Abstract
The algebraic multi-channel theory for heavy-ion reactions proposed by Alhassid and Iachello is based on a dynamic SO(3,1) symmetry for the scattering matrix S, written in the form S = gamma (J + I + iV) / gamma (J + I - iV), where the arguments of the Euler gamma functions are complex n x n matrices, n being the number of reaction channels, and are written as a combination of the total angular momentum, J, and the complex potential matrix, V; 1 is the n x n identity matrix. Computing S requires diagonalization of the complex matrix, V, and inversion of the matrix of the eigenvectors of V. These operations are to be repeated for some hundred values of J. Thus, the computer time becomes a rapidly increasing function of the maximum J value; therefore, it is important to choose efficient high-precision routines. Starting from a version of the program where the mathematical routines had been taken from version 9 of the IMSL library, an improvement has been obtained by choosing the more efficient versions, DEVCCG and DLINCG, available in version 1.1 of the IMSL MATH library; the routine DEPICG was used for evaluation of the performance index of
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Citation Formats
Vaccari, M, Ventura, A, Lichtenthaler Filho, R, and Zuffi, L.
Using IMSL routines in algebraic scattering theory for heavy ions.
Italy: N. p.,
1992.
Web.
Vaccari, M, Ventura, A, Lichtenthaler Filho, R, & Zuffi, L.
Using IMSL routines in algebraic scattering theory for heavy ions.
Italy.
Vaccari, M, Ventura, A, Lichtenthaler Filho, R, and Zuffi, L.
1992.
"Using IMSL routines in algebraic scattering theory for heavy ions."
Italy.
@misc{etde_10148570,
title = {Using IMSL routines in algebraic scattering theory for heavy ions}
author = {Vaccari, M, Ventura, A, Lichtenthaler Filho, R, and Zuffi, L}
abstractNote = {The algebraic multi-channel theory for heavy-ion reactions proposed by Alhassid and Iachello is based on a dynamic SO(3,1) symmetry for the scattering matrix S, written in the form S = gamma (J + I + iV) / gamma (J + I - iV), where the arguments of the Euler gamma functions are complex n x n matrices, n being the number of reaction channels, and are written as a combination of the total angular momentum, J, and the complex potential matrix, V; 1 is the n x n identity matrix. Computing S requires diagonalization of the complex matrix, V, and inversion of the matrix of the eigenvectors of V. These operations are to be repeated for some hundred values of J. Thus, the computer time becomes a rapidly increasing function of the maximum J value; therefore, it is important to choose efficient high-precision routines. Starting from a version of the program where the mathematical routines had been taken from version 9 of the IMSL library, an improvement has been obtained by choosing the more efficient versions, DEVCCG and DLINCG, available in version 1.1 of the IMSL MATH library; the routine DEPICG was used for evaluation of the performance index of the complex eigenvalue-eigenvector computation. The calculations were carried out on the IBM-3090 computer of the ENEA (the Italian Agency for Energy, New Technologies and the Environment) research centre in Bologna. As an application, differential cross sections for elastic and inelastic scattering of O/sup 16/ on Cu/sup 65/ based on the algebraic scattering formalism are computed and compared with recent experimental data.}
place = {Italy}
year = {1992}
month = {Dec}
}
title = {Using IMSL routines in algebraic scattering theory for heavy ions}
author = {Vaccari, M, Ventura, A, Lichtenthaler Filho, R, and Zuffi, L}
abstractNote = {The algebraic multi-channel theory for heavy-ion reactions proposed by Alhassid and Iachello is based on a dynamic SO(3,1) symmetry for the scattering matrix S, written in the form S = gamma (J + I + iV) / gamma (J + I - iV), where the arguments of the Euler gamma functions are complex n x n matrices, n being the number of reaction channels, and are written as a combination of the total angular momentum, J, and the complex potential matrix, V; 1 is the n x n identity matrix. Computing S requires diagonalization of the complex matrix, V, and inversion of the matrix of the eigenvectors of V. These operations are to be repeated for some hundred values of J. Thus, the computer time becomes a rapidly increasing function of the maximum J value; therefore, it is important to choose efficient high-precision routines. Starting from a version of the program where the mathematical routines had been taken from version 9 of the IMSL library, an improvement has been obtained by choosing the more efficient versions, DEVCCG and DLINCG, available in version 1.1 of the IMSL MATH library; the routine DEPICG was used for evaluation of the performance index of the complex eigenvalue-eigenvector computation. The calculations were carried out on the IBM-3090 computer of the ENEA (the Italian Agency for Energy, New Technologies and the Environment) research centre in Bologna. As an application, differential cross sections for elastic and inelastic scattering of O/sup 16/ on Cu/sup 65/ based on the algebraic scattering formalism are computed and compared with recent experimental data.}
place = {Italy}
year = {1992}
month = {Dec}
}