Rare-earth Region Research Articles

Transition probabilities in the U(6) limit of the symplectic interacting vector boson model

The tensor properties of the algebra generators and the basis are determined in respect to the reduction chain Sp($12,R$) \ensuremath{\supset} U(6) \ensuremath{\supset} U(3) \ensuremath{\bigotimes} U(2) \ensuremath{\supset} O(3) \ensuremath{\bigotimes} U(1), which defines one of the dynamical symmetries of the interacting vector boson model. The action of the Sp($12,R$) generators as transition operators between the basis states is presented. Analytical expressions for their matrix elements in the symmetry-adapted basis are obtained. As an example the matrix elements of the $E2$ transition operator between collective states of the ground band are determined and compared with the experimental data for the corresponding intraband transition probabilities of nuclei in the actinide and rare-earth region. On the basis of this application the important role of the symplectic extension of the model is analyzed.

Core-cluster partitions of actinide nuclei

We generate the core-cluster partitions of even-even nuclei in the rare-earth region using a form of the core-cluster interaction employed previously in an analysis of nuclei in the actinide region. The correlations between the core-cluster charge products thus obtained and various nuclear observables are found to display similar characteristics in the two mass regions.

Extended locus of regular nuclei along the Arc of Regularity

Recently, the first nuclei to lie along an arc of regularity in the collective symmetry triangle were identified. These nuclei are predicted to display significantly more ordered spectra than their neighbors. The nuclei identified all lie in the rare earth region from $A=156--180$. Here we present the results of a search of all known nuclei from $A=90--208$ and have identified an additional set of such candidates for regular nuclei using a particular degeneracy condition as a signature.

NUCLEI WITH TETRAHEDRAL SYMMETRY

We discuss a point-group-theory based method of searching for new regions of nuclear stability. We illustrate the related strategy with realistic calculations employing the tetrahedral and the octahedral point groups. In particular, several nuclei in the Rare Earth region appear as excellent candidates to study the new mechanism.

Extensive investigation of0+states in rare earth region nuclei

The nature of 0+ excitations, especially in transitional and deformed nuclei, has attracted new attention. Following a recent experiment studying 158Gd, we investigated a large group of nuclei in the rare-earth region with the (p,t) pickup reaction using the Q3D magnetic spectrograph at the University of Munich MP tandem accelerator laboratory. Outgoing tritons were recorded at various lab angles, and their angular distributions are compared to those calculated using the distorted-wave Born approximation. Using the unique shape of the L=0 angular distribution, more than double the number of 0+ states than were previously known are identified. The distribution of 0+ energies and cross sections is discussed in terms of collective and noncollective degrees of freedom, and the density of low-lying 0+ states is discussed as a corroboration of a characteristic feature of phase transition regions. The degree of level mixing, as extracted from Brody distribution fits to the energy spacings of adjacent 0+ levels, is also explored.

Connecting the X(5)-β2, X(5)-β4, and X(3) models to the shape/phase-transition region of the interacting boson model

The parameter independent (up to overall scale factors) predictions of the X(5)-$\beta^2$, X(5)-$\beta^4$, and X(3) models, which are variants of the X(5) critical point symmetry developed within the framework of the geometric collective model, are compared to two-parameter calculations in the framework of the interacting boson approximation (IBA) model. The results show that these geometric models coincide with IBA parameters consistent with the phase/shape transition region of the IBA for boson numbers of physical interest (close to 10). Nuclei within the rare-earth region and select Os and Pt isotopes are identified as good examples of X(3), X(5)-$\beta^2$, and X(5)-$\beta^4$ behavior.

Probing the maximally deformed light rare-earth region around the drip-line nucleus 130Sm

The neutron deficient rare-earth nuclei of the A∼130 region are of particular interest since highly deformed prolate ground states are expected. Indeed these nuclei are predicted to show maximal ground-state deformations of β2 ∼ 0.40 (axis ratio of 3:2), comparable to the deformation deduced for superdeformed cerium isotopes at high spin. A fusion–evaporation experiment was performed with radioactive ion beams at GANIL in October 2004 which had the goal to reach very proton-rich exotic nuclei located near the proton drip-line. A radioactive 76Kr beam, delivered by the SPIRAL facility, was used to bombard a thin 58Ni target. Emitted γ-rays were detected by the EXOGAM γ-ray spectrometer which was, for the first time, coupled with both the DIAMANT charged-particle array and the VAMOS spectrometer.

Enhanced density of low-lying 0+ states: A corroboration of shape phase transitional behavior

A (p, t) study of eight nuclei in the rare earth region identified 96 0 + states (67 new). Their density at low energy is used to corroborate a fundamental property of quantum phase transitional behavior and to provide a new signature of nuclei near the critical point.

