Quadrupole Excitations Research Articles

Complete spectroscopy of the 162Dy nucleus

States in 162Dy have been populated by ( n , γ ) , ( n , e − ) , and ( α , 2 n ) reactions in order to characterize a complete set of low K bands below 2 MeV. The ( n , γ ) and ( n , e − ) measurements were made using high precision curved crystal and β − spectrometers. Gamma–gamma coincidence and DCO measurements were made following the ( α , 2 n ) reaction using an array of Compton-suppressed Ge detectors. Using all these data and employing the Ritz combination principle, a level scheme was developed which represents one of the most complete and extensive spectra of levels available for comparison with nuclear models. The observed positive and negative parity bands are discussed in terms of collective quadrupole and octupole vibrational excitations as well as 2 quasi-particle excitations.

Resonant inelastic X-ray scattering in d and f electron systems

Recent progress in the study of resonant inelastic X-ray scattering (RIXS) spectroscopy in d and f electron systems is described. The main space is devoted to the theoretical investigations, some typical experimental data and the comparison of calculated and experimental results, putting emphasis on the underlying physical mechanisms. We confine ourselves mainly to the studies performed since 2000, and discuss the following topics: (1) RIXS in high Tc cuprates, (2) f0 and d0 systems, (3) other transition metal compounds, (4) RIXS by electric quadrupole excitation, and (5) magnetic circular dichroism in RIXS of ferromagnetic systems. Some brief description is also given on the future prospect of the RIXS study.

Generalized oscillator strengths for the valence-shell excitations of neon

The generalized oscillator strengths for the valence-shell excitations to $2{p}^{5}3s$, $2{p}^{5}3p$, and $2{p}^{5}4s$ of neon were measured with an angle-resolved fast-electron energy-loss spectrometer at an incident electron energy of $2500\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. The transition multipolarities for these excitations were elucidated with the help of the calculated intermediate-coupling coefficients using the COWAN code. The generalized oscillator strength profiles for the electric monopole, electric dipole, and electric quadrupole excitations were analyzed and their positions of the extrema were obtained. Furthermore, the experimental generalized oscillator strength ratios between the excitations to $2{p}^{5}4s{[3∕2]}_{1}$ and $2{p}^{5}4{s}^{\ensuremath{'}}{[1∕2]}_{1}$ were determined and found to be in agreement with the calculated intermediate-coupling coefficient ratio.

Dynamical core deformation effects on single-nucleon knockout reactions at fragmentation beam energies

The effects of core deformation and of its dynamical reorientation and rotational excitation on the inclusive single-neutron knockout reaction cross sections on light spherical nuclei are examined. The projectile nuclei are modeled within the framework of a weak-coupling, quadrupole-deformed core-plus-neutron two-body model. We formulate the inclusion of this non-spectator-core degree of freedom within the nonperturbative eikonal model and calculate the diffractive break up and stripping neutron-removal cross sections. We apply the methods to model the single-neutron removal reactions induced by 11Be and 17C and secondary fragmentation beams incident on a 9Be target. Our calculations indicate that dynamical deformation effects on the diffractive break up component of the knockout cross section can be significant. For the two reactions studied here, the diffractive break up cross section is significantly enhanced. This effect is found to be very surface localised, thus the importance of core deformation is increased the more tightly bound the projectile system. The quadrupole deformation parameter and excitation energy of the core also influence the magnitude of this enhancement of the diffractive cross section, which is relatively insensitive to the projectile energy. The stripping cross section is found to be virtually unchanged by the inclusion of the deformed core degree of freedom.

Excitation of Giant Resonances in Deuteron Stripping Reactions on 10B far below the Coulomb Barrier

The reaction threshold for deuteron induced reactions on 10 B amounts to 25.2 MeV, which enables an excitation of the giant resonances (GR) in the compound nucleus 12 C even at very low projectile energies. In our recent experimental and theoretical investigations of the 10 B(d,p) 11 B reaction, we have found a strong reaction contribution arising from the giant dipole resonance (GDR) excitation. This kind of transition is only possible due to a significant isospin impurity of the GDR in 12 C. In the present work, we study an influence of the GDR as well as of the giant quadrupole (GQR) excitation on the 10 B(d,p) 11 B reaction cross section for transitions to the ground as well as the first three excited states at astrophysically relevant deuteron energies below 3 MeV. Based on our new measurement of angular distributions and absolute cross sections as well as on experimental results of other authors we have determined the total astrophysical S-factor of the 10 B(d,p) 11 B reaction down to deuteron energies close to zero. Additionally, the importance of the interference between resonant and direct reaction amplitudes is discussed.

