Nuclear Structure and Electromagnetic Transitions Investigation in Er Isotopes within Framework of Interacting Boson Model

Interacting Boson Model-2 (IBM-2) is used to determine the Hamiltonian for Er nuclei. Fit values of parameters are used to construct the Hamiltonian, energy levels and electromagnetic transitions (B(E2), B(M1)) multipole mixing ratios (δ(E2/M1)) for some even-even Er nuclei and monopole transition probability are estimated. New ideas are used for counting bosons number at N = 64 and results are compared with previous works.     

Nuclear structure of <Superscript>128–140</Superscript>Nd in IBM

We determined the most appropriate Hamiltonian that is needed for calculations of nuclei in the A ≅ 130 region from the viewpoint of the interacting boson model (IBM). Using the best-fitted values of parameters in the Hamiltonian, we have calculated energy levels and B(E2) values for a number of transitions in some doubly even Nd nuclei of 128 ⩽ N ⩽ 140. The results were compared with the previous experimental and theoretical data, and it is observed that they are in good agreement. The calculations have been extended to Nd isotopes for which some B(E2) values are still not known. The text was submitted by the author in English.     

Microscopic interacting boson model calculations for even-even <Superscript>128–138</Superscript>Ce nuclei

In this study, we determined the most appropriate Hamiltonian that is needed for the present calculations of energy levels and B(E2) values of ^128–138Ce nuclei which have a mass around A≅130 using the interacting boson model (IBM). Using the best-fitted values of parameters in the Hamiltonian of the IBM-2, we have calculated energy levels and B(E2) values for a number of transitions in ^{128,130,132,134,136,138}Ce. The results were compared with the previous experimental and theoretical (PTSM model) data and it was observed that they are in good agreement. Also some predictions of this model have better accuracy than those of PTSM model. It has turned out that the interacting boson approximation (IBA) is fairly reliable for calculating spectra in the entire set of ^{128,130,132,134,136,138}Ce isotopes and the quality of the fits presented in this paper is acceptable.      

U(5)-SU(3) nuclear shape transition within the interacting boson model applied to dysprosium isotopes

In the framework of the interacting boson model (IBM) with intrinsic coherent state, the shape Hamiltonian from spherical vibrator U(5) to axially symmetric prolate deformed rotator SU(3) are examined. The Hamiltonian used is composed of a single boson energy term and quadrupole term. The potential energy surfaces (PES’ s) corresponding to the U(5)-SU(3) transition are calculated with variation of a scaling and control parameters. The model is applied to ^150–162Dy chain of isotopes. In this chain a change from spherical to well deformed nuclei is observed when moving from the lighter to heavier isotopes. ¹⁵⁶Dy is a good candidate for the critical point symmetry X(5). The parameters of the model are determined by using a computer simulated search program in order to minimize the deviation between our calculated and some selected experimental energy levels, B(E2) transition rates and the two neutron separation energies S_2n. We have also studied the energy ratios and the B(E2) values for the yrast state of the critical nucleus. The nucleon pair transfer intensities between ground-ground and ground-beta states are examined within IBM and boson intrinsic coherent framework.     

中重核中单粒子与集体运动的竞争效应(英文)

