Comparison between formulas of rotational band for axially symmetric deformed nuclei

The experimental rotational spectra of the deformed nuclei available in even-even and odd-A nuclei in the rare-earth and actinide regions are systematically analyzed with several rotational spectra formulas, including Bohr-Mottelson's I(I+1)-expansion, Harris' ω²-expansion, ab and abc formulas. It is shown that the simple 2-parameter ab formula is much better than the widely used 2-parameter Bohr-Mottelson's AB formula and Harris'αβ formula. The available data of the rotational spectra of both ground-state band in even-even nuclei and one-quasiparticle band in odd-A nuclei can be conveniently and rather accurately reproduced by ab formula and abc formula. The moment of inertia and the variation with rotational frequency of angular momentum can be satisfactorily reproduced by ab and abc formulas.     

α Decay Properties of Even-Even Nuclei~(296-308)120 Within the Two-Potential Approach

In the present work,we predict the α decay half-lives of unknown even-even nuclei ~(296-308)120 within the two-potential approach,whose α decay energy Qa is calculated using WS3+mass model.To reduce the deviations between the predictions and experimental data due to nuclear shell effect,the analytic formula of α decay hindrance factor is introduced to the two-potential approach,whose parameters had been extracted from even-even nuclei in the region of 82 Z 126 and 152 N 184 in our previous work [Deng et al.,Chin.Phys.C 42(2018) 044102].In addition,for comparing,we use a type of α decay general formula Universal Decay Law(UDL) and a semi-empirical formula in the superheavy nucleus(SEMFLS) to calculate the half-lives of even-even nuclei ~(296-308)120.The results indicate that our predicted values and the calculated values of the above two empirical formulas are mutually confirmed.Meanwhile,we systematically study α decay chains of ~(296-308)120 and predict the decay modes for superheavy nuclei to help to identify new superheavy isotopes.     

稀土区奇A核晕带存在从转动到振动形状演化的直接证据(英文)

原子核的形状演化效应是核结构研究的重要基础问题之一。通常认为,A=160质量区的奇A核位于大形变核区域,它们的激发态能谱将呈现出典型的转动激发特征。然而,基于E-GOS曲线方法,发现随着角动量的增加,该质量区奇A核的晕带具有显著地从转动激发演化成为振动激发的形状演化现象。此外,为深入理解原子核形状演化的微观机制,采用Total-Routhian-Surface（TRS）方法针对稀土区的奇A核进行了理论计算,结果表明,165Yb和157Dy同位素在低激发态时具有稳定的长椭形变,当角动量大于0.50 MeV后,核芯的四极形变显著减小并开始产生三轴形变。The phase transition of nuclei with increasing angular momentum (or spin) and excitation energy is one of the most fundamental topics of nuclear structure research. The odd-N nuclei with A ≈160 are widely considered belonging to the well-deformed region, and their excitation spectra are energetically favored to exhibit the rotational characteristics. In this work, however, the evidence suggesting that the nuclei changes from rotation to vibration along the yrast lines as a function of spin was found. The simple method, named as E-Gamma Over Spin (E-GOS) curves, would be used to discern the evolution from rotational to vibrational structure in nuclei for various spin ranges. Meanwhile, in order to understand the band structure properties of nuclei, theoretical calculations have been performed for the yrast bands of the odd-A rare-earth nuclei within the framework of the total routhian surface (TRS) model. The TRS plots predict that the 165Yb and 157Dy isotopes have large quadrupole shapes at low spin states. At higher rotational frequency (hω~ >0.50 MeV), a clear reduction of the quadrupole deformation is indicated by the present results, and the isotopes become rigid in the γ deformation.     

Shell Effect of Superheavy Nuclei in Self-consistent Mean-Field Models

We analyze in detail the numerical results of superheavy nuclei in deformed relativistic mean-field model and deformed Skyrme-Hartree-Fock model. The common points and differences of both models are systematically compared and discussed. Their consequences on the stability of superheavy nuclei are explored and explained. The theoreticalresults are compared with new data of superheavy nuclei from GSI and from Dubna and reasonable agreement is reached.Nuclear shell effect in superheavy region is analyzed and discussed. The spherical shell effect disappears in some cases due to the appearance of deformation or superdeformation in the ground states of nuclei, where valence nucleons occupysignificantly the intruder levels of nuclei. It is shown for the first time that the significant occupation of vaJence nucleons on the intruder states plays an important role for the ground state properties of superheavy nuclei. Nuclei are stable in the deformed or superdeformed configurations. We further point out that one cannot obtain the octupole deformation of even-even nuclei in the present relativistic mean-field model with the σ,ω and ρ mesons because there is no parityviolating interaction and the conservation of parity of even-even nuclei is a basic assumption of the present relativistic mean-field model.     

