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Spallation nuclear reactions in the range of 0.2 to 1.2 GeV are studied using the CRISP code. A new approach for the deexcitation stage of the compound nucleus was introduced. For the calculations of the level densities, this approach is based on the Back-shifted Fermi gas model (BSFG), which takes into account pairing effects and shell corrections, whereas the calculation of the fission barriers were performed by means of the Extended Thomas-Fermi plus Strutinsky Integral (ETFSI) method, which is a high-speed approximation to the Hartree-Fock method with pairing correlations treated as in the usual BCS plus blocking approach. This procedure is more appropriate to calculate level densities for exotic nuclei. Satisfactory results were obtained and compared with experimental data obtained in the GSI experiments. As another important result, we highlight some directions for the development of a qualitatively superior version of the CRISP code with the implementation of more realistic and suitable physical models to be applied in stable and exotic nuclei that participate in the process. This new version of the code includes several substantial changes in the decay of the hot compound nucleus which allow satisfactory agreement with the experimental data and a reduction of the adjustment parameters. [ABSTRACT FROM AUTHOR]

This paper proposes that the study of Sturm sequences is invaluable in the numerical computation and theoretical derivation of eigenvalue distributions of random matrix ensembles. We first explore the use of Sturm sequences to efficiently compute histograms of eigenvalues for symmetric tridiagonal matrices and apply these ideas to random matrix ensembles such as the β-Hermite ensemble. Using our techniques, we reduce the time to compute a histogram of the eigenvalues of such a matrix from O( n2+ m) to O( mn) time where n is the dimension of the matrix and m is the number of bins (with arbitrary bin centers and widths) desired in the histogram ( m is usually much smaller than n). Second, we derive analytic formulas in terms of iterated multivariate integrals for the eigenvalue distribution and the largest eigenvalue distribution for arbitrary symmetric tridiagonal random matrix models. As an example of the utility of this approach, we give a derivation of both distributions for the β-Hermite random matrix ensemble (for general β). Third, we explore the relationship between the Sturm sequence of a random matrix and its shooting eigenvectors. We show using Sturm sequences that assuming the eigenvector contains no zeros, the number of sign changes in a shooting eigenvector of parameter λ is equal to the number of eigenvalues greater than λ. Finally, we use the techniques presented in the first section to experimentally demonstrate a O(log n) growth relationship between the variance of histogram bin values and the order of the β-Hermite matrix ensemble. [ABSTRACT FROM AUTHOR]