Yrast Superdeformed Band Research Articles

Nucleon localization function in rotating nuclei

Background: An electron localization function was originally introduced to visualize bond structures in molecules. It became a useful tool to describe electron configurations in atoms, molecules and solids. In nuclear physics, a nucleon localization function (NLF) has been used to characterize clusters in light nuclei, fragment formation in fission and pasta phases in the inner crust of neutron stars. Purpose: We use the NLF to study the nuclear response to fast rotation. Methods: We generalize the NLF to the case of nuclear rotation. The extended expressions involve both time-even and time-odd local densities. Since current density and density gradient contribute to the NLF primarily at the surface, we propose a simpler spatial measure given by the kinetic-energy density. Illustrative calculations for the superdeformed yrast band of $^{152}$Dy were carried out by using the cranked Skyrme-Hartree-Fock method. We also employed the cranked harmonic-oscillator model to gain insights into patterns revealed by the NLF at high angular momentum. Results: In a deformed rotating nucleus, several NLFs can be introduced, depending on the definition of the spin-quantization axis and self-consistent symmetries of the system. The oscillating pattern of the NLF can be explained by a constructive interference between the kinetic-energy and particle densities. The nodal pattern seen in the NLF along the major axis of a rotating nucleus comes from single-particle orbits with large aligned angular momentum. The variation of the NLF along the minor axis is traced back to deformation-aligned orbits. Conclusions: The NLF allows a simple interpretation of the shell structure evolution in the rotating nucleus in terms of the angular-momentum alignment of individual nucleons. We expect that the NLF will be useful for the characterization of other collective modes and time-dependent processes.

Lifetime measurements with improved precision in S30,32 and possible influence of large-scale clustering on the appearance of strongly deformed states

The formation of large size clusters and/or their relative motion as possible excitation mode are suggested to be closely related to the origin of deformation in specific cases. In $^{32}\mathrm{S}$, the consideration of some excitations in this nucleus as based on the existence of two doubly magic $^{16}\mathrm{O}$ clusters offers a possible solution to the long-standing problem of missing quadrupole collectivity in shell-model calculations aiming to describe electromagnetic $E2$ transition strengths and quadrupole moments. To experimentally check again this collectivity, lifetime measurements were performed on $^{30}\mathrm{S}$ and $^{32}\mathrm{S}$. In $^{32}\mathrm{S}$, at least, the reproduction of a number of observables supports the cluster scenario. Additionally, the superdeformed yrast band in $^{80}\mathrm{Zr}$ could find an explanation as based on the relative motion of two $^{40}\mathrm{Ca}$ clusters. Simultaneously, a necessity arises to revise experimentally some lifetimes derived in the past within the Blaugrund approximation when using the Doppler-shift attenuation method.

Properties of superdeformed bands in A ∼ 190 region within the framework of three parameters nuclear softness model

The three parameters nuclear softness model (NS3) have been applied to eleven superdeformed (SD) bands of A ≈190 mass region namely: 191Hg(SD2,SD3), 192Hg(SD1), 194Hg(SD1,SD2), 193Tl(SD1,SD2), 194Tl(SD1,SD3, SD5) and 194Pb(SD1). The level spins and the model parameters are determined by fitting the electric quadrupole transition energies Eγ with the experimental ones, by using a computer simulated search program. Rotational frequencies ħω, kinematic J(1) and dynamic J(2)moments of inertia and the quadrupole deformation parameter β2 have been calculated. In all cases of our selected SD bands the results obtained are in good agreement with experimental ones. J(2) reveal a steady increase with ħω, this can be attributed to the successive alignment of πi13/2 (N = 6) and υj15/2 (N = 7) intruder orbitals in the presence of dynamical pairing correlations. The presence of ΔI = 2 staggering in the two SD bands 1,2 of 194Hg and in the three SD bands 1,3,5 of 194Tl have been investigated by calculating the staggering parameter which represent the fourth order derivative of the gamma-ray transition energies. Also the ΔI = 1 staggering in SD bands of odd nuclei has been investigated in the signature partner pairs 191Hg (SD2, SD3) and 193Tl (SD1, SD2). The yrast SD bands in the isotones 194Pb and 192Hg have almost identical transition energies which implies that their J(2) are also identical. This indicates that either the two occupied 5/2+[642] protons have a very weak influence on Eγ and J(2).

