^{1,a)}and P. R. Berman

^{2,b)}

### Abstract

The intensity of Rayleigh scattering is proportional to the number of scatterers in a dilute gas. In contrast, for liquids or solids at low temperatures, any lateral Rayleigh scattering can be suppressed significantly. Microscopically, it is not obvious why the lateral Rayleigh scattering is diminished as the density in the medium increases. We use simple exactly solvable models to show that the suppression of Rayleigh scattering is proportional to the ratio of the interparticle correlation length to the interparticle distance. The wavelength of the scattered radiation is much larger than both these quantities in many cases of interest and does not play an explicit role in the suppression of lateral Rayleigh scattering.

The authors would like to thank Alejandro García, William Andersen, W. Ford, Mark Newman, and Stephen Fahy for helpful discussions. In particular, Fahy told them that he and others have used arguments similar to those they give in arriving at Eq. (29). A.G.R. acknowledges support from the Research Corporation.

I. INTRODUCTION

II. QUALITATIVE DISCUSSION

A. Random positions

B. Equal spacing

III. STATISTICAL EXCLUSION MODEL

A. Mathematical details

B. Correlation length

IV. FLUCTUATIONMODEL

A. Tonks model

B. Connection with the statistical model

V. SUMMARY

### Key Topics

- Rayleigh scattering
- 26.0
- Particle scattering
- 21.0
- Particle fluctuations
- 11.0
- Light scattering
- 9.0
- Molecule scattering
- 9.0

## Figures

Scattering of an incident field by particles aligned along the axis. The figure is not drawn to scale because . The bold arrow gives the propagation direction of the incident field, which is polarized in the direction. The origin of the coordinate system is at the midpoint of the line of scatterers.

Scattering of an incident field by particles aligned along the axis. The figure is not drawn to scale because . The bold arrow gives the propagation direction of the incident field, which is polarized in the direction. The origin of the coordinate system is at the midpoint of the line of scatterers.

Particles placed on a line at random with nearest neighbors removed. It is clear from the figure that removal of nearest neighbors builds in correlation between particle positions.

Particles placed on a line at random with nearest neighbors removed. It is clear from the figure that removal of nearest neighbors builds in correlation between particle positions.

Graphs of the structure function as a function of for several values of : (a) , (b) , (c) , (d) . The approximate expression (24) is used for (a)–(c) and the exact expression (21) with is used for (d). A region of the order of about the origin is excluded because it is assumed that .

Graphs of the structure function as a function of for several values of : (a) , (b) , (c) , (d) . The approximate expression (24) is used for (a)–(c) and the exact expression (21) with is used for (d). A region of the order of about the origin is excluded because it is assumed that .

Experimental curves of the structure factor for x-ray diffraction from rubidium (Ref. 16) [ corresponds to our ]. The lowest curve corresponds to a dense gas and the other curves to the liquid phase.

Experimental curves of the structure factor for x-ray diffraction from rubidium (Ref. 16) [ corresponds to our ]. The lowest curve corresponds to a dense gas and the other curves to the liquid phase.

The particles are divided into bins, each bin containing a large number of oscillators. The spatial phase factor is approximately constant for each particle within a given bin.

The particles are divided into bins, each bin containing a large number of oscillators. The spatial phase factor is approximately constant for each particle within a given bin.

particles randomly distributed over a wavelength distance. The sine wave is replaced by a square wave to illustrate the importance of the scattered signal on particle fluctuations.

particles randomly distributed over a wavelength distance. The sine wave is replaced by a square wave to illustrate the importance of the scattered signal on particle fluctuations.

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