Decay of heavy and superheavy nuclei

We present here, an overview and progress of the theoretical works on the isomeric state α decay, α decay fine structure of even–even, even–odd, odd–even and odd–odd nuclei, a study on the feasibility of observing α decay chains from the isotopes of the superheavy nuclei Z = 115 in the range 271 ≤A ≤ 294 and the isotopes of Z = 117 in the range 270 ≤A ≤ 301, within the Coulomb and proximity potential model for deformed nuclei (CPPMDN). The computed half-lives of the favoured and unfavoured α decay of nuclei in the range 67 ≤Z ≤ 91 from both the ground state and isomeric state, are in good agreement with the experimental data and the standard deviation of half-life is found to be 0.44. From the α fine structure studies done on various ranges of nuclei, it is evident that, for nearly all the transitions, the theoretical values show good match with the experimental values. This reveals that CPPMDN is successful in explaining the fine structure of even–even, even–odd, odd–even and odd–odd nuclei. Our studies on the α decay of the superheavy nuclei ^271?294115 and ^270?301117 predict 4 α chains consistently from ^284,285,286115 nuclei and 5α chains and 3α chains consistently from ^288?291117 and ²⁹²117, respectively. We thus hope that these studies on ^284?286115 and ^288?292117 will be a guide to future experiments.     

On the Possibility of Delayed Fission of Nuclei in the Region of Superheavy Transuranium Elements

Delayed fission of atomic nuclei was discovered in 1966. It is observed primarily in odd–odd nuclei for which the energy released in beta decay (K capture) is commensurate with the fission barrier in the nucleus formed after this process. Delayed fission was found in four nuclide regions: neutrondeficient isotopes in the Pb region, neutron-deficient isotopes in the Ac and Pa regions, and neutrondeficient and neutron-rich isotopes of transuranium elements. In the wake of investigations into the properties of isotopes of superheavy transuranium elements, numerous calculations were performed in order to determine the masses of new nuclei and to predict their decay properties. Explored and predicted properties of superheavy-element nuclides, where, for some odd–odd nuclei of transuranium elements, the K-capture energy is commensurate with the fission barriers in the corresponding daughter nuclei formed after K capture, are analyzed. Estimates of the delayed-fission probability are presented for some isotopes of elements whose charge number Z ranges from 103 to 107.     

Charge radii and structural evolution in Sr,Zr, and Mo isotopes

The evolution of the ground-state nuclear shapes in neutron-rich Sr, Zr, and Mo isotopes, including both even-even and odd-A nuclei, is studied within a self-consistent mean-field approximation based on the D1S–Gogny interaction. Neutron separation energies and charge radii are calculated and compared with available data. A correlation between a shape transition and a discontinuity in those observables is found microscopically. While in Sr and Zr isotopes the steep behavior observed in the isotopic dependence of the charge radii is a consequence of a sharp prolate–oblate transition, the smooth behavior found in Mo isotopes has its origin in an emergent region of triaxiality.     

Systematic study of odd-mass 151-161Pm and 154,156Pm isotopes using projected shell model

Inspired by the availability of recent experimental as well as theoretical data on the energy levels of odd-mass ^151-161Pm and odd-odd ^154,156Pm, we applied the theoretical framework of the projected shell model to further understand the nuclear structure of these nuclei. The calculations closely reproduced the experimental data reported for the yrast bands of these isotopes by assuming an axial (prolate) deformation of ~0.3. Other properties along the yrast line, such as transition energies and transition probabilities, have also been discussed. Band diagrams are plotted to understand their intrinsic multi-quasiparticle structure, which turn out to be dominated by 1-quasiparticle bands for the odd-mass Pm isotopes and 2-quasiparticle bands for the doubly-odd Pm isotopes under study. The present study not only confirms the recently reported experimental/theoretical data, but also extends the already available information on the energy levels and adds new information regarding the reduced transition probabilities.     

Calculation of nucleon densities in calcium,nickel, and molybdenum isotopes on the basis of the dispersive optical model

The radial distributions of proton and neutron densities in the even–even isotopes ^40?70Cа and ^48?78Ni and the analogous distributions of neutron densities in the even–even isotopes ^92?138Mo were calculated on the basis of the mean-fieldmodel involving a dispersive optical potential. The respective root-mean-square radii and neutron-skin thicknesses were determined for the nuclei under study. In N > 40 calcium isotopes, the calculated neutron root-mean-square radius exhibits a fast growth with increasing N, and this is consistent with the prediction of the neutron-halo structure in calcium isotopes near the neutron drip line.     

