Showing papers by "R. F. Casten published in 2007"

Staggering in γ-band energies and the transition between different structural symmetries in nuclei

Abstract: The experimental energy staggering in \ensuremath{\gamma} bands of rare earths and actinides exhibits three distinct patterns as a function of angular momentum that are typical of well-deformed structural benchmarks: \ensuremath{\gamma}-soft for nuclei situated between a vibrator and a deformed \ensuremath{\gamma}-soft structure, axially symmetric for those between a vibrator and a rigid rotor, and triaxial \ensuremath{\gamma}-rigid for nuclei between a vibrator and a rigid triaxial rotor. The three patterns are reproduced by appropriate special solutions of the Bohr Hamiltonian, as well as by interacting boson approximation calculations. A particular quantity called S(4), which is proportional to the displacement of the ${3}_{\ensuremath{\gamma}}^{+}$ level relative to the average of the ${2}_{\ensuremath{\gamma}}^{+}$ and ${4}_{\ensuremath{\gamma}}^{+}$ levels, can vary in magnitude and sign for different shapes and is found to give a good indication of structure and the evolution of structure. A sudden change in the \ensuremath{\gamma}-band staggering occurring between the vibrator and the axially symmetric rotor limits seems to be connected to the known presence of a first-order phase/shape transition in this region.

Exactly separable version of the Bohr Hamiltonian with the Davidson potential

Abstract: An exactly separable version of the Bohr Hamiltonian is developed using a potential of the form $u(\ensuremath{\beta})+u(\ensuremath{\gamma})/{\ensuremath{\beta}}^{2}$, with the Davidson potential $u(\ensuremath{\beta})={\ensuremath{\beta}}^{2}+{\ensuremath{\beta}}_{0}^{4}/{\ensuremath{\beta}}^{2}$ (where ${\ensuremath{\beta}}_{0}$ is the position of the minimum) and a stiff harmonic oscillator for $u(\ensuremath{\gamma})$ centered at $\ensuremath{\gamma}={0}^{\ifmmode^\circ\else\textdegree\fi{}}$. In the resulting solution, called the exactly separable Davidson (ES-D) solution, the ground-state, $\ensuremath{\gamma},$ and ${0}_{2}^{+}$ bands are all treated on an equal footing. The bandheads, energy spacings within bands, and a number of interband and intraband $B(E2)$ transition rates are well reproduced for almost all well-deformed rare-earth and actinide nuclei using two parameters (${\ensuremath{\beta}}_{0},\ensuremath{\gamma}$ stiffness). Insights are also obtained regarding the recently found correlation between \ensuremath{\gamma} stiffness and the \ensuremath{\gamma}-bandhead energy, as well as the long-standing problem of producing a level scheme with interacting boson approximation SU(3) degeneracies from the Bohr Hamiltonian.

Empirical proton-neutron interactions and nuclear density functional theory: global, regional, and local comparisons

Abstract: Calculations of nuclear masses, using nuclear density functional theory, are presented for even-even nuclei spanning the nuclear chart. The resulting binding energy differences can be interpreted in terms of valence proton-neutron interactions. These are compared globally, regionally, and locally with empirical values. Overall, excellent agreement is obtained. Discrepancies highlight neglected degrees of freedom and can point to improved density functionals.

High-spin states in 191,193 Au and 192 Pt: Evidence for oblate deformation and triaxial shapes

Abstract: High-spin states of {sup 191,193}Au and {sup 192}Pt have been populated in the {sup 186}W({sup 11}B, xn) and {sup 186}W({sup 11}B, p4n) reactions, respectively, at a beam energy of 68 MeV and their {gamma} decay was studied using the YRAST Ball detector array at the Wright Nuclear Structure Laboratory at Yale University. The level scheme of {sup 193}Au has been extended up to I{sup {pi}}=55/2{sup +}. New transitions were observed also in {sup 191}Au and {sup 192}Pt. Particle-plus-Triaxial-Rotor (PTR) and Total Routhian Surface (TRS) calculations were performed to determine the equilibrium deformations of the Au isotopes. The predictions for oblate deformations in these nuclei are in agreement with the experimental data. Development of nonaxial shapes is discussed within the framework of the PTR model.

Isospin Purity of T=1 States in the A=38 Nuclei Studied Via Lifetime Measurements in K38

Abstract: The Doppler Shift Attenuation Method was used to measure lifetimes for levels in $^{38}\mathrm{K}$ at excitation energies of 1698, 2404, 2830, 2996, and 3671 keV, populated using the $^{40}\mathrm{Ca}$(d, \ensuremath{\alpha})$^{38}\mathrm{K}$ reaction at a beam energy of 4.5 MeV. Values of 109(29), 95(22), 457(63), 130(40), and 160(50) fs, respectively, were measured and are compared with previous values obtained using different stopping powers. The matrix element for the transition between the ${J}^{\ensuremath{\pi}}={2}_{T=1}^{+}$ and ${0}_{T=1}^{+}$ states in this ${T}_{z}=0$ nucleus is compared with the analogous transition in the other nuclei in the $T=1$ triplet, $^{38}\mathrm{Ca}$ (${T}_{z}=\ensuremath{-}1$) and $^{38}\mathrm{Ar}$ (${T}_{z}=+1$), and with the results of shell-model calculations.

High-resolution study of 0+ and 2+ excitations in 168Er with the (p,t) reaction

Abstract: Excited states in the deformed nucleus 168Er have been studied with high energy resolution in the (p, t) reaction, with the Munich Q3D spectrograph. A large number of excited 0+ states (25) and 2+ states (64) have been assigned up to 4.0-MeV excitation energy. This allows detailed investigations along two directions of current interest: first, an extension of microscopic model interpretations into the region of medium level density above the pairing gap; second, a first analysis of the statistical fluctuation (order/chaos) properties of pure sequences of levels, in one deformed nucleus. Predictions of two models (the quasiparticle-phonon model and the projected shell model) are compared to the data, and it is concluded that, in both cases, mixing of more configurations is required in the wave functions.

Spectroscopy of Zr-91(51) at medium to high spins

Abstract: = 3167 keV have been identified for thefirst time in this work, a tentative decay scheme of near-yrast states toexcitation energies in excess of 10 MeV has been constructed. These statesare of relevance to shell model structures formed via limited valence-spaceconfigurations in this semi-magic N = 51 nucleus.PACS numbers: 21.10.–k, 21.60.Cs, 27.60.+j, 29.30.Kv

g factor of the 2 + 1 state of 170 Hf

Abstract: The $g$ factor of the ${2}_{1}^{+}$ state of $^{170}\mathrm{Hf}$ was measured by perturbed \ensuremath{\gamma}-\ensuremath{\gamma} angular correlation in a static external magnetic field. The result, $g({2}_{1}^{+})=0.28$(5), extends the systematics of $g$ factors of even-even Hf isotopes to $N=98$ and enables a better test of theoretical models. The $g({2}_{1}^{+})$ experimental values of these isotopes exhibit a remarkable constancy as a function of neutron number. This phenomenon, which was also observed for other isotopic chains in the Gd--W range, is explained in terms of a recently proposed empirical model.