从原子核的电四极跃迁强度B（E2）中可以提取出原子核集体性和单粒子性质竞争的重要信息,其中一个重要的观测量是B（E2;4₁+ →2₁+）/B（E2;2₁+ →g.s.）的比值（B_4/2）。B_4/2一般要大于1,而且对于原子核转动和振动,我们应有B_4/2=1.4和2.0,但球形半满壳核一般会有不一样的性质。这些核的性质主要受对关联效应影响。介绍了几种超出我们一般认识的奇特衰变性质。Te同位素的基态带有鲜明的振动特性,但114Te的E2跃迁性质却更符合转动性。这些性质可以通过大规模壳模型计算来描述。对于填充j=9/2轨道的半满壳核,它们的4+和6+显示出很强的辛若数部分守恒性质。这种奇特的部分守恒可以被解析证明。而且我们的计算表明辛若数部分守恒对相关的E2跃迁影响很大。对于N=90附近具有量子相变行为的核素,其B_4/2也会也表现出相似的奇异特性。The E2 transition strength, B(E2), gives particularly precise information on the competition between the collective and single-particle degree of freedom. An important observable to study the development of collectivity is the B(E2; 4₁+ →2₁+)/B(E2; 2₁+ →g.s.) (B_4/2). The B_4/2 ratio is usually greater than unity. These values are 1.4 and 2.0 for an ideal rotor and a vibrator, respectively. Whereas the seniority scheme usually leads to different behaviours. In this contribution I will show examples that contrast with our standard understanding. The yrast spectra of Te isotopes show a vibrational-like equally-spaced pattern but the few known E2 transitions show anomalous rotational-like behaviour, which cannot be reproduced by collective models. Large-scale shell model calculations reproduce well the equally-spaced spectra of those isotopes as well as the constant behaviour of the B(E2) values in 114Te. For nuclei involving protons or neutrons in j=9/2 orbitals, the partial conservation of seniority can lead to dramatic changes to the E2 decay pattern that have never been seen before. The B_4/2 ratios in quantum phase transitional nuclei around N=90 also show a similar exotic feature.     

原子核过渡区的量子相变

在相互作用玻色子模型(IBM) 基础上用O(6) 高阶项代替传统的SU(3) 四极-四极相互作用来研究原子核从振动到转动过渡区的量子相变行为。利用U(5)-SU(3) 和UQ 两种方案,在玻色子数分别为N = 8 和N = 20 不同情况下,研究了原子核的一些低激发态的能级比和电四极跃迁比。结果表明:随着玻色子数N 的增大,系统的量子相变行为得到加强;两种方案都可以用来描述从振动到转动过渡区的原子核的量子相变特征且O(6) 高阶项方案下量子相变行为更为明显。在此基础上,进一步应用这两种方案具体讨论了152Sm 核的低激发态能级和电四极跃迁性质并与实验数据进行对比分析。结果表明,用O(6) 高阶项可以更为合理地描述带内跃迁及不同带之间的带间跃迁性质。With the framework of Interacting Boson Model(IBM), transitional patterns from the spherical to the axially deformed limit of the IBM with a schematic Hamiltonian are studied by replacing the SU(3) quadrupole-quadrupole term with O(6) cubic interaction. But, we use the two schemes to investigate some energy ratios and B(E2) ratios for different bosons N = 8 and N = 20. The results show that with the increasing of the numbers of bosons, the transitional behaviors can be enhanced; the transitional behaviors are very similar in the two schemes. However, there are some distinctive differences for some quantities across the entire transitional region, such as energy levels and ratios, B(E2) values and ratios, and expectation values of the shape variables. Generally speaking, the transition is smoother and the nuclear shape is less well defined in the new scheme. Then we apply the two schemes to the critical point symmetry candidate, such as 152Sm, and find the overall fitting quality of the UQ scheme is better than that of the U(5)-SU(3) scheme, especially for the inter-band E2 transitions in 152Sm.     

带三体势的IBM1的O(6)极限对偶偶Pt核的应用

通过在IBMI哈密顿中,引入一种简单的等效三体势,O(6)核能谱可得到不同程度的修正.本文具体计算了^192—198Pt偶偶同位素核的能谱和E2跃迁几率,理论计算值与实验数据符合较好.     

偶偶Ge和Se同位素核的形变HF态及负宇称带研究

将具有负宇称的fp轨道空间扩大到包含具有正宇称的1g_9/2轨道,采用修正的表面δ相互作用,对⁶⁴Ge,⁶⁶Ge,⁶⁸Ge,⁷⁰Se,⁷²Se和⁷⁴Se等6个偶偶核做了形变HF计算.得到了基态和一些激发态的解.同时,还用近似角动量投影形变Hartree-Fock(PDHF)方法,对⁶⁴Ge和⁷⁴Se进行了能谱计算,得到其正、负宇称带的解,计算结果与实验谱基本一致.     

