Γ-vibrational Band Research Articles

Collective γ-vibrational bands in 165Ho and 167Er

The nuclear structures of 165Ho and 167Er have been investigated by means of Coulomb excitation. These nuclei excited at moderate spins exhibit γ-vibrational bands with K π = 11 2 −, 3 2 − in 165Ho and K π = 11 2 + in 167Er. The γ-vibrational bands in 165Ho are found to be isospectral; heaving very nearly identical in-band γ-ray energies. Gamma-ray branching ratios are analysed to extract information on collectivity and Coriolis mixing. Experimental results are compared with calculations performed with the Cranked Shell Moedl + RPA + particle-vibration coupling and by invoking the generalized intensity relations (GIR) in the unified model scheme. Although this model explains many features of the data, puzzling aspects such as identical transition energies for the bands in 165Ho remain unexplained. The role of the K quantum number in identical bands is discussed.

Quadrupole and octupole collectivity in 148Nd

The role of quadrupole and octupole collectivity in the shape-transitional nucleus 148Nd has been studied by Coulomb excitation using beams of 58Ni and 92Mo, and a beam of 148Nd (using a 208Pb target). The extracted E1, E2 and E3 matrix elements involving states up to 12 + ·in the ground band and 13 − in the negative-parity band are presented, and compared to calculations that assume a vibrational and rotational octupole nature for the negative-parity band. The positive-parity ground-band states are well described in terms of a prolate deformed shape with Q 20 ≈ 400 e fm 2 ( β 2 rms ≈ +0.18). The present results suggest a vibrational octupole nature for the low-spin negative-parity states, with an intrinsic moment Q 30 ≈ 1500 e fm 3 ( β 3 rms ≈ 0.12). The E2 and E3 matrix elements connecting these bands to the β- and γ-vibrational bands (and within these bands) are also presented, and compared to calculations incorporating the coupling between the rotational and vibrational modes. These calculations describe reasonably well the E2 matrix elements involving the gamma band, but do not reproduce the measured E2 matrix elements for the beta band, implying a complicated intrinsic structure for the beta band. The strong enhancement of the measured E3 matrix elements connecting the negative-parity band to the beta band could be indicative of a significant component of the two-phonon octupole vibration in the wavefunction of the so-called beta band.

Two-phonon γ-vibrational states in 166Er

The nucleus 166Er has been Coulomb excited using a beam of 58Ni. In addition to the ground-and γ-vibrational bands three states were observed, a new state at 1943 keV, a previously known 4 + state at 1978 keV and a new state at 2029 keV suggested to have also spin and parity 4 +. The two 4 + states decay to the 2 + and 3 + states of the one-phonon γ-vibrational band, and their B(E2) values to the 2 γ + state are measured to 49 −25 +20 and 267 −100 +100 e 2 fm 4, respectively. It is suggested that the 1978 keV state has a small and the 2029 keV state a large component of the K π = 4 + two-phonon γ vibrational configuration in their wave functions.

G-factors in the ground state and γ-bands in 164,166,168Er

Abstract The g -factors of the ground state band members up to the 10 + level and of the 2 + state in the γ-vibrational band have been measured in 164,166,168 Er using the Coulomb excitation transient field technique. In the g-band the g -factor values were found to be nearly constant as a function of spin. For the 2 + states of the γ-band, values about 20% larger than those in the g-band have been determined. This latter fact is consistent with the known decay properties of the γ-band.

Rotational bands in 238U

A thick foil of 238 U was bombarded with 209 Bi beams at 1130 and 1330 MeV, delivered by the TASCC facility at Chalk River Laboratories. Gamma-ray spectroscopy of states populated in multiple Coulomb excitation was performed with the 8π spectrometer, an instrument comprising 20 Compton-suppressed HPGe detectors and 71 BGO ball elements. The event trigger required that 3 BGO elements and 2 HPGe detectors fire in coincidence. The experiment achieved a high degree of sensitivity, the weakest rotational band observed had about 0.16% intensity of the ground state rotational band. Several bands were observed to high spin for the first time, including the γ-vibrational band (spin 27 + ) and the octupole bands with K = 0 (spin 31 − ), K = 1 (spin 28 − ) and K = 2 (spin 25 − ). Results for positive and negative parity vibrational bands are compared with cranked RPA calculations. Although this theory can explain some features of the data, many puzzling aspects remain to be explored.

On-line nuclear orientation study of184Au

The184Au→184Pt decay, studied on-line with the UNISOR facility at HHIRF, is discussed. Gamma-ray and conversion-electron spectroscopy of184Pt as well as on-line nuclear orientation measurements of184Au were done. A new low-lying level scheme of184Pt is proposed. Two coexisting bands with different deformations and their respective γ-vibrational bands are established. Internal conversion coefficients for interband transitions between states with the same spin are extracted from the spectroscopy measurements. The relative E0 contents of the transitions are determined by combining internal conversion coefficients with E2/M1 mixing ratios deduced from gamma-ray anisotropies measured from oriented nuclei.

