Fully self-consistent calculation ofβ-decay half-lives within Skyrme energy density functional

β-decay half-lives of some magic and semi-magic nuclei have been studied in a fully self-consistent Skyrme Hartree-Fock(HF) plus charge-exchange random phase approximation(RPA).The self-consistency is addressed,in that the same Skyrme energy density functional is adopted in the calculation of ground states and Gamow-Teller excited states.First,the impact of J2 terms on the β-decay half-lives is investigated by using the SGII interaction,revealing a large influence.Subsequently,numerical calculations are performed for the selected nuclei with Skyrme energy density functionals SGII,LNS,SKX,and SAMi.Finally,comparisons to available experimental data and predictions of different theoretical models are discussed.     

Competition between α-decay and β-decay for heavy and superheavy nuclei

In this work, the β-stable region for Z 90 is proposed based on a successful binding energy formula.The calculated β-stable nuclei in the β-stable region are in good agreement with the ones obtained by Mo¨ller et al. The half-lives of the nuclei close to the β-stable region are calculated and the competition between α-decay andβ-decay is systematically investigated. The calculated half-lives and the suggested decay modes are well in line with the experimental results. The decay modes are mostly β--decay above the β-stable region. Especially for Z 111,all the decay modes are β--decay. Regarding the nuclei above the β-stable region, α-decay and β--decay(α+β-)can occur simultaneously when Z 112. This is a very interesting phenomenon. The competition between α-decay and β-decay is very complex and drastic below the β-stable region. The predictions for half-lives and decay modes of the nuclei with Z =107–110 are presented in detail.     

Calculation of multidimensional potential energy surfaces for even-even transuranium nuclei: systematic investigation of the triaxiality effect on the fission barrier

Static fission barriers for 95 even-even transuranium nuclei with charge number Z = 94-118 have been systematically investigated by means of pairing self-consistent Woods-Saxon-Strutinsky calculations using the potential energy surface approach in multidimensional(β_2, γ, β_4) deformation space. Taking the heavier (252)~Cf nucleus(with the available fission barrier from experiment) as an example, the formation of the fission barrier and the influence of macroscopic, shell and pairing correction energies on it are analyzed. The results of the present calculated β_2 values and barrier heights are compared with previous calculations and available experiments. The role of triaxiality in the region of the first saddle is discussed. It is found that the second fission barrier is also considerably affected by the triaxial deformation degree of freedom in some nuclei(e.g., the Z =112-118 isotopes). Based on the potential energy curves, general trends of the evolution of the fission barrier heights and widths as a function of the nucleon numbers are investigated. In addition, the effects of Woods-Saxon potential parameter modifications(e.g.,the strength of the spin-orbit coupling and the nuclear surface diffuseness) on the fission barrier are briefly discussed.     

Competition between α-decay and β-decay for heavy andsuperheavy nuclei

In this work, the β-stable region for Z≥90 is proposed based on a successful binding energy formula. The calculated β-stable nuclei in the β-stable region are in good agreement with the ones obtained by Möller et al. The half-lives of the nuclei close to the β-stable region are calculated and the competition between α-decay and β-decay is systematically investigated. The calculated half-lives and the suggested decay modes are well in line with the experimental results. The decay modes are mostly β^--decay above the β-stable region. Especially for Z≤111, all the decay modes are β^--decay. Regarding the nuclei above the β-stable region, α-decay and β^--decay (α+β^-) can occur simultaneously when Z≥112. This is a very interesting phenomenon. The competition between α-decay and β-decay is very complex and drastic below the β-stable region. The predictions for half-lives and decay modes of the nuclei with Z=107-110 are presented in detail.     

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.     

An improved α-decay energy formula for heavy and superheavy nuclei

Based on the liquid-drop model and using the first derivative of the normalized Gaussian function to consider the shell correction, a simple α-decay energy formula is proposed for heavy and superheavy nuclei. The values of corresponding adjustable parameters are obtained by fittingα-decay energies of 209 nuclei ranging from Z = 90 to Z = 118 with N ≥ 140. The calculated results are in good agreement with the experimental data. The average and standard deviations between the experimental data and...     

