Lu Nuclei Research Articles

Interpretation of the large-deformation high-spin bands in selectA=158–168 nuclei

The high-spin rotational bands in 168Hf and the triaxial bands in Lu nuclei are analyzed using the configuration-constrained Cranked Nilsson-Strutinsky (CNS) model. Special attention is given to the up-sloping extruder orbitals. The relative alignment between the bands which appear to correspond to triaxial shape is also considered, including the yrast ultra-high spin band in 158Er. This comparison suggests that the latter band is formed from rotation around the intermediate axis. In addition, the standard approximations of the CNS approach are investigated, indicating that the errors which are introduced by the neglect of off-shell matrix elements and the cut-off at 9 oscillator shells (N_{max}=8) are essentially negligible compared to other uncertainties. On the other hand, the full inclusion of the hexadecapole degree of freedom is more significant; for example it leads to a decrease of the total energy of ~ 500 keV in the TSD region of 168Hf.

Triaxial superdeformed bands in odd–odd [formula omitted] isotopes

The triaxial superdeformed rotational bands in the odd–odd Lu 160 ∼ 168 isotopes are investigated by performing the configuration dependent three-dimensional total routhian surface calculations. About fifty low lying triaxial superdeformed bands have been found for these odd–odd nuclei within the excitation energy of 3 MeV above the normal deformed yrast bands. The calculated equilibrium elongation, triaxial and hexadecapole deformations for these triaxial superdeformed bands are close to the values of ε 2 ∼ 0.4 , γ ∼ 20 ° and ε 4 ∼ 0.03 , respectively. The configurations of calculated triaxial superdeformed bands have been assigned based on the total routhian surface calculations and the analysis of quasiparticle routhians in the rotating frame. The observed yrast triaxial superdeformed band of 164Lu, where the linking transitions between superdeformed and normal deformed states are measured, have been reproduced by the present calculation in the relative energy to the normal deformed band. We show that the stability of superdeformed triaxial shapes in the odd–odd Lu isotopes is similar to that presented in odd–even Lu nuclei, and thus the wobbling excitations could be expected to occur in odd–odd Lu isotopes. The deformation driving effect of the proton high-j low-K orbit play an important role in the formation of the triaxial superdeformed states in both odd–odd and odd–even Lu isotopes, while the shell effect is a fundamental factor for the triaxial superdeformed shapes. The shell gaps and the positions of the deformation driving intruder orbits which are responsible for the triaxial superdeformed minima have been localized, particularly, the neutron N = 94 gap and the position of the proton [ 660 ] 1 / 2 orbit in the deformed single particle diagram provide the basis for a microscopic understanding of the observed triaxial superdeformed bands in the mass region.

Wobbling mode inTa167

The collective wobbling mode, the strongest signature for the rotation of a triaxial nucleus, has previously been seen only in a few Lu isotopes in spite of extensive searches in nearby isotopes. A sequence of transitions in the N = 94 Ta-167 nucleus exhibiting features similar to those attributed to the wobbling bands in the Lu nuclei has now been found. This band feeds into the pi i(13/2) band at a relative energy similar to that seen in the established wobbling bands and its dynamic moment of inertia and alignment properties are nearly identical to the i(13/2) structure over a significant frequency range. Given these characteristics, it is likely that the wobbling mode has been observed for the first time in a nucleus other than Lu, making this collective motion a more general phenomenon.

Triaxial strongly deformed bands inTm160,161

High-spin states in Tm-160,Tm-161 were populated using the Te-128(Cl-37, 5n and 4n) reactions at a beam energy of 170 MeV. Emitted gamma rays were detected in the Gammasphere spectrometer. Two rotational bands with high moments of inertia were discovered, one assigned to Tm-160, while the other tentatively assigned to Tm-161. These sequences display features similar to bands observed in neighboring Er, Tm, Yb, and Lu nuclei which have been discussed in terms of triaxial strongly deformed structures. Cranked Nilsson Strutinsky calculations have been performed that predict well-deformed triaxial shapes at high spin in Tm-160,Tm-161.

