Unified theory of nuclear reactions

A compilation of charged-particle induced thermonuclear reaction rates

A Unified Theory of Nuclear Reactions, II

The statistical properties of the characteristic values of a matrix the elements of which show a normal (Gaussian) distribution are well known (cf. [6] Chapter XI) and have been derived, rather recently, in a particularly elegant fashion.1 The present problem arose from the consideration of the properties of the wave functions of quantum mechanical systems which are assumed to be so complicated that statistical considerations can be applied to them. Since the physical problem has been given rather recently in some detail in another journal [3], it will not be reviewed here. Actually, the model which underlies the present calculations shows only a limited similarity to the model which is believed to be correct. Nevertheless, the calculation which follows may have some independent interest; it certainly provided the encouragement for a detailed investigation of the model which may reproduce some features of the actual behavior of atomic nuclei.

Characteristic Vectors of Bordered Matrices with Infinite Dimensions II

https://escholarship.org/content/qt2dj9p3h4/qt2dj9p3h4.pdf?t=pmi3bw

ENDF/B-VIII.0: The 8th Major Release of the Nuclear Reaction Data Library with CIELO-project Cross Sections, New Standards and Thermal Scattering Data

R-Matrix Theory of Nuclear Reactions

In the consideration of the independent-particle model, a distinction can be made between the spacing $D$ of the levels of the whole nucleus and the spacing $d$ of the levels of individual nucleons. Except in the immediate neighborhood of the normal state of closed-shell nuclei, $d\ensuremath{\gg}D$. In the "giant-resonance" interpretation considered here, the deviations from the independent-particle model are strong enough to mix many states of the whole nucleus, but the mixing is restricted to an energy range which is less than the order of $d$. According to this interpretation, the reduced particle widths of the levels of the compound nucleus are, on the average, anomalously large close to the energy values of those states of the independent-particle model which correspond to an unexcited target nucleus and a virtual level of the incident particle. As a consequence, the nuclear cross sections have a gross structure which is similar to a giant resonance, such as is implied by the complex square well representation of the nucleon-nucleus interaction. The position, width, and height of these maxima in the average cross sections are expressed in terms of the parameters of the independent-particle model and the departure of the actual nuclear potential which are responsible for the inaccuracy of this model. It is shown, however, that the conventional nuclear potential gives far too large values for the widths of the giant resonances (that is, for the imaginary part of the presentative complex square well potential).

A. M. Lane

Papers

R-Matrix Theory of Nuclear Reactions

Giant Resonance Interpretation of the Nucleon-Nucleus Interaction

Evaluation of the imaginary part of the nuclear complex potential

Nuclear theory : pairing force correlations and collective motion