Mössbauer Diffraction. II. Dynamical Theory of Mössbauer Optics

Abstract

The dynamical theory of Mossbauer optics is developed utilizing the multiple-scattering equations derived in the preceding paper (I). The general optical equations obtained are analogous to the equations of the dynamical theory of x-ray diffraction, but are generalized to account for the very strong polarization mixing which occurs in Mossbauer optics. This polarization mixing leads to a number of interesting features, such as Faraday effects, selective absorption, and selective critical reflection. The cases of Bragg reflection, Laue transmission, critical reflection, and off-Bragg transmission are treated in detail. 12

Stroboscopic detection of nuclear resonance in an arbitrary scattering channel

“…The index τ specifies the open scattering channel (Hannon & Trammell, 1969;Sturhahn & Gerdau, 1994). The scattering matrix T (r) (E − E v ) of the reference sample depends on the Doppler-shifted energy E − E v , where the channel index τ is omitted for forward scattering.…”

“…Theories that expand the coherent elastic scattering to the case of sharp nuclear resonances Hannon & Trammell, 1968;Hannon & Trammell, 1969;Hannon et al, 1985a) have been applied to various scattering geometries. The simplest cases are the onebeam cases, such as forward and off-Bragg scattering, and the two-beam cases, the Bragg-Laue scattering (Hannon & Trammell, 1969;Sturhahn & Gerdau, 1994) and the grazing incidence scattering (Röhlsberger et al, 2003;Hannon & Trammell, 1969;Hannon et al, 1985b;Irkaev et al, 1993;Deák et al, 1996). In the grazing incidence limit, an optical model was derived from the dynamical theory (Hannon & Trammell, 1969;Hannon et al, 1985b), which has been implemented in numerical calculations (Röhlsberger et al, 2003).…”

“…The simplest cases are the onebeam cases, such as forward and off-Bragg scattering, and the two-beam cases, the Bragg-Laue scattering (Hannon & Trammell, 1969;Sturhahn & Gerdau, 1994) and the grazing incidence scattering (Röhlsberger et al, 2003;Hannon & Trammell, 1969;Hannon et al, 1985b;Irkaev et al, 1993;Deák et al, 1996). In the grazing incidence limit, an optical model was derived from the dynamical theory (Hannon & Trammell, 1969;Hannon et al, 1985b), which has been implemented in numerical calculations (Röhlsberger et al, 2003). The reflectivity formulae given by Deák et al (1996) and Deák et al (2001) are suitable for fast numerical calculations in order to actually fit the experimental data (Spiering et al, 2000) and, as has been shown , this optical method is equivalent to that of the other approaches in the literature (Röhlsberger et al, 2003;Hannon et al, 1985b).…”

Measurement of synchrotron-radiation-excited Kossel patterns

“…4(e), without detailed theoretical discussion. The calculations are based on the theory worked out by Hutton et al (1985), Hannon & Trammell (1969) and Hannon et al (1974a,b). In both cases, the phase converged to the expected 0 value within 10 .…”

Superradiance of an ensemble of nuclei excited by a free electron laser

“…Similar to the 'collective dipole' of atoms coupled to the light field in an infrared optical cavity [10][11][12] , the 'compound' excited state 16,17 of an ensemble of nuclei under diffraction 15 or forward-scattering 18,19 conditions leads to enhancement of emission and strong 'speed-up' of the collective response [15][16][17][18][19][20][21][22][23] . In contrast to the optical regime, the theory of the quantum mechanical ensemble of nuclei and X-rays [20][21][22][23] is relatively tractable, as for short wavelengths the system is in the limit of dynamical diffraction 24 . This computational simplification allows the spatial extent of the sample to be easily incorporated and results in the close agreement of closed-form theory with nearly all observations 15,18,19,23,25 .…”