Nuclear Anomalous Dispersion inFe57by the Method of Total Reflection

Abstract

The recoil-free coherent resonant scattering of the 14.4-keV Fe 67 gamma rays has been investigated by employing the techniques of the Mossbauer effect together with those of total reflection. Of particular interest are the observed large interference effects attributed to the coherent superposition of the several resonant nuclear contributions and the nonresonant electronic contribution to the scattering amplitude in the forward direction. Gamma rays from a 300-mCi Co 57 source, diffused into the thin edge of a stainless steel plate, were reflected at small glancing angle 0 by an optically flat Fe 67 mirror through a narrow slit into a Nal scintillation detector. The resonant frequency spectrum of the Fe 67 nuclei in the mirror was scanned by varying the source velocity v. Values of the absolute reflectivity R (0,v) were obtained by comparison of the direct and reflected measured intensities. In an auxiliary experiment R(v) was measured with an external magnetic field applied to the mirror. The results of these measurements were compared with computerprogrammed calculations based on the classical optical theory of total reflection. Appropriately averaged quantum-mechanical expressions were introduced for the coherent resonant nuclear scattering amplitude in the forward direction. Separate computations were made for each polarization state of the incident radiation; these were averaged to give R(9,v) appropriate for an unpolarized source and a polarizationinsensitive detector. Suitable integrations were performed to take into account the frequency spread and angular width of the incident radiation. For 0 = 4 mrad, R(v), computed with the six resonances of normal ferromagnetic Fe 57 , agreed in shape and magnitude with the observed reflectivity, when the resonance width was assumed to be four times the natural width. For 0 -2 mrad, where the gamma-ray penetration depth is small, anomalies in the magnetic and chemical environment of the Fe 67 nuclei near the mirror surface required the introduction of additional resonances for FeO and for nonmagnetic Fe.

Nuclear resonance reflectivity from a [57Fe/Cr]30multilayer with the Synchrotron Mössbauer Source

“…This is the reason why the Fourier transform of the reflectivity amplitude, sensitive only to the variable part of the function, tends to 0 as goes to zero, and it explains the specific shape of the NRR curve measured in the time-domain experiments. Note that exactly this shape of the reflectivity curves was observed in the first Mö ssbauer experiment on reflectivity (Bernstein & Campbell, 1963) in which the validity of the Fresnel formalism for the nuclear resonant scattering was tested. The interference of the nuclear resonant and electronic scattering amplitudes is revealed as an asymmetric distortion of the lines in Mö ssbauer reflectivity spectra mostly pronounced near the critical angle of the total external reflection.…”

“…The interference of the nuclear resonant and electronic scattering amplitudes is revealed as an asymmetric distortion of the lines in Mö ssbauer reflectivity spectra mostly pronounced near the critical angle of the total external reflection. The lines in Mö ssbauer reflectivity spectra appear as dips at angles lower than the critical angle, as dispersive-like curves at the critical angle, and as asymmetric peaks at higher angles (Bernstein & Campbell, 1963;Irkaev et al, 1993aIrkaev et al, ,b, 1995Isaenko et al, 1994;Andreeva et al, 1998Andreeva et al, , 2017a.…”

“…Mö ssbauer reflectivity experiments (Bernstein & Campbell, 1963) started soon after the discovery of the Mö ssbauer effect. The dispersive shape of the lines in Mö ssbauer reflectivity spectra, varying from dips to peaks with the change of incidence angle, was clearly demonstrated and explained using the Fresnel formula and taking into account the interference between the nuclear resonant and electron scattering.…”

“…The selection rules for nuclear transitions between magnetic hyperfine sublevels lead to a specific line ratio in the Mö ssbauer spectra and its angular dependence, different for the cases ofand -polarized incident radiation. It is worthwhile noting that in reflectivity spectra the lines are characterized by a peculiar shape, considerably changing with grazing angle variation (Bernstein & Campbell, 1963;Isaenko et al, 1994). This adds a complexity to the correct interpretation of the Mö ssbauer reflectivity spectra.…”

Interferometric phase detection at x-ray energies via Fano resonance control

“…The interference of a narrow bound state with a continuum is known to give rise to asymmetric Fano resonances [22][23][24]. Note that asymmetric line shapes for nuclear resonances have previously been predicted or observed [25][26][27][28][29][30], though not interpreted as Fano resonances. However, they are also well known at hard x-ray energies [31,32].…”