Influence of proton-skin thickness on the α decays of heavy nuclei

We investigate the effect of proton-skin thickness on the α decay process. We consider 188 neutrondeficient nuclei belonging to the isotopic chains from Te(Z = 52) to Pb(Z = 82). The calculations of the half-life are carried out in the framework of the preformed cluster model, with the Wentzel-Kramers-Brillouin penetration probability and assault frequency. It is shown that the proton-skin thickness(?p) of the daughter nucleus gives rise to a total α-daughter nucleus interaction potential of relatively wide deep internal pocket and a thinner Coulomb barrier of less height. This increases the penetration probability but decreases the assault frequency. The overall impact of the proton-skin thickness appears as a decrease in the decay half-life. The proton-skin thickness decreases the stability of the nucleus. The half-lives of the proton-skinned isotopes along the isotopic chain decrease exponentially with increasing the proton-skin thickness, whereas the Qα-value increases with ?p. α-decay manifests itself as the second favorite decay mode of neutron-deficient nuclei, next to the β+-decay and before proton-decay. It is indicated as main, competing, and minor decay mode, at 21%, 7%, and 57%, respectively, of the investigated nuclei.     

Global α-decay study based on the mass table of the relativistic continuum Hartree-Bogoliubov theory

The α-decay energies(Qα) are systematically investigated with the nuclear masses for 10 Z 120 isotopes obtained by the relativistic continuum Hartree-Bogoliubov(RCHB) theory with the covariant density functional PC-PK1, and compared with available experimental values. It is found that the α-decay energies deduced from the RCHB results present a similar pattern to those from available experiments. Owing to the large predicted Qαvalues( 4 Me V), many undiscovered heavy nuclei in the proton-rich side and super-heavy nuclei may have large possibilities for α-decay. The influence of nuclear shell structure on α-decay energies is also analysed.     

The contribution of the first forbidden transitions to the nuclear β~--decay half-life

β-decay half-life is a key quantity for nuclear structure and nucleosynthesis studies.There exist large uncertainties in the contributions of allowed and forbidden transitions to the total β-decay life,which limits the resolution of the predicted β-decay half-life.We systematically study the contribution of the first forbidden(FF) transitions to the β~--decay half-life,and quantify it with a formula based on simple physics considerations.We also propose a new formula for calculation of the β~--decay half-life that includes the FF contribution.It is shown that the inclusion of the contribution of FF transitions significantly improves the precision of calculations of the β~--decay half-life.By fitting of the RQRPA results for neutron-rich Z=47,57 isotopes and N=80,94 isotones,the formula for the contribution of the FF transitions gives similar results as the RQRPA calculations.However,because of limited experimental data for the branching ratios of unstable nuclei,the fit parameters are not fully constrained.Therefore,the proposed formula for the β~--decay half-life is more suitable for calculations of half-lives than of the FF contributions.The formula could be used to predict the β~--decay half-life in nuclear structure studies as well as nucleosynthesis calculations in stars.     

Shell model Monte Carlo studies of N = Zpf-shell nuclei with pairing-plus-quadrupole Hamiltonian

We perform shell model Monte Carlo calculations of selected N = Z pf-shell nuclei with a schematic Hamiltonian containing isovector pairing and quadrupole-quadrupole interactions. Compared to realistic interactions, this Hamiltonian does not give rise to the SMMC “sign problem”, while at the same time resembles essential features of the realistic interactions. We study pairing correlations in the ground states of N = Z nuclei and investigate the thermal dependence of selected observables for the odd-odd nucleus ⁵⁴Co and the even-even nuclei ⁶⁰Zn and ⁶⁰Ni. Comparison of the present results to those with the realistic KB3 interaction indicates a transition with increasing temperature from a phase of isovector pairing dominance to one where isoscalar pairing correlations dominate. In addition, our results confirm the qualitative reliability of the procedure used to cure the sign problem in the SMMC calculations with realistic forces.     

Systematic study of decay properties of heaviest elements

Decay properties and stability of heaviest nuclei with Z ?? 132 are studied within the macro-microscopical approach for nuclear ground-state masses. We use phenomenological relations for the half-lives with respect to ??-decay, ??-decay and spontaneous fission. Our calculations demonstrate that the ??-stable isotopes ²⁹¹Cn and ²⁹³Cn with a half-life of about 100 years are the longest-living superheavy nuclei located on the first island of stability. We found the second island of stability of superheavy nuclei in the region of Z ?? 124 and N ?? 198. It is separated from the ??continent?? by the ??gulf?? of short-living nuclei with half-lives shorted than 1 ??s.     

Systematic study of properties of Hs nuclei

The ground-state properties of Hs nuclei are studied in the framework of the relativistic mean-field theory. We find that the more relatively stable isotopes are located on the proton abundant side of the isotopic chain. The last stable nucleus near the proton drip line is probably the ²⁵⁵Hs nucleus. The a \alpha -decay half-lives of Hs nuclei are predicted, and together with the evaluation of the spontaneous-fission half-lives it is shown that the nuclei, which are possibly stable against spontaneous fission are ^263-274Hs . This is in coincidence with the larger binding energies per nucleon. If ^271-274Hs can be synthesized and identified, only those nuclei from the upper Z = 118 isotopic chain, which are lighter than the nucleus ²⁹⁴118 , and those nuclei in the corresponding a \alpha -decay chain lead to Hs nuclei. The most stable unknown Hs nucleus is ²⁶⁸Hs . The density-dependent delta interaction pairing is used to improve the BCS pairing correction, which results in more reasonable single-particle energy level distributions and nucleon occupation probabilities. It is shown that the properties of nuclei in the superheavy region can be described with this interaction.     

