Further Discussion on the Spin-Determination of Superdeformed Bands in the A～190 Region

The 27 superdeformed bands, whose spin determinations aren't in agreement with two-parameter, three-parameter and four-parameter I(I+1) expansions, are analyzed. The results show that the angular momenta of 18 superdeformed bands can be determined by comparison with the variation of the kinematic and dynamic moments of inertia with rotational frequency and their mutual relation. The angular momenta of superdeformed bands like ¹⁹²Hg(2), which have bands cross, can also determined by analyzing the spectra before bands cross and by comparison with the variation of the kinematic and dynamic moments of inertia with rotational frequency and their mutual relation.     

Microscopic Mechanism of the ω Variation in Moments of Inertia for the Series of Yrast SD Bands 192—198Pb(1) and 198Po(1)

The variations in moments of inertia (J⁽²⁾ and J⁽¹⁾) with rotational frequency for the series of yrast SD bands in even-even nuclei, ^192—198Pb(1) and ¹⁹⁸Po(1), are investigated by using the particle-number conserving method for treating the pairing interaction (monopole and quadrupole). The observed co variations of J⁽²⁾ and J⁽¹⁾ are reproduced quite well in the PNC calculation, particularly the microscopic mechanism (the contributions from each major shell and each cranked Nilsson orbital) is clearly displayed. It is found that the smooth rise of J⁽²⁾ with ω is attributed to the contribution from the intruder shells (neutron N=7 and proton N=6).     

190区超形变带自旋指定的再讨论

利用两类转动惯量随转动频率的变化及其相互关系,对190区Bohr-Mottelson的两参数、三参数和四参数I(I+1)展开公式指定自旋不一致的27条超形变带进行分析,发现其中18条超形变带,它们的带首自旋I₀能够从两类转动惯量随转动频率的变化及其相互关系中可靠地定出.¹⁹²Hg(2)等发生带交叉的超形变带,它们的带首自旋也可通过分析带交叉以前、两类转动惯量随转动频率的变化及其相互关系定出.     

190区超形变核中转动带的组态结构

通过系统研究A～190区超形变核中转动带的转动惯量、角动量顺排、旋称分裂随转动频率的变化规律, 结合我们用处理对力的粒子数守恒方法的计算结果, 对A～190区所有转动带的组态结构给出了一个整体的描述. 绝大多数超形变带都建立在强耦合轨道上, 例如中子[512]5/2, [624]9/2. 少数超形变带则建立在高j闯入轨道上, 即中子[761]3/2, [752]5/2. 根据我们提出的组态结构所进行的理论计算结果表明, A～190区所有转动带的一般行为、反常变化和带交叉都得到了满意的解释.     

Nuclear Superdeformed States

The recent development of the investigations of nuclear superdeformed (SD) states are briefly reviewed with emphasis on the phenomenological analyses of nuclear SD rotational bands,including the determination of the angular momenta of SD bands,the variation of the kinematic and dynamic moments of inertia with rotational frequency and their mutual relation,etc.A plausible scheme to account for the so-called "identical"SD bands is given,which seems to be consistent with the available microscopic calculations and in which no pseudospin alignment is involved.     

Observation of superdeformed states in 88Mo

High-spin states in ⁸⁸Mo were studied using the Gammasphere germanium detector array in conjunction with the Microball CsI(Tl) charged-particle detector system. Three γ-ray cascades with dynamic moments of inertia showing similar characteristics to superdeformed rotational bands observed in the neighbouring A= 80 region have been identified and assigned to the nucleus ⁸⁸Mo. The quadrupole moment of the strongest band, deduced by the Residual Doppler Shift Method, corresponds to a quadrupole deformation of β₂≈ 0.6. This confirms the superdeformed nature of this band. The experimental data are interpreted in the framework of total routhian surface calculations. All three bands are assigned to two-quasi-particle proton configurations at superdeformed shape. Received: 20 May 1999 / Revised version: 25 August 1999     

The limited angular momentum in strongly deformed rotational bands

The moments of inertia of rotational bands in the cranked harmonic oscillator are explored. The important role played by the maximum spin is pointed out. A qualitative agreement is found with the properties of recently observed superdeformed bands.     

