# Interaction of Thermal Neutrons and Photons with Matter

Chapter

## Abstract

Spectroscopy is concerned with measurement of the structure and dynamics of the ground state or low lying excited states of a condensed matter. A radiation is useful as a tool for spectroscopy if it couples weakly (in a sense to be discussed later) to the many body system. Because in this case the double differential cross-section (per unit solid angle, per unit energy transfer) for the radiation scattering can be written schematically as (see Figure 1): where the first factor (dσ/dΩ)

$$\frac{{{d^2}}}{{d\Omega d\omega }} \sim {\left( {\frac{{d\sigma }}{{d\Omega }}} \right)_0}\;{\sum\limits_{i,f} {{P_i}\left| { < f\left| {\sum\limits_{\ell = 1}^n {{e^{i\left( {{{\underline k }_1} - {{\underline k }_2}} \right) \cdot {{\underline r }_\ell }}}} } \right|i > } \right|} ^2}\delta \left( {\hbar \omega - E{}_i + {E_f}} \right)$$

(1)

_{Q}refers to differential scattering cross-section from the basic unit of scattering in the system and the second factor, usually called the dynamic structure factor, represents the time dependent structure of the system as seen by the radiation. This clear separation of the basic scattering problem, as embodies in the first factor, from the dynamic structure of the system itself, is only possible when the radiation couples weakly to the system and therefore the use of Born-approximation in deriving Equation (1) is valid. Both thermal neutrons and photons with energy up to x-ray region satisfy this criterion and thus are useful as probes for condensed matter structures.## Keywords

Thermal Neutron Compton Scattering Rayleigh Scattering Random Walk Model Dynamic Structure Factor
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## References

- 1.J. S. Higgins, L. K. Nicholson, and J. B. Hayter, “Observation of single chain motion in a polymer melt,” preprint (1980).Google Scholar
- 2.V. F. Sears, “Dynamic theory of neutron diffraction,” Can. J. Phys. 56: 1262 (1978).ADSCrossRefGoogle Scholar
- 3.Bound scattering length refers to scattering length of a nucleus which is fixed in space. Measurement of scattering length is normally made in a situation where the nucleus is free to recoil. The measurement gives free scattering length a which is related to b by b = [(A+1)/A]a where A is atomic weight of the nucleus. See G. E. Bacon, Neutron Diffraction, 2d ed., Oxford (1975) for tabulation of values of b.Google Scholar
- 4.H. Rauch, and D. Petrascheck, “Dynamical neutron diffraction and its application,” in Neutron Diffraction, ed. by H. Dachs, Springer-Verlag, Berlin (1978).Google Scholar
- 5.The Fermi approximation is discussed clearly in R. G. Sachs, Nuclear Theory, Addison-Wesley, Reading, Mass. (1953). p. 91.Google Scholar
- 6.See for example, L.D. Landau, and E. M. Lifshitz, Electrodynamics of Continuous Media, Addison-Wesley, Reading, Mass. (1960). Chapter 15.MATHGoogle Scholar
- 7.P. Eisenberger, and P. M. Platzman, “Compton scattering of X-rays from bound electrons,” Phys. Rev. A2: 415 (1970).ADSGoogle Scholar
- 8.A detailed discussion of this transformation can be found in E. A. Power, and T. Thirunamachandran, “On the nature of the Hamiltonian for the interaction of radiation with atoms and molecules,” Am. J. Phys. 46: 370 (1978).MathSciNetADSCrossRefGoogle Scholar
- 9.See for example, P. Nozieres, Theory of Interacting Fermi Systems, W. A. Benjamin, New York (1964).MATHGoogle Scholar
- 10.C. Kittel, Quantum Theory of Solids, John Wiley, New York (1963).Google Scholar
- 11.See derivation of Equation (92) from Equation (91) in S. H. Chen, “Structure of liquids,” in Physical Chemistry — An Advanced Treatise, ed. by H. Eyring, D. Henderson, and W. Jost, vol. VIIIA, Academic Press, New York (1971).Google Scholar
- 12.G. E. Uhlenbech, and L. S. Ornstein, “On the theory of Brownian motion,” Phys. Rev. 36: 823 (1930).ADSCrossRefGoogle Scholar
- 13.S. H. Chen, Y. Lefevre, and S. Yip, “Kinetic theory of collision line narrowing in pressurized hydrogen gas,” Phys. Rev. A8: 3163 (1973).ADSGoogle Scholar
- 14.M. Holz, and S. H. Chen, “Quasielastic light scattering from migrating chemostatic bands of E. Coli,” Biophys. J. 23: 15 (1978).ADSCrossRefGoogle Scholar
- 15.K, Kawasaki, “Mode coupling and critical dynamics,” in Phase Transitions and Critical Phenomena, ed. by C. Domb, and M. S. Green, vol. Va, Academic Press, New York (1976).Google Scholar
- 16.S. H. Chen, C. C. Lai, and J. Rouch, “Experimental confirmation of renormalization-group prediction of critical concentration fluctuation rate in hydrodynamic limit,” J. Chem. Phys. 68: 1994 (1978); andADSCrossRefGoogle Scholar
- 16a.C. C. Lai, Ph.D. thesis, “Light Intensity Correlation Spectroscopy and Its Application to Study of Critical Phenomena and Biological Problems,” MIT (1972).Google Scholar

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© Plenum Press, New York 1981