Quasirelativistic quasilocal finite wave-function collapse model

A Markovian wave function collapse model is presented where the collapse-inducing operator, constructed from quantum fields, is a manifestly covariant generalization of the mass density operator utilized in the nonrelativistic Continuous Spontaneous Localization (CSL) wave function collapse model. However, the model is not Lorentz invariant because two such operators do not commute at spacelike separation, i.e., the time-ordering operation in one Lorentz frame, the "preferred" frame, is not the time-ordering operation in another frame. However, the characteristic spacelike distance over which the commutator decays is the particle's Compton wavelength so, since the commutator rapidly gets quite small, the model is "almost" relativistic. This "QRCSL" model is completely finite: unlike previous, relativistic, models, it has no (infinite) energy production from the vacuum state. QRCSL calculations are given of the collapse rate for a single free particle in a superposition of spatially separated packets, and of the energy production rate for any number of free particles: these reduce to the CSL rates if the particle's Compton wavelength is small compared to the model's distance parameter. One motivation for QRCSL is the realization that previous relativistic models entail excitation of nuclear states which exceeds that of experiment, whereas QRCSL does not: an example is given involving quadrupole excitation of the $^{74}$Ge nucleus.

Dipole and quadrupole excitations inSr88up to6.8MeV

Dipole and quadrupole excitations in the semimagic N=50 nucleus {sup 88}Sr were investigated at the superconducting Darmstadt electron linear accelerator S-DALINAC with bremsstrahlung of an end-point energy of 6.8 MeV. Many new dipole excitations could be identified, and their reduced excitation probabilities were determined. The experimental findings are discussed in the context of quasiparticle-phonon-model and shell-model calculations. A breaking of the N=50 core is essential to describe the structure of the observed excitations. The two-phonon quadrupole-octupole J{sup {pi}}=1{sup -} state exhibits unusual features which are presently not understood.

Three-phonon excitations in 124Sn

The low-lying levels of 124Sn have been explored using the ( n , n ′ γ ) reaction to identify multiphonon quadrupole excitations. Yields of γ rays as a function of incident neutron energy, γ– γ coincidences, and γ-ray angular distributions have been measured. From the excitation functions and coincidence measurements, the level and decay schemes were determined with good confidence in the γ-ray placements. The angular distributions provide multipolarity information on the decay γ rays which lead to spin assignments for levels and also enable the determination of lifetimes or lifetime limits from Doppler shifts. A close-lying triplet of levels, representing the two-phonon multiplet, occurs near an additional 4 + level which mixes with the 4 + two-phonon excitation. A three-phonon quintet of levels has been found, including one new level, which decays almost exclusively to the two-phonon triplet. No other levels in the three-phonon energy region decay other than weakly to the two-phonon excitations; only one other level has observable decays to the two-phonon triplet.

Coulomb-nuclear interference (CNI) results of the collective quadrupolar excitations in odd and even Ru isotopes

The study of the odd 99;101Ru nuclei complements the investigation of the collectivity of the first quadrupolar excitations in 100;102;104Ru. Angular distributions for the 99;101Ru(d, d') reactions at 13 MeV were obtained in the Pelletron Laboratory using nuclear emulsion plates on the focal plane of the Enge spectrograph. A Coulomb-Nuclar Interference analysis employing DWBA-DOMP predictions with global optical potential parameters was applied to the excitation of states which could belong to the multiplet built on the first quadrupolar excitation of the core. In the analysis, three states were identified for each of the isotopes and associated, respectively, with adopted levels in the Nuclear Data Sheets Compilation of Jpi= 5=2+, 7=2+ and 9=2+. Through the comparison of experimental and predicted cross section angular distributions, the values of (<IMG SRC="/img/revistas/bjp/v34n3a/a14img01.gif">)² and of the ratio C = <IMG SRC="/img/revistas/bjp/v34n3a/a14img01.gif" >/ <IMG SRC="/img/revistas/bjp/v34n3a/a14img02.gif" >were obtained.

Coulomb nuclear interference with deuterons in even palladium isotopes

Angular distributions for the inelastic scattering of 13.0 MeV deuterons on 104;106;108;110Pd were measured with the Sao Paulo Pelletron-Enge-Spectrograph facility in the range of 120 < qlab < 640. A Coulomb-Nuclear Interference analysis, employing the Distorted Wave Born Approximation with the Deformed Optical Model as transition potential, under well established global optical parameters, was applied to the first quadrupolar excitations. The values of C = / , the ratio of charge to isoscalar deformation lengths, and of ()2 were extracted through the comparison of experimental and predicted cross section angular distributions. The ratios of reduced charge to isoscalar transition probabilities, B(EL) to B(ISL) respectively, are related to the square of the parameter C and were thus obtained with the advantage of scale uncertainties cancellation. For 104Pd, and preliminary for 108Pd, the respective values of C = 1.18(3) and C = 1.13(4) reveal an enhanced contribution of the protons relative to the neutrons to the excitation, while a smaller effect is found for 106Pd, C = 1.06(3) and for 110Pd, C = 1.07(3), in comparison with the value C = 1.00 expected for homogenous collective excitations.

