Charles E. Porter

FURTHER REMARKS ON ENERGY LEVEL SPACINGS

Abstract First, a discussion is given of the next-nearest neighbour-energy level spacing distribution based on earlier work. Secondly, a unified approach to the discussion of the class of all quantal measuring devices with the same mean level density is presented. Some very brief remarks concerning number operator ensembles are included.

RANDOM MATRIX DIAGONALIZATION--SOME NUMERICAL COMPUTATIONS

Numerical results of Monte‐Carlo calculations of spacing and eigenvalue distributions for the invariant and independent Gaussian orthogonal ensemble of Hamiltonian matrices are presented. Many of the histograms should be useful for comparison with experimental data. A table of the first few moments of each distribution is given. For the spacing distributions, such moments are equivalent to spacing correlation coefficients, and hence these are also made available indirectly.

Statistical fluctuations of energy levels: The unitary ensemble

Abstract The next-nearest neighbour energy level spacing distribution for complex systems with non-time-reversal-invariant interactions is derived from the Gaussian unitary ensemble in three dimensions and is compared to the similar result for the orthogonal ensemble. Since it has been shown for other spacing distributions that low-dimensional results are within a few per cent of infinite-dimensional results in regions of significant probability, the three-dimensional results developed here probably have rather wide numerical validity.

Neutron-nucleus optical model parameter effects on s-wave transmission coefficients

Abstract Numerical calculations of the s-wave transmission coefficients at a neutron energy of 1 keV for a nuclear optical model are presented in order to display the effects of model parameter variation. Particular attention is given to the effects of the surface diffuseness distance and of the strength of the imaginary part of the optical potential. Both volume and surface-peaked absorption are considered. In addition, some comments are made concerning the difficulties encountered in using one-dimensional models to infer three-dimensional behaviour of the complex scattering length.

STATISTICS OF ATOMIC RADIATIVE TRANSITION PROBABILITIES

A brief preliminary examination of ntomic radiative transition probability data recently made available is reported. It is concluded that the number of degrees of freedom in atomic radiative transition probability data is probably small and may not be grossly inconsistent, at least for complex atoms, with one degree of freedom when the accuracy of the data and the possible missing of small levels are taken into account. (W.D.M.)