Quadrupole Excitations Research Articles

Laser-induced fluorescence for ion tomography in a Penning trap

Laser-induced ion fluorescence of laser-desorbed Ba + ions provides a measure of the relative number of ions near the center of the Penning trap of a Fourier transform ion cyclotron resonance mass spectrometer. Here, we report the detection of Penning-trapped ions by ion fluorescence, subject to radially outward ion cloud expansion (because of ion–neutral collisions), radially inward ion cloud compression (because of quadrupolar axialization), and the effects of buffer gas pressure and electrostatic trapping potential on those processes. At high pressure and high trapping voltage, radial ejection is far more rapid than axial ejection; quadrupolar axialization increases the number of ions near the center of the trap as well as the length of time that ions may be trapped; higher pressure results in faster magnetron radial expansion; and the choice of azimuthal quadrupolar excitation waveform significantly affects the efficacy of axialization. Based on these results, we suggest that directly detected laser-induced ion fluorescence provides a general new tool for mapping the ion distribution and its time evolution in response to various excitatory and damping effects.

Collisional damping of nuclear collective vibrations in a non-Markovian transport approach

A detailed derivation of the collisional widths of collective vibrations is presented in both quantal and semiclassical frameworks by considering the linearized limits of the extended time-dependent Hartree-Fock and the Boltzmann-Uehling-Uhlenbeck model with a non-Markovian binary collision term. Damping widths of giant dipole and giant quadrupole excitations are calculated by employing an effective Skyrme force, and the results are compared with giant dipole resonance measurements in lead and tin nuclei at finite temperature. {copyright} {ital 1998} {ital The American Physical Society}

Isovector quadrupole excitations in the valence shell of the vibrator nucleus136Ba:Evidence from photon scattering experiments

Photon scattering experiments have been performed on the nucleus ${}^{136}$Ba with photon energies of ${E}_{\ensuremath{\gamma}}<~4.1$ MeV and ${E}_{\ensuremath{\gamma}}<~2.8$ MeV. At 2.1 MeV clear evidence for the ${2}_{\mathrm{ms}}^{+}$ state has been found. From the measured lifetime we extract signatures for the isovector quadrupole excitation in the valence shell: a weakly collective $E2$ decay to the ground state and a strong $M1$ decay to the ${2}_{1}^{+}$ state. As the resonant photon scattering with bremsstrahlung is a complete reaction, we can conclude that the ${2}^{+}$ state at 2129 keV is a rather pure ${2}_{\mathrm{ms}}^{+}$ state with little fragmentation. This is in contrast to the ${1}^{+}$ scissors state. A comparison with an IBM-2 calculation is given.

Proton polarization in the p(e,e′p)π0 reaction and the measurement of quadrupole components in the N to Δ transition

The recoil proton polarization in the π0 production off the proton with longitudinally polarized electron beam has been studied as a means to measure quadrupole components in the N to Δ transition. On top of the Δ resonance a high sensitivity to a possible Coulomb quadrupole excitation is found in parallel kinematics. The ratio of S 1+/M 1+ multipole amplitudes can be determined from the ratio of the two in-scattering-plane recoil proton polarization components. Avoiding the absolute measurement of the polarizations, such a ratio allows small experimental uncertainties. Furthermore, the electron helicity independent proton polarization component enables the characterization of resonant and non-resonant pieces.

Three-body continuum structure and response functions of halo nuclei (I): 6He

Three-body scattering states of the Borromean two-neutron halo nuclei are explored in a core + n + n model using the method of hyperspherical harmonics. We analyse the continuum structure (the properties of the continuum wave functions) separately from the continuum response (the magnitudes of one-step transitions from the ground state to the continuum). Predictions are made for the positions and strengths of the isoscalar monopole, electric dipole and quadrupole excitations, as well as for nuclear inelastic and charge-exchange response functions, for the 6He nucleus. The known 2 + resonance in 6He is reproduced. We find 1 − strength concentrations at lower energies in the proximity of the three-body threshold, and predict new 2 +, 1 + (and possibly 0 +) resonances at slightly higher energies in 6He.

