Level Densities from Proton Resonances

Detailed information about nuclear level densities is obtained by direct counting of individual resonances. A collection of individual resonances with the same spin and parity follows the predictions of the Gaussian Orthogonal Ensemble (GOE) version of Random Matrix Theory (RMT). RMT predictions are used to determine the corrections due to the imperfections in the measurement. We derived a general expression for the probability distribution for imperfect eigenvalue sequences. The missing level correction for the number of levels is obtained by two methods, the newly developed eigenvalue (or spacing) analysis and the more traditional reduced width analysis. Proton resonances in three nuclei are analyzed using the two methods. Improved values for the level densities are obtained, and the parity dependence of level density is considered.