SYSTEMATIC ANALYSIS OF CRITICAL POINT NUCLEI IN THE RARE-EARTH REGION WITH RELATIVISTIC MEAN FIELD THEORY

The shape phase transition between spherical U (5) and axially deformed SU (3) nuclei is investigated systemically for the rare-earth region nuclei by the constrained relativistic mean field theory with the interactions NL3. The properties of ground state for Nd , Gd and Dy isotopes are described fairly well as compared with experiments. By examining the potential energy curve and quadruple deformation β2 obtained with this microscopic approach, the possible critical point nuclei are suggested to be 148,150 Nd for Nd isotopes, but 148 Nd is the best candidate, and 150 Nd is slightly to the rotor side of the phase transition. For Gd and Dy isotopes, 150,152 Gd and 152,154 Dy are suggested to be the critical point nuclei. Similar conclusions are also drawn from the microscopic neutron single particle spectra.

Systematic exploration of 0+ states in structurally diverse nuclei

The puzzling nature of 0+ excitations, especially in transitional and deformed nuclei, has attracted new attention. Following a recent experiment studying 158Gd, we investigated 15 additional nuclei in and near the rare earth region. Our aim was to map out the energies of as many 0+ states as possible. A series of (p, t) experiments was performed at the Q3D magnetic spectrograph at the University of Munich MP tandem accelerator laboratory. These reactions are particularly sensitive to 0+ states. Outgoing tritons were recorded at various lab angles, and their relative cross sections are compared to those calculated using the distorted wave Born approximation (DWBA). The L = 0 angular distribution is easily discerned. New 0+ states are found in each of these nuclei, and their systematics are discussed.

β-delayed proton decays near the proton drip line

We briefly reviewed and summarized the experimental study on $\ensuremath{\beta}$-delayed proton decays published by our group over the last 8 years, namely the experimental observation of $\ensuremath{\beta}$-delayed proton decays of nine new nuclides in the rare-earth region near the proton drip line and five nuclides in the mass 90 region with $N~Z$ by utilizing the $p\text{\ensuremath{-}}\ensuremath{\gamma}$ coincidence technique in combination with a He-jet tape transport system. In addition, important technical details of the experiments were provided. The experimental results were compared to the theoretical predictions of some nuclear models, resulting in the following conclusions. (1) The experimental half-lives for $^{85}\mathrm{Mo},\phantom{\rule{0.3em}{0ex}}^{92}\mathrm{Rh}$, as well as the predicted ``waiting point'' nuclei $^{89}\mathrm{Ru}$ and $^{93}\mathrm{Pd}$ were 5--10 times longer than the macroscopic-microscopic model predictions of M\"oller et al. [At. Data Nucl. Data Tables $66,131(1997)$]. These data considerably influenced the predictions of the mass abundances of the nuclides produced in the rp process. (2) The experimental assignments of spin and parity for the drip-line nuclei $^{142}\mathrm{Ho}$ and $^{128}\mathrm{Pm}$ could not be well predicted by any of the nuclear models. Nevertheless, the configuration-constrained nuclear potential-energy surfaces calculated by means of a Woods-Saxon-Strutinsky method could reproduce the assignments. (3) The ALICE code overestimated by one or two orders of magnitude the production-reaction cross sections of the nine studied rare-earth nuclei, while the HIVAP code overestimated them by approximately one order of magnitude.

Interpretation of Correlations between Nuclear Observables in Rare-Earth Nuclei

We have recently obtained the optimal core-cluster decompositions for an extensive set of heavy even-even nuclei in the rare-earth region. The core-cluster charge products thus deduced are found to be closely correlated with the corresponding B(E2) values. We investigate here the strong resemblance of these correlations to the corresponding Casten plots, and find that the cluster model also predicts a further correlation between core-cluster charge products and the nuclear excitation energies, suggesting a new form of Casten plot for these energies.

Ground-state properties and phase/shape transitions in the IBA

Detailed fits to energies and electromagnetic transition rates for isotopic chains in the rare-earth region were performed using a simple IBA-1 Hamiltonian. The resulting parameters were then used to calculate two-neutron separation energies, isomer and isotope shifts. Comparison of the isotope shift behavior with other observables in this mass region suggests that the isotope shift could provide an indication for a first-order phase transition.

The ion-trap facility SHIPTRAP

The Penning-trap mass spectrometer at the ion trap facility SHIPTRAP is in the final stage of commissioning. First on-line mass measurements of neutron-deficient radionuclides in the rare-earth region around A = 147 were performed in July 2004. Systematic investigations in order to determine systematic errors are ongoing. Further improvements of the efficiency of the system are in preparation, e.g. improved detection schemes and further optimization of the stopping cell. SHIPTRAP will then address exotic nuclides produced in fusion-evaporation reactions at the velocity filter SHIP. This production technique will give access to nuclei not available at ISOL facilities, especially in the transuranium region.

Evidence of nuclear clustering throughout a major shell

We apply a cluster model to an extensive set of heavy even-even nuclei in the rare-earth region and determine the optimal core-cluster decomposition of each nucleus from a least-squares fit to the energy spectrum of its ground-state band. Good fits are obtained using a mass-symmetric form of the core-cluster interaction. We find that the core-cluster charge products deduced from the fits and the corresponding $B(E2)$ values are strongly correlated, in support of an underlying cluster picture of these nuclei.