Wavelength resolved laser-induced fluorescence emission of [formula omitted] trapped in an ion cyclotron resonance cell

We have measured the wavelength resolved fluorescence emission laser-induced fluorescence (LIF) spectrum of C 6 F 3 H 3 + confined in an open cylindrical ion cyclotron resonance Penning trap. Ion cyclotron resonant azimuthal quadrupolar excitation successfully mass-selects and traps the ions for 10 s for repeated laser interrogation, and establishes that the observed fluorescence is from C 6 F 3 H 3 + ions. Electron-induced fluorescence (EIF) emission spectra of the same species were acquired for comparison. Vibrational structure was resolved for both LIF and EIF, and our assignments are consistent with prior literature values in the absence of ion trapping and high magnetic field (3 T). This work represents the first determination of wavelength resolved LIF emission spectra of organic ions in a Penning trap.

Investigation of dipole excitations inCe142using resonant photon scattering

A photon scattering experiment with bremsstrahlung has been performed on the vibrational nucleus $^{142}\mathrm{Ce}$ up to a photon endpoint energy of $4.1\phantom{\rule{0.3em}{0ex}}\text{MeV}$. Fourteen dipole excitations have been observed between 2.1 and $3.9\phantom{\rule{0.3em}{0ex}}\text{MeV}$, five of them for the first time. A candidate for the ${1}^{\ensuremath{-}}$ dipole member of the recently proposed quintuplet of negative parity ${({2}_{1,\text{ms}}^{+}\ensuremath{\bigotimes}{3}_{1}^{\ensuremath{-}})}^{({J}^{\ensuremath{-}})}$, involving the ${2}_{1,\text{ms}}^{+}$ isovector quadrupole excitation in the valence shell, has been identified. This exotic ${1}_{\text{ms}}^{\ensuremath{-}}$ state has been predicted within the $sdf$-IBM-2 and is expected to be accessible to photon scattering measurements. Solely one of nine $J=1$ states in the energy region of interest shows a decay pattern compatible with the model predictions for the ${1}_{\text{ms}}^{\ensuremath{-}}$ state.

A digital ion trap mass spectrometer coupled with atmospheric pressure ion sources.

In a digital ion trap (DIT), the quadrupole trapping and excitation waveforms are generated by the rapid switching between discrete d.c. voltage levels. As the timing of the switch can be controlled precisely by digital circuitry, the approach provides an opportunity to generate mass spectra by means of a frequency scan in contrast to the conventional voltage scan, thus providing a wider mass range of analysis. An instrument has been constructed which employs a 'non-stretched' ion trap and the field fault around the aperture of the end-cap electrode can be corrected electronically using a field-adjusting electrode. The ion trap was coupled with electrospray ionization (ESI) and atmospheric pressure matrix-assisted laser desorption/ionization (AP-MALDI) sources to demonstrate the capability of the digital method. AP-MALDI mass spectra of singly charged ions with mass-to-charge ratios upto 17 000 Th were generated using a trapping voltage of only 1000 V. Forward and reverse mass scans at resolutions up to 19 000 and precursor ion isolation at resolutions up to 3500 with subsequent tandem mass spectrometric analysis were demonstrated. The method of generating the digital waveforms and period scan is described. Discussion of the issues of mass range, scan speed, ion trapping efficiency and collision-induced dissociation efficiency are also provided.

Quadrupole and scissors modes and nonlinear mode coupling in trapped two-component Bose-Einstein condensates

We theoretically investigate quadrupolar collective excitations in two-component Bose-Einstein condensates and their nonlinear dynamics associated with harmonic generation and mode coupling. Under the Thomas-Fermi approximation and the quadratic polynomial ansatz for density fluctuations, the linear analysis of the superfluid hydrodynamic equations predicts excitation frequencies of three normal modes constituted from monopole and quadrupole oscillations, and those of three scissors modes. We obtain analytically the resonance conditions for the second harmonic generation in terms of the trap aspect ratio and the strength of intercomponent interaction. The numerical simulation of the coupled Gross-Pitaevskii equations vindicates the validity of the analytical results and reveals the dynamics of the second harmonic generation and nonlinear mode coupling that lead to nonlinear oscillations of the condensate with damping and recurrence reminiscent of the Fermi-Pasta-Ulam problem.