Shell Effect of Superheavy Nuclei in Self-consistent Mean-Field Models

We analyze in detail the numerical results of superheavy nuclei in deformed relativistic mean-field model and deformed Skyrme-Hartree-Fock model. The common points and differences of both models are systematically compared and discussed. Their consequences on the stability of superheavy nuclei are explored and explained. The theoretical results are compared with new data of superheavy nuclei from GSI and from Dubna and reasonable agreement is reached. Nuclear shell effect in superheavy region is analyzed and discussed. The spherical shell effect disappears in some cases due to the appearance of deformation or superdeformation in the ground states of nuclei, where valence nucleons occupy significantly the intruder levels of nuclei. It is shown for the first time that the significant occupation of valence nucleons on the intruder states plays an important role for the ground state properties of superheavy nuclei. Nuclei are stable in the deformed or superdeformed configurations. We further point out that one cannot obtain the octupole deformation of even-even nuclei in the present relativistic mean-field model with the σ, ω and ρ mesons because there is no parity violating interaction and the conservation of parity of even-even nuclei is a basic assumption of the present relativistic mean-field model.     

Spherical and Deformed Shell Closures in Superheavy nuclei

The structure of superheavy nuclei has been studied using the macroscopic-microscopic model. The macroscopic energy was calculated with the continuous medium model in which the energy is expressed as a function of nucleon densities. The deformations and structures of superheavy nuclei were systematically investigated. Calculations reproduce well the available data of experimental α-decay energies and half-lives. The investigation of single-particle levels shows that the shell structure is deformation and isospin dependent. Potential-energy-surface calculations display that superheavy nuclei have in general harder shapes than the nuclei of other mass regions.     

Particle-number conserving analysis for the 2-quasiparticle and high-K multi-quasiparticle states in doubly-odd 174,176Lu

Two-quasiparticle bands and low-lying excited high-K four-, six-, and eight-quasiparticle bands in the doubly-odd 174,176 Lu are analyzed by using the cranked shell model (CSM) with the pairing correlations treated by a particle-number conserving (PNC) method, in which the blocking effects are taken into account exactly. The proton and neutron Nilsson level schemes for 174,176Lu are taken from the adjacent odd-A Lu and Hf isotopes, which are adopted to reproduce the experimental bandhead energies of the one-quasiproton and one-quasineutron bands of these odd-A Lu and Hf nuclei, respectively. Once the quasiparticle configurations are determined, the experimental bandhead energies and the moments of inertia of these two- and multi-quasiparticle bands are well reproduced by PNC-CSM calculations. The Coriolis mixing of the low-K (K=|Ω1Ω2 |) two-quasiparticle band of the Gallagher-Moszkowski doublet with one nucleon in the Ω=1/2 orbital is analyzed.     

Description of Superdeformed Bands of the Nuclei in A ～60 Mass Region

Using the supersymmetry scheme including many-body interactions, we investigate the superdeformed (SD) bands of the nuclei in A ～ 60 mass region systematically. Quantitatively good results of the γ-ray energy spectra and the dynamical moments of inertia are obtained. It shows that the supersymmetry approach is powerful to describe the generic rotational property of SD states of light nuclei.     

Description of the Superdeformed Bands of the Odd-Odd Nuclei in A ～ 150 Region

With the supersymmetry scheme including many-body interactions, the global property and the △I ＝ 4bifurcation in the superdeformed (SD) bands of odd-odd nuclei in A ～ 150 mass region are investigated systematically.Good results for the γ-ray energies, the dynamical moments of inertia, and energy differences △ Eγ - △ Erefγ are obtained.It shows that this approach is quite powerful in describing not only the SD bands in even-even and odd-A nuclei butalso those in odd-odd nuclei in the mass region.     

Effects of shell correction on α decay properties

The shell correction effects on the α decay properties of heavy and superheavy nuclei have been studied in a macroscopic-microscopic manner. The macroscopic part is constructed from the generalized liquid drop model(GLDM), whereas the microscopic part, namely, the shell correction energy, brings about certain effects on the potential barriers and half-lives under a WKB approximation, which is emphasized in this work. The results show that the shell effects play a significant role in the estimation of the α decay half-lives within the actinide region.Predictions of the α decay half-lives are then generated for superheavy nuclei, which will provide useful information for future experiments.     

Particle-Number Conserving Analysis for High K Multi-Quasiparticle Bands in Odd-A Deformed Nuclei 173,175Hf

Using the Particle-number Conserving (PNC) method for treating the cranked shell model, the high K multi-quasiparticle bands in odd-A deformed nuclei ^173,175Hf are analyzed, including the variation with rotational frequency of the moment of inertia, angular momentum alignment and occupation probability of each cranked Nilsson orbital. No free parameters are involved in the PNC calculation and the experimental results are reproduced well. The microscopic mechanism of the difference between the multi-quasiparticle high K bands and the yrast bands in neighboring even-even nuclei is investigated, where the blocking effects of high j intruder orbitals near the Fermi surface play a crucial role.     

稀土变形奇A核173,175Hf的多准粒子高K转动带的粒子数守恒分析

用处理推转壳模型的粒子数守恒方法分析了稀土奇A变形核^173,175Hf的3准粒子和5准粒子高K转动带,包括转动惯量、顺排角动量,以及推转Nilsson能级上的粒子填布几率随转动角频率的变化.计算中无自由参数.实验观测结果在计算中得到较好地重现.分析了多准粒子带与相邻偶偶核基态带的转动惯量变化规律不同的微观机制.在这里Fermi面邻近高j闯入态的堵塞效应起了举足轻重的作用.     

