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Journal de physique

Phase and distance effects in rf modulation of Mössbauer radiation under stationary conditions

N.I. Ognjanov, Ludmil Todorov Tsankov

Published Jan 1, 1983• 4 citations
Publisher

Abstract

The phase effects, appearing in a system consisting of a Mössbauer source and a Mössbauer absorber, both vibrating at ultrasonic frequency, are theoretically investigated. It is shown that the intensity of the transmitted recoilless radiation depends on both the absolute phase shift between the vibrations of the source and those of the absorber, and on the effective dephasing due to the finite propagation time of the electromagnetic wave between them (the so-called « distance effect »). The relation between the distance effect and general relativity theory is critically discussed.

DOI
10.1051/jphys:01983004407086500

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The phase effects, appearing in a system consisting of a Mössbauer source and a Mössbauer absorber, both vibrating at ultrasonic frequency, are theoretically investigated. It is shown that the intensity of the transmitted recoilless radiation depends on both the absolute phase shift between the vibrations of the source and those of the absorber, and on the effective dephasing due to the finite propagation time of the electromagnetic wave between them (the so-called « distance effect »). The relation between the distance effect and general relativity theory is critically discussed.
A theoretical analysis is made of the influence of ultrasonic vibrations in a sample containing Mössbauer nuclei on the propagation of resonant gamma radiation. The problem is tackled by simultaneous solution of the Maxwell equations and equations for the density matrix. An exact solution of the problem is obtained for continuous sources and observation conditions without any restrictions on the frequency and amplitude of ultrasonic vibrations. The dependence of the absorption of gamma rays on their polarization and on the absorber thickness is derived. It is shown that the propagation of gamma radiation across a system of resonant absorbers vibrating at the same frequency but with different phases depends on the relationship between the phases and the distances between the absorbers. Experimental applications of the theory are considered.
Classical phase-modulation theory is applied to describe the interference of the recoil-free gamma-radiaton fields emitted by a M\"ossbauer source and a resonant absorber in forward-scattering geometry. During the exponential decay of the excited state in the source the resonant absorber develops and emits a coherent field, which interferes destructively with the source field. A stepwise phase change of the source field relative to the absorber field is introduced by a fast mechanical displacement of the source. As a result, an intense pulse of gamma rays is observed in the time dependence of the resonantly filtered radiation. This coherent transient phenomenon is called a gamma echo. The time reference of the gamma-echo experiment is the moment of formation of the excited state in the source. This is in contrast to earlier transient M\"ossbauer experiments in which the measurements were synchronized to the phase of the modulation and averaging occurred over all possible times of formation of the excited state. By choosing a suitable shape for the phase-modulation function in the echo experiment, short pulses of gamma radiation with desired duration and amplitude can be generated within a time frame defined by the lifetime of the excited nuclear state. Here, a detailed description of the experimental and theoretical aspects of stepwise phase modulation in a coincidence scheme is given. Theoretical results are presented in a general form, taking into account the experimental nonidealities. The properties of the mechanical drive system are discussed in detail. Gamma-echo data are presented. Good agreement between the theoretical calculations and the experimental data has been established.
The so-called gamma-echo effect has been observed experimentally and analyzed using the semiclassical optical theory. Here the effect is reinterpreted using a new 1D quantum mechanical model. This leads to a different interpretation of the effect as a π phase-shift induced transparency. In the basic time-differential Mössbauer spectroscopic technique the forward-scattered recoil-free radiation is observed, in delayed coincidence, after passing through a nuclear-resonant absorber. The effect in question is produced most efficiently when the source of recoil-free radiation is moved abruptly causing a π phase shift of the source radiation during its radiative lifetime. Using the 1D model the effect is seen to arise from the constructive interference between the source radiation at a later time, and the radiation coming from the absorber excited at an earlier time. The exact form of the source modulation and the nuclear-resonant thickness of the resonant absorber determines the shape of the time-differential resonant gamma ray transmission spectrum. Numerical results are given using the familiar 57Fe recoil-free resonant transition. The π phase-shift-induced transparency allows the resonant gamma radiation, incident on the resonant absorber, to be transmitted through the absorber without appreciable attenuation.
A quantum mechanical calculation of the time-dependent M\"ossbauer transmission has been performed neglecting solid-state effects. The source considered consists of nuclei which decay via a two-photon cascade, the second of which is emitted without recoil and is subject to resonant absorption by a foil whose resonance may be shifted due to a small relative velocity between source and absorber. The transmission is obtained when the transmitted recoiless photon is measured in coincidence with the first photon of the cascade. The result is in agreement with that obtained by considering the absorber as a classical dielectric slab capable of absorption and dispersion. The initial condition has been investigated in detail by considering the full cascade. In this manner, one sees that the usual simple assumption that the nucleus is in the first excited state immediately after the emission of the first photon, gives the correct boundary condition.
The transmission of the Mössbauer γ-quanta through a vibrating absorber is analyzed in the framework of the quantum theory.For this aim the photons are described by the Bialynicki -Birula's wave function.We calculated time dependence of the wave packets, which describe the transmitted γ-photons.It is shown that the squared modulus of their wave function determines the detection rate of γ-photons in full analogy with particles having a mass.The effect of anomalous transmission of Mössbauer radiation, caused by high-frequency periodic swings of the absorber, and the corresponding suppression of reactions is studied.
The radiation from a Mössbauer source of 57Co in a copper matrix is frequency-modulated by vibrating the source with a quartz piezo-crystal driven by an oscillator. If the radiation passes through a resonant absorber (a "filter"), a time structure containing the oscillator frequency and its harmonics appears in the resulting counting rate. It may be seen by sorting the time of each count with respect to the cross-over time of a subharmonic of the oscillator. These quantum beats are caused by interferences between the frequency components of the photon amplitude, and vanish unless there is some alteration of relative phase or amplitude of the original radiation by the filter. The harmonic constitution of the beats is a sensitive function of the relative shift of source and filter and may be used as a sensitive probe of small shifts. This is demonstrated by measuring the temperature shift in 57Fe-Be. If a velocity spectrum is made with counts collected during only a part of the vibration cycle, prominent dispersion effects are seen, with counting rates higher than background in some portions of the spectrum. A classical optical theory of the phenomenon is presented in summary. It explains the beats, the dispersion effects, and the sensitivity of the harmonic ratios to relative shifts.