Electric dipole transitions in neutron-rich nuclei

The structure of neutron-rich nuclei in several isotopes is investigated by shell model calculations. We study the electric dipole (E1) transitions in C isotopes focusing on the interplay between the low-energy Pigmy strength and the giant dipole resonance (GDR). Reasonable agreement is obtained with available experimental data for the photoreaction cross sections in ¹²C, ¹³C, and ¹⁴C with the inclusion of the quenching effects. A low-energy peak in the dipole strength in ¹⁵C is associated with a single-particle motion of the 1s_1/2 valence neutron relative to the ¹⁴C core. The calculated transition strength below the GDR in C isotopes heavier than ¹⁵C is found to exhaust about 50–80% of the cluster sum rule value and 12–16% of the classical Thomas-Reiche-Kuhn sum rule value. Next, we point out that the quadrupole and magnetic moments in the odd C isotopes strongly depend on configuration, which will be useful to determine the spin parities and the deformations of the ground states of these nuclei. The electric quadrupole (E2) transitions in even C isotopes are also studied. The isotopic dependence of the E2 transition strength is found to be reasonably well explained, although the calculated strength largely overestimates the unexpectedly small strength observed in ¹⁶C. The E1 strength in ¹⁸N and ¹⁹N as well as in Ne isotopes is also investigated.     

New states in 44,46Ar isotopes from deep-inelastic heavy ion reaction studies

In-beam γ-rays in neutron-rich sdfp shell nuclei, produced in deep-inelastic collisions of ⁴⁸Ca projectiles on ⁴⁸Ca target nuclei, have been studied using Ge multidetector array EU-ROBALL III. New yrast states in heavy argon isotopes have been identified. Received: 11 November 1999     

Consistency tests of Ampcalculator and chiral amplitudes in SU(3) Chiral Perturbation Theory: A tutorial-based approach

The positive-parity yrast bands of ^{79, 81, 83, 85, 87, 89}Y isotopes have been studied using the projected shell model (PSM). Nuclear-structure properties like yrast spectra, transition energies, band diagrams, kinetic moment of inertia, rotational frequencies and reduced transition probabilities (B(M1) and B(E2) are calculated. The results obtained from the PSM calculations are also compared with the available experimental as well as theoretical data and, in general, a reasonable agreement is obtained between them. Calculations in the present work also predict that these isotopes have multi-quasiparticle structure.     

Properties of lead isotopes in the vicinity of the neutron drip line

On the basis of the Hartree-Fock method with Skyrme forces of the Ska, SkM*, and Sly4 type, the position of the neutron drip line and the properties of neutron-rich lead isotopes are studied with allowance for deformations. It is shown that, in extremely neutron-rich nuclei, the neutron and proton density distributions are characterized by an anomalously large deformation parameter of β ～ 0.6. Also, nuclei of superdeformed lead isotopes have anomalously large root-mean-square radii. The existence of the isotopes ^266–288Pb, which are stable to the emission of one neutron, is predicted.     

The FBCS model and the inverse gap equations applied to the tin isotopes

The FBCS model for odd nuclei and the inverse gap equations are applied to a whole sequence of tin isotopes,viz.^111–125Sn. From spectroscopic data on the odd isotopes, the single-particle energies and interaction strengths are obtained. With these parameters the lowest states of the even isotopes are calculated by a number-projected two-quasiparticle diagonalization and by the usual BCS one. This is done with two Gaussian interactions and the SDI. In the case of the Gaussian forces the experimental energies are well reproduced by the number-projected treatment. Effective charges for Eλ transitions, which are required to reproduce the experimental transition rates, are rather constant for the whole series of isotopes, in case of the number-projected treatment. In addition a number of spectroscopic factors for one-nucleon transfer reactions are calculated and good agreement with experiments is observed.     

