抄録
A simple analyses is presented concerning the total response observed in neutron wave experiments under conditions outside the asymptotic mode region in finite polycrystalline media.
A discontinuity of the pseudo-fundamental eigenvalue due to sub-Bragg neutrons and the disappearance of the cold-neutron dominated discrete eigenvalue are indicated in the low-frequency region in finite polycrystalline media under ordinary experimental conditions. The analytically continued dispersion relation cannot explain the space- (or time-) dependent and system dimension-dependent experimental results in the pseudo-fundamental mode region. Here, the total solution including such contaminating components as the sub-Bragg neutron continuum or the spatial higher mode is obtained in an integral making use of suitable models and simple approximations.
The portion having the largest excitation amplitude in the solution is analyzed by a "saddle-point method" appled to the integral, and a simple relation for the effective relaxation coefficient observed in the experiment is derived. Numerical calculations give satisfactory agreement with experimental results in graphite, and the experimental conditions desirable for the exact observation of the pseudo-fundamental eigenvalue are discussed as well as practical results obtained for graphite.
