On the theory of scattering measurements in nuclear emulsion

Abstract

Moliere's theory of multiple scattering measurements in nuclear emulsion is here treated in a mathematically simpler way. The distribution functions of the second, third, and fourth differences of coordinates arising from true scattering and noise are derived for the constant-cell method. In the derivation, the parameters B/sub r/ are not assumed to be all equal as was assumed by Moliere. As a consequence the scattering constant agrees better with experimental results than the scattering constant calculated by Gottstein et al. lt is shown that the relation between the mean noise epsilon /sub r/ for the r/ sup th/ differences and the error sigma of a coordinate measurement is epsilon /sub 2/ = l.96 sigma /sub N/, epsilon /sub epsilon / = 3.56 sigma /su b N/ and epsilon /sub 4/= 6.68 sigma /sub N/. Therefore, to obtain a noise level of 0.l5 mu for second differences the error sigma /sub N/ should be less than 0.075 mu . In this case epsilon /sub 3/= 0.28 mu and epsilon /sub 4/= 0.50 mu . The effect of the finite size of the nucleus on the distribution functions of the coordinate differences is evaluated in an approximate way. (auth)