowed Gamow-Teller β-decay and the corresponding strengths derived from shell model wave functions computed in the full basis of the major shell. It is found that the experimental transitions are, on the average, slower than the theoretical by the square of ρψ = 0.897±0.035. This is to be compared with the outcome of an earlier study in which a corresponding factor was extracted in an almost-wave-function-free way using the isoscalar magnetic moments of mirror pairs which gave ρ_μ = 0.902±0.046.     

Resonance structure of strength functions for first-forbidden β +/EC transitions

Experimental data obtained by measuring the fine structure of the strength function S _?? (E) in spherical and deformed nuclei were analyzed. The use of modern nuclear-spectroscopy methods made it possible to reveal the nuclear-deformation-induced splitting of peaks in S _?? (E) for transitions of the Gamow-Teller type. For first-forbidden transitions, the resonance nature of S _?? (E) was proven experimentally both for spherical and for deformed nuclei. It is shown that, at some values of the excitation energy, the intensity of first-forbidden transitions in nuclei can be commensurate with the intensity of Gamow-Teller transitions.     

Cross sections for evaporation residue production near theN=126 shell closure

In fusion reactions of⁴⁰Ar with isotopes of Ho, Tm, Yb, Lu, Hf and Ta, cross sections for the production of proton-rich evaporation-residues near the 126 neutron shell were measured. This first comprehensive study of very fissile spherical residues reveals a surprisingly low stabilizing influence of the sphericalN=126 shell on the survival probability. The experimental results are compared with evaporation calculations. Conclusions for the production of superheavy nuclei are drawn.     

Extraction of weak transition strengths via the (3He, t) reaction at 420 MeV

Differential cross sections for transitions of known weak strength were measured with the (3He, t) reaction at 420 MeV on targets of 12C, 13C, 18O, 26Mg, 58Ni, 60Ni, 90Zr, 118Sn, 120Sn, and 208Pb. Using these data, it is shown that the proportionalities between strengths and cross sections for this probe follow simple trends as a function of mass number. These trends can be used to confidently determine Gamow-Teller strength distributions in nuclei for which the proportionality cannot be calibrated via beta-decay strengths. Although theoretical calculations in the distorted-wave Born approximation overestimate the data, they allow one to understand the main experimental features and to predict deviations from the simple trends observed in some of the transitions.     

Simple relations for nuclear moments

Various relations for nuclearg-factors are extended, applied and discussed in view of recent experimental data. It is shown that the additivity relation can be used such that most of the corrections to theg-factor are accounted for. The isoscalar and isovector parts of theg-factor are studied in the mass regionA≦55 under the assumption of purej ⁿ configurations. For the isoscalar part the discrepancies with experiment are compatible with those for large shell-model calculations. Good results are obtained for the isovector part of theg-factor of ground states in mirror nuclei if both Gamow-Teller matrix elements, extracted from experimentalft values with an effective coupling constant ratio for Fermi and Gamow-Teller transitions, and assumptions on the seniority of the wave functions are used.     

Partial level density of n-quasiparticle excitations, radiative strength functions and new experimental information on the dynamics of nuclear structure change in the B n range

The most reliable at present values of the level density in the fixed spin window and the sums of radiative strength functions of cascade gamma transitions are obtained from analysis of intensities of two-step cascades excited upon thermal neutron capture for approximately 40 nuclei in the mass range 40 ≤ A ≤ 200. The maximal reliability of these data is provided by the experimental conditions—minimum possible propagation error coefficients and practically unique solution of the problem of determination of gamma decay parameters from measured spectra. The experimental data are approximated by the sum of partial level densities corresponding to excitation of n quasiparticles. Steplike structures in the level density at excitation energies smaller than 3–4 MeV are described with good accuracy as the superposition of two-quasiparticle (three-quasiparticle in odd A nuclei) and vibrational excitations with the coefficient of collective density enhancement K _coll ≈ 10?20. They correspond to excitation-energy-correlated maximum enhancement of the radiative strength functions of primary gamma transitions. The level density at larger excitation energies is well reproduced if the breakup of at least two more Cooper pairs of nucleons is taken into account. The increase in the number of excited quasiparticles in the nucleus corresponds to unconditional reduction of the radiative strength functions of primary gamma transitions of the compound state decay. However, the maximum possible value of partial widths of primary transitions increases regularly with decreasing energy. Some ambiguity in the results of approximation and divergence from existing theoretical ideas of the energy dependence of nucleon correlation functions in an excited nucleus point to the possibility of direct extraction from experiment of fundamentally new information on the structure of excited nuclear levels in the range of the neutron binding energy. These are, first of all, the parameters of dependence of nucleon correlation functions on the excitation energy of the nucleus.     

Spin-dependent nuclear weak processes and nucleosynthesis in stars

Spin dependent nuclear weak processes and nucleosynthesis in stars are investigated based on recent advances in shell model studies of stable and unstable exotic nuclei. Three topics on (1) neutrino-nucleus reactions in supernova explosions and nucleosynthesis of light elements as well as Mn, (2) electron capture reaction rates on Ni and Co isotopes at high densities and temperatures in the core-collapse process, and (3) new β-decay half-lives of N=126 isotones obtained by including both the Gamow-Teller and the first-forbidden transitions, and the effects on the element abundance in the r-process at the third peak region (A∼195), are studied with the use of new shell model Hamiltonians.     

Gamow-Teller strengths in the A = 14 multiplet: a challenge to the shell model

A new experimental approach to the famous problem of the anomalously slow Gamow-Teller (GT) transitions in the beta decay of the A=14 multiplet is presented. The GT strength distributions to excited states in 14C and 14O were studied in high-resolution (d,2He) and (3He,t) charge-exchange reactions on 14N. No-core shell-model calculations capable of reproducing the suppression of the beta decays predict a selective excitation of Jpi=2+ states. The experimental confirmation represents a validation of the assumptions about the underlying structure of the 14N ground state wave function. However, the fragmentation of the GT strength over three 2+ final states remains a fundamental issue not explained by the present no-core shell model using a 6homega model space, suggesting possibly the need to include cluster structure in these light nuclei in a consistent way.