Systematics of band moment of inertia of yrast and excited SD bands of even–even nuclei in A~150 mass region

A four parameter formula has been applied to all the yrast and excited superdeformed (SD) bands of even–even nuclei in the A~150 mass region to obtain band moment of inertia J0. In even–even nuclei, totally three yrast SD bands and 16 excited SD bands have been fitted. The measured Qt values and hence the axes ratios have been used to calculate the rigid body J0 values and compared with the fitted values of J0. It is interesting to look at the yrast SD band 152 Dy (1), the doubly magic SD nucleus and the first one to be discovered that the J0 values are quite larger than that extracted from Qt measurement. We found that all the excited SD bands in even–even nuclei are signature partner SD bands because the J0 value of each signature partner SD band is almost identical. Among all these excited SD bands, 150 Gd (4) is found to be super-rigid in nature having J0 value larger than that observed from the measured Qt value.

Description of the yrast superdeformed bands in even-even nuclei in A $\sim$ 190 region using the nuclear softness model

A two-parameter nuclear softness (NS2) model for the transition energies is proposed by treating the variation of the moment of inertia with spin. The model has been applied to the yrast superdeformed (SD) bands in even-even nuclei in the mass region A � 190. The model parameters have been determined from thetting procedure in order to minimize the relative root mean square deviation between the experimental E2 transition -ray energies and the calculated ones. The basic experimental data on SD bands are given in the form of a series of -ray transitional energies and the spins were determined in our previous works. The excellent agreement between the theory and the experiment give good support to the model. The presence of identical bands between the two isotopes 192 Hg and 194 Pb is investigated because their differences in -ray energies are small and constant up to rotational frequency ℏ! � 0.25 MeV. Our analysis also leads to the appearance of ∆ I = 2 staggering effect in 194 Hg (SD1). A comment on equilibrium

Discrete decay of the yrast superdeformed band in theTb151nucleus

The Euroball array has been used to search for linking transitions between the superdeformed (SD) and the normal deformed (ND) wells in Tb-151. Many. rays in the energy range 2-4 MeV have been observed in coincidence with the yrast SD band. It is proposed that the highest energy transition of 3748 keV and the strongest line (2818 keV) of the previously observed transitions both decay from the same SD level as their links with the ND states have been identified. The current spectra have insufficient statistics to completely identify the decay point in the SD band. Theoretical calculations covering SD bands in the A approximate to 150 region enable the two possible spin assignments to be compared with experimental data on proposed links in Gd-149 and Dy-152. It is concluded that the energy of the lowest SD band member in Tb-151 has an excitation energy of 12861 keV and a spin of 65/2(+).

Selective studies of the excited rotational bands in the superdeformed nucleusTb151

The experimental study of the unresolved rotational bands, forming ridge structures in $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ spectra, has been performed on the superdeformed nucleus $^{151}\mathrm{Tb}$. \ensuremath{\gamma} transitions from the reaction $^{27}\mathrm{Al}$, at 155 MeV, on $^{130}\mathrm{Te}$ were measured with EUROBALL IV in high fold coincidence. The analysis of the intensities and count fluctuations of the ridge structures shows the existence of $\ensuremath{\approx}30$ discrete rotational bands of superdeformed nature, half of which is in direct coincidence with the superdeformed yrast band. A comparison with band mixing model predictions and with a previous work on the superdeformed nucleus $^{143}\mathrm{Eu}$ is presented.

STATIC AND DYNAMIC NON-AXIAL OCTUPOLE DEFORMATIONS SUGGESTED BY SKYRME-HF AND SELFCONSISTENT RPA CALCULATIONS

On the basis of the symmetry-unrestricted, cranked Skyrme-Hartree-Fock (SHF) calculations, we discuss superdeformed (SD) rotational bands in (1) the 40 Ca region along the N=Z line, and (2) neutron-rich Sulfur isotopes up to the neutron-drip line. The calculation was carried out with the use of the three-dimensional (3D) coordinate-mesh representation without imposing any symmetry restriction. Stability of the SD bands against exotic deformations breaking both reflection and axial symmetries were carefully examined. The analysis indicates possible appearance of negative-parity rotational bands associated with octupole shape vibrational excitations built on the SD yrast band. We then present results of selfconsistent RPA calculation for such a new type of collective vibrational modes. The selfconsistent RPA calculations based on the SD local minima obtained by the SHF calculation were carried out by means of the mixed representation on the 3D Cartesian mesh in a box.

Octupole vibration in superdeformed 152(66)Dy86.

Nine transitions of dipole character have been identified linking an excited superdeformed (SD) band in 152Dy to the yrast SD band. As a result, the excitation energy of the lowest level in the excited SD band has been measured to be 14 238 keV. This corresponds to a 1.3 MeV excitation above the SD ground state. The levels in this band have tentatively been determined to be of negative parity and odd spin. The measured properties are consistent with an interpretation in terms of a rotational band built on a collective octupole vibration.

