Quadrupole Vibrations Research Articles

Elementary Excitations of a Trapped Bose Gas at Zero Temperature

Starting from the equations of Gross–Pitaevskii for the order parameter we investigate the collective modes of a trapped Bose-condensed gas. These excitations are analogous to the propagation of phonons in homogeneous Bose superfluids. The coupling between the monopole and quadrupole vibrations in a deformed trap is explicitly investigated and the predictions are successfully compared with recent experimental data.

Quadrupole and Hexadecapole Vibrational Excitations in Deformed Nuclei

Energies, wave functions of the quadrupole and hexadecapole states, B(Eλ) and B(M1) values are calculated within the quasiparticle-phonon nuclear model in a number of well-deformed even-even nuclei in the rare earth region. Reasonably good overall agreement with available experimental data is obtained. Specific properties of the Kπ = 0+ and two-gamma vibrational states are discussed. The distributions of the M1 strength is studied. It is shown that the M1 strength is more strongly fragmented in Er isotopes compared to Gd and Dy isotopes. The fragmentation of one- and two-phonon states is investigated. The fragmentation of one-phonon states strongly affects the Eλ and M1 strength distribution at energies above 2.5–3.0 MeV. The wave functions in the energy range 2–4 MeV contain specific nuclear structure information and these states cannot be treated as chaotic.

Excited levels in 145Pm.

High-spin states in {sup 145}Pm have been studied with TESSA3 operating at NSF Daresbury, through the {sup 134}Xe({sup 15}N,4{ital n}) compound nucleus reaction using a solid xenon target. To determine conversion coefficients and properties of low-spin excitations electron-{gamma} and {gamma}-{gamma} coincidences have been measured following the {sup 146}Nd({ital d},3{ital n}) reaction. An extended level scheme of {sup 145}Pm is proposed and interpreted in terms of single-particle excitations with collective quadrupole and octupole vibrations coupled to them. {copyright} {ital 1996 The American Physical Society.}

Doppler-shift attenuation method lifetime measurements of low-lying states in 111In.

The lifetimes of nine low-lying excited states in $^{111}\mathrm{In}$ have been measured with the Doppler-shift attenuation method in the $^{111}\mathrm{Cd}$(p,n\ensuremath{\gamma}) reaction. A comparison of experimental quantities with predictions based on the interacting boson-fermion model unravels the states due to the coupling of a ${\mathit{g}}_{9/2}$ proton hole to the quadrupole vibrations of the core. \textcopyright{} 1996 The American Physical Society.

Active stabilization of mechanical quadrupole vibrations for linear colliders

To achieve luminosities of some 1033 cm−2 s−1, all linear collider schemes currently under study require extremely low beam emittances to achieve spot sizes of some 10 nm height and some 100 nm width at the interaction point. Therefore, high beam position stability is required in order to provide central collisions of the opposing bunches. Since ground motion amplitudes are likely to be larger than the required tolerances of 85 nm rms for the 500 GeV and 43 nm rms for the 1 TeV S-band linear collider SBLC, some means of active stabilization is necessary to damp quadrupole motion to the desired value. Therefore, an inexpensive active stabilization system to be installed in the S-band test accelerator at DESY has been developed and successfully tested. It damps quadrupole motion in the frequency range 2–30 Hz by up to 14 dB, thus leading to rms values of approximately 25 nm even in very noisy environments. Since the system is based on geophone type motion sensors with an internal noise level corresponding to 1.1 nm at 2 Hz, it is likely that this system allows stabilization below the 10 nm level.

Atoms and ions in superfluid helium

Optical spectra, level population and nonradiative deexcitation processes of atomic impurities in liquid helium have been investigated. The recombination of electrons and positive metal ions are described by the tunneling model. This model explains the population gap of 1.8 eV below the ionisation limit which was observed for several neutral defect atoms in liquid helium. In the framework of a pseudopotential theory excited singlet levels of Ba, Ca and Na atoms are recalculated and compared to experimental data. Non-spherical atomic defects for excited p-states are treated also. Quadrupole vibrations of these distorted defect structures are assumed to be responsible for inducing multiphonon transitions between excited atomic states.

