Magnetic rotation — past,present and future

Magnetic-dipole rotational (MR) bands were discovered about 15 years ago without any theoretical prediction in contrast to the super-deformed (SD) bands which were predicted long ago. First identification of a quasirotational structure as MR band occurred around 1992 although Kr isotopes probably have the first set of data having the signatures of MR bands as shown by us. Our first compilation of MR bands listed 120 MR bands in 56 nuclides which have now grown to more than 180 bands in 80 nuclides. We have observed new MR bands in the A = 130 mass region in ¹³⁷Pr, ¹³⁹Nd and ¹³⁵Ba nuclei. This led to the observation of the smallest MR bands in ¹³⁷Pr, multiple minima in the γ deformation in ¹³⁵Ba, coexistence of band structure based on these minima and band crossing of MR bands in A = 130 region. Some of these results have been reviewed in this paper along with theoretical calculations. There are still a number of questions related to MR bands which have not been fully resolved. The role of neutrons/protons in magnetic rotation still needs to be delineated. Do the MR bands follow the I(I + 1) behaviour? Are these structures as regular as normal rotational bands? How important is the existence of deformation for MR bands? We address some of these questions in this paper.     

Dipole bands in nucleus ~(139)pm

High-spin states in nucleus (~139)Pm have been studied using the reaction ~(116)Cd(~(27)Al, 4n)~(139)Pm. Two dipole cascades have been found. Spin and parity assignments were based on the Directional Correlation of Oriented Nuclei (DCO) ratios and systematic behavior in neighboring odd-proton nuclei. The level structures of ~(139)pm are compared with those of the N = 78 isotone ~(141)Eu in which two dipole bands have been confirmed as magnetic rotational bands. The close similarity between them suggests that the dipole bands in ~(139)Pm may be magnetic rotational bands.     

Vibration-rotation bands of hydrogen halides dissolved in liquefied noble gases

Fundamental absorption bands of hydrogen halides have been studied in dilute solutions in liquefied Ar, Kr, and Xe. The second band moments obtained from experimental profiles are in agreement with the theoretical values for vibration-rotation bands. Extensive rotational structure of the HCl and HF bands has been recorded in Kr and Xe solutions. The observed rotational lineshifts and linewidths are compared with the available gas phase data.     

Average g-factors for high-spin states in 78Kr

Inverse reactions of ^{63, 65}Cu beams on ^{18, 16}O targets have been used to populate states of ⁷⁸Kr by fusion-evaporation reactions. The excited nuclei recoiled at high velocity v/c ≈ 7 % through a polarized iron (⁵⁴Fe) layer and were stopped in a copper layer. During the period in iron, 0.05–0.65 ps, the nuclei were subjected to the intense transient magnetic field (initially ～ 3500 T). The resulting precession of the high-spin nuclear states populated during this time was determined by measuring the time integral rotation angle of the discrete γ-ray transitions at low spin.The average g-factor at low spin 2 ≦ J ≦ 8 compared to that at higher spin 8 ≦ J ≦ 12 in ⁷⁸Kr was found to be identical within the experimental uncertainties of ～ 15 %. This result implies that either there are no rotational alignment effects at the backbend in ⁷⁸Kr or more plausibly, proton (g ≈ 1) and neutron (g ≈ 0) aligned bands are equally competitive and both populated in the reaction. It is then likely that the resulting g-factor represents an average over many populated proton and neutron aligned bands.     

Band crossing phenomena inN=Z nuclei a probe toT=0 pairing correlations?

The structure of theN=Z nuclei⁶⁰Zn,⁶²Ga,⁶⁴Ge, and⁷²Kr has been investigated at GASP. Total Routhian surface (TRS) calculations have been performed for theN=36, 38 and 40 Kr isotones. In the case of⁷²Kr the four quasi-particleg _9/2 alignment is observed to be significantly delayed in rotational frequency with respect to the heavier Kr isotopes. Such a delay contradicts the predictions of mean field calculations and may be viewed as the first sign of additional correlations in theT=0 pairing channel.     

Dipole bands in nucleus ~(139)Pm

High-spin states in nucleus 139Pm have been studied using the reaction 116Cd(27Al,4n)139Pm.Two dipole cascades have been found.Spin and parity assignments were based on the Directional Correlation of Oriented Nuclei(DCO) ratios and systematic behavior in neighboring odd-proton nuclei.The level structures of 139Pm are compared with those of the N =78 isotone 141Eu in which two dipole bands have been confirmed as magnetic rotational bands.The close similarity between them suggests that the dipole bands in 139...     