Multipole analysis of pion photoproduction based on fixed t dispersion relations and unitarity

We have analyzed pion photoproduction imposing constraints from fixed t dispersion relations and unitarity. Coupled integral equations for the S and P wave multipoles were derived from the dispersion relations and solved by the method of Omnès and Muskhelishvili. The free parameters were determined by a fit to the most recent data for π + and π 0 production on the proton as well as π − production on the neutron, in the energy range 160 MeV ⩽ E γ ⩽ 420 MeV. The lack of high precision data on the neutron and of polarization observables leads to some limitations of our results. Especially the multipole M 1− connected with the Roper resonance P 11 (1440) cannot be determined to the required precision. Our predictions for the threshold amplitudes are in good agreement with both the data and chiral perturbation theory. In the region of the Δ(1232) we have determined the ratio of electric quadrupole and magnetic dipole excitation. The position of the resonance pole is obtained in exellent agreement with pion-nucleon scattering, and the complex residues of the multipoles are determined with the speed-plot technique.

Identification of Quadrupolar Excitation Channels at theL3Edge of Rare-Earth Compounds

Resonant inelastic x-ray scattering spectra are recorded at the ${L}_{3}$ absorption edge of rare-earth ions in ${R}_{2}{\mathrm{Fe}}_{14}\mathrm{B}$. In all cases, weak resonances are observed at energies below the dipolar white line resonance, originating from $2p\ensuremath{\rightarrow}4f$ quadrupolar excitations. Their energy position is in excellent agreement with that of preedge features in the x-ray magnetic circular dichroism (XMCD) spectra of the same samples. Our results therefore evidence the systematic appearance of quadrupolar excitation channels and the importance of their inclusion in the correct interpretation of the XMCD at the ${L}_{3}$ edges of rare-earth systems.

Two-plate vs. four-plate azimuthal quadrupolar excitation for FT-ICR mass spectrometry

Azimuthal quadrupolar excitation has become one of the most useful techniques for ion axialization and translational cooling for FT-ICR mass spectrometry, leading to order(s)-of-magnitude improvement in mass selectivity, resolving power, mass accuracy, remeasurement efficiency, etc. Recently, Hendrickson et al. (J. Am. Soc. Mass Spectrom. 6 (1995) 448–452) showed that axialization may be achieved by 2-plate azimuthal quadrupolar excitation, in which an rf voltage of the same amplitude and phase is applied to a single pair of opposed side electrodes, while grounding the other orthogonal opposed pair (rather than applying an rf voltage of equal amplitude but shifted in phase by 180° to the second pair as in prior 4-plate experiments). Here, we analyze theoretically and test experimentally the performance of these two electrode geometries. As previously shown, either geometry can achieve axialization by resonant excitation at the unshifted ion cyclotron frequency, ( ω c = qB/ m). For either excitation configuration, excitation at twice the reduced cyclotron frequency, 2ω +, leads to unwanted exponential growth of the ion cyclotron radius. For 2-plate geometry, we show that excitation at twice the axial oscillation frequency, 2 ω z, leads to exponential growth in z-oscillation amplitude, whereas excitation at ω c = ω + + ω − and ω p = ω + − ω − (‘parametric’ frequency) leads to complex ion behavior. Finally, we discuss the effect of azimuthal quadrupolar excitation amplitude (as well as frequency) on axialization.

Antiscreening channels for ion–ion collisional excitations in dense plasmas

Plasma-screening effects are investigated on antiscreening channels for excitation of a one-electron target by a one-electron projectile in dense plasmas. The interaction Hamiltonian in dense plasmas is obtained by an appropriate form of the nonspherical Debye–Hückel potentials. Semiclassical straight-line trajectory method is applied to the ion projectile path in order to visualize the antiscreening transition probability in dense plasmas as a function of the impact parameter and the collision energy. The plasma screening effects reduce the transition probabilities, especially, in the dipole–dipole transition. The maximum position of the transition probability is receding from the target nucleus with increasing projectile energy for the dipole–dipole and dipole–quadrupole excitations. However, in the quadrupole–quadrupole excitation, the maximum position is getting closer to the target nucleus with increasing projectile energy. The quadrupole transitions (dipole–quadrupole and quadrupole–quadrupole) show the second maximum which is due to the double peaks of the 2s radial distribution function.

