__Yu.A. Semerenko__

*B.Verkin Institute for Low Temperature Physics and
Engineering, **National** **Academy** of Sciences of the **Ukraine**, **Kharkov**, **Ukraine*

It has been known [1], that for real crystal
with defects the damping decrement _{} and defect of
the dynamic Young's modulus _{} are defined by
statistical averaging for a Debye expressions [1] on the whole energy activation
spectrum *U* of local structural imperfections (relaxators), which is
characterized by the statistical distribution function *P*(*U*):

were _{}, *t*_{0} - the period of attacks, *U* - the activation
energy, *k* – the Boltzmann constant, D_{0} - the elementary
relaxators "power", *C _{r}* - the relaxators concentration.

It has
been shown in Ref. [2] that the energy spectrum
of acoustic relaxation in high-purity Fe single crystal of orientation
<731> can be described by a quasi-Gaussian function _{}. In this assumption the theoretical dependences well
describe experimental temperature spectra _{} and _{} in the vicinity
of a-peak (*U*_{0}=0.037 eV, t_{0}=2.4·10^{-11}
s) which is observed at temperature »54 К (vibration frequency of the order of 88
kHz). However at the temperatures around 15 К it was observed some discrepancy of
experimental and theoretical dependences. It
is represented expedient to decide a inverse problem - recovering *P*(*U*) from
experimental dependences _{} or _{} and carrying
out the comparison of the *P*(*U*) with the
"guessed" expression *P ^{G}*(

1.A.S. Nowick, and B.S. Berry,
Anelastic Relaxation in Crystalline Solids, Academic Press,

2.V.D. Natsik, P.P. Pal-Val, L.N. Pal-Val,
and Yu.A. Semerenko // Fiz. Nizk. Temp. **26**,
711 (2000) [Low Temp. Phys. **26**, 522
(2000)].

3.A.N. Tikhonov, V.Ya. Arsenin The methods for
solution of ill-posed problems [in Russian], Nauka,

4.P.P. Pal-Val, V.D. Natsik, *Phil. Mag*. **A 56**, 407 (1987).