Rearrangements in neutron shell closures far from stability

A survey of experimental results obtained at GANIL (Caen, Prance) on the study of the properties of very neutron-rich nuclei (Z = 6–20, A = 20–60) near the neutron drip line and resulting in an appearance of further evidence for the new magic number N = 16 is presented. Very recent data on mass measurements of neutron-rich nuclei at GANIL and some characteristics of binding energies in this region are discussed. Nuclear binding energies are very sensitive to the existence of nuclear shells and together with the measurements of instability of doubly magic nuclei ¹⁰He and ²⁸0 they provide information on changes in neutron shell closures of very neutron-rich isotopes. The behaviour of the two-neutron separation energies S_2n derived from mass measurements gives a very clear evidence for the existence of the new shell closure N = 16 for Z = 9 and 10 appearing between 2s_1/2 and ld_3/2 orbitals. This fact, strongly supported by the instability of C, N and O isotopes with N > 16, confirms the magic character of N = 16 for the region from carbon up to neon while the shell closure at N = 20 tends to disappear for Z ≤ 13. Decay studies of these hardly accessible short-lived neutron-rich nuclei from oxygen to silicon using the in-beam γ-ray spectroscopy are also reported.     

Gammasphere上裂变丰中子核核结构若干前沿领域的新进展(Ⅰ:第一和第二部分)(英文)

(第一和第二部分):使用Gammasphere多探测器系统对252Cf裂变源瞬发γ射线进行γ-γ-γ和γ-γ(θ)符合测量,裂变丰中子原子核核结构若干前沿领域的深入研究获得了新的进展。高达5.7×1011以上的三重和更高重符合事件的数据统计,以及更少压缩的三维数据为宽广未知丰中子核区的寻找和研究提供了有利的条件。在具有重要物理意义的若干丰中子核区首次建立,或显著扩展了一批包括转晕态和转晕附近能态的高自旋能级纲图。在偶-偶丰中子核110,112Ru和108Mo中鉴别出了手征对称破缺结构。丰中子110,112Ru附近核的三轴形变基态具有最低的能量,在它们之中已确认了接近最大值的三轴形变。在这些Ru和Mo同位素中观察到的手征双线能带展示出手征破缺的一切特征,特别是其理想的能量简并,表明它们在迄今已报道的手征破缺结构中,具有最好的手征特性。研究了手征结构从具有γ软度的108Ru到具有大三轴形变的110,112Ru的过渡。斜轴推转(TAC)和随机相近似(RPA)理论计算成功地拟合了在这些偶-偶丰中子核中观察到的手征双线能带的特性,并指定其为软手征振动态。在这些偶-偶核中观察到的手征破缺不可能归纳为奇-奇核中那样的简化的几何图像。前者来自闭壳外所有中子的相互作用。对双幻核132Sn附近N=83同中素链的系统研究为这个极富吸引力的核区提供了大量新的谱学信息。N=83同中素135Te(Z=52),136I(Z=53),137Xe(Z=54),138Cs(Z=55)和139Ba(Z=56)的最新能级信息,特别是首次建立的138Cs高自旋能级纲图和壳模型理论计算表明,Z=50质子闭壳外少数g7/2价质子激发同N=82中子闭壳外之唯一f7/2价中子的耦合对该核区能级结构具有关键作用。观察到了132Sn和208Pb附近核区谱学信息的相似性和相对应的三粒子和五粒子态。在135Te中观察到了磁转动,这是在双幻核132Sn附近观察到的首例磁转动。     

Microscopic aspects of identical bands in 78Sr and 78Rb

Recent investigations of the shape transition and shape coexistence phenomena dominating the structure of the even-even N ? Z nuclei in the A ? 80 mass region are extended to the odd-odd nucleus ⁷⁸Rb. Special attention is paid to the structure of some “identical” bands which have been recently identified in ⁷⁸ Sr and ⁷⁸Rb. The ground band of⁷⁸ Sr and the yrast as well as excited negative parity bands in ⁷⁸Rb are studied within the EXCITED VAMPIR approximation using complex Hartree-Fock-Bogoliubov transformations in a relatively large model space. The results are compared with the available experimental data. The emerging picture reveals the role played by the strong quadrupole deformation on the appearance of identical bands as well as the influence of the shape coexistence on their evolution. Predictions for the electromagnetic and alignment properties of the bands are presented.     