Parametrizations of triaxial deformation andE2transitions of the wobbling band

There are various different definitions for the triaxial deformation parameter '{gamma}'. It is pointed out that the parameter conventionally used in the Nilsson (or Woods-Saxon) potential, {gamma}(pot:Nils) [or {gamma}(pot:WS)], is not appropriate for representing the triaxiality {gamma} defined in terms of the intrinsic quadrupole moments. The difference between the two can be as large as a factor two in the case of the triaxial superdeformed bands recently observed in Hf and Lu nuclei, i.e., {gamma}(pot:Nils){approx_equal}20 deg. corresponds to {gamma}{approx_equal}10 deg. In our previous work, we studied the wobbling excitations in Lu nuclei using the microscopic framework of the cranked Nilsson mean-field and the random phase approximation. The most serious problem was that the calculated B(E2) value is about factor two too small. It is shown that the origin of this underestimate can mainly be attributed to the small triaxial deformation parameter {gamma}{approx_equal}10 deg. that corresponds to {gamma}(pot:Nils){approx_equal}20 deg. If the same triaxial deformation parameter is used as in the analysis of the particle-rotor model, {gamma}{approx_equal}20 deg., the calculated B(E2) gives correct magnitude of the experimental data.

Evidence for particle–hole excitations in the triaxial strongly-deformed well of 163Tm

Two interacting, strongly-deformed triaxial (TSD) bands have been identified in the Z=69 nucleus {sup 163}Tm. This is the first time that interacting TSD bands have been observed in an element other than the Z=71 Lu nuclei, where wobbling bands have been previously identified. The observed TSD bands in {sup 163}Tm appear to be associated with particle--hole excitations, rather than wobbling. Tilted-axis cranking (TAC) calculations reproduce all experimental observables of these bands reasonably well and also provide an explanation for the presence of wobbling bands in the Lu nuclei, and their absence in the Tm isotopes.

Observation of states beyond band termination in 156, 157, 158Er and strongly deformed structures in 173, 174, 175Hf

High-spin terminating bands in heavy nuclei were first identified in nuclei around 158Er90. While examples of terminating states have been identified in a number of erbium isotopes, almost nothing is known about the states lying beyond band termination. In the present work, the high-spin structure of 156, 157, 158Er has been studied using the Gammasphere spectrometer. The subject of triaxial superdeformation and ‘wobbling’ modes in Lu nuclei has rightly attracted a great deal of attention. Very recently four strongly or superdeformed (SD) sequences have been observed in 174Hf, and cranking calculations using the Ultimate Cranker code predict that such structures may have significant triaxial deformation. We have performed two experiments in an attempt to verify the possible triaxial nature of these bands. A lifetime measurement was performed to confirm the large (and similar) deformation of the bands. In addition, a high-statistics, thin-target experiment took place to search for linking transitions between the SD bands, possible wobbling modes, and new SD band structures.

Beyond band termination in 157Er and the search for wobbling excitations in strongly deformed 174Hf

High-spin terminating bands in heavy nuclei were first identified in nuclei around 158Er90. While examples of special terminating states have been identified in a number of erbium isotopes, almost nothing is known about the states lying beyond band termination. In the present work the high-spin structure of 157Er has been studied using the Gammasphere spectrometer.The subject of triaxial superdeformation and ‘wobbling’ modes in Lu nuclei has rightly attracted a great deal of attention. Very recently, four strongly or superdeformed (SD) sequences have been observed in 174Hf and ultimate cranker calculations predict such structures may have significant triaxial deformation. We have performed two experiments in an attempt to verify the possible triaxial nature of these bands. A lifetime measurement was performed to confirm the large (and similar) deformation of the bands. In addition, a high-statistics, thin-target experiment was run to search for linking transitions between the SD bands and possible wobbling modes.

Wobbling excitations in strongly deformed Hf nuclei?

