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.     

The decay-out of superdeformed bands in theA=190 region: What have we learned?

One-step decay transitions linking the superdeformed (SD) bands 1 and 3 in¹⁹⁴Hg to yrast levels are discussed. Inter-band transitions between bands 1 and 3 have also been identified. For the first time, the spin, parity and excitation energy have been determined for two SD bands in the same nucleus. The low excitation energy of the excited band supports the view that it is based on an octupole excitation. It is believed that Porter-Thomas fluctuations play a major role in determining the strength of the one-step transitions as suggested by the fact that only one other SD band has been linked in theA=190 mass region (¹⁹⁴Pb) at the present time. When Porter-Thomas fluctuations prevent the observation of one-step or two-step linking transitions, as e.g. in the case of¹⁹²Hg, the analysis of the quasi-continuous part of the decay-out spectrum provides an alternative method for the determination of the excitation energy and spin of an SD band. This method is discussed in detail.     

Octupole vibrations of the superdeformed196Pb nucleus

The study of the superdeformed (SD)¹⁹⁶Pb nucleus has been revisited using the Eurogam Phase 2 spectrometer. All of the three observed excited SD bands were found to decay to the yrast SD band through, presumably,E1 transitions, allowing relative spin and excitation energy assignments. Comparisons with calculations using the random-phase approximation suggest that all three excited bands can be interpreted as octupole vibrational structures.     

Superdeformed bands in194Tl

Two superdeformed (SD) bands have been found in¹⁹⁴Tl using the reactions¹⁷⁶Yb(²³Na,5n) and¹⁸¹Ta(¹⁸O,5n). The mass assignments were made from excitation function data. These are the first SD bands found in the mass-190 region that are not in Hg nuclei. The energies of many of the transitions of one of these new SD bands are similar in energy to those in the SD band of¹⁹²Hg.     

Simple model calculations of spin and quantized aligment for the A ∼ 60–90 superdeformed mass region

We have used a simple model based on the rotational energy formula E(I, K) to study the structure of the superdeformed (SD) mass region 60–90. The higher order inertial parameters A and B of such model were determined by using the Marquardt method of nonlinear least-squares routines to fit the proposed transition energies with their observed values. A good agreement between the calculated and corresponding experimental transition energies of the SD bands is obtained which supports our proposed model. In addition, the frequency dependence of the dynamic, θ⁽²⁾, and static, θ⁽¹⁾, moments of inertia is used to determine the lowest spin (I_f) and the K-value of the considered SD bands; namely, ⁵⁸Ni(b1), ⁵⁸Cu, ⁵⁹Cu(b1), ⁶¹Zn, ⁶²Zn, ⁶⁵Zn, ⁶⁸Zn, ⁸⁴Zr, ⁸⁶Zr(b1), ⁸⁸Mo(b1, b2, b3) and ⁸⁹Tc. As a result of the identity exist among some of the considered SD bands, we have studied the incremental alignment and also the angular momentum alignment.     

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.     

Lifetime measurements and decay of superdeformed bands in Hg isotopes

The lifetimes of states in Superdeformed (SD) bands in ^192,194Hg have been measured using the Doppler shift attenuation method. Intrinsic quadrupole moments have been extracted for band 1 of ¹⁹²Hg and for bands 1, 2, and 3 of ¹⁹⁴Hg. It was found that the quadrupole moments for the “identical” SD bands in these nuclei are the same. In the same experiment, one-step transitions linking SD states to yrast and near yrast states for bands 1 and 3 of ¹⁹⁴Hg have been identified. From this observation, excitation energies, spins and probable parities have been assigned to SD states in these bands.     

Evidences for magicity in superdeformed shapes

Many empirical evidences that point to the existence of preferred magic nucleon numbers for superdeformed (SD) shapes are presented in this paper. We use a simple premise based on the 4-parameter formula fitted using observed γ-rays of SD bands. In particular, plots of γ-ray energy ratios, nuclear softness parameter values and the number of SD bands for given N and Z are used to pinpoint the magicity (N, Z numbers) that are most favoured as the SD magic numbers. This analysis also leads to several new predictions on the occurrence of SD bands specially in neutron-rich nuclei.     

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.     

Superdeformed bands in195Tl

Two superdeformed (SD) bands have been found and assigned to¹⁹⁵Tl on the basis of excitation function and cross bombardment results. The two bands are almost identical in transition energies to those observed in¹⁹³Tl. They are signature partners with a splitting, presumably due to the proton i_13/2 (=5/2) orbital, characteristic of all known SD bands in the thallium isotopes. Their alignments relative to the¹⁹³Tl bands were found to be zero.On leave from Comision National de Energia Atomica 1429 Buenos Aires, Argentina.     