Deformed shell model for T = 0, 1 and 2 bands in <Superscript>52</Superscript>Fe and <Superscript>72</Superscript>Kr

Deformed configuration mixing shell model based on Hartree-Fock states with extension to include isospin projection (DSMT) for two- and four-particle configurations (generated by particle-hole excitations) is applied to study the structure of the low-lying T = 0, 1 and 2 bands (or levels) in the even-even N = Z nuclei ⁵²Fe and ⁷²Kr. The pf-shell KB3 interaction for ⁵²Fe and a modified Kuos interaction for ⁷²Kr are employed in the calculations. In this first application of DSMT with four-particle T projection, low-spin (J 10) members of the T = 0, 1 and 2 bands in ⁵²Fe are compared with experiment including the known E2 transition strengths. The agreement between DSMT and experiment is reasonably good. Similarly, the low-spin members of the observed (prolate) yrast band in ⁷²Kr are also well described by DSMT.     

Sp(4, R) symmetry in light nuclei

A classification of nuclear states according to the non-compact Lie algebra Sp(4, R) is investigated. This model strikes a compromise between the Sp(6, R) and Sp(2, R) models and furnishes a practical, yet algebraically simple means for selecting those shell-model core excitations which are needed for the development of quadrupole collectivity in rotational bands of deformed nuclei. Applications to rotational bands in ²⁴Mg and ¹⁶O, including shell-model excitations with excitation energies up to 10?ω, show that the core excitations needed to fit observed E2 rates in these nuclei are too large to be treated by perturbation theory. Despite this, a definite symplectic band structure emerges. The nature of the core excitations is very simple, so that it may be feasible to incorporate such symplectic excitation structures into more detailed shell-model calculations.     

双奇核172Re的高自旋

对149Sm(27Al, 4n)172Re反应产生的172Re在束γ的实验数据进行了重新分析, 新发现了可归属于172Re的3个转动带, 由此建立了由6个转动带构成的172Re高自旋态能级纲图。依据相邻核的带结构知识和推转壳模型分析方法, 对新发现的3个转动带的准粒子组态进行了指定, 讨论了它们的转动特征。We have re analyzed the experimental data of in beam γ spectroscopy for 172Re via the 149Sm(27Al, 4n)172Re reaction. Three rotational bands have been newly found and assigned to 172Re. A new level scheme of 172Re, consisting of 6 bands, is thus presented. Based on the existing knowlegde from the neighboring nuclei and the cranked shell model, the quasiparticle configurtions have been assigned to the 3 newly observed bands and their structure properties have been dicussed.     

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.     

Shape coexistence and evolution in neutron-def icient krypton isotopes

Total Routhian Surface(TRS) calculations have been performed to investigate shape coexistence and evolution in neutron-deficient krypton isotopes72,74,76 Kr. The ground-state shape is found to change from oblate in72 Kr to prolate in74,76 Kr, in agreement with experimental data. Quadrupole deformations of the ground states and coexisting 0+2states as well as excitation energies of the latter are also well reproduced. While the general agreement between calculated moments of inertia and those deduced from observed spectra confirms the prolate nature of the low-lying yrast states of all three isotopes(except the ground state of72Kr), the deviation at low spins suggests significant shape mixing. The role of triaxiality in describing shape coexistence and evolution in these nuclei is finally discussed.     

Levels in 74Se, 78, 80Kr and 84Sr and systematics of quasi-γ bands

Quasi-band structures in ⁷⁴Se, ^{78, 80}Kr and ⁸⁴Sr have been investigated using (p, 2nγ) reactions. The members of the quasi-γ band have been observed up to 5⁺ in ⁷⁴Se, ^{78, 80}Kr and up to 3⁺ in⁸⁴Sr. The analyses of the energy systematics of the quasi-γ bands studied in this mass region as well as in other regions make clear the evolution of the quasi-γ band to the γ-band in well-deformed nuclei. In addition to these positive-parity bands, negative-parity levels were observed in ⁷⁴Se, ⁸⁰Kr and ⁸⁴Sr.     