The structural part of reduced interband E2-transition probabilities

Abstract The nonlinearity of the Mikhailov plot for deformed doubly even nuclei is discussed. The spectral and electromagnetic properties of 158 Dy and 232 Th are calculated within the simple phenomenological mixing model. The results of numerical calculations and theoretical analysis within perturbation theory have shown that the discussed nonlinearity is caused by mixing of β- and γ-vibrational bands.

Collective states in 230Ra fed by β − decay of 230Fr

The γ-rays following the β − decay of 230Fr have been investigated by means of γ-ray singles including multispectrum analysis and γγ coincidence measurements using Ge(Li) detectors. The half-life of 230Fr was measured to be 19.1 ± 0.5 s. Most of the observed transitions could be placed in a level scheme comprising 23 new excited states of 230Ra, ten of them grouped into the K π = 0 + ground-state band, the K π = 0 − band with its 1 − state at 710.9 keV and a K π = 2 + γ-vibrational band with its head at 734.8 keV. It is concluded that 230Ra is a better rotator than the lighter radium isotopes, and has no ground-state octupole deformation.

Mass number dependence of hexadecapole ( Y42) excitation of the γ-vibrational band in proton inelastic scattering for 152⩽ A⩽192

Inelastic scattering exciting the 2 + and 4 + members of the K π =2 + γ-vibrational band in 152, 154Sm, 160Gd, 164Dy, 166, 168Er, 176Yb, 182, 184W and 192Os has been measured with 65 MeV polarized protons. The quadrupole ( Y 22) and hexadecapole ( Y 42) transition strengths to the γ-vibrational band have been extracted systematically for the first time. They show strong mass number dependences, which are explained qualitatively by a simple geometrical picture.

States in 160,162Gd Studied with the (t, p) Reaction

Angular distributions from the 158,160Gd (t, p) 160,162Gd reactions were studied, with 17 MeV tritons from the McMaster University tandem Van de Graaff accelerator. The reaction products were analyzed with a magnetic spectrograph and detected with photographic emulsions. Members of the ground state bands were populated up to 6+, and γ-vibrational bands were populated up to spin 4+ in both nuclides. Compared to the L = 0 strengths to the ground states, the excited strengths are as different as 20% and 50% for 160Gd and 162Gd. The considerable excited L = 0 strength found for 162Gd is interesting as there are no sudden changes of deformation or prominent shell structures in this region.

Two-quasiproton states in 168Er studied by the [formula omitted] reaction

The 169 Tm( t , α) 168 Er reaction has been studied using 17 MeV polarized tritons from the Los Alamos National Laboratory tandem Van de Graaff accelerator. The α-spectra were analyzed with a Q3D magnetic spectrometer. The overall energy resolution was typically ~ 15 keV (FHWM) and angular distributions of cross sections and analyzing powers were obtained for levels up to ~ 2.7 MeV. The fact that spins and parities for all levels up to ⩾ 2 MeV were previously known from an extensive series of (n, γ) studies made it possible to determine specific two-quasiproton structures for many bands from the present results. The K π = 2 + γ-vibrational band was found to have a large 3 2 + [411] p + 1 2 +[411] p admixture, consistent with the predicted microscopic composition of this phonon, but no 5 2 [413] p − 1 2 + [411] p component was observed. The K π = 0 4 + band at 1833 keV has ∼ 25% of the 1 2 + [411] p − 1 2 +[411] p two-quasiproton strength. This is in excellent agreement with the Soloviev model but is inconsistent with the interacting boson model, in which the K π = 0 4 + band is composed almost completely of multiphonon configurations that should not be populated in a single-nucleon transfer reaction. The K π = 4 −, 7 2 −[523] p + 1 2 + [411] p two-quasiproton and the K π = 4 −, 7 2 +[633] n + 1 2 −[521] n two-quasineutron states are mixed strongly with each other, but the two K π = 3 − bands composed of antiparallel couplings of the same particles are not. A good qualitative explanation of this mixing pattern is provided in terms of the effective neutron-proton interaction.

Inelastic proton scattering exciting the γ-vibrational band in 168Er and the necessity of the hexadecapole degree of freedom in the γ-motion

Inelastic scattering exciting the 2 2 + and 4 2 + members of the γ-vibrational band in 168Er has been investigated with 65 MeV polarized protons. A coupled-channel analysis has been performed assuming both the γ-vibrational model and the asymmetric-rotor model. A large hexadecapole term ( Y 42 + Y 4−2) in the γ-motion is necessary in order to reproduce the experimental data.

Band crossings at low rotational frequency in 166Yb

The 166Er( 3He, 3nγ) and 164Er(α, 2nγ) reactions were used to populate rotational side-bands in the N = 96 nucleus 166Yb. The aligned v( i 13 2 ) 2 S-band was observed from I π = 8 +to 12 +, while the β- and γ-vibrational bands were observed from the bandheads to I π = 10 +and 12 +, respectively. Negative-parity bands with K π = 0 −, (2 −) and 5 − were also observed. Band crossings and interaction effects are seen in both the positive- and negative-parity excitations below about h ̵ ω = 0.25 MeV , the frequency at which the first yrast backbend occurs.