Alpha decay chains from superheavy nuclei

Magic islands for extra-stable nuclei in the midst of the sea of fission-instability were predicted to be around Z=114, 124 or, 126 with N=184, and Z=120, with N=172. Whether these fission-survived superheavy nuclei with high Z and N would live long enough for detection or, undergo α-decay in a very short time, remains an open question. α-decay half lives of nuclei with 130≥Z≥100 have been calculated in a WKB framework using density-dependent M3Y interaction with Q-values from different mass formulae. The results are in excellent agreement with the experimental data. Fission survived Sg nuclei with Z=106, N=162 is predicted to have the highest α-decay half life (∼3.2 h) in the Z=106-108, N=160-164 region called small island/peninsula. Superheavy nuclei with Z>118 are found to have α-decay half lives of the order of microseconds or less.     

rp-process nucleosynthesis at extreme temperature and density conditions

We present nuclear reaction network calculations to investigate the influence of nuclear structure on the rp-process between Ge and Sn in various scenarios. Due to the lack of experimental data for neutron-deficient nuclei in this region, we discuss currently available model predictions for nuclear masses and deformations as well as methods of calculating reaction rates (Hauser-Feshbach) and β-decay rates (QRPA and shell model). In addition, we apply a valence nucleon (N_pN_n) correlation scheme for the prediction of masses and deformations. We also describe the calculations of 2p-capture reactions, which had not been considered before in this mass region. We find that in X-ray bursts 2p-capture reactions accelerate the reaction flow into the Z ≥ 36 region considerably. Therefore, the rp-process in most X-ray bursts does not end in the Z = 32–36 region as previously assumed and overproduction factors of 10⁷–10⁸ are reached for some light p-nuclei in the A = 80–100 region. This might be of interest in respect of the yet unexplained large observed solar system abundances of these nuclei. Nuclei in this region can also be produced via the rp-proces in accretion disks around low mass black holes. Our results indicate that the rp-process energy production in the Z > 32 region cannot be neglected in these scenarios. We discuss in detail the influence of the various nuclear structure input parameters and their current uncertainties on these results. It turns out that rp-process nucleosynthesis is mainly determined by nuclear masses and β-decay rates of nuclei along the proton drip line. We present a detailed list of nuclei for which mass or β-decay rate measurements would be crucial to further constrain the models.     

对力对于锕系核性质的影响

本文用处理对力的粒子数守恒方法来分析对力对于锕系核性质的影响,其中包括奇A核和偶偶核的内部激发谱、β衰变、α衰变等。文中首先根据实验测得的寄A核的内部激发谱,计及对力的影响,定出了单粒子能级的Nilsson参数(见表3和5)。然后利用此单粒子能级进一步分析了偶偶核的内部激发谱和β衰变。由于现有数据的限制,只分析了Th²²⁸,Th²³⁰,U²³²,U²³⁴和Cm²⁴⁴等核。由能级位置和β衰变的分析,     

A shell-model description of 0+ intruder states in even-even nuclei

Starting from the nuclear shell structure in medium-heavy and heavy nuclei, the excitation energy for low-lying 0⁺ intruder states is studied. Taking as a simplified model two particle-two hole (2p-2h) excitations across closed shells, the effects of the pairing and the proton-neutron (monopole and quadrupole component) residual interaction on the unperturbed energies are calculated. Application to major closed-shell (fZ = 50, Z = 82) and to subshell (Z = 40, Z = 64) regions is performed. We especially concentrate on 0⁺ intruder states in the even-even Pb nuclei.     

A new study of 25Mg(\alpha,n) 28Si angular distributions at E_{\alpha} =3-5 MeV

Heavy neutron-rich nuclei close to N = 126 were produced by fragmentation of a 1A GeV ²⁰⁸Pb beam at the FRS at GSI. The β-decay half-lives of 7 nuclides have been determined using a novel numerical analysis method. The half-lives of ^202,199Ir, ^200,199Os and ¹⁹⁶Re are reported for the first time. The comparison of the data with model calculations provides indications on the importance of first-forbidden transitions on the β-decay of nuclei around N = 126 and Z < 82.