0000000000117067
AUTHOR
Martin Kretzschmar
The Ramsey method in high-precision mass spectrometry with Penning traps: Experimental results
The highest precision in direct mass measurements is obtained with Penning trap mass spectrometry. Most experiments use the interconversion of the magnetron and cyclotron motional modes of the stored ion due to excitation by external radiofrequency-quadrupole fields. In this work a new excitation scheme, Ramsey's method of time-separated oscillatory fields, has been successfully tested. It has been shown to reduce significantly the uncertainty in the determination of the cyclotron frequency and thus of the ion mass of interest. The theoretical description of the ion motion excited with Ramsey's method in a Penning trap and subsequently the calculation of the resonance line shapes for differ…
A note on Δn ≠ 0 Stark transitions in hydrogenlike atoms
In a gaseous helium or hydrogen target slow muons or antiprotons are captured into orbits with a high principal quantum number (n = 15 to 50) to form (μ− α)+ ions, (pα)+ ions, or (pp) atoms respectively. In the subsequent deexcitation process Stark mixing of the intermediary states plays an important role. The successful Mainz Cascade Model assumed Δn = 0 for the Stark transitions, although formally no such selection rule exists. This note examines the reasons why Δn ≠ 0 Stark transitions play only a negligible role in the deexcitation cascade.
Theory of the elliptical Penning trap
Abstract An ideal “Elliptical Penning Trap” is an ideal cylindrically symmetric Penning trap with an additional electrostatic quadrupolar potential ∝ κ ( x 2 − y 2 ) . This configuration is here investigated for arbitrary strength κ of the additional potential. Aside from the decoupled axial motion the system is characterized by a generalized cyclotron and a generalized magnetron frequency. While the former depends only weakly on κ , the magnetron frequency decreases rapidly with increasing κ , vanishing at a maximum value κ max which represents the stability limit for the magnetron motion. Magnetron orbits are elliptical, with their numerical excentricity tending toward unity as κ approa…
The Ramsey method in high-precision mass spectrometry with Penning traps: Theoretical foundations
Abstract This paper presents in a quantum mechanical framework a theoretical description of the interconversion of the magnetron and modified cyclotron motional modes of ions in a Penning trap due to excitation by external rf-quadrupole fields with a frequency near the true cyclotron frequency. The work aims at a correct description of the resonance line shapes that are observed in connection with more complicated excitation schemes using several excitation pulses, such as Ramsey’s method of separated oscillating fields. Quantum mechanical arguments together with the “rotating wave approximation” suggest a model Hamiltonian that permits a rigorous solution of the corresponding Heisenberg eq…
Single particle motion in a Penning trap: description in the classical canonical formalism
This paper aims at the development of methods for the calculation of the characteristic frequencies of a Penning trap, taking into account deviations of the actual geometry from the ideal one, anharmonicities of the electric potential, misalignments and inhomogeneities of the magnetic field, additional time dependent electromagnetic fields, and so on. The paper starts by describing the motion of a single charged particle in an ideal hyperbolic Penning trap using the formalism of classical hamiltonian mechanics. The usefulness of rotating coordinates is pointed out, and the importance of conservation of canonical angular momentum is stressed. After transformation to action-angle variables th…
Buffer-gas-free mass-selective ion centering in Penning traps by simultaneous dipolar excitation of magnetron motion and quadrupolar excitation for interconversion between magnetron and cyclotron motion
A new excitation scheme of the radial ion-motional modes is introduced for Penning-trap ion-cyclotron-resonance experiments. By simultaneous dipolar excitation of the magnetron motion and resonant quadrupolar excitation for the conversion between magnetron motion and cyclotron motion, a mass-selective recentering of the ions of interest is performed while all other (contaminant) ions are ejected from the trap. This new technique does not rely on the application of a buffer gas as presently used [G. Savard, St. Becker, G. Bollen, H.-J. Kluge, R.B. Moore, Th. Otto, L Schweikhard, H. Stolzenberg, U. Wiess, Physics Letters A 158 (1991) 247] and will thus prevent charge-exchange reactions and da…
Time-separated oscillatory fields for high-precision mass measurements on short-lived Al and Ca nuclides
High-precision Penning trap mass measurements on the stable nuclide 27Al as well as on the short-lived radionuclides 26Al and 38,39Ca have been performed by use of radiofrequency excitation with time-separated oscillatory fields, i.e. Ramsey's method, as recently introduced for the excitation of the ion motion in a Penning trap, was applied. A comparison with the conventional method of a single continuous excitation demonstrates its advantage of up to ten times shorter measurements. The new mass values of 26,27Al clarify conflicting data in this specific mass region. In addition, the resulting mass values of the superallowed beta-emitter 38Ca as well as of the groundstate of the beta-emitte…
g-factor measurement of hydrogenlike28Si13+as a challenge to QED calculations
Using a phase-detection method to determine the cyclotron frequency of a single trapped ion in a Penning trap allowed us to perform a measurement of the $g$ factor of the bound electron in hydrogenlike ${}^{28}$Si${}^{13+}$ with a statistical uncertainty of $4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11}$. Furthermore, we reevaluated the image-charge shift as the main source of uncertainty. Our result challenges bound-state quantum-electrodynamical calculations by probing two-loop contributions of order (Z$\ensuremath{\alpha}$)${}^{6}$ and paves the way towards a more precise determination of fundamental constants as the electron mass.