Comparison between formulas of rotational band for axially symmetric deformed nuclei

The experimental rotational spectra of the deformed nuclei available in even-even and odd-A nuclei in the rare-earth and actinide regions are systematically analyzed with several rotational spectra formulas,including Bohr-Mottelson's I(I+l)-expansion,Harris'w2-expansion,ab and abc formulas.It is shown that the simple 2-parameter ab formula is much better than the widely used 2-parameter Bohr-Mottelson's AB formula and Harris'αβ formula.The available data of the rotational spectra of both ground-state band in even-even nuclei and one-quaasiparticle band in odd-A nuclei can be conveniently and rather accurately reproduced by ab formula and abc formula.The moment of inertia and the variation with rotational frequency of angular momentum can be satisfactorily reproduced by ab and abc formulas.     

用推广的Viola-Seaborg公式计算α衰变寿命

根据Audi等编评的最新核数据表, 对Z≥84, N≥128的核的α衰变实验寿命用Viola-Seaborg公式进行最小方差拟合, 得到一套新参数. 用新拟合参数计算的偶偶核的衰变寿命与实验寿命很好地符合, 平均偏差1.3倍.而对奇A和奇奇核理论寿命与实验寿命相差较远. 考虑到处于基态时奇A和奇奇核与偶偶核的主要区别在于自旋和宇称, 对Viola-Seaborg公式做了推广. 在公式中引入了离心势垒(即α粒子轨道角动量)对衰变寿命的影响. 由推广公式计算的奇A和奇奇核的寿命与实验寿命平均偏差2.5倍,最大偏差5—6倍.     

From discrete rotational bands to damped rotational motion

We present shell model calculations for warm rotating nuclei, combining the cranked Nilsson mean field and a residual surface-delta two-body interaction. The model is used to describe the transition from the region of well-defined rotational bands into the region dominated by rotational damping, and the results are in overall agreement with the experimental findings.     

Dynamic rotational characteristics of actinides on empirical approach

In the paper calculation of the moments of inertia for nuclei from the region 87 ≤ Z ≤ 100 and 130 ≤ N ≤ 156 was made in dependence on the angular momentum of their rotational states. The experimental values of the moments of inertia were calculated for rotational energy of the classic rotor in its quantum form, with the use of a simple formula. The moment of inertia term appearing in the formula was treated as a variable. The calculations were carried out on the basis of experimental data for the energies of the rotational levels for 51 bands built on ground states for even-even nuclei and for nuclei with odd mass number A. In addition, 30 rotational bands built on excited states were also analysed in the investigated region in case of even-even nuclei. For many bands and nuclei the considered dependence of the moment of inertia on angular momentum has been found in the analytical form by fitting polynomials to the experimental data. It turned out that obtained results for the moments of inertia made it possible to describe the energies of rotational levels with a relative deviation not greater or only slightly greater than 1%. In general, in the case of 12 bands of ground level the maximum relative deviation of obtained level energies is smaller than 1%.      

Odd-Even Difference of Moment of Inertia of NuclearSuperdeformed States in A～190 Region

By fitting the E2 transition spectra of superdeformed bands in A～190 region, the coefficients of Bohr-Mottelson's I(I+1) expansion are determined and moments of inertia of band head are calculated out. All results show that the moments of inertia of odd-A nuclei are systematically larger than those of the neighboring even-even nuclei, and the moments of inertia of odd-odd nuclei are systematically larger than those of the neighboring odd-A nuclei. The odd-even difference of moment of inertia of nuclear superdeformed states is obvious.     

Description of the Superdeformed Bands of the Odd-Odd Nuclei in A～150 Region

With the supersymmetry scheme including many-body interactions, the global property and the ΔI=4 bifurcation in the superdeformed (SD) bands of odd-odd nuclei in A～150 mass region are investigated systematically. Good results for the γ-ray energies, the dynamical moments of inertia, and energy differences ΔE_γ-ΔE_γ^ref are obtained. It shows that this approach is quite powerful in describing not only the SD bands in even-even and odd-A nuclei but also those in odd-odd nuclei in the mass region.     

Shell effects on rotational damping in superdeformed nuclei

Damping of collective rotational motion in A ∼ 190 and A ∼ 150 superdeformed nuclei is studied by means of the cranked shell model with two-body residual force. Numerical calculations predict that in a typical A ∼ 190 superdeformed nucleus, ¹⁹²Hg, the rotational damping width is significantly small, Γ_rot ∼ 30 keV, and that the number of superdeformed bands in the offyrast region amounts up to 150 at a given rotational frequency. These features are quite different from the prediction for A ∼ 150 superdeformed nuclei and rare-earth normally deformed nuclei. It is shown that the single-particle alignments of the cranked Nilsson orbits have strong shell oscillation. It affects significantly the properties of rotational damping in superdeformed ¹⁹²Hg.