Physics of the Nucleus

A Multilevel Formalism for Neutron Elastic Scattering Cross Sections

“…In equation (9) Sz and Pz are the shift factor and penetration factor for which a table of values is given by Preston (1962).…”

On the Non-invariance of Distributions of Reaction Matrix Parameters Under Changes in Boundary Conditions

“…and the residues are (8) Equation (4) was shown by Teichmann (1950) to be equivalent to the differential form…”

“…In order to study the statistics of R-matrix parameters, Wigner (1956) introduced the concept of the statistical R-function in which the reduced widths Y~ and level spacings D A' given by (11) have definite distributions which are independent of the sampling range. We shall consider the statistical R-function defined by equation (1) in which the s~mmation over.\ extends from -00 to + 00.…”

“…Lane and Thomas (1958) claimed this on physical grounds and supported their view with a plausibility argument. Teichmann and Wigner (1952), by considering the effect of changes in the boundary conditions, suggested the existence of correlations between the level spacings and the reduced widths. On the other hand, Lane and Thomas dismiss this argument as being based on mere speculation.…”

“…Distribution laws for level spacings and reduced widths have been derived by Wigner (1956) and Porter and Thomas (1956) respectively. Though no formal proof has ever been given, it is usually assumed that the statistical distributions of R-matrix parameters are independent of the boundary conditions used in the definition ofthe R-matrix.…”