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Journal of Modern Optics

Mössbauer spectra narrowing by the ‘magic-angle‘ technique

Petr M. Anisimov, Yuri V. Rostovtsev, Olga A. Kocharovskaya

Published Nov 10, 2005• 1 citation
Publisher

Abstract

We conduct a numerical study of the possibility of using the `magic-angle' technique to suppress inhomogeneous broadening of Mössbauer spectra. We use the Floquet-state perturbation theory for the rf modulation of the Mössbauer resonance, which was adjusted to suit our purpose. A system of two nuclei of 57Fe coupled by the dipole–dipole interaction is considered. The analysis here completes studies started in 2004, by including the dipole–dipole interaction between one nucleus in the ground state and the other in the excited state. We show that partial suppression of inhomogeneous broadening remains possible.

DOI
10.1080/09500340500275660

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We conduct a numerical study of the possibility of using the `magic-angle' technique to suppress inhomogeneous broadening of Mössbauer spectra. We use the Floquet-state perturbation theory for the rf modulation of the Mössbauer resonance, which was adjusted to suit our purpose. A system of two nuclei of 57Fe coupled by the dipole–dipole interaction is considered. The analysis here completes studies started in 2004, by including the dipole–dipole interaction between one nucleus in the ground state and the other in the excited state. We show that partial suppression of inhomogeneous broadening remains possible.
We study theoretically resonance absorption of \ensuremath{\gamma} rays by nuclei exposed to an external radio-frequency (rf) magnetic field. The external field is taken to couple directly to the nuclear magnetic moments. Perturbation theory is developed for M\"ossbauer spectroscopy in terms of Floquet eigenstates that incorporate the rf field exactly. The present treatment allows for calculation of the conventional time-averaged absorption spectrum, as well as analysis of the time dependence of absorption, resolved on the scale of a period of the rf field. An efficient numerical implementation of the theory is described and comparisons with the equally general approach of Salkola and Stenholm [M. Salkola and S. Stenholm, Phys. Rev. A 41, 3838 (1990)] are made. We demonstrate that even at off-resonance frequencies a strong modulation leads to shifts of the original static hyperfine lines. Examples of line splittings of NMR's associated with Rabi flopping are also shown. \textcopyright{} 1996 The American Physical Society.
Modification of nuclear resonant absorption by means of laser radiation is analyzed both theoretically and experimentally. Theoretical analysis is done on the basis of four-level model of atom. This model includes both electronic and nuclear excitations. It is predicted that under coherent laser driving nuclear resonant Mossbauer absorption can be significantly modified, e.g. new Mossbauer resonances can appear, some of the existing resonances can vanish, both can be Rabi-split, broadened by laser action. In addition, it is predicted that Mossbauer absorption can be completely suppressed due to coherent population trapping. Experimental observation of laser-induced transformations of Mossbauer spectra of 57Fe2+ : MgO is accomplished. New Mossbauer lines appear with laser driving while the existing are broadened. Possible explanations of the observed changes in 57Fe2+ : MgO Mossbauer spectra are population of higher-lying electronic states of iron ion and significant modification of electronic relaxation processes due to modified Jahn-Teller interaction.
In this paper we derive a complete semiclassical description of M\"ossbauer spectroscopy with arbitrary external or internal perturbations of the active levels. The \ensuremath{\gamma} rays are taken to be weak enough to allow us to evaluate the linear M\"ossbauer response to lowest order in the intensity, in which case the \ensuremath{\gamma}-ray field can be treated classically. It induces transitions between level manifolds that can have arbitrary interactions inside themselves. The nuclear system is described by a density matrix. In principle, time-dependent perturbations can be handled by the formalism, but the equations are easier to solve for systems that display steady-state behavior. We consider, in particular, the case of magnetic radio-frequency modulation of the M\"ossbauer levels. Utilizing a matrix-continued-fraction technique, we solve for the absorption spectrum, and we choose numerical illustrations with parameters such that they describe the nucleus 57Fe^{57}\mathrm{Fe}57Fe. In this paper we treat mainly the case of magnetic modulation, but other experimental arrangements are discussed too. The calculations are able to treat both saturation and interference effects, which become important when the radio-frequency modulation is very strong. The new feature that emerges is the occurrence of resonances arising from the interference of different physical processes. The calculational method and its results are discussed and compared with other works.
As part of our general programme to develop the field of quantum nucleonics, we have studied Mössbauer spectroscopy when there is Zeeman splitting of the nuclear levels and a further interaction due to an applied rf-radiation field. We have applied the `dressed' state concept, developed in quantum electronics, to this situation. In particular, we have studied the case when the rf frequency is in the neighbourhood of the ground state (spin =1/2) splitting. The dressed-state approach in this case treats the coupling of nuclear Zeeman levels, due to an rf field, by considering the total system made up of nucleus, static magnetic field and rf field as one global quantum system. This allows the time evolution of the system to be handled straightforwardly. The energy levels and corresponding eigenstates of the system are calculated as a function of the rf frequency and the magnitude of the rf magnetic flux density. Mössbauer spectra are calculated for the case in which the source is subjected to both the static and radiation fields while the absorber nuclear levels are unsplit. Spectra are given as a function of the rf frequency, the magnitude of rf-field magnetic flux density, as well as the photon direction.