Investigation of the Type of Quadrupole Pairing Force in Superdeformed Nuclei

The variations of moments of inertia of superdeformed (SD) bands ¹⁹⁴Hg(1)and ¹⁹²Hg(1) with angular momentum (rotational frequency) are investigated using the particlenumber conserving (PNC) method for treating the cranked shell model. Calculations show that if both the monopole and Y₂₀ quadrupole pairing forces are taken into account, the observed co variation of the moments of inertia of ¹⁹⁴Hg(1) and ¹⁹²Hg(1) can be reproduced very well both in the low-and high- ranges, in particular the J⁽²⁾ downturn of ¹⁹⁴Hg(1) and the flattening in J⁽²⁾ of ¹⁹²Hg(1) at>0.40MeV. On the contrast, the calculated J⁽²⁾'s with the Y_2±1 or Y_2±2 quadrupole pairing forces are in disagreement with the experiments. The microscopic mechanism of the co variation of J⁽²⁾ is clearly exhibited in the PNC calculation (the contributions to J⁽²⁾ from various major Shells and individual cranked Nilsson orbitals, the occupancy of each cranked Nilsson Orbital etc). The variation of moment of inertia is the result of the competition among the shell effect (single particle motion in a deformed potential), pairing correlation, Pauli blocking effect and Coriolis (anti-pairing) interaction.     

A microscopic study on shape transition and shape coexistence in superdeformed nuclei

Superdeformed nuclei at high-spin states in several mass regions are investigated within a microscopic approach using cranked Nilsson-Strutinsky formalism to explore the equilibrium deformations in the ground state and their evolution with spin. Shape transition from normal deformed to superdeformed states with increasing spin is studied and a clear picture of shape coexistence is provided. Detailed information on spin, rotational energy, dynamical moment of inertia, and rotational frequency of superdeformed rotational bands is presented and the general features of superdeformed bands in certain mass regions are outlined. Rotational energy and dynamical moment of inertia are compared with available experimental data and the impact of temperature and pairing on superdeformed configuration are discussed.     

Backbendings of superdeformed bands in ~(36,40)Ar

Experimentally observed superdeformed(SD) rotational bands in ~(36)Ar and ~(40)Ar are studied by the cranked shell model(CSM) with the pairing correlations treated by a particle-number-conserving(PNC) method.This is the first time that PNC-CSM calculations have been performed on the light nuclear mass region around A=40.The experimental kinematic moments of inertia J~((1))versus rotational frequency are reproduced well. The backbending of the SD band at frequency around ω =1.5 Me V in ~(36)Ar is attributed to the sharp rise of the simultaneous alignments of the neutron and proton 1 d_(5/2)[202]5/2 pairs and 1 f_(7/2)[321]3/2 pairs, which is a consequence of the band crossing between the 1 d_(5/2)[202]5/2 and 1 f_(7/2)[321]3/2 configuration states. The gentle upbending at low frequency of the SD band in ~(40)Ar is mainly affected by the alignments of the neutron 1 f_(7/2)[321]3/2 pairs and proton 1 d_(5/2)[202]5/2 pairs.The PNC-CSM calculations show that besides the diagonal parts, the off-diagonal parts of the alignments play an important role in the rotational behavior of the SD bands.     

Identical superdeformed bands

The phenomenon of identical bands is studied by analyzing the distributions of fractional changes in the dynamical moments of inertia of pairs of bands in superdeformed (SD) nuclei. These distributions are found to exhibit a peak with a centroid at nearly zero. Their widths increase in going from the SD bands in the massA～150, to the SD bands in the mass ～190 and to the normally-deformed bands in the rare-earth region. These differences may be attributed to the weaker pairing correlations and the stabilizing role of intruder orbitals on the structures of SD bands. Precise level lifetimes have been measured for various pairs of identical SD bands in Gd and Dy isotopes. By comparing the derived quadrupole moments with calculations performed in the framework of the cranking Skyrme-Hartree-Fock model, it is shown that, independently of the intrinsic configuration and of the proton and neutron numbers, the charge moments calculated with respect to the doubly-magic SD core of¹⁵²Dy can be expressed in terms of independent contributions from the individual hole and particle orbitals.     

Criteria of the Spin Assignment of Rotational Band

Based on the very general properties of the rotational band of axially symmetric nucleus, some rules of the I variation of the kinematic and dynamic moments of inertia are obtained, which may serve as the effective criteria of the spin assignment of rotational band. Extensive analysis of large amount of ro tational bands (below bandcrossing) of normally deformed eveneven nuclei whose spins were established shows that these rules do hold without exception. The spins of the yrast superdeformed bands of even-even nuclei in the actinide region (fission isomeric bands), and in the A～190, 150 regions are analyzed also. The spin of the lowest observed level of the yrast superdeformed band in ¹⁵²Dy is determined to be I₀ = 26, rather than I₀ = 22 or 24.     

