Law of corresponding states in elastic scattering theory

The idea of corresponding states has been successfully utilized in Statistical Mechanics in numerous ways, e.g., to summarize and correlate empirical data, to study the quantum effects in various properties of matter, to predict the properties of a substance from the experimental data of other substances where no satisfactory theoretical treatment existed--to name a few. Similar possibilities for utilizing the idea of corresponding states exist in the elastic scattering where one is faced with the practically impossible theoretical problem of evaluating the T-matrix when calculating the scattering cross-section in analogy with a similarly difficult problem of calculating the partition function in Statistical Mechanics. Analogous to the Law of Corresponding States (LCS) of Statistical Mechanics, a law of corresponding states in elastic scattering theory is derived by means of operator methods, enabling us to relate cross sections of different scattering systems. Applications of LCS in elastic scattering are given where experimental data is used to relate hitherto theoretically unrelated scattering cross-sections. For the case of H--Ar where the potential has been determined indirectly, a linear equation relating sigma/sup 1/2/ and log E is predicted by means of LCS