Dynamical symmetries of nuclear collective models

The construction of algebraic models has become popular over the past twenty years. However, the fact that almost every dynamical model has an underlying algebraic structure is often overlooked. Indeed, a model is often described as geometric to distinguish it from models that are manifestly algebraic. In fact, the algebraic and geometric perspectives of a model are complementary and emerge naturally when the model is expressed in terms of its dynamical symmetry group. There is much to be gained by examining the dynamical symmetry of a model. For example, dynamical group transformations map out phase spaces and reveal the dynamical content of a model in classical terms. On the other hand, the unitary representations of a model's Lie algebra provide a quantization of its dynamics and the means to classify basis states and do calculations. Even more important, perhaps, is the discovery that identifying the dynamical symmetry of a phenomenological model provides a means to determine if the model is compatible with the microscopic many-nucleon structure of the nucleus and, when it is. give it a microscopic interpretation. Finally, as discussed in the last section of this review, dynamical symmetry concepts can be invoked to discover if the dynamics associated with two different models are compatible and can be combined. The models considered in this review are restricted (because of page limitations) to those which concern quadrupole vibrations and rotational motions.

Collisional damping of giant resonances in a non-Markovian approach.

Employing a non-Markovian collision term, the relaxation rates of giant resonances in nuclei are calculated using a diffuse nuclear surface, and energy and angle dependent cross sections obtained by a parametrization of the nucleon-nucleon scattering data. The calculations show that the collisional damping of giant quadrupole vibrations is sizable and accounts for about 40--60 % of the observed widths, while for giant dipole and giant monopole vibrations it accounts for only 25--30 % of the observed widths.

Study of excited levels in 147Pm

Abstract Excited states in 147 Pm have been studied through the 136 Xe( 15 N,4n) and 148 Nd(d,3n) compound nucleus reactions. A solid xenon target has been used to populate high-spin states in 147 Pm. Conversion coefficients of weak transitions were determined measuring electron-γ coincidences. The half-life of the isomeric level at 649.3 keV has been remeasured to be 27 ± 3 ns. An extended level scheme is proposed, which is discussed in terms of single-particle excitations and collective quadrupole and octupole vibrations coupled to them. The possible presence of octupole deformation is considered.

Coexistence in even-even Cd nuclei: global structure and local perturbations

Abstract The even-even Cd nuclei near neutron number N = 66 are indicative of the presence of two rather distinct families of excitations: anharmonic quadrupole vibrations and more deformed intruder particle-hole excitations. We discuss these excitations as mainly coexisting families of states forming the global structure of these nuclei. Then, we investigate how local large perturbations can cause strong mixing between the two families. The coupling is studied in detail and a particular set of selection rules governing the mixing leads to the introduction of a new basis in order to discuss the interaction between vibrational and intruder excitations. Numerical applications are carried out for 112,114 Cd.

Isoscalar Vibrational States in Hot Nuclei

We study the collective response .function for typical isoscalar modes on the basis of the selfconsistent transport theory. For the quadrupole vibration we find the usual low energy and giant resonance peaks at low temperature whereas all strength is concentrated in a low energy mode above a transition temperature of around 1.5 MeV. On the other hand, the peak of the resonance for the monopole vibration does not move to lower frequency for the increasing temperature. Only the peak becomes somewhat broader.

Isoscalar Vibrational States in Hot Nuclei

We study the collective response function for typical isoscalar modes on the basis of the selfconsistent transport theory. For the quadrupole vibration we find the usual low energy and giant resonance peaks at low temperature whereas all strength is concentrated in a low energy mode above a transition temperature of around 1.5 MeV. On the other hand, the peak of the resonance for the monopole vibration does not move to lower frequency for the increasing temperature. Only the peak becomes somewhat broader.

Spin-dependent generalized collective model in relation to the j=3/2 interacting boson fermion model.

The linearized collective Schroedinger equation for nuclear quadrupole vibrations describes nuclei with spin 3/2 in the ground state. Another model, which has been developed for nuclei with spin 3/2, is the [ital j]=3/2 interacting boson fermion model. We use a special property of the Clifford algebra, which appears in the linearized collective Schroedinger equation, to establish a connection between both models. We also compare the predictions of both approaches for various spin-3/2 nuclei.