Persistence of rotational bands in a coupled SU(3) model

To understand better the emergence of rotational structures in a variety of situations, a model in which two SU(3) irreps are coupled via a quadrupole-quadrupole (Q·Q) interaction is considered. Strong coupling of different SU(3) irreps gives rise to low-lying rotor bands. We study the excited bands that occur and the perturbation effects of the rotational decoupling. Persistence of rotational-like bands for a large range of coupling strengths is observed. However, although for very weak interaction strengths the electromagnetic transition rates are consistent with those of the rotor model, the excitation energy ratios look more vibrational, a phenomenon which has been observed in many nuclei.     

High-spin structure of N\simeq Z nuclei around the A = 72 region

High-spin states have been studied in ⁷²Kr and ⁷²Br using the ⁴⁰Ca + ⁴⁰Ca and ³⁶Ar + ⁴⁰Ca reactions at 164 and 145 MeV, respectively. The properties and configurations of the high-spin bands observed have been interpreted using unpaired cranked Nilsson-Strutinsky (CNS), and for ⁷²Kr, paired cranked relativistic Hartree-Bogoliubov (CRHB) calculations. In ⁷²Kr a new band has been identified that has the properties expected for the doubly aligned S-band configuration. In ⁷²Br the previously known bands have been extended to higher spin. This has lead to a re-interpretation of the configurations.Received: 31 October 2002, Published online: 24 February 2004PACS: 21.10.Re Collective levels - 23.20.Lv transitions and level energies - 27.50. + e      

The Interacting Boson Model of Dipole-Octupole Strong Correlations in SU(3) Limit for Positive Parity States

Within the framework of the Usdpf(16) interacting boson model (IBM), the effects of strong correlations of the dipole (p--boson) and the octupole (f--boson) degree of freedom on the positive-parity states of even-even nuclei in SU(3) limit are discussed. It is shown that configurations of an even number of many p- and f-bosons can not only be incorporated into the usual low-lying collective rotational bands, such as the ground state band, β- and γ-vibrational bands, but also naturally form the Kπ＝ 1+, 3+ rotational bands, etc. These results are similar to that of Usdg (15)-IBM and in agreement well with the experimental data of the 176 72 Hf 104 nucleus. Besides, several intraband E2 transition probabilities are given, which are consistent with that of Usd(6)-IBM.     

A microscopic description of boson and fermion alignment in octupole bands of actinide nuclei

The rotational alignment of the octupole boson in negative-parity bands of actinide nuclei is investigated in the framework of the cranked random-phase approximation (CRPA).     

Magnetic rotation and chiral symmetry breaking

The deformed mean field of nuclei exhibits various geometrical and dynamical symmetries which manifest themselves as various types of rotational and decay patterns. Most of the symmetry operations considered so far have been defined for a situation wherein the angular momentum coincides with one of the principal axes and the principal axis cranking may be invoked. New possibilities arise with the observation of rotational features in weakly deformed nuclei and now interpreted as magnetic rotational bands. More than 120 MR bands have now been identified by filtering the existing data. We present a brief overview of these bands. The total angular momentum vector in such bands is tilted away from the principal axes. Such a situation gives rise to several new possibilities including breaking of chiral symmetry as discussed recently by Frauendorf. We present the outcome of such symmetries and their possible experimental verification. Some possible examples of chiral bands are presented.     

Pseudobands in non-SU(3) odd-mass nuclei and coherent state structures of quadrupole phonons

Ground state symmetric rotor bands are described as coherent-state structures of deformation in a quadrupole-phonon model. These structures are shown to be very different from the phonon composition of pseudobands which are culled from the excited state spectrum of nuclei such as⁷⁵Se,⁷⁵Kr, and⁷⁷Kr. The pseudobands are shown to be only a subset of more complete excitation spectra, which occur in most unique-parity odd-nucleon nuclei with a transitional core and can be expected to occur throughout the chart of the nuclides.     

Particle-Number Conserving Analysis for High K Multi-Quasiparticle Bands in Odd-A Deformed Nuclei 173,175Hf

Using the Particle-number Conserving (PNC) method for treating the cranked shell model, the high K multi-quasiparticle bands in odd-A deformed nuclei ^173,175Hf are analyzed, including the variation with rotational frequency of the moment of inertia, angular momentum alignment and occupation probability of each cranked Nilsson orbital. No free parameters are involved in the PNC calculation and the experimental results are reproduced well. The microscopic mechanism of the difference between the multi-quasiparticle high K bands and the yrast bands in neighboring even-even nuclei is investigated, where the blocking effects of high j intruder orbitals near the Fermi surface play a crucial role.