Microscopic Mechanism of the ω Variation in Moments of Inertia for the Yrast Superdeformed Bands 194Tl(1a,1b)**The project supported by National Natural Science Foundation of China under Grant Nos 1047205, 19835010, and 10047001, the Major State Basic Research Development Program under Grant No. G2000-0774-07 and the Knowledge Innovation Project of the Chinese Academy of Sciences under Grant No.KJCX2-SW-NO2

The variation in moments of inertia (J(1) and J(2)) with rotational frequency for the superdeformed bands in odd-odd nuclei, 194Tl(1a,1b), is investigated by using the particle-number conserving method for treating the pairing interaction (monopole and quadrupole). The observed variations of J(1) and J(2) with ω are reproduced quite well in the calculation and the contributions from each major shell are clearly displayed.

Quantum tunneling of the excited rotational bands in the superdeformed nucleus 143Eu

The properties of the thermally excited rotational motion up to the region of rotational damping are studied experimentally in the superdeformed nucleus 143Eu. The effective lifetime of the excited discrete rotational bands forming ridge structures in γ– γ matrices is measured at the EUROBALL array using the DSAM technique, giving a quadrupole moment Q t ≈10 e b, consistent with the deformation of the superdeformed yrast band. In addition, the effective number of excited superdeformed bands is extracted by a statistical analysis of the ridge structure, for transition energies down to the region where the effect of the decay-out into the normal deformed well shows up. The experimental data are compared with microscopic cranked shell model calculations including a residual interaction of surface delta type. Satisfactory agreement between data and theory is obtained when the quantum tunneling of the excited superdeformed states is included in the model.

Probing nuclear structure at finite temperature and spin via decay of superdeformed bands in lead nuclei

The 174Yb(25Mg, 5n)194Pb and 173Yb(24Mg, 5n)192Pb reactions were used to probe the decay of superdeformed (SD) bands. The total γ-ray spectra associated with the SD bands in 192,194Pb have been studied to determine the energy and angular momenta associated with each step of the cascade, from entry population to decay to the ground state. In particular, the γ-ray spectra associated with the quasicontinuous, non-discrete decay of their respective yrast SD bands has been extracted. Using various model assumptions, the quasicontinuous decay spectrum is expected to have a rapid rise in intensity at an energy associated with the gap, or backshift parameter, in level density; such a rise is observed in the quasicontinuous decay of the SD bands in 194,192Pb. Values of Egap ≈ 0.9(1) MeV for 194Pb at ≈ 6ℏ and Egap ≈ 0.4+0.3-0.1 MeV for 192Pb at ≈ 10ℏ have been deduced.

Accurate Lifetime Measurements of Superdeformed Bands inA∼80Nuclei

Comparative measurements of the lifetimes of yrast superdeformed (SD) states in ${}^{80--83}\mathrm{Sr}$, ${}^{83}\mathrm{Y}$, and ${}^{84}\mathrm{Zr}$ have been performed using the Doppler-shift attenuation method. Thus, the transition quadrupole moments ( ${Q}_{t}$) of these structures have been determined accurately. The yrast SD bands in ${}^{80--83}\mathrm{Sr}$ possess ${Q}_{t}\ensuremath{\sim}3.5e\mathrm{b}$, while the ${}^{83}\mathrm{Y}$ and ${}^{84}\mathrm{Zr}$ cases display ${Q}_{t}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}4.4e\mathrm{b}$ and $5.6e\mathrm{b}$, respectively. Intruder orbital assignments based on these results demonstrate a previously unnoticed transition in the structure of the SD bands when the proton number changes from $Z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}38$ to $Z\ensuremath{\ge}39$.

Decay-out of the yrast superdeformed band in136Nd: Towards an experimental extraction of the neutron pairing gap at large deformation

A study of the 136Nd nucleus has been performed with the EUROBALL III multidetector to establish the decay-out of the yrast superdeformed (SD) band. Three discrete linking transitions (754, 1456, and 1493 keV) have been discovered, establishing the position of the SD band at 7.03 MeV excitation energy with proposed spin and parity 17(−) for the lowest observed SD state. Neutron pairing gap parameters for SD shapes have been extracted in Nd isotopes, using the strong-coupling model and odd-even mass difference formulas. The major conclusion of our phenomenological analysis is that the pairing correlations do subsist in the SD configurations of nuclei in the A=130 mass region.Received 15 October 1998DOI:https://doi.org/10.1103/PhysRevC.60.064313©1999 American Physical Society

First evidence for linking transitions between the superdeformed yrast band and the normal deformed states in 149Gd

Double step resolved γ-ray transitions linking the yrast superdeformed (SD) band of 149Gd to the normal deformed (ND) level scheme have been observed using the EUROGAM phase II spectrometer. The excitation energy of the 47/2 − SD state above the 7/2 − ground state has thus been determined to be 10.625 MeV. The most likely multipolarity of the linking transitions is deduced, which permits the assignment of the most probable spins for this SD band. This measurement represents the first observation of discrete γ-ray transitions linking SD and ND states in the A∼150 mass region of the nuclear chart.