Algebraic models of nuclear collective motion

The focus of this review is on the use of algebraic structure in the development of nuclear collective theory. The objective is a theory which takes full advantage of: (a) the geometrical perspectives of the traditional collective model, (b) the independent-particle concepts of the shell model and unified models, and (c) the mathematical tools of the algebraic models. For the purpose of this review, I adopt the premise that the most important correlations in the nucleus, as far as the description of quadrupole vibrations and rotations are concerned, are of the independent-particle, pairing and quadrupole types. I shall concentrate on the complementary approaches adopted in the Interacting Boson Model and in the Symplectic Model and the ways these models relate to the shell model and the Bohr-Mottelson-Frankfurt collective model.

Low-lying surface vibrations in the pair-hopping model.

The pair-hopping model of large amplitude motion is applied to the calculation of the frequency of low-lying quadrupole and octupole vibrations in atomic nuclei. Theory provides an overall account of the experimental findings.

An Experimental Study of the 4-0 and 5-0 Quadrupole Vibration Rotation Bands of H 2 in the Visible

Pressure shifts and collisional narrowing effects of the molecular hydrogen (H 2) 4-0 and 5-0 vibration rotation bands have been studied in greater detail than before. A high-resolution ring dye laser has been coupled to a multi-pass absorption cell with a base length of 22 m at Denison University in Granville, Ohio. Signal averaging periods of several hours, with an absorbing layer of 24 km-atm, were required to obtain acceptable measurements. A zero-density position and shift coefficient of 15 535.7441 ± 0.0036 cm −1 and −6.29 ± 1.29 × l0 −3 cm −1/Amagat, respectively, have been determined for the 4-0 S(0) line. For the 4-0 S(1) line the corresponding values are 15 699.8011 ± 0.0010 cm −1 and −4.22 ± 0.36 × 10 −3 cm −1/Amagat. The 5-0 S(1) line has been observed in the laboratory for the first time; its position has been located at 18 907.5160 ± 0.0200 cm −1. Linestrengths were also determined in this study and the results are 2.31 ± 0.55 × l0 −5 cm −1/(km Amagat) for the 4-0 S(0) line, 1.37 ± 0.17 × l0 −4 for the 4-0 S(1)line, and 1.76 ± 0.99 × 10 −5 for the 5-0 S(1) line. Collisional narrowing was clearly evident for the 4-0 S(0) and 4-0 S(1) lines.

Cluster-phonon model applied to the 91Zr nucleus.

The structure of the low-lying levels of the $^{91}\mathrm{Zr}$ nucleus is discussed in a framework of the cluster-phonon coupling model. In order to describe simultaneously positive- and negative-parity states, octupole as well as quadrupole vibrations of the $^{88}\mathrm{Sr}$ core are allowed. The cluster states include two single protons coupled to a single neutron. The residual interaction among the cluster particles is assumed to be the modified surface \ensuremath{\delta} interaction. Energy levels and electromagnetic properties are calculated and compared with the experimental data.

Ground state correlations and charge transition densities

The effect of the ground state correlations on the charge transition densities of the quadrupole vibration states in spherical nuclei is studied. The problem for the ground state correlations beyond the RPA leads to a non-linear system of equations, which is solved numerically. The calculations when the ground state correlations are taken into account give a 30% depletion of the charge transition density in the nuclear interior in comparison with the RPA calculation.

Gross-shell effects in nuclear response functions

We study nuclear collective vibrations and try to separate contributions from quasi-particle excitations close to the Fermi level from statistically averaged quantities. In this paper we concentrate on the variation coming from the quasi-particle component. As theoretical means we use linear response functions and their semiclassical expansions over trajectories. We study gross-shell effects in vibrating spherical nuclei and evaluate these expansions for the case of an infinitely deep square well, and thus for surface peaked interactions. We calculate strength functions for monopole and quadrupole vibrations. Restricting to only a few dominating terms in the semiclassical expansion we obtain simple expressions which can easily be evaluated numerically. For the case of the quadrupole we find good agreement with available data and with previous computations in the frame of conventional RPA, both for the excitation energies itself as well as their distribution within an energy-weighted sum. The resonance behaviour of the strength function, or its quasi-particle component rather, is determined by the distance between gross shells. The latter is related to the mean period of the shortest periodic orbits.

Collective potential and mass parameters derived from the generator coordinate method

The collective hamiltonian for the axial quadrupole vibrations was derived from theQQ+PP model. The generator coordinate method was applied and the results obtained through the symmetric moments expansion and the gaussian overlap approximation were compared. It was found that the collective potential and the average magnitude of the mass parameter obtained in both approximations are close to each other.