Magnetic Circular Dichroism of Resonant X-Ray Emission Spectra by Electric Quadrupole Excitation

We give a theoretical prediction for the angle dependence of the magnetic circular dichroism in resonant X-ray emission spectroscopy (MCD-RXES) by the electric quadrupole excitation. After general analytic calculations with an atomic model, we perform numerical calculations of L 2,3 – M 4,5 MCD-RXES for Sm 3+ , where the 2 p –4 f electric quadrupole excitation, as well as the 2 p –5 d electric dipole excitation, is followed by the 3 d –2 p X-ray emission by the electric dipole transition. Tuning the incident X-ray energy in the pre-edge region of the L 3 X-ray absorption, the change of the spectral shape of MCD-RXES is studied in detail with the change of the incident and emitted X-ray angles. We also discuss the possibility of detecting the signal of the electric quadrupole excitation in the MCD-RXES spectra, separately from that of the electric dipole excitation, by changing the incident and emission angles.

Theoretical aspects of resonant X-ray emission spectroscopy

We report recent theoretical topics for resonant X-ray emission spectroscopy (RXES) in d and f electron systems: (1) RXES in high T c cuprates, (2) effects of electric quadrupole excitation, and (3) magnetic circular dichroism (MCD) in RXES for ferromagnetic systems. In high T c cuprates, RXES with Cu 1s excitation detects a 6 eV charge transfer excitation whose intensity is affected by the Zhang–Rice (Z–R) singlet formation in the intermediate state. Very recently the Zhang–Rice singlet excitation is studied both theoretically and experimentally in RXES with O 1s excitation. On the electric quadrupole excitation at the L edge of rare earth systems, RXES is a powerful tool to detect it, whereas the quadrupole excitation is almost invisible in the conventional X-ray absorption spectroscopy (XAS). Theoretical calculations have recently been made for a spectral splitting of the quadrupole excitation in light rare earth elements from La to Eu, and compared with experimental results so far made. Finally, recent theoretical calculations of MCD in RXES for ferromagnetic systems show that when the incident X-ray direction is perpendicular to the magnetization of the system the MCD is caused by the interference effect characteristic of the coherent second order optical process. This effect has been confirmed by experimental observations of MCD-RXES with Gd L edge of a Gd–Co amorphous alloy.

A self-consistent approach to the quadrupole dynamics of medium heavy nuclei

We present a study of the collective quadrupole excitations in some medium heavy transitional nuclei, namely 102Zr, 104Mo, 110Ru, 110Pd, 124Xe and 126Ba, within the frame of a self-consistent model with the Skyrme SIII forces. The full five-dimensional collective dynamics is treated through the Bohr Hamiltonian with mass parameters and moments of inertia calculated microscopically. We discuss consequences stemming from the approximate inclusion of Thouless–Valatin corrections as well as effects of various shapes of the pairing interactions ( G force, δ and density dependent δ forces).

Finite-temperature excitations of a trapped Bose-Fermi mixture

We present a detailed study of the low-lying collective excitations of a spherically trapped Bose-Fermi mixture at finite temperature in the collisionless regime. The excitation frequencies of the condensate are calculated self-consistently using the static Hartree-Fock-Bogoliubov theory within the Popov approximation. The frequency shifts and damping rates due to the coupled dynamics of the condensate, noncondensate, and degenerate Fermi gas are also taken into account by means of the random-phase approximation and linear-response theory. In our treatment, the dipole excitation remains close to the bare trapping frequency for all temperatures considered, and thus is consistent with the generalized Kohn theorem. We discuss in some detail the behavior of monopole and quadrupole excitations as a function of the Bose-Fermi coupling. At nonzero temperatures we find that, as the mixture moves towards spatial separation with increasing Bose-Fermi coupling, the damping rate of the monopole (quadrupole) excitation increases (decreases). This provides us a useful signature to identify the phase transition of spatial separation.

Instabilities of off-centered vortices in a Bose-Einstein condensate

We study numerically the excitations of off-centered vortices in a Bose-Einstein condensate. The displacement of a single vortex and the separation of a doubly quantized vortex are considered. We find that the core-localized excitations of the precessing vortices continue to feature the property which implies that the vortices are unstable. The core-localized, dipolar, and quadrupolar excitations are found to deform continuously as functions of vortex displacements and intervortex separation.

Resonant X-Ray Emission Spectra by the Electric Quadrupole Excitation at the MnK-Edge of MnO

We study the incident, the scattering and the azimuthal angle dependences of the Mn K β resonant x-ray emission spectroscopy (RXES) due to the electric quadrupole excitation by tuning the incident photon energy to the pre-edge region of the Mn K -edge for a MnO single crystal both experimentally and theoretically. RXES caused by the electric quadrupole excitation shows a strong sensitivity to these angles, and the agreement between theory and experiment is good. Different angle dependences are shown between the excitation to the T 2 g orbital and that to the E g one. It is discussed that RXES can be a powerful tool to separate the electric quadrupole and dipole contributions in the pre-edge region of the transition-metal K -edge in transition metal compounds.