Scattering of electrons on metal clusters and fullerenes

It is shown that the main contribution to the elastic cross section of fast electrons on metal clusters and fullerenes results from scattering on the frozen cluster potential, which is determined by the electron density distribution of the ground state of the target cluster. The specific shape of the electron distribution in fullerenes and metal clusters manifests itself in the diffraction behaviour of the elastic differential cross section. The analysis of the total elastic cross section dependence upon projectile velocity, the number of atoms in the cluster and its size is provided. The cross section of elastic scattering on a cluster surpasses the sum of the individual scattering cross sections on the equivalent number of isolated atoms. This occurs because of the coherent interaction of the projectile electron with electrons delocalized in the cluster volume. We have demonstrated that collective electron excitations sensitive to the many-electron correlations dominate inelastic scattering. The surface plasmon resonances can be observed in the differential cross section for inelastic scattering. We found a condition for the quadrupole and higher multipole plasmon excitations to contribute relatively little to the electron energy loss spectrum. The results obtained have been compared with experimental data for the electron - fullerene collision. Reasonable agreement between theoretical and experimental results is reported. We have also demonstrated that plasmon excitations provide the main contribution to the total inelastic cross section over a wide energy range. We have calculated the dependence of the total inelastic cross section on collision energy and compared the result obtained with the experimental data available, giving an interpretation for the plateau region in the cross section as caused by plasmon excitations rather than the cluster fragmentation process. We have shown that the single-particle jellium approximation fails to describe this experiment. Our analysis is performed for metal clusters and fullerenes, However, it can also be applied to other polarizable systems, possessing plasmon or giant collective resonances.

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.

Self-consistent description of the excited superdeformed bands in 191Hg

Abstract The superdeformed ground and excited bands of the nucleus 191 Hg are calculated self-consistently within the Hartree-Fock-Bogoliubov theory with approximate particle number projection. In the numerical calculations we use the finite range density dependent Gogny force. We describe quadrupole moments, excitation energies and moments of inertia the experimentally observed four superdeformed bands. Former band assignments based in a more phenomenological approximation are confirmed. The agreement with the available experimental results is very satisfactory.

X-ray resonant Raman scattering from Gd3Fe5O12

The Fe 3p3/2,1/2→1s X-ray Resonant Raman Scattering (RRS) from Gd3Fe5O12 shows an intense resonating feature in the vicinity of the K absorption edge and a pronounced satellite in the emission spectrum above threshold. Comparison with Gd 3d5/2→2p3/2 RRS reveals common characteristics. The results are explained by inclusion of quadrupolar (E2) excitations in the intermediate states and electron correlation effects in the final states of the inelastic scattering process. Experimental aspects on how inelastic scattering spectra are recorded are briefly discussed.

Filtered white noise and repetitive chirp broadband quadrupolar excitation Fourier transform ion cyclotron resonance mass spectrometry at 1 tesla

Radiofrequency (RF) chirp and filtered white noise are compared as waveforms for broadband quadrupolar excitation. Ions are formed by matrix-assisted laser desorption Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry and axialized by quadrupolar excitation. Both quadrupolar excitation waveforms are capable of axializing ions over a range of masses. Remeasurement efficiencies for repetitive chirp excitation are greater than 98%. Remeasurement efficiencies for noise excitation are lower, 80%. The duration of transients recorded using either broadband excitation method is several orders of magnitude longer than for ions that have not been axialized.

A 4.7 Tesla internal MALDI-FTICR instrument for high mass studies: performance and methods

A 4.7 Tesla internal source matrix-assisted laser desorption ionization (MALDI) ion cyclotron resonance (FTICR) (MALDI-FTICR) has been constructed to examine ions in the 1000–10000 Da mass range. This instrument combines several recent innovations for enhancing the trapping and detection of ions of high mass-to-charge. Ions up to m/z 11 000 have been efficiently trapped and detected with high signal-to-noise (S/N). By using quadrupolar excitation to axialize ions, resolutions of 1.5 million for gramicidin S, 65 000 for insulin, and 85 000 for the 146-mer of polyethylene glycol have been obtained. 100% remeasurement efficiency is shown for 200 remeasurement cycles at m/z 2000 at high S/N with normal detection energies. By using quadrupolar excitation for ion remeasurement, effects from detection parameters such as trapping voltage and r.f. excitation power are examined under conditions that are independent of ionization yield. A tuning method is presented that uses the ions produced by one laser shot to systematically optimize signal strength and resolution for FTICR detection.

Deconvolution of lifetime broadening at rare-earth LIII edges compared to resonant inelastic x-ray scattering measurements.