Identification of Bandhead Spin and Identical Bands for Odd-A Nuclei in $A\sim190$ Superdeformed Mass Region

The dynamical moment of inertia is estimated with its even-power expansion of the rotational frequency and in accordance we determine the intermediate spins of the superdeformed (SD) rotational bands. Using Marquardt method of nonlinear least-squares routines, we determine the expansion coefficients by fitting the proposed dynamical moment of inertia with its recent experimental data of the SD nuclei in the A=190 mass region. The comparison between our theoretical and available experimental data for the dynamic moment of inertia and spin shows good agreements. Also, we have calculated the static moment of inertia at three alternative values of spin. The value of spin at which the two moments of inertia are nearly equals is to be regarded as a bandhead spin of the corresponding band. These studies are carried out for eighteen bands of odd-A nuclei of the superdeformed region 190, namely ¹⁸⁹Hg(b1), ¹⁹¹Hg(b1, b2, b3, b4), ¹⁹³Hg(b2, b3, b5), ¹⁹⁵Hg(b1, b2, b3, b4), ¹⁹³Tl(b1, b2, b3, b5), ¹⁸⁹Tl(b1), and ¹⁹⁷Bi(b1). We also notice the occurrence of identical SD bands with near identical transition energies among the considered SD bands.     

Observation of superdeformed bands in194Hg

Two rotational bands, with energy spacings characteristic of superdeformed shapes, have been observed following bombardment of¹⁵⁰Nd with⁴⁸Ca. The more intensively populated band consists of 18 transitions and is assigned to¹⁹⁴Hg. The depopulation of this band occurs around spin 10. The second band, consisting of at least 16 transitions, was populated less strongly and is tentatively assigned to¹⁹⁴Hg also. The lowest level in this band is assigned spin 8. The energy differences between transitions for both bands decrease from ～40 keV at low rotational frequencies to ～30 keV at the highest observed frequencies. The moments of inertia of the bands are similar to those of the two previously observed superdeformed bands in^191,192Hg. The similarities and differences of the four known bands in the mercury region are discussed.     

转动谱的若干理论及其对超形变带的研究

简述了若干转动谱理论及其对超形变带的应用 ,并用 Bohr- Mottelson的 I(I+1 )展开公式分析了 A=1 90区超形变带的性质和指定了它们的能级自旋 ,用 Harris的ω2 展开公式 J(1) =2α+(4/3 )βω2 +(6 /5 )γω4分析了 A=1 5 0区 Tb和 Dy同位素 2 0条超形变带的性质 ,指定了它们的能级自旋 .对于首次发现的152 Dy(1 )超形变带 ,带首自旋指定为 2 6 h,与实验结果更加符合. The recent developments of rotational spectral theories and its application to superdeformed bands were briefly reviewed. The superdeformed bands in A ≈190 region were analyzed and the spins of energy level were determined by the least square fitting experimental transition energy with the formula of Bohr Mottelson’s I(I+1) expansions. The superdeformed bands in A ≈150 region were analyzed by using the kinematic moments of inertia formula J (1) =2α+(4/3)βω 2+(6/5)γω 4 in...     

Description of Properties of Triaxial Superdeformed Bands in Odd-A Lu Isotopes

Properties of the triaxial superdeformed （TSD） bands of odd-A Lu isotopes are investigated systematically within the supersymmetry scheme including many-body interactions and a perturbation possessing the S0（5） （or SU（5）） symmetry on the rotational symmetry. Quantitatively good results of the γ-ray energies, the dynamical moments of inertia and the spin of the TSD bands in odd-A Lu isotopes are obtained. The calculation shows that the competition between the pairing and anti-pairing effects exists in these TSD bands. Meanwhile, the SU（3） symmetry in TSD bands are broken more seriously than in superdeformed （SD） bands.     

A comparison of the known SD bands in the mass A≈80 region

The mass A≈80 region is now firmly established as the newest region of superdeformation, with up to 11 nuclei exhibiting as many as 21 superdeformed bands. The dynamic moments of inertia of these bands reveal a variety of interesting features, such as superdeformed band crossings and the first pair of identical superdeformed bands in the mass A≈80 region. Cranked shell model calculations have been performed and the bands are interpreted in terms of the number of high-N intruder orbitals occupied. The differences in dynamic moments of inertia and the proposed single particle configurations are discussed.     

Expansion of moment of inertia at high temperature

The moment of inertia of hot nuclei is expanded in powers of the rotational frequency ω. The first two expansion coefficients are determined for temperatures above T_c, where the equilibrium shape is spherical at ω = 0. It is shown how the moment of inertia varies with temperature, rotational frequency, proton number, and neutron number.     

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, 176}Lu 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=|Ω₁-Ω₂|) two-quasiparticle band of the Gallagher-Moszkowski doublet with one nucleon in the Ω = 1/2 orbital is analyzed.