质子数Z 分别位于Ru 之上和之下的A~(100~126) 丰中子原子核三轴形变在原子核形状变迁和共存中的重要作用(英文)

基于Ru (Z = 44) 丰中子同位素中存在最大三轴形变的理论预言和实验证据,综述了近年来Rh (Z = 45),Pd (Z =46), Ag (Z =47), Cd (Z =48)(质子数Z 位于Ru,Z =44 之上)及Zr (Z =40), Nb (Z =41), Mo (Z =42),Tc (Z =43)(质子数Z 位于Ru,Z =44 之下) 的A~ (100~126) 丰中子同位素中关于三轴形变的形状变迁和形状共存系统性研究的重要进展。252Cf 自发裂变瞬发 射线-- 三重符合、特别是新建立的--- 四重符合数据的系统观测和研究,在Ru, Pd, Cd 和Nb 丰中子同位素中显著扩展或首次观测到了一系列能带,为这个核区原子核形状的研究提供了新的、重要的实验数据。联系此前报道的有关进展,使用PES, TRS, PSM, CCCSM 和SCTAC 理论模型计算拟合新的实验数据,在该核区沿同中素和同位素链,并随自旋和激发能变化各自由度,跟踪原子核形状渐进变化,获得了新的系统性研究成果,显著扩展和深化了人们对原子核形状变迁和形状共存的认知。对于Ru 及其上的Rh (Z = 45), Pd (Z = 46), Ag (Z = 47) 和Cd (Z = 48) 丰中子同位素的研究表明:Rh 丰中子核具有比最大值稍小的三轴形变,γ = 28°,并在103{106Rh 同位素链上鉴别出了手征对称破缺;在三轴形变核112Ru和114Pd(N = 68)中发现了三轴原子核的摆动运动,该摆动运动也可能在114Ru (N = 70)中存在;观察到了从具有最大三轴形变的110,112Ru 中手征破缺到稍小三轴形变的112,114,116Pd 中扰动的手征破缺的过渡;在较软的Ag 核中观察到了丰富的谱学结构,在104,105Ag 中鉴别出了可能的手征对称破缺,在较重的115,117Ag 中提出了趋于三轴形变的软度;具有小形变的Cd核的能级结构被解释为准粒子耦合、准转动和软三轴形变;最近的库伦激发的研究提供了Z = 50, N = 82满壳附近122,124,126Cd 核中出现核集体性的实验和理论证据;上述研究成果展现出从Ru中的最大三轴形变(γ=30°,三轴形变极小增益为0.67 MeV), 经具有大三轴形变的Rh核γ=28°),到Pd核中的稍小、但稳定于中等自旋到高自旋区的三轴形变(γ~41°,三轴形变极小增益为0.32 MeV),再经Ag核中的软度,最后到具有很小形变、但仍出现集体性质、包括软三轴形变的Cd核的过渡。对于Pd核转动带交叉系统性的研究揭示了其第一带交叉(νh_11/2)2 中子转动顺排的上行驱动,和第二带交叉(πg_9/2)2质子转动顺排的下行驱动效应,成功地解释了114Pd 中的三轴摆动运动,并给出了110-118Pd同位素链中理论早已预言、而比早期理论预言更为完整准确的形状渐进变迁和形状共存的图像。根据该核区的系统研究,发现最大三轴形变出现在112Ru,而在相邻的偶Z(Pd)同位素链,三轴形变极小的中心在114Pd, 两者均为N = 68。上述系统性研究沿相邻的Ru和Pd偶Z同位素链,在N =68同中素中鉴别出最大三轴形变,均比理论预言的108Ru 和110Pd 多4个中子。在Z值位于Ru (Z = 44) 之下的Zr (Z = 40), Nb (Z = 41), Mo (Z = 42) and Tc (Z = 43) 丰中子同位素中,Y和Zr核具有很强的轴对称四极形变,而在较重的Zr同位素中出现了自由度;较重的Nb核(A = 104~106) 基态具有中等程度的软三轴形变和强四极形变,随着自旋和激发能的增加,过渡到接近于轴对称的强四极形变;而较轻的Nb核(A≤103) 基态均接近轴对称形状;在Nb同位素链上基态由球形到强四极形变的形状突变发生在100Nb(N = 59),在100-106Nb同位素链中基态的软三轴形变随中子数增加而增加;在Nb核中还观察到关于软三轴形变的形状共存;Mo核具有大的三轴形变,观察到了振动和手征对称破缺;Tc核具有比最大值稍小的三轴形变,γ=26°,并观察到了手征对称破缺。质子数Z从41到48的A~(100~126)丰中子同位素,特别是Pd和Nb 同位素,呈现出关于三轴形变的过渡特征。This paper reviews the systematic investigations and understanding for the shape transitions and coexistence with regard to triaxial deformations in A s 100 to 126 neutron-rich Rh (Z = 45), Pd (Z = 46), Ag (Z = 47), Cd (Z = 48) and Zr (Z = 40), Nb (Z = 41), Mo (Z = 42), Tc (Z = 43) isotopes with Z beyond and below Ru (Z = 44), respectively, in Ru the maximal triaxial deformation having been predicted and deduced. The recent measurements and studies of prompt triple- and four-fold, γ-γ-γ and γ-γ-γ-γ, coincidence data from the spontaneous fission of 252Cf using Gammasphere have yielded considerable expansion and extension or first observation of the bands in Ru, Pd, Cd, and Nb isotopes,which provided important data for the studies of nuclear shapes in this region. Combined with previous investigations, recent systematic studies of the new data well reproduced by PES, TRS, PSM, CCCSM and SCTAC model calculations have traced shape changes along the isotonic and isotopic chains, respectively,and with changing excitations/spins as well, significantly expanding our knowledge of shape transitions/coexistence in nuclei.For the neutron-rich Ru and beyond, Rh, Pd, Ag and Cd isotopes, triaxial deformations γ= 28°,slightly smaller than the maximal value, were deduced in Rh (Z = 45) isotopes, with chiral symmetry breaking