Microscopic descriptions of superdeformed bands with the Gogny force: Configuration mixing calculations in theA∼190 mass region

A quantal Hamiltonian ${\stackrel{^}{\mathcal{H}}}_{\mathrm{coll}}$ expressed in terms of the five collective quadrupole coordinates is built for eight nuclei ${(}^{190,192,194}$Hg, ${}^{192,194,196}$Pb, and ${}^{196,198}$Po) which display secondary minima at large elongation in their potential energy surface. These surfaces as well as the tensor of inertia entering ${\stackrel{^}{\mathcal{H}}}_{\mathrm{coll}}$ are deduced from constrained Hartree-Fock-Bogoliubov calculations based on Gogny force. A two-center basis method employed to solve ${\stackrel{^}{\mathcal{H}}}_{\mathrm{coll}}$ is presented. The stability of predicted collective spectra is discussed. Yrast and vibrational $\ensuremath{\pi}=+$ superdeformed (SD) bands are predicted together with collective bands at normal deformation (ND). The predicted yrast SD bands at low spin display properties which compare favorably with experimental information. Quite good agreement is in particular obtained for the isomeric energies of nuclei for which the link between SD and ND levels is experimentally known. Among the excited SD bands which are here predicted, those built on top of $\ensuremath{\beta}$ vibrations are lower in energy. Only for the ${}^{196,198}$Po isotopes are these excitation energies falling in the low energy range $E\ensuremath{\sim}$0.8--1.0 MeV. These properties should favor an experimental discovery of $\ensuremath{\beta}$-vibrational SD bands in the $A\ensuremath{\sim}$190 mass region.

Theoretical Constraints for Observation of Superdeformed Bands in the Mass-60 Region

The lightest superdeformed nuclei of the mass-60 region are described using the Projected Shell Model. In contrast to the heaviest superdeformed nuclei where a coherent motion of nucleons often dominates the physics, it is found that alignment of $g_{9/2}$ proton and neutron pairs determines the high spin behavior for superdeformed rotational bands in this mass region. It is predicted that, due to the systematics of shell fillings along the even--even Zn isotopic chain, observation of a regular superdeformed yrast band sequence will be unlikely for certain nuclei in this mass region.

Quadrupole moments and identical superdeformed bands in149Tb

Five superdeformed (SD) bands have been observed in ${}^{149}\mathrm{Tb},$ using the Gammasphere spectrometer. The measurement was performed with a backed target to obtain lifetime information from a Doppler-shift attenuation method analysis. It is proposed that the yrast SD band corresponds to the ${}^{148}\mathrm{Gd}(\mathrm{yrast})\ensuremath{\bigotimes}\ensuremath{\pi}{6}^{3}$ intruder configuration. The first excited band (band 2) is found to be identical to the ${}^{150}\mathrm{Tb}$ yrast SD band. Band 3 is proposed to correspond to the $\ensuremath{\pi}[301]1/2(\ensuremath{\alpha}=\ensuremath{-}1/2)\ensuremath{\rightarrow}[651]3/2(\ensuremath{\alpha}=\ensuremath{-}1/2)$ proton-hole excitation coupled to the $\ensuremath{\pi}{6}^{4}\ensuremath{\nu}{7}^{1}(\ensuremath{\nu}[651]{1/2)}^{\ensuremath{-}1}$ intruder configuration. Bands 4 and 5, the weakest SD bands seen in the present work, show similarities with band 3 and are most likely associated with a similar intruder configuration.

Superdeformed Bands of 150Gd in the Interacting Boson Model

The electric quadrupole transition γ-ray energies and the dynamical moments of inertia of the five superdeformed (SD) bands of 150Gd have been investigated with a four parameter approach inspired of the interacting boson model. The calculated results agree with experimental data well. It indicates that the four parameter approach is powerful in describing both the yrast SD band and the excited SD bands of even-even nucleus no matter whether the bands are built upon some extra single particle excitations.

Quadrupole moment of superdeformed bands in 151Tb

The quadrupole moments of the first two superdeformed (SD) bands in the nucleus 151Tb have been measured with the Doppler Shift Attenuation Method (DSAM) using the EUROGAM γ-ray spectrometer. The first excited band (B2) is identical to the yrast SD band of 152Dy in terms of dynamical moments of inertia and γ-ray energies. The measured relative quadrupole moments of the yrast band (B1) with respect to the band B2 are nicely reproduced by self-consitent Hartree-Fock calculations. The variation of the Q0 value at the bottom of the yrast band suggests a large admixture between wave functions in the normal and the SD wells. This could explain the rather high deexcitation spin for the yrast band.