Two Gammasphere experiments have been performed in order to establish the possible triaxial nature of strongly deformed (SD) bands in 174Hf. A lifetime measurement, using the Doppler-shift attenuation method, confirmed the large deformation of the four previously observed bands in this nucleus with transition quadrupole moments ranging from 12.6 to 13.8 b. These values are significantly larger than those predicted for triaxial minima by ultimate cranker (UC) calculations. A thin-target, high-statistics experiment was also carried out to search for linking transitions between the SD bands. No such transitions, which represent an experimental signature for wobbling modes, were observed. Four additional SD bands were found in 174Hf together with a single SD band in 173Hf. These results indicate that the strongly deformed sequences of N≈102 Hf isotopes behave differently than the triaxial strongly deformed (TSD) bands found in Lu nuclei near N=92. The interpretation of these bands in terms of possible stable triaxial deformation is confronted with the experimental findings and UC predictions.

Highly deformed Bands inHf175

Two high-spin regularly spaced rotational bands with large dynamical moments of inertia have been identified in Hf-175 with the Gammasphere spectrometer. These new bands are very similar to the previously identified superdeformed bands in the hafnium nuclei. However, the new bands in Hf-175 have been linked into the known level scheme and thereby provide the first firm spin assignments for these structures in this region. In order to understand the new bands, theoretical calculations have been performed based on the ULTIMATE CRANKER code. The new bands in Hf-175 are deduced to be built upon highly deformed structures. No experimental evidence for triaxiality was established and this work suggests that the structure of the so-called triaxial superdeformed bands in the Hf nuclei may be quite different from those identified in the lighter mass Lu nuclei. Since the two highly deformed bands in Hf-175 are associated with different deformations, this work also identifies the role of the intruder orbits in polarizing the nuclear shape.

First triaxial superdeformed band in 170Hf

First evidence is presented for triaxial superdeformation in 170Hf. High-spin states in this nucleus have been investigated in a γ-ray coincidence measurement using the EUROBALL spectrometer array. A new band was discovered which has moments of inertia that are very similar to the ones of triaxial superdeformed bands in neighbouring Hf and Lu nuclei. The intensities with which these bands are populated are different from what may be expected from calculated potential-energy minima.

The Triaxial Superdeformed Bands in163Lu

Triaxial superdeformed bands in 163 Lu are analysed by applying the Holstein-Primakoff transformation both to the total and single-particle angular momenta. Quite good agreements with the experimental values are reproduced in the energy difference between two superdeformed bands as a function of angular momentum, and also in the ratio of E2 transitions among these bands. The results coming from the exact diagonalization of the particle plus rotor Hamiltonian are compared with the approximate calculation. Recently, triaxial superdeformed bands in 163 Lu nucleus 1) have been observed, which are interpreted as the wobbling motion. 2) We have already proposed the theory for the triaxially deformed bands nearly thirty years ago. 3) The difference between our treatment and Bohr-Mottelson’s text book is in the quantization axis and in the order of approximation. We chose z-axis as the quantization axis, while BohrMottelson chose x-axis. We included the whole effect coming from 1/I where I is the total angular momentum. These two differences help us to get the exact energy eigenvalue at the axially symmetric limit. Moreover, our paper is the first work that applied the Holstein-Primakoff transformation to the nuclear physics. In this paper we extend our old theory to the odd nuclei by introducing two kinds of bosons for the total angular momentum I and the single-particle angular momentum j. Here, we pay attention to the symmetry of the nucleus. Both the rotor and the intrinsic Hamiltonian have D2-symmetry, and are also the function of deformations β and γ. There appears another symmetry in 5-dimensional space (three Eulerian angles, β and γ), which is called Bohr’s symmetry. 4) Thus, it is different from the classical precession around rigid body given in the text book by Landav-Lifshits. 5) We adopt an approximate wave function as, [D I φΩ +( −) I−j+κ D I −K φ−Ω], where κ = Ω − K is restricted to the even value because of the Bohr’s symmetry. Then the energy eigenvalue becomes the average of κ and −κ, and the energy difference between κ+2 and κ becomes constant independent from I. We adopt the irrotational flow formula for the moments of inertia as Ji = Cβ 2 sin 2 (γ− 2π 3 i), and the quadrupole moments are proportional to these moments of inertia. In the numerical analysis for 163 Lu, we adopt the state for the triaxially deformed superdeformed band 1 (TSD1) as K = 1 Ω = 1 (κ = 0), and for the triaxially deformed superdeformed band 2 (TSD2) as K = − 3 Ω = 1 (κ = 2). We adopt γ =1 9 ◦ , and unique-parity level i13/2 for the last nucleon. The band head energies of TSD1 and TSD2 are adjusted to the experimental energies. Three moments of inertia become J irr