Rare-earth nuclei and the pseudo-SU(3) model

An extended version of the pseudo-SU(3) model is used to describe low-energy positive-parity states of three rare-earth nuclei in a full proton-neutron formalism. Along with other residual interactions, the Hamiltonian includes the pairing which induces mixing between different representations of SU(3). Excitation energies, B(E2) values, B(M1) values, quadrupole moments, andg _R factors of¹³⁶Xe,¹³⁸Ba, and²⁰⁴Hg are calculated in a truncation free environment and the results are compared with the experimental data and other theories.     

Quasi-SU(3) truncation scheme for even–even sd-shell nuclei

The quasi-SU(3) symmetry was uncovered in full pf and sdg shell-model calculations for both even–even and odd–even nuclei. It manifests itself through a dominance of single-particle and quadrupole–quadrupole terms in a Hamiltonian used to describe well-deformed nuclei. A practical consequence of the quasi-SU(3) symmetry is an efficient basis truncation scheme. In [C.E. Vargas et al., Phys. Rev. C 58 (1998) 1488] it is shown that when this type of Hamiltonian is diagonalized in an SU(3) basis, only a few irreducible representations (irreps) of SU(3) are needed to describe the yrast band, the leading S=0 irrep augmented with the leading S=1 irreps in the proton and neutron subspaces. In the present article the quasi-SU(3) truncation scheme is used, in conjunction with a “realistic but schematic” Hamiltonian that includes the most important multipole terms, to describe the energy spectra and B(E2) transition strengths of ^20,22Ne, ²⁴Mg and ²⁸Si. The effect of the size of the Hilbert space on both sets of observables is discussed, as well as the structure of the yrast band and the importance of the various terms in the Hamiltonian. The limitations of the model are explicitly discussed.     

Coulomb excitation of radioactive 132,134,136Te beams and the low B(E2) of 136Te

The B(E2;0(+)-->2+) values for the first 2+ excited states of neutron-rich 132,134,136Te have been measured using Coulomb excitation of radioactive ion beams. The B(E2) values obtained for 132,134Te are in excellent agreement with expectations based on the systematics of heavy stable Te isotopes, while that for 136Te is unexpectedly small. These results are discussed in terms of proton-neutron configuration mixing and shell-model calculations using realistic effective interactions.     

Isovector magnetic dipole sum rules in (d s)- shell

Linear-energy weighted sum-rules (LEWSR) are calculated for isovector magnetic dipole transitions from the ground state in some (d s)-shell nuclei. It is found that the well-known Kurath sum rule is inadequate to explain the experimental transition strengths in these nuclei. A significant contribution to the sum-rule is seen to arise from the two-body part of the Hamiltonian. The calculations are made using the spectral distribution methods.     

原子核的反常宇称能谱研究

将具有负宇称的 fp 空间扩大到包含1g9/2 轨道, 采用修正的表面相互作用(MSDI), 对64Ge, 66Ge, 68Ge, 70Se, 72Se, 74Se, 76Kr 和 78Kr等偶偶核作了形变Hartree Fock计算, 得到了基态和一些激发态的解. 同时, 还用近似角动量投影形变Hartree Fock（PDHF）方法对偶偶核64Ge, 74Se和奇A核79Kr进行了能谱计算, 得到其正、 负宇称带的解, 计算结果与实验谱基本一致.Using modified surface delta interaction, enlarging the fp configuration space to include the 1g9/2 orbit with the abnormal parity, the deformed Hartree Fock calculations for the eight nuclei: 64Ge, 66Ge, 68Ge, 70Se, 72Se , 74Se, 76Kr and 78Kr are performed. The ground state and some particle hole excited configurations are obtained. The approximate angular momentum projected deformed Hartree Fock (PDHF) method is applied to even even nuclei 64Ge and 74Se and odd A nuclus 79Kr. Both of their normal and abnormal parity bands are obtained. The calculated energy spectra are consistent well with experimental spectra.     