The elliptical Penning trap: Experimental investigations and simulations
Abstract The application of an additional azimuthal quadrupolar electrostatic field to a Penning trap leads to a field configuration referred to as an elliptical Penning trap. The resulting changes of the radial ion motions have been investigated experimentally and by use of simulations. The eigenfrequencies, i.e., the magnetron frequency ω ˜ − and the reduced cyclotron frequency ω ˜ + , are found to be shifted with respect to those of the standard Penning trap ω − , ω + , respectively. As the shift of the magnetron frequency ω ˜ − is larger than that of the reduced cyclotron frequency ω ˜ + their sum ω ˜ + + ω ˜ − is also a function of the ellipticity and no longer equal to the cyclotron f…
Octupolar excitation of ion motion in a Penning trap: A theoretical study
Abstract High-precision Penning-trap mass spectrometry uses the resonant conversion of the magnetron motional mode into the cyclotron motional mode to determine the cyclotron frequency of the ions under investigation. Usually the conversion process is performed by interaction of the ions with external quadrupolar rf-fields. Recently it was found that conversion by means of octupolar rf-fields entails a tremendous increase in mass resolution and is thus of great interest. However, the conversion results depend in an intricate way on the amplitudes and phases of the octupolar rf-field and of the motional modes of the ions. Experimental progress was hampered by the lack of an underlying theory…
On the phase dependence of the interconversion of the motional modes in a Penning trap by quadrupolar excitation
Abstract The interconversion of the radial motional modes in a Penning trap (magnetron and cyclotron modes) by an external quadrupolar rf-field with a frequency near the true cyclotron frequency ω c plays an important role in the measurement cycle of Penning trap mass spectrometry. Ions to be measured are prepared in a state of magnetron motion which is then resonantly converted into cyclotron motion. The data analysis is usually carried out under the assumption that the initial motional state of the ions has been a pure magnetron state. In reality, however, a small component of cyclotron motion is always present in the ion's initial motional state. This component introduces a dependence on…
Theoretical investigations of different excitation modes for Penning trap mass spectrometry
Abstract In Penning trap mass spectrometry the motion of trapped ions is manipulated by external radio-frequency fields. This paper describes a general theoretical framework to classify the various types of excitation of the ion's motional modes, to identify the resonance frequencies, and to find the effective interaction Hamiltonians which are valid in the vicinity of the resonances. Instead of Cartesian or cylindrical coordinates and momenta our theoretical approach uses the complex oscillator amplitudes of the cyclotron, magnetron, and axial oscillators as its basic dynamical variables. Equations of motion are set up, which can be simplified in the vicinity of resonances by the resonatin…
The interconversion of the radial motional modes of an ion in a Penning trap mass spectrometer by 4n-polar external radio frequency fields (n= 1,2,3,4)
In Penning trap mass spectrometry ion masses are determined by measuring the free cyclotron frequency via the resonant conversion of the magnetron into the cyclotron motional mode, induced by the interaction with an external radio-frequency field. With octupolar rf-fields of frequency the mass resolution has been improved by more than an order of magnitude as compared to conventional quadrupolar fields of frequency and with the same pulse duration. This result raises the question what one might expect from using 12-polar rf-fields with frequency or even 16-polar rf-fields with frequency . In this paper the theoretical model for the interconversion of the radial modes by quadrupolar and octu…
Theory of simultaneous dipole and quadrupole excitation of the ion motion in a Penning trap
Abstract Penning traps confine ions of atoms and molecules as well as other charged particles by a combination of static electric and magnetic fields to the central region of the trap, where these objects can be studied. Most experiments employ pulses of dipolar radio-frequency radiation followed by pulses of quadrupolar radio-frequency radiation to manipulate the motional state of the trapped particles. Instead of a sequential procedure an excitation of the ion motion by the simultaneous application of dipolar and quadrupolar rf-fields is also conceivable. This paper investigates the theory of simultaneous excitation under very general assumptions, with inclusion of possible damping terms.…
Damping effects in Penning trap mass spectrometry
Abstract Collisions of ions with residual gas atoms in a Penning trap can have a strong influence on the trajectories of the ions, depending on the atom species and the gas pressure. We report on investigations of damping effects in time-of-flight ion-cyclotron resonance mass spectrometry with the Penning trap mass spectrometers ISOLTRAP at ISOLDE/CERN (Geneva, Switzerland) and SHIPTRAP at GSI (Darmstadt, Germany). The work focuses on the interconversion of the magnetron and cyclotron motional modes, in particular the modification of the resonance profiles for quadrupolar excitation due to the damping effect of the residual gas. Extensive experiments have been performed with standard and Ra…