Recoil-free fraction and Debye-Waller factor

We have now reached the stage of realising that, for a y-emitter in a solid, there is a finite probability that the y-ray can be emitted essentially without recoil or thermal broadening and that the width of the hne derives from the Heisenberg uncertainty principle. We next seek to calculate what this probability will be. [Pg.9]

4 Recoil-free Fraction and Debye-Waller Factor We have already seen qualitatively that the recoil-free fraction or probability of zero-phonon events will depend on three things [Pg.9]

Thus / will be greater the smaller the probability of exciting lattice vibrations, [Pg.9]

From a quantitative viewpoint, the probability W of zero-phonon y-emission from a nucleus embedded in a solid which simultaneously changes its vibration state can be calculated by dispersion theory [3, 5] it is proportional to the square of the matrix element connecting the initial i and final f I states. [Pg.9]

Further, since j is a random vibration vector, can be replaced by a , the component of the mean square vibrational amphtude of the emitting atom in the direction of the y-ray. Since U = Tf = Ey/ificY, where X is the wavelength of the y-ray, we obtain [Pg.10]

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