### ASA 126th Meeting Denver 1993 October 4-8

## 2aPAb1. On statistical fluctuations in single scattering by an ensemble of
scatterers.

**George H. Goedecke
Michael De Antonio
**

**
**
*Dept. of Phys., NMSU, Las Cruces, NM 88003-0001
*

*
*
**Harry J. Auvermann
**

**
**
*Army Res. Lab., Battlefield Environment Directorate, WSMR, NM 88002-5501
*

*
*
Expressions in terms of the presumed known scattering cross section of the
objects are derived for the ensemble average single scattering differential
cross section (sigma)[sub N] and its rms deviation (Delta)(sigma)[sub N] due to
a homogeneous ensemble of N identical objects randomly positioned with no
corrections in an observed volume V. For wavelength (lambda), it is well known
that, if N(lambda)[sup 3]/V(less than or equal to)1, there is considerable
diffuse scattering, while, if N(lambda)[sup 3]/V>>>1, the scattering is
essentially forward and coherent. Apparently not so well known is the result of
(Delta)(sigma)[sub N]/(sigma)[sub N] depends on another parameter
(alpha)(identically equal to)C((theta))N((lambda)[sup 3]/V)[sup 4/3], when
C((theta)) is a numeric of order unity and depends on scattering angle (theta).
It is shown that, if (alpha)>>1, then (Delta)(sigma)[sub N]/(sigma)[sub
N](alpha)N[sup -1/2] and is very small, while if (alpha)(less than or equal
to)1, then (Delta)(sigma)[sub N](approximately equal to)(sigma)[sub N].
Application involving numerical simulation is made to single scattering of
acoustic waves by an ensemble of turbules.