proposed in 103-106Rh; onset of wobbling motions were identified in 112Ru and 114Pd (N =68),and probably also in 114Ru (N =70); evolution from chiral symmetry breaking in 110,112Ru with maximal triaxial deformations to disturbed chirality in 112,114,116Pd with less pronounced triaxial deformations was proposed; rich nuclear structure was proposed in soft Ag isotopes with possible chiral doubling structure suggested in 104,105Ag, and softness towards triaxial deformation proposed in heavier 115,117Ag;quasi-particle couplings, quasi-rotations and soft triaxiality were suggested in Cd (Z =48) isotopes with small deformations; onset of collectivity was recently suggested in 122,124,126Cd in the vicinity of Z =50 and N = 82 closed shells by studies of Coulomb excitations; shape evolutions from maximal triaxial deformations in Ru (γ=30°, with triaxial minimum energy gain of 0.67 MeV), through Rh with large triaxial deformations ( γ=28°), to less pronounced triaxiality in Pd (with triaxial minimum energy gain of 0.32 MeV), then soft triaxiality in Ag, and finally to slightly deformed Cd isotopes but with emergence of collectivity and soft triaxiality were proposed. The systematic studies of the band crossings in Pd revealed up-rising drivings of the first band crossings caused by (νh_11/2)2 and down-sloping drivings of the second band crossings by (πg_9/2)2, explained the onset of wobbling motions in 114Pd,and showed a long-sought picture of shape evolution and coexistence in the Pd isotopic chain which is more complete but complex than earlier predictions. Based on the systematic studies in the mass region,maximal triaxial deformation is found to be reached in 112Ru and less-pronounced triaxiality centered at 114Pd, both for N =68, four neutrons more than predicted in earlier theoretical calculations.In the neutron-rich Zr (Z =40), Nb (Z =41), Mo (Z =42) and Tc (Z =43) isotopes with Z just below Ru, large quadrupole deformations of axially symmetric shapes were deduced in Y and Zr isotopes, with emergence of the degree of freedom having been suggested for heavier Zr isotopes; medium triaxial deformations were deduced for the ground states of heavier (A > 104) Nb isotopes, and, with increasing excitations and spins, evolution from medium triaxial deformations with strong quadrupole deformations at ground states to nearly axially-symmetric shapes were deduced; light Nb isotopes (A6103) have near axially-symmetric shapes with strong quadrupole deformations; combining with the identification of onset of strong quadrupole deformation at 100Nb in the Nb isotopic chain, an increase of soft triaxiality with increasing neutron number was proposed in 100-106Nb. Shape coexistence with regard to soft triaxiality is also proposed in Nb isotopes; large triaxial deformations, vibrations and chiral doublets were proposed in Mo isotopes; chiral doubling and large triaxial deformations (γ ~26°) slightly smaller than the maximal triaxiality were suggested in Tc isotopes.The neutron-rich nuclei with Z ranging from 41 through 48 and A ~100 to 126, especially the Pd and Nb isotopes are thus found to be transitional nuclei with regard to triaxiality.     