High spin states in162Lu

An experimental investigation of the odd-odd {sup 162}Lu nucleus, following the {sup 148}Sm({sup 19}F,5n) reaction at beam energy E{sub lab}=112MeV, has been performed through in-beam gamma-ray spectroscopy. It revealed three signature-split bands. The yrast band based on {pi}h{sub 11/2}{circle_times}{nu}i{sub 13/2} configuration exhibits anomalous signature splitting (the unfavored signature Routhian lying lower than the favored one) whose magnitude {Delta}e{sup {prime}}{approx}25keV, is considerably reduced in contrast to sizable normal signature splitting {Delta}e{sup {prime}}{approx}125 and 60 keV observed in the yrast {pi}h{sub 11/2} bands of the neighboring odd-A {sup 161,163}Lu nuclei, respectively. The signature inversion in this band occurs at spin {approximately}20{h_bar} (frequency=0.37MeV). The second signature-split band, observed above the band crossing associated with the alignment of a pair of i{sub 13/2} quasineutrons, is a band based on the four-quasiparticle [{pi}h{sub 11/2}[523]7/2{sup {minus}}{circle_times}{nu}h{sub 9/2}[521]3/2{sup {minus}}{circle_times}({nu}i{sub 13/2}){sup 2}], i.e., EABA{sub p}(B{sub p}), configuration. The third signature-split band is also likely to be a four-quasiparticle band with configuration similar to the second band but involving F quasineutron, i.e., FABA{sub p}(B{sub p}). The experimental results are discussed in comparison with the existing data in the neighboring nuclei and in the framework of the cranking shell model. {copyright} {ital 1997} {ital The American Physical Society}

Analysis of175Lu NMR data on dilute alloys of Lu in Tb and Dy

Results of Sano, Shimizu and Itoh on NMR frequencies of175Lu in ferromagnetic Lu0.02Tb0.98 and Lu0.02Dy0.98 alloys are fitted by use of a model with five adjustable parameters. Two of these are related to the magnitude and asymmetry of the electric-field-gradient (EFG) tensor at a Lu nucleus, and three others specify the magnitude of the magnetic hyperfine field and its orientation with respect to the principal axes of the EFG tensor. For LuDy it is found that (i) the hyperfine field is tilted with respect to these axes, and (ii) the asymmetry of the EFG tensor differs in magnitude from published calculated values based on a point-change model. For LuTb at least one of these two statements is shown to be true. Tilting of the hyperfine field is consistent with inferences from neutron scattering data that the 4f moment is tipped away from the b axis in Tb metal.

Nuclear orientation of 177Lu in iron, cobalt and nickel

Nuclear orientation measurements were performed on 177Lu implanted in iron, cobalt, and nickel to obtain the hyperfine field on the Lu nucleus. Also the M2/E1 and the E2/M1 mixing ratios of the 208 keV and 113 keV transitions have been determined.

NMR of Lu175 in Ferromagnetic Lu-Tb and Lu-Dy Alloys

The NMR of Lu 175 in ferromagnetic Lu(2%)-Tb and Lu(2%)-Dy alloys was investigated at 1.4 K. Assuming the asymmetry factors calculated by Holden et al. which are 0.32 and 0.35 for Tb and Dy respectively, the experimental results are analysed. The effective fields at the Lu nuclei are found to be 302 kG (Tb alloy) and 239 kG (Dy alloy). The principal values of the electric field gradients along the c -axis are 1.91×10 24 cm -3 (Tb alloy) and 1.92×10 24 cm -3 (Dy alloy). The conduction electron contribution to the electric field gradient is about 70% of that produced by the lattice charges.

The magnetic hyperfine field in gadolinium metal

The perturbed angular correlation technique has been employed for measuring the magnetic fields acting on the Gd and Lu nuclei in Gd x Lu 1− x alloys. From these measurements, the various contributions to the hyperfine field in Gd metal were determined.