Shape Coexistence and Band Termination in Doubly Magic Nucleus 40Ca

Shape coexistence and band structure near yrast line of the Z=N doubly magic nucleus ⁴⁰Ca have been investigated by the configuration-dependent cranked Nilsson-Strutinsky approach. The observed normal deformed and superdeformed bands are explained and the terminating states are confirmed by the calculations. The transition quadrupole moment Q_t of the calculated superdeformed band is in good agreement with the observed one at high spin. There is shape coexistence within the same configuration. Possible normal deformed and superdeformed bands with rotation around the intermediate axis in several interesting configurations of ⁴⁰Ca are discussed. Possible favored superdeformed band terminations in ³⁸Ca and ³⁸Ar are predicted. The experimental results in ³⁸Ar are discussed simply.     

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.     

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...     

丰中子锶同位素的投影壳模型研究

利用考虑跨壳激发的投影壳模型（PSM）方法,研究了质子数Z=38、中子数N=63和64大形变丰中子101,102Sr同位素的结构性质。主要计算了转动谱、转动惯量和电磁跃迁性质等（如B（E2）和g因子）,并与相应的实验数据进行系统比较和相关的理论预言。结果表明,PSM可以利用理论计算的能带图解释101,102Sr同位素的转动惯量、电磁跃迁随自旋的变化,分析晕带的结构。PSM理论可以很好地再现实验结果,说明PSM方法及其采用的有效相互作用可以外推研究丰中子核区101,102Sr同位素的原子核结构。对于101,102Sr同位素,核子开始填布质子g_9/2和中子h_11/2轨道,通过更为仔细地分析能带图中来自质子g_9/2和中子h_11/2轨道对各转动带的组态成分的贡献,清晰地表明丰中子核结构性质对不同核子填布的依赖。Recently, we have carried out systematically studies on the structural properties of proton number Z=38, neutron number N=63 and 64 neutron-rich isotopes 101,102Sr by using the projected shell model (PSM) with consideration of cross shell excitation. The rotation spectra, the moment of inertia and the electromagnetic transition properties (such as B(E2) and g-factor) are calculated and compared with the corresponding experimental data in this paper. Furthermore, more high spin states are predicted in the calculation and expected to be confirmed experimentally. The results show that the PSM can not only well analyze the structural properties of yrast bands in 101,102Sr but also interpret the variation of the moment of inertia, electromagnetic transition with spins in terms with the theoretical band diagram. The good agreement with the experimental data suggests that the PSM with the adopted effective interactions can be generalized to study the nuclear structure of 101,102Sr isotopes in neutron-rich mass region. For 101,102Sr isotopes, the nucleons begin to fill proton g_9/2 and neutron h_11/2 orbital, the dependence of nuclear structure and properties on the different orbital occupies is described by carefully analyzing the contribution from proton g_9/2 and neutron h_11/2 orbital to the configuration of rotational bands in band diagram.     

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.     

Superdeformation in Pb: Observation of three additional excited bands

The superdeformed nucleus ¹⁹³Pb has been studied following a heavy-ion fusion-evaporation reaction with the Gammasphere spectrometer array. Three new superdeformed bands, two of them probably signature partners, have been observed, bringing the total number of superdeformed bands known in this nucleus to nine. An estimate of the g-factor associated with one of the previously known pairs of strongly coupled excited bands has been made, confirming their configuration. The properties of the bands are compared with the results of cranked shell model calculations; good agreement is found and configurations are assigned to each band. The two new signature partner bands are suggested to be based on the two signatures of the [512]5/2 neutron orbital. The third new band is probably based on the 7₃ intruder orbital. In addition, the high-energy region of the spectrum in coincidence with the yrast superdeformed bands has been carefully studied. The current data provide no evidence for the previously reported transitions linking the superdeformed and normal-deformed states with energies around 2.2–2.4 MeV.     

Re-discussion of the Spin Assignments of the Superdeformed Bands in A≈190 Region (Ⅱ) Odd Superdeformed Nuclei

The influence of the I=1 staggering and the fluctuation in observed γ-tyanstion energies on the spin assignments of superdeformed bands is taken into account properly. An improved approach for removing the fluctuations from the observed y transition energies is proposed. The smoothed transition energies are fitted by the ah expression or its modification to assign the spins of the superdeformed bands in the odd-A nuclei in A≈190 region. The assigned spins for some superdeformed bands are different from those given in other approaches.     

Evidence for multiple band terminations in Pd

The level structure of ¹⁰²Pd has been investigated using data collected with the Eurogam 2 array. Several cascades of γ-rays have been established up to high spins. Termination of rotational bands has been observed at I^π = 28⁻ and 32⁺, and tentatively at I^π = 38⁺ and 42⁺. The nucleus ¹⁰²Pd is the first case where rotational bands built on valence space configurations are followed from spin close to zero up to termination and, at higher spins, a smooth rotational band which appears to terminate is built on core excited configurations.     

Study for Superdeformed Bands in A～190 Region with Quantum Group Uqp(u2) Model

superdeformed bands in the A～190 region are systematically analyzed by using the twoparameter expansion of quantum group U_qp(u₂) Model. The calculated results of E2 transition γ ray energies are in agreement with experimental data. According to three different methods for the spin assignment of rotational bands, the spin values of the band head I₀ of the yrast SD bands in ¹⁹⁴Hg(1) and ¹⁹⁴Pb(1) are assigned. Furthermore, the physical meaning of the nuclear softness is discussed, and these nuclear softness values of a signature partner are almost equal.     

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.     

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.     