Clustering in neutron-rich nuclei

Clustering in nuclei is discussed putting emphasis on the investigation of the role of nuclear clustering in neutron-rich nuclei. The subjects we discuss include clustering in neutron-rich Be, B and C isotopes, clustering in the island of inversion around N = 20, and clustering in the region with A ≈ 40. Be isotopes present us typical examples of clustering in neutron-rich nuclei not only in their ground band states but also in their excited band states, for which we show the analyses based on antisymmetrized molecular dynamics (AMD). Clustering in Be isotopes near neutron dripline is intimately related to the breaking of the neutron magic number N = 8. In this connection we report our study about the possible relation of the clustering with the breaking of the neutron magic number N = 20 in the island of inversion including ³²Mg and ³⁰Ne. Our discussion is not only about the positive parity states but also about negative parity states. Recently in the latter half of sd shell and in the pf shell many excited rotational bands with large deformation have been found to exist. Since the first excited K ^π = 0⁺ and K ^π = 0^- bands in ⁴⁰Ca have been regarded as constituting inversion doublet bands having the ³⁶Ar + α structure, and since the first excited K ^π = 0^- band in ⁴⁴Ti has been concluded to have ⁴⁰Ca + α structure through the α transfer reaction and by using the unique α optical potential on ⁴⁰Ca, it is important to investigate the role of α clustering in these newly-found rotational bands with large deformation. We will report the AMD study about this problem.     

The deformation of the ground and excited states in the Ag and Sn nuclei

The microscopic calculation of the potential energies in the ground and excited states of Ag and Sn nuclei has been performed. The single particle Nilsson potential and the shell correction Strutinski method have been used. The weak sensitivness to nonaxial deformation has been found for even neighbours of these nuclei. The small tendency towards prolate deformation of the ground and excited one-quasiparticle states originating from theg _9/2 proton subshell in^101–105Ag odd isotopes has been noticed. The behaviour with quadrupole e and hexadecapole ε₄ deformation of the ground and two-quasiparticle excited 0⁺ states originating from thed _5/2,g _9/2 andg _7/2 proton subshells andh _11/2 neutron subshell in^112–118Sn has been investigated. The small quadrupole deformation of the excited 0⁺ states has been found what is in agreement with the experimental data concerning the rotational bands build on the first excited 0⁺ states in Sn isotopes.     

High-Spin States and Negative Parity Levels in Neutron-Rich 116,118,120Cd Nuclei

High spin states in neutron-rich ^116,118,120Cd nuclei have been investigated by observing high-fold prompt γ-ray coincidence events from the spontaneous fission of ²⁵²Cf with the Gammasphere detector array. The yrast bands have been extended with spin up to 18h in¹¹⁸Cd and 16h in ^116,120Cd respectively. The band structures are calculated using the cranked shell model and possible origination for the backbends in the yrast bands is discussed. Proposed 5^－ and 7^－ levels are observed in each of these cadmium isotopes, and possible explanation for the negative states is discussed based on systematic comparison. A quasi-rotational band based on 7^－ level in ¹¹⁸Cd has been established.     

Beta-decay energies and masses of short-lived isotopes of rubidium,caesium, francium,and radium

Total decay energies have been measured for a number of neutron-deficient Rb and Cs isotopes, as well as for some neutron-rich isotopes of Fr and Ra. Mass separated sources were produced at the ISOLDE on-line separator at CERN. By applying two differentβ-γ coincidence methods,Q values or their lower limits were determined for^76–78Rb,⁸⁰Rb,^121–124Cs,²²²Fr,^224–226Fr,²²⁹Ra-²²⁹Ac. For many of these nuclei, the atomic mass excesses could be derived, allowing the comparison of masses of far unstable nuclei with predictions from mass formulae. The odd-odd nuclei⁷⁶Rb and⁷⁸Rb appear to be 1?1 1/2 MeV more strongly bound than expected from the systematics.