Triplet cooper pairing in nuclear matter and rotational states of superdeformed nuclei

One hundred and sixty-one rotational bands of superdeformed states in nuclei are considered on the basis of a model that admits triplet Cooper pairing in superfluid nuclear matter. The behavior of the dynamical moment of inertia for such states is investigated within this model, which is shown to comply well with available experimental data and to describe successfully the rotational spectra of superdeformed states.     

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.     

Double-Blocking Effects in Odd-odd Superdeformed Nucleus 194Tl

Six superdeformed bands of odd-odd nucleus ¹⁹⁴Tl in A～190 mass region are studied using the particle-number conserving method for treating the cranked shell model with pairing interactions. Calculated results agree with experiments very well. Based on our calculation the configurations of the six superdeformed bands are assigned and the influence of blocking effects of proton and neutron on moments of inertia is investigated in detail. The variation of moments of inertia with rotational frequency is mainly attributed to the intruder shells (neutron N=7 and proton N=6), whereas the contributions to moment of inertia from other shells remain almost unchanged with rotational frequency.     

Energy Staggering in Ground Bands of 232Th and 236,238U Nuclei Using the Interacting Vector Boson Model

The ΔI=2 and ΔI=4 staggering parameters of transition energies E_γ for normally deformed positive parity ground bands in ²³²Th and ^236,238U nuclei are studied in framework of the symplectic extension of the interacting vector boson model. The model parameters are obtained from the fitting procedure between the calculated excitation energies and the corresponding experimental ones. The staggering parameters represent the finite difference approximations to higher order derivatives dⁿE_γ/d Iⁿ of the γ -ray transition energies in a ΔI=2 and ΔI=4 bands, which yielding multipoint formulae. The first order derivative (two-point formula) provides us with information about the dynamical moment of inertia. The staggering oscillation for the fourth order derivative (five-point formula) is about 0.5 KeV and is even larger than that in superdeformed bands. The quite similarity in dynamical moments of inertia of the isotopes ^236,238U up to high spin states indicate that the phenomenon of identical bands is not restricted to superdeformed bands.     

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.     

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.     

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.     

Band head spin assignment of superdeformed bands in 86Zr

Two parameter expressions for rotational spectra viz. variable moment of inertia (VMI), ab formula and three parameter Harris ω² expansion are used to assign the band head spins (I₀) of four rotational superdeformed bands in ⁸⁶Zr. The least-squares fitting method is employed to obtain the band head spins of these four bands in the A~80 mass region. Model parameters are extracted by fitting of intraband γ-ray energies, so as to obtain a minimum root-mean-square (rms) deviation between the calculated and the observed transition energies. The calculated transition energies are found to depend sensitively on the assigned spins. Whenever an accurate band head spin is assigned, the calculated transition energies are in agreement with the experimental transition energies. The dynamic moment of inertia is also extracted and its variation with rotational frequency is investigated. Since a better agreement of band head spin with experimental results is found using the VMI model, it is a more powerful tool than the ab formula and Harris ω² expansion.     

Systematic Study on the Superdeformed Bands of Double Odd Nuclei in A～130 Region

Properties of the superdeformed bands of odd-odd nuclei in A～130 mass region are investigated systematically within the supersymmetry scheme including many-body interactions and a perturbation possessing the SO(5) (or SU(5)) symmetry on the rotational symmetry. The obtained γ-ray energies, the dynamical moments of inertia, and energy differences △Eγ - △Eγ^ref agree wlth experimental data. It shows that this approach is quite powerful in describing odd-odd nuclei in 130 mass region.     

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.     

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...     

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.     

Description of the Superdeformed Bands in A～190 Region with a Three-Parameter Formula

The q-deformed moment of inertia, formulated by was first introduced as the mechanical moment of inertia of superdeformed (SD) nuclei. The E2 transition γ-ray energies and the dynamical moment of inertia of the lowest-formed bands in Hg, Ph, and TI isotopes are calculated. The calculated results indicate that the SD bands may be described by the ided-rotor with the q-deformed mpment of inertia.     

Description of the Superdeformed Bands of Double Odd Nuclei in A ～ 190 Region

With the supersymmetry scheme including many-body interactions and aperturbation possessing the SO(5)(or SU(5)) symmetry on the rotational symmetry, the superdeformed bands and △I＝4 bifurcation of odd-odd nuclei in A ～ 190 mass region are investigated systematically. Good results for the γ-ray energies, the dynamical moments of inertia, and energy differences △Eγ - △Eref γ are obtained. It shows that this approach is quite powerful in describing odd-odd nuclei in the region.     

Description of the Superdeformed Bands of Odd-Odd Nuclei in A ～ 80 Region

Properties of the superdeformed bands of odd-odd nuclei in A～80 mass region are investigated systematically within the supersymmetry scheme including many-body interactions and a perturbation possessing the SO(5) (or SU(5)) symmetry on the rotational symmetry. The obtained γ-ray energies, and the dynamical moments of inertia agree with experimental data. It shows that this approach is quite powerful in describing odd-odd nuclei in A～80 mass region.     

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.     

Triaxial superdeformation in Lu

High-spin states in ¹⁶³Lu have been investigated using the Euroball spectrometer array. The previously known superdeformed band has been extended at low and high energies, and its connection to the normal-deformed states has been established. From its decay the mixing amplitude and interaction strength between superdeformed and normal states are derived. In addition, a new band with a similar dynamic moment of inertia has been found. The experimental results are compared to cranking calculations which suggest that the superdeformed bands in this mass region correspond to shapes with a pronounced triaxiality (γ≈±20°).     

Detailed spectroscopy in the superdeformed second minimum of 240Pu

Spectroscopic studies in the superdeformed shape isomer of ²⁴⁰Pu using γ-spectroscopy, conversion electron spectroscopy and transmission resonance spectroscopy have been performed. In a high-resolution and high-efficiency γ-spectroscopy experiment the out-of-band decays of several excited superdeformed rotational sequences with K=2^? and 1^? could be identified together with evidence for a weakly populated 0^? octupole band. Surprisingly, no low-lying collective quadrupole excitations could be observed. Complementary information could be obtained in conversion electron measurements in coincidence with isomeric fission, resulting in the first identification of the lowest ß-vibrational K=0⁺ band. For all rotational bands the variation of the moment of inertia with spin could be studied. A predominant population of negative parity states in the second well could be observed, which can be explained by the selective population and depopulation of the second minimum. Complementary transmission resonance measurements have been performed, yielding new information on the fine structure of high-lying (ß-)vibrational multi-phonon states. A new method could be established to determine the excitation energy of the fission isomer ground state from measured level densities.     

Superdeformation in142Eu

A rotational band with 15 transitions has been observed in¹⁴²Eu in an experiment with the GASP Ge detector array by the¹¹⁰Pd(³⁷Cl,5_n) reaction. The average energy spacing between the neighbouring transitions is 60 keV, which is similar to the energy spacings in the superdeformed bands in the mass 140 region. The band has a constant dynamic moment of inertia as suggested by Cranked Shell Model calculations.     

New Method for Spin Assignment of Superdeformed Rotational Bands

A new method for spin assignment of superdeformed rotational bands is proposed and it turns out to be more efficient than other methods used before. The application is made to superdeformed bands in A～190 and A～150 mass regions. By analyzing the standard deviation of the fixed gamma-ray energies of an SD band in different methods, the advantage of the present method over the other methods is presented. This method brings then a comprehensive interpretation of the methods used in spin assignment.