The lifetime broadening of some rare-earth ${L}_{\mathrm{III}}$-edge x-ray absorption spectra (XAS) is partially removed by deconvolving high quality data. The ligand field splitting of dipolar resonances is clearly resolved. Exposed pre-edge structure is compared to atomic multiplet calculations of the $2p\ensuremath{\rightarrow}4f$ quadrupolar excitations. Ratios are thereby determined for the quadrupolar/dipolar oscillator strengths. Deconvolved XAS data of Ho${(\mathrm{N}{\mathrm{O}}_{3})}_{3}$ are compared to inelastic x-ray scattering measurements showing experimentally that the latter cannot reproduce a narrowed XAS.

Fourier Transform Mass Spectrometry

The fundamental principles of Fourier transform mass spectrometry (FTMS) are presented. The motion of ions in a FTMS analyzer can be understood in terms of the magnetic and electric fields present in the FTMS analyzer cell. Ion motion is illustrated with the results of ion trajectory calculations under both collision-free conditions and at high pressure. Dipolar and quadrupolar excitation are described and compared. Practical considerations in obtaining ultra-high-mass resolution and accuracy are discussed. The FTMS experiment is a series of events (ionization excitation, detection) that occur in sequence. Pulse sequences for mass spectrometric and tandem mass spectrometric experiments are presented.

Efficient Ion Remeasurement Using Broadband Quadrupolar Excitation FTICR Mass Spectrometry

Quadrupolar excitation is achieved over a wide mass range by using repetitive chirp excitation, filtered noise excitation, and high-amplitude, single-frequency excitation for matrix-assisted laser desorption FTICR mass spectrometry. These methods efficiently axialize ions over a wide range of masses in a 4.7 T FTICR spectrometer. Remeasurement efficiencies are >99.5% for broadband repetitive chirp excitation, 99% with filtered white noise, and 99.4% with high-amplitude, single-frequency broad-band quadrupolar excitation. Results indicate that z-axis ejection of ions during detection is the primary mechanism for ion loss during remeasurement experiments. Capacitive coupling of the excitation signal to the trapping plates of the open-ended cylindrical analyzer cell is required for high remeasurement efficiency.

Laser-induced Fluorescence of Ba+ Ions Trapped and Mass-selected in a Fourier Transform Ion Cyclotron Resonance Mass Spectrometer

We present the design and preliminary results from a Fourier transform ion cyclotron resonance (ICR) mass spectrometer developed for the direct detection of UV/visible laser-induced fluorescence of trapped, mass-selected, gas-phase ions. A 3 T superconducting magnet and an open-ended multi-section cylindrical Penning trap capture and confine ions created by electron impact or laser desorption. Azimuthal quadrupolar excitation in the presence of ion/neutral collisions cools, axializes and mass selects ions as they fill the trap. A pulsed dye laser pumped by an Nd:YAG laser provides electronic energy excitation. A Brewster window and baffles on each side of the vacuum chamber reduce the scattered light from the excitation laser. Laser-induced fluorescence is collected from mirrors and lenses and directed through a quartz window and fiber-optic bundle to a photomultiplier. The ICR and optical events are controlled by a modular ICR data station and GPIB and RS-232 interfaces. An excitation spectrum is demonstrated for atomic Ba+ ions, and should extend to laser-induced fluorescence of virtually any stable positive or negative gas-phase ions of arbitrary molecular weight: molecular or quasimolecular ions, fragment ions, adduct ions, and ions formed from ion/molecule reactions.

In-cell matrix-assisted laser desorption-ionization fourier transform ion cyclotron resonance mass spectrometry

A new internal matrix-assisted laser desorption-ionization (MALDI) Fourier transform ion cyclotron resonance-mass spectrometry (FTICR-MS) method is introduced. The target is directly positioned at one trapping electrode of a single cylindrical ion cyclotron resonance (ICR) cell and becomes a part of it. The ionization occurs inside the ICR cell in contrast to external or near-cell MALDI-FTICR-MS techniques. Very efficient trapping and mass resolving power better than unit resolution of singly charged peptides and proteins ions up to 2000 u is possible by using only basic FTICR-MS techniques. The sole application of a pulsed retarding potential increases the mass range to 6000 u. No collisional cooling and quadrupolar excitation was done. Sensitivities below 1 fmol, and ion storage times of more than 15 s are shown. High resolving powers of 16,000 and 56,000 are obtained on bovine insulin (5.7 ku) and gramicidin D (1.9 ku), respectively.