Quadrupole moments of superdeformed bands in 193Tl

Lifetimes of states in the two strongest superdeformed (SD) bands in ¹⁹³Tl were measured using the Doppler-shift attenuation method. The reaction ¹⁷⁶Yb(²³Na,6n)¹⁹³Tl at a beam energy of 129 MeV was used and γ-rays were detected by the Gammasphere array. Quadrupole moments of 18.3(10) eb and 17.4(10) eb were extracted for SD bands 1 and 2, respectively, using the fractional Doppler-shifts of the SD transitions. The previously reported linking transitions of these SD bands to normal deformed near yrast levels could not be confirmed. No other candidates for linking transitions could be established. Received: 27 April 1999     

Band terminations in valence-space and core-excited configurations in102Pd

The level structure of¹⁰²Pd has been investigated using the Eurogam Phase2 array. Termination of rotational bands has been observed atI=28^? andI=32⁺, and tentatively atI=38⁺ andI=42⁺. Three other bands evolving towards termination have also been identified. These terminating bands are explained in terms of valence-space and core-excited configurations.     

Systematic study of rotational energy formulae for superdeformed bands in La and Ce isotopes

The experimental rotational spectra of superdeformed(SD) bands of ~(130)La, ~(131)Ce(1,2), ~(132)Ce(1,2,3) and133 Ce(1,2,3) in the A～130 mass region are systematically analyzed with the four parameter formula, power index formula, nuclear softness formula, and VMI model. It is observed that out of all the formulae, the four parameter formula suits best for the study of the ~(130)La, ~(131)Ce(1,2), ~(132)Ce(2,3) and ~(133)Ce(1,2,3) SD bands. The four parameter formula works efficiently in determining the band head spin of the ~(130)La, ~(131)Ce(1,2) ~(132)Ce(2,3) and ~(133)Ce(1,2,3) SD bands. Good agreement is seen between the calculated and observed transition energies whenever the accurate spin is assigned. In ~(132)Ce(1), the power index formula is found to work better than the other three formulae. The dynamic moment of inertia is also calculated for all the formulae and its variation with the rotational frequency is investigated.     

New results on the superdeformed 196Pb nucleus: decay of the excited bands to the yrast band

The study of the superdeformed ¹⁹⁶Pb nucleus has been revisited using the EUROGAMphase 2 array. In addition to the known yrast and two excited SD bands, a third excited SD band has been found. All of the three excited bands were found to decay to the yrast SD band through presumably E1 transitions. Comparisons with calculations using RPAapproximation indicate that the excited bands can be interpreted as octupole-vibrational structures.     

Collective and two-quasiparticle states in 158Gd observed through study of radiative neutron capture in 157Gd

The level structure of ¹⁵⁸Gd has been studied using the prompt γ-rays and conversion electrons emitted following neutron capture in ¹⁵⁷Gd. The γ-ray energy and intensity measurements were made using both Ge(Li) detectors and a curved-crystal spectrometer. Conversion-electron energy and intensity measurements were made using two separate magnetic spectrometers: one to measure the primary electron spectrum and the other to measure the lower energy secondary electron spectrum. Some γ-γ coincidence measurements were also made among the secondary γ-rays. From these data, a neutron separation energy of 7937.1 ± 0.5 keV has been determined for ¹⁵⁸Gd. A level scheme containing 59 excited states with energies < 2.25 MeV, for which de-excitation modes have been identified, is proposed for ¹⁵⁸Gd. Many of these states have been grouped into rotational bands. A total of thirteen excited rotational bands with band-head energies below 2.0 MeV are contained in the level scheme. Features of the proposed level scheme include: the K^π = 0^?, 1^? and 2^? octupole-vibrational bands with band-head energies of 1263, 977 and 1793 keV, respectively; the γ-vibrational band at 1187 keV; three excited K^π = 0⁺ bands with band-head energies of 1196, 1452 and 1743 keV; several two-quasiparticle bands with band-head energies in keV (and K^π assignments) of 1380 (4⁺), 1636 (4^?), 1847 (1⁺), 1856 (1^?), 1920 (4⁺) and 1930 (1⁺). An analysis of (d, p) reaction data is presented which permits definite two-quasiparticle configuration assignments to be made to most of these latter bands. Evidence is presented which suggests strong mixing of some two-neutron and two-proton bands. A phenomenological four-band mixing analysis is made of the energy and E2 transition-probability data for the ground-state band and the three lowest-lying excited collective positive-parity bands. Good agreement with experiment is obtained. A Coriolis-mixing analysis of the octupole bands has been carried out and good agreement with the data on level energies and E1 transition probabilities to the ground-state band has been achieved. Values of Z, the ratio of the E1 transition matrix element with ΔK = 1 to that with ΔK = 0, involving the octupole bands and the first four 0⁺ bands are derived. For three of these 0⁺ bands, absolute values of these matrix elements are deduced. An interesting alternation in the sign of Z is observed for these four 0⁺ bands.     