E0 transition and coupling between quadrupole and pairing-vibrational modes

Using a theory of mode-mode coupling between the two-phonon 0⁺ mode and the pairing-vibrational mode, we have extensively investigated the first excited 0⁺(0₂²) states in spherical and transitional nuclei. The results tell us that the 0₂⁺ states in a wide range of nuclei are strongly mixed states of both the modes. By making use of these results, the matrix elements for the E0 transitions from the 0₂⁺ states to the ground states are calculated for the Zn, Ge, Se, Kr, Sr, Zr, Mo, Ru, Pd, Cd and Sn isotopes. For some of the Cd and Sn isotopes, the matrix elements between the 0₂⁺ and 0₂⁺ states are also obtained. These numerical calculations make a rather good fit to the E0 experiments.     

用推转玻尔-莫特森哈密顿量研究A～190区超形变带

用推转玻尔－莫特森哈密顿量研究了Ａ～１９０区２０个核的５５条超形变带．通过拟合实验测得的Ｅ２跃迁能量值，确定了各带的能级自旋，得到了质量参量Ｂ１和硬度参数Ｃ０．Ｂ１和Ｃ０都显示出明显的奇偶性. superdeformed bands in 20 nuclei of the A ～190 region are studied with formulas derived from the Cranking Bohr Mottelson Hamiltonian. From fitting the experimental E γ , the level spins are determined and mass parameter B 1 and rigidity parameter C 0 are obtained. The B 1 and C 0 values show clear odd even effects.     

Influence of giant angular resonances on the electromagnetic characteristics of low-lying states

The two-rotor model0 with the Feshbach projection operator method is applied for investigating the properties of the positive parity low-lying collective states in the rare earth nuclei. The calculations of the energy spectra, E2-transition probability and magnetic properties of the states of β- and γ-bands are carried out for the isotopes ^{164, 166, 168}Er. The B(M1) values from 1⁺ states to the ground band are estimated.     

ON THE MECHANISM OF BACKBENDING PHENOMENA OF SOME EVEN-EVEN NUCLEI

The energy levels, B(E2) values and gyromagnetic ratio g of some even-even nuclei have been calculated with a double band scheme of band-crossing. Based on these results, the mechanism of backbending phenomena is analyzed, and the possible criterion to distinguish the effects of shape transition, rotation-alignment and pairing collapse are also discussed.     

Quasi-exactly solvable decatic model description of nuclei near the X(5) critical point

The Bohr Hamiltonian with axially deformed shape confined in a quasi-exactly solvable decatic β-part potential is studied.It is shown that the decatic model can well reproduce the X(5)model results as far as the energy ratios in the ground and beta band and related B(E2)values are concerned.Fitting results to the low-lying energy ratios and relevant B(E2)values of even-even X(5)candidates ¹⁵⁰Nd,¹⁵⁶Dy,¹⁶⁴Yb,¹⁶⁸Hf,¹⁷⁴Yb,^176,178,180Os,and ^188,190Os show that the decatic model provides the best fitting results for the energy ratios,while the X(5)model is the best at reproducing the B(E2)values of these nuclei,in which the beta-bandhead energy is lower than that of the gamma band.While for even-even nuclei,such as ^154,156,158Gd,with bandhead energies of the beta and gamma bands more or less equal within the X(5)critical point to the axially deformed region,our numerical analysis indicates that the decatic model is better than the X(5)model in describing both the low-lying level energies and related B(E2)values.     

In-beam γ-spectroscopy with relativistic radioactive ion beams

This work demonstrates the feasibility of in-beam %-spectroscopy employing radioactive ion beam species at relativistic energies of E = 210 ~ 280 A · MeV. Neutron-rich nuclei below ⁴⁸Ca with neutron number between the two magic numbers 20 and 28 have been investigated. Using a Pb target, single step inelastic excitation originating mainly from Coulomb interaction takes place populating preferentially low-lying low-spin states and enabling the extraction of B(E2) values. On a C target, nucleon removal reactions are dominating and medium-spin states are populated thus offering spectroscopic information in neighboring nuclei. Cross sections of inelastic excitation are determined and compared to coupled-channels calculations. Two new states of the very neutron-rich nucleus ⁴⁴Ar at 1.78(8) MeV and 2.61(16) MeV are deduced from %-transitions.