β-delayed proton decays near the proton drip line

We briefly reviewed the experimental study on β-delayed proton decays near the proton drip line published by our group during the period of 1996–2004, namely the first observation of the β-delayed proton decays of 9 new nuclides in the rare-earth region and the new measurements of β-delayed proton decays of 5 nuclides in the mass ∼90 region near theN=Z line with the aid of the “p-y” coincidence in combination with a He-jet tape transport system. In the meantime some important experimental technique details were supplemented. The experimental results, including the half-lives, spins, parities, deformations and production reaction cross sections for the 14 nuclei were summarized and compared with the current nuclear-model predictions, and then the following points were represented. (1) The experimental half-lives for85Mo and92Rh as well as the predicted “waiting point” nuclei89Ru and93Pd are 5–10 times longer than the theoretical predictions given by Moller et al. using a macroscopic-microscopic model. It considerably influences the predictions of the abundances of the nuclides produced in the rp-process. (2) The current-model predictions are not consistent with the experimental assignments of the spins and parities for the proton drip-line nuclei142Ho and128Pm. However, the nuclear potential energy surface (PES) calculated by using a Woods-Saxon-Strutinsky method reproduced the experimental results. (3) The Alice code overestimated the production reaction cross sections of the studied 9 rare-earth nuclei by one order of magnitude or two, while HIVAP code overestimated them by one order of magnitude approximately.

Systematics in the structure of low-lying, nonyrast bandhead configurations of strongly deformed nuclei

An empirical investigation of the trends in the properties of the nonyrast ${K}^{\ensuremath{\pi}}={2}_{\ensuremath{\gamma}}^{+}$ and ${K}^{\ensuremath{\pi}}={0}_{2}^{+}$ bandhead configurations in nuclei that are related to one another through the addition or removal of $\ensuremath{\alpha}$-particle-like structures, reveals their complex and changing behavior in contrast to the smooth behavior of the yrast states. A systematic application of the pseudo-SU(3) model for such a sequence of deformed nuclei from the rare earth region leads to an accurate and unified description of not only yrast, but nonyrast collective bands. The onset of deformation as manifested through the position of the excited bandheads in the spectra is understood and interpreted by using a realistic model Hamiltonian in conjunction with a microscopic distribution of the eigenstates across allowed proton and neutron strong-coupled SU(3) configurations.

Mapping the interacting boson approximation symmetry triangle: New trajectories of structural evolution of rare-earth nuclei

The discovery of a set of analytic solutions to describe nuclei at the critical point of spherical-deformed phase transitions has led to an increased interest in the properties of ${0}^{+}$ excited states. This idea provides the motivation for the present investigation to determine sets of interacting boson model (IBA) parameters that reproduce the properties of all low-lying, positive-parity excitations, including the first excited ${0}^{+}$ state, for a wide range of even-even, collective nuclei. Detailed fits of isotopic chains in the rare-earth region are shown to reproduce the energies of the positive-parity states and to provide a reasonable description of their transition matrix elements. Two neutron separation energies, isomer shifts, and isotope shifts are also described using a truncated IBA-1 Hamiltonian. A proposed set of polar coordinates allows for a mapping of these parameters into the IBA symmetry triangle and a comparison of trajectories for different isotopic chains.

Signature inversion in the semidecoupled $\pi h_{9/2} \otimes \nu i_{13/2}$ band of the odd-odd nucleus 172 Lu

High-spin states in the odd-odd nucleus 172Lu have been populated in a 170Er(7Li,5n) reaction at 51 MeV and the emitted $\gamma$ -radiation was detected with the GASP array. A new semidecoupled band with the proposed $\pi 1/2^-[541] \otimes \nu 7/2^ + [633]$ configuration has been established exhibiting a signature inversion. A systematic study of the signature inversion in odd-odd nuclei of the rare-earth region is presented. The variation of the inversion spin remains nearly constant for nuclei with the same N-Z, increases with N for an isotopic chain and decreases with Z for an isotonic chain. On the basis of the systematics a change of the spins by $1\hbar$ is proposed for the semidecoupled bands in 180Re, 182,184Ir and 184,186Au.

Phase transitions and critical points in the rare-earth region

A systematic study of isotope chains in the rare-earth region is presented. For chains ${}_{60}^{144\ensuremath{-}154}\mathrm{Nd},$${}_{62}^{146\ensuremath{-}160}\mathrm{Sm},$${}_{64}^{148\ensuremath{-}162}\mathrm{Gd},$ and ${}_{66}^{150\ensuremath{-}166}\mathrm{Dy},$ energy levels, E2 transition rates, and two-neutron separation energies are described by using the most general (up to two-body terms) interacting boson model (IBM) Hamiltonian. For each isotope chain a general fit is performed in such a way that all parameters but one are kept fixed, to describe the whole chain. In this region, nuclei evolve from spherical to deformed shapes and a method based on catastrophe theory, in combination with a coherent-state analysis to generate the IBM energy surfaces, is used to identify critical phase transition points.