Interaction between the S-band and the β- and γ-vibrational bands in 166Yb

After crossing the gsb at I = 14, the S-band of 166Yb crosses the γ-band at I = 10 and the β-band at I = 8. The β- and γ-bands are highly aligned below the crossing point, suggesting that the ν( i 13 2 ) 2 strength may be fractionated at low spin.

Band structures of 76Se and 78Se

Band structures of 76Se and 78Se have been studied with the 74,76Ge(α, 2nγ) 76,78Se reactions by using a variety of in-beam γ-techniques : γ-ray singles spectra, γ-ray excitation functions, γ- γ- t coincidences, γ-ray angular distributions and γ-ray linear polarizations. Spins and parities have been assigned uniquely for many new levels in 76Se and 78Se and four bands have been identified in both nuclei: (i) the ground-state band, (ii) a positive-parity ΔJ = 1 band built on the second 2 + state (γ-vibrational band), (iii) a negative-parity Δ J = 2 band built on the 3 − state (octupole band) and (iv) a ΔJ = 2 band built on the high-lying J = 4 state. In addition, the second 8 + and 10 + states, which are possibly the lowest members of a band, have been found in both nuclei. Systematics of the band structures obtained are discussed. Level energies of the band members and B(E2) ratios for some of the inter-band transitions between γ- and ground-state bands have been calculated with the proton-neutron interacting boson model IBM-2 and a reasonable agreement with the present data has been obtained.

A study of the rotational side-bands in 162Dy

Rotational side-bands in 162Dy have been studied using the 160Gd(α, 2nγ) 162Dy reaction. Seven side-bands are observed, with K π = 2 +, 2 −, (0) −, 0 +, 5 −, 4 + and (6 −). Four of these bands have collective structure at low spin: the K π = 2 + γ-vibrational band, the K π = 0 + β-vibrational band, and the K π = 2 − and (0) − octupole vibrational bands. Of the remaining bands, the 4 + band is deformation coupled while the 5 − and (6 −) bands are rotation-aligned. Several bandcrossings are observed in this nucleus. The β and γ-bands are crossed at I = 6 h ̵ and 12 h ̵ , respectively, by a highly aligned ( i 13 2 ) 2 S-band; extrapolation of this S-band to higher spin suggests that it crosses the g.s.b. between I = 18 h ̵ and 20 h ̵ . The 2 − octupole band is crossed by the 5 − band at I = 9 h ̵ and again by the (6 −) band at I = 12 h ̵ . The latter bandcrossings are discussed in terms of two-quasiparticle plus rotor calculations.

The nature of M1 admixtures in intra-band transitions in the γ-vibrational band

Abstract The M1 admixtures in the 74.6 keV (3+ → 2+), 122.8 KeV (5+ → 4+) and 146.3keV (6+ → 5+) transitions in the γ-vibrational band of 168Er have been determined to be 33 ± 1, 29 ± 2 and 22 ± 6 percent from measurements of L subshell conversion line intensity ratios. It is shown that the M1 admixtures in the intra-band transitions in the γ-band are a general and suprisingly constant feature in deformed rare-earth nuclei. This suggests that they are the result of a collective effect. The theory of Greiner, which takes the diferent deformation of the proton and nuetron cores into account, is found to be able to give a quantitative explanation of the observed M1 admixtures.

Governor model for asymmetric deformed nuclei

The governor model is extended to include the asymmetric shape of nuclei which allows a simultaneous analysis of the data for both the ground state and the γ-vibrational bands in deformed even–even nuclei. The rotationally invariant core is assumed to be a spheroid with an axis of symmetry parallel to the axis of rotation. The calculations are carried out under the assumption of no stretching. The static γ-deformation results are compared with the VMI(ARM) and Krutov values, and the calculated energies are in good agreement with the experimental data.

Inadequacy of the dynamic collective model in describing inelastic photon scattering in 166Er

Quasi-monochromatic photons in the range E γ = 14.4−16.6 MeV have been used to study inelastic scattering to the 2 +, γ-vibrational band head in 166Er. The results for transitions to this branch are drastically smaller (by a factor ≈3–5) than the predictions of the dynamic collective model (DCM).

Study of subnanosecond high-spin isomers in 186, 188, 190Pt by conversion electron spectroscopy

High spin states in 186,188, 190Pt have been populated using ( 16, 18 O, x n) reactions with 172, 174, 176Yb targets. The decay chains and lifetimes of high spin subnanosecond isomers have been measured using a solenoid spectrometer with Si(Li) detectors. The decay of the isomeric 12 + level in 188Pt via the γ-vibrational band and via the ground state band was established by e − -e − and e − -γ coincidence measurements. The B(E2) values to three 10 + states were determined for the first time in these nuclei. No isomeric 12 + state has been observed in 186Pt. The half-lives of the 7 − isomers in 186, 188, 190Pt were measured. The B(E2) values of the 7 − → 5 − transitions are larger than predicted from theory, but indicate, that even in 186Pt the rotation alignment of high spin particles can occur. Comparison with the rotational alignment model indicates a great γ-softness of 186Pt while for 188Pt all experimental results are in accordance with oblate deformation.