Anomalous behaviour of transition probabilities in75Kr

Two collective bands of⁷⁵Kr have been extended up to spin 21/2 using the compound reactions⁶⁴Zn(¹⁴N,p2n)⁷⁵Kr and⁵⁰Cr(²⁸Si, 2pn)⁷⁵Kr. Spins and parities were assigned from neutron-gatedγ-ray angular distributions and excitation functions using the OSIRIS anti-Compton spectrometer. The bands are interpreted to be built on the well-deformed Nilsson states: [442] 5/2 and [301] 3/2. Energies for both bands and the order of magnitude of the mixing ratios in thef _5/2 band can be reproduced within the single-particle-plus-rotor model, while the experimentalQ(I→I?1)/Q(I→I?2) ratios, deduced from mixing ratios and branching ratios, exhibit large deviations by a factor 4 to 6 from theoretical values (which are around one). An explanation of this effect may be found by treating the two rotational bands each as a result of mixing between rotational bands of oblate and prolate states; thus explaining the large difference between B(E2,I→I?1) andB(E2, I →I?2) in the bands of⁷⁵Kr.     

Microscopic aspects of identical bands in 78Sr and 78Rb

Recent investigations of the shape transition and shape coexistence phenomena dominating the structure of the even-even N ? Z nuclei in the A ? 80 mass region are extended to the odd-odd nucleus ⁷⁸Rb. Special attention is paid to the structure of some “identical” bands which have been recently identified in ⁷⁸ Sr and ⁷⁸Rb. The ground band of⁷⁸ Sr and the yrast as well as excited negative parity bands in ⁷⁸Rb are studied within the EXCITED VAMPIR approximation using complex Hartree-Fock-Bogoliubov transformations in a relatively large model space. The results are compared with the available experimental data. The emerging picture reveals the role played by the strong quadrupole deformation on the appearance of identical bands as well as the influence of the shape coexistence on their evolution. Predictions for the electromagnetic and alignment properties of the bands are presented.     

A reevaluation of the assignment of the vibrational fundamentals and the rotational analysis of bands in the high-resolution infrared spectra of trans- and cis-1,3,5-hexatriene

Assignments of the vibrational fundamentals of cis- and trans-1,3,5-hexatriene are reevaluated with new infrared and Raman spectra and with quantum chemical predictions of intensities and anharmonic frequencies. The rotational structure is analyzed in the high-resolution (0.0013-0.0018 cm⁻¹) infrared spectra of three C-type bands of the trans isomer and two C-type bands of the cis isomer. The bands for the trans isomer are at 1010.96 cm⁻¹ (ν₁₄), 900.908 cm⁻¹ (ν₁₆), and 683.46 cm⁻¹ (ν₁₇). Ground state (GS) rotational constants have been fitted to the combined ground state combination differences (GSCDs) for the three bands of the trans isomer. The bands for the cis isomer are at 907.70 cm⁻¹ (ν₃₃) and 587.89 cm⁻¹ (ν₃₅). GS rotational constants have been fitted to the combined GSCDs for the two bands of the cis isomer and compared with those obtained from microwave spectroscopy. Small inertial defects in the GSs confirm that both molecules are planar. Upper state rotational constants were fitted for all five bands.     

Carbon suboxide: The infrared spectrum from 1800 to 2600 cm−1

The infrared spectrum of carbon suboxide has been recorded from 1800 to 2600 cm^?1 at a resolution of 0.003 cm^?1. About 7% of the ca. 40 000 lines observed have been assigned and analyzed, belonging to 36 different bands. Most of these are associated with the fundamental ν₃, at 2289.80 cm^?1, and the combination band ν₂ + ν₄, at 2386.61 cm^?1, each of which give rise to a system of sum bands, difference bands, and hot bands involving the low-wave-number fundamental ν₇ at 18 cm^?1. A few other tentative assignments are made. The bands have been analyzed for vibrational and rotational constants.     

Absorption spectrum of VO2+ in zinc cesium sulphate hexahydrate

Results of optical absorption spectra of VO²⁺ ion doped in zinc cesium sulphate hexahydrate are reported. The observed bands have been assigned transitions from the ground ²B_2g state to the excited ²E_g, ²B_ig and ²A_1g states. From the nature and position of the bands a successful interpretation of all observed bands could be made. The crystal field and molecular orbital coefficients are reported.