J. Phys. C: Solid State Physics, Vol. 12, 1979 PP 615-631

On excitation of isometric nulcear states in a crystal by synchrotron 
radiation

Yu. Kagan, A. M. Afanas'ev and V. G. Kohn

The time dependence of delayed radiation is investigated when a pulse of 
synchrotron radiation undergoes resonance Bragg scattering by the nuclei 
in a crystal that have an isomeric level with a Mossbauer transition. 
Instead of the usual exponential law exp(-t/tau_0) characteristic of an 
isolated nucleaus, a time dependence in the form (tau_0/t)^2exp(-t/tau_0) 
was discovered at small deviations alpha from the Bragg angle. The 
acceleration of the decay is connected with the collective nature of the 
excitation of the nuclei in the crystal -- the nuclear exciton formation. 
The exponential law remains at large alpha but the intensity decreases as 
1/alpha^2. In the case of large divergence of the incident beam the law 
(tau_0/t)exp(-t/tau_0) is obeyed. The frequency distribution of the 
reflected pulse and the possibility of formation of a resonance structure 
with sufficient resolution are analysed in detail. The problem of time 
evolution of the synchrotron radiation pulse in transimssion trough two 
crystals -- the Bragg reflector and resonance absorber -- is solved. It is 
found that the requirements for the maximum intensity of the delayed 
radiation and the necessary frrequency distribution contradict one 
another. For example, when alpha or the delay time are small the resonance 
structure vanishes. Therefore, for Mossbauer-type experiments it is 
expedient to measure the intensity integrated over time with the exception 
of an appreciable initial time interval after the pulse, and with 
effective use of the reflection corresponding to a deviation from the 
Bragg angle by the value characteristic for the angle interval of the 
Bragg scattering.