Programs in Physics & Physical Chemistry
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|Manuscript Title: Quantum mechanical coupled channels code for Coulomb excitation.|
|Authors: F. Rosel, J.X. Saladin, K. Alder|
|Program title: AROSA-FOR-COULOMB-EXCITATION-I|
|Catalogue identifier: ABOY_v1_0|
Distribution format: gz
|Journal reference: Comput. Phys. Commun. 8(1974)35|
|Programming language: Fortran.|
|Computer: PDP 1077.|
|Operating system: FORSE (32A).|
|RAM: 39K words|
|Word size: 36|
|Peripherals: magnetic tape, disc.|
|Keywords: Nuclear physics, Excitation amplitudes, Coulomb excitation, Coupled channels, Excitation cross-section, Schrodinger equation.|
Nature of problem:
AROSA calculates amplitudes and cross sections for Coulomb excitation of even even nuclei (g.s.spin and parity 0+). Up to five excited states may be included in the calculation. All reduced E2 and E4 matrix elements between these states may be taken into account.
The set of radial second-order differential equations resulting from the Schrodinger equation is solved by outward integration from the vicinity of the origin. The integration method is based on the Taylor expansion whose coefficients are obtained from recursion relations. At larger distances a WKB procedure is employed. Convergence of the scattering amplitudes with the number of partial waves is improved by using a procedure which is related to the Pade approximation.
The Sommerfeld parameter eta must be smaller than 30, but methods are discussed for extrapolation of results to larger eta values.
Due to the long-range nature of the Coulomb force it is necessary to carry out the integration of the radial equations to large distances, and to assure convergence as a function of orbital angular momentum. The integration can be carried out to arguments rho=kr=800 and the convergence as a function of l is improved by the use of an iterative procedure related to the Pade approximation. The program can be executed in two parts with part I supplying data on cards for part II. Alternatively, the two sections can be run consecutively with intermediate data stored on disc.
The running time is roughly proportional to the square of the number N of couplings which is given by N= Sigma n(In+1) where In is the spin of the nth state. A calculation involving three states with spins and parities 0+,2+,4+ and all by selection rules permissable E2 and E4 matrix elements between them, requires on the PDP 1077 about 35 minutes.
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