Isospin and Symmetry Structure in 36Ar

The interacting boson model-3(IBM-3) has been used to study the isospin excitation states and electromagnetic transitions for ³⁶Ar nucleus. The mixed symmetry states and superdeformed band at low spin are also analyzed. The theoretical calculations are in agreement with experimental data, and the ³⁶Ar is superdeformed rotational nucleus close to the SU(3) limit. The present calculations indicate that the 2₄⁺ state is the lowest mixed symmetry state and the lowest isospin T=1 excitation state and at about 6.2 MeV, and the bandhead of superdeformed band is 0₂⁺ state.     

Cranked Skyrme–Hartree–Fock calculation for superdeformed and hyperdeformed rotational bands in N=Z nuclei from S to Cr

With the use of the symmetry-unrestricted cranked Skyrme–Hartree–Fock method in the three-dimensional coordinate-mesh representation, we have carried out a systematic theoretical search for the superdeformed and hyperdeformed rotational bands in the mass A=30–50 region. Along the N=Z line, we have found superdeformed solutions in ³²S, ³⁶Ar, ⁴⁰Ca, ⁴⁴Ti, and hyperdeformed solutions in ³⁶Ar, ⁴⁰Ca, ⁴⁴Ti, ⁴⁸Cr. The superdeformed band in ⁴⁰Ca is found to be extremely soft against both the axially symmetric (Y₃₀) and asymmetric (Y₃₁) octupole deformations. An interesting role of symmetry breaking in the mean field is pointed out.     

127La转动带及带终止

组态相关推转壳模型 Nilsson势研究了 C.M.Parry组最近用 EUROBALL谱仪观测到的 12 7La高自旋态结构 .实验上观测的 12 7La的宇称和辛量子数为 (π,α) =(+,- 1 /2 )的带自旋达到(83/2 ) h.理论计算结果表明该带可能具有组态 π(h11/2 ) 2 ν(h11/2 ) 6.并且几乎达到该带的带终止理论预言值 I=47.5h.该带的形变在 I≤ 40 h内处于正常形变区 (ε2 ≈ 0 .2 2 ,γ≈ 0°) ,随着角动量的增加 γ值逐渐增加 ,直到 γ=60°时带终止. HJ4/9]The configuration dependent shell correction approach with cranked Nilsson potential is employed for explaining the experimental high spin spectra in 127 La. The experimental high spin band with parity and signature (+, -1/2) consists of two parts with a crossing around I =20 . It is most like to have the configuration [02, 6], π (h 11/2 ) 2 ν (h 11/2 ) 6 and almost reaching the maximum angular momentum at I =47.5 . It is in normal deformation region with ...     

Total Routhian Surface Calculations on Hf Isotopes

The two-dimensional total routhian surface calculations have been carried out to study the triaxial superdeformed structure of a neutron-rich nucleus ¹⁷³Hf firstly. In particular the effects of the rotational frequency ω and pairing-energy gap parameter Δ are discussed in detail in the course of shaping its triaxial superdeformation; additionally the neutron-shell correction energy is analyzed with emphasis in the confirmed triaxial superdeformed nucleus ¹⁷³Hf. Finally, more systematical results have been investigated for some confirmed superdeformed nuclei experimentally and a few predicted triaxial superdeformed nuclei theoretically with quadropole deformation ε₂≈0.4 and triaxial deformation γ≈20^º or 30^º in the Z=72 region.     

Band head spin assignment of superdeformed bands in Hg isotopes through power index formula

The power index formula has been used to obtain the band head spin(I_0) of all the superdeformed(SD) bands in Hg isotopes. A least squares fitting approach is used. The root mean square deviations between the determined and the observed transition energies are calculated by extracting the model parameters using the power index formula. Whenever definite spins are available, the determined and the observed transition energies are in accordance with each other. The computed values of dynamic moment of inertia J~((2)) obtained by using the power index formula and its deviation with the rotational frequency is also studied. Excellent agreement is shown between the calculated and the experimental results for J~((2)) versus the rotational frequency. Hence, the power index formula works very well for all the SD bands in Hg isotopes expect for ~(195)Hg(2, 3, 4).     

Rb晕带signature反转的机理

将角动量投影壳模型应用到84Rb核，对组态为πg9/2νg9/2的正宇称晕带和组态为π(p3/2,f5/2)νg9/2的负宇称晕带理论计算和实验结果进行了比较，特别是对正宇称晕带中的signature反转机理进行了探讨.角动量投影壳模型计算显示正宇称晕带中的signature反转是原子核随自旋增加形状发生变化的信号，其间原子核从低自旋的长椭球通过三轴形变变到高自旋的扁椭球.此外，还确定了此两带的原子核形状.     

Rotational co-existence in selenium isotopes

High spin states of ^72,73,74Se nuclei are discussed using calculations from the cranked Nilsson Strutinsky method with tuning to fixed spins. The low spin anomaly in the yrast bands of these nuclei is interpreted in a rotational co-existence picture. High K rotational isomers are proposed for I ^π =4⁺ in ⁷²Se and 6⁺ in ⁷⁴Se.     

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.     

Superdeformed band in Gd. First observation of band crossing

A discrete superdeformed band is found in ¹⁴⁶Gd. Lifetime measurements yield an average quadrupole moment of 12±2 e b. A band crossing corresponding to an alignment of ≈2 is observed at a rotational frequency of 0.65 MeV. A theoretical analysis suggests that the band has a π6²v7¹ configuration with odd spins and odd parity. Arguments are given that the [651 1/2] and [642 5/2] single-particle states are involved in the band crossing.