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Differential cross sections for electric quadrupole coulomb excitation I
(2-129 COMPUTER PHYSICS COMMUNICATIONS 3 (1972) 118-129. NORTH-HOLLAND PUBLISHING COMPANY
DIFFERENTIAL CROSS SECTIONS FOR ELECTRIC QUADRUPOLE COULOMB EXCITATION I * Suzanne M. LEA **, Vinaya JOSHI Physics Department, Duke University, Durham, North Carolina 27706, USA and
A. B. LOPEZ-CEPERO *** University o f Texas, Austin, Texas, USA
Received 10 August 1971
PROGRAM SUMMARY Title o f program: DXS1 Catalogue number: ABQE Computer for which the program is designed and others upon which it is operable Computer: IBM 360/75. Installation: Triangle University Computation Center, Research Triangle Park, North Carolina Operating system or monitor under which the program is executed: OS-360-MVT Programming languages used: FORTRAN-IV (G) High speed store required: 35 000 word~ No. o f bits in a word: 32 Is the program overlaid? No No. o f magnetic tapes required: None What other peripherals are used? Card Reader; Line Printer No. oi" cards in combined program and test deck: 1172 Keywords descriptive o f problem and method o f solution: Nuclear, Electric Quadrupole, Coulomb Excitation, Differential Cross Section, Inelastic Scattering, Radial Coulomb Integrals, Finite Sums. Nature o f the physical problem The program calculates the differential cross section for inelastic scattering of a structureless charged particle through E2 excitation of a point nucleus. It is assumed that all nuclear effects can be ignored.
* Research supported in part by the National Science Foundation and the Army Research Office (Durham). ** Present address: Davidson County Community College, Lexington, North Carolina, USA. *** Work done at Duke Univexsity.
Method o f solution The numerical calculation closely follows the well-known quantum-mechanical theory of Coulomb excitation [1, 2] in the distorted wave Born approximation. The target and projectile axe assumed to be point particles. Radical integrals are calculated in the long wavelength (of the transferred photon) limit. Restrictions on the complexity o f the problem The calculation is non-relativistic and in the center of mass coordinates. In spite of the program's capability to consider up to 300 partial waves, even that may not provide good resuits with a combination of very small energy loss and small scattering angles.
(2-130 S. M. Lea et al., Differential cross sections for electric quadrupole Coulomb excitation I Unusual features o f the program The capacity for considering up to 300 partial waves is necessaxy to get reliable results for small angle scattering. The spherical harmonics are calculated by a recursion relation that is very stable for high angular momenta [3], as are the techniques for computing the Clebsch-Gordan and Racah coefficients. The finite-sum method [4] is used for calculating the radial integrals. This methods is remarkably fast and stable with respect to errors; at present there axe no available codes for Coulomb excitation that incorporate this method. Typical running time In the IBM 360/75 the program takes about 52 seconds to compile and the running time depends on the number of pax-
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tial waves used. Typically for about 60 partial waves it takes about 2 minutes to calculate the radial integrals and an extra 15 seconds for each angle. Running time increases significantly with increase in the number of partial waves used. References [ 1 ] K. Alder, A. Bohr, T. Huus, B. Mottelson and A. Winther, Rev. Mod. Phys. 28 (1956) 432. [2] L. C. Biedenharn and P. J. Brussaard, Coulomb excitation (Clarendon Press, Oxford, 1965). [3] S. L. Belousov, Tables of normalized associated Legendre polynomials (MacMillan, New York, 1962). [4] M. Goldstein, R. M. Thaler and L. C. Biedenharn, A tabulation of the radial Coulomb integrals (n, m,/), LASL Report LA-2106 (1957).
DIFFERENTIAL CROSS SECTIONS FOR ELECTRIC QUADRUPOLE COULOMB EXCITATION I * Suzanne M. LEA **, Vinaya JOSHI Physics Department, Duke University, Durham, North Carolina 27706, USA and
A. B. LOPEZ-CEPERO *** University o f Texas, Austin, Texas, USA
Received 10 August 1971
PROGRAM SUMMARY Title o f program: DXS1 Catalogue number: ABQE Computer for which the program is designed and others upon which it is operable Computer: IBM 360/75. Installation: Triangle University Computation Center, Research Triangle Park, North Carolina Operating system or monitor under which the program is executed: OS-360-MVT Programming languages used: FORTRAN-IV (G) High speed store required: 35 000 word~ No. o f bits in a word: 32 Is the program overlaid? No No. o f magnetic tapes required: None What other peripherals are used? Card Reader; Line Printer No. oi" cards in combined program and test deck: 1172 Keywords descriptive o f problem and method o f solution: Nuclear, Electric Quadrupole, Coulomb Excitation, Differential Cross Section, Inelastic Scattering, Radial Coulomb Integrals, Finite Sums. Nature o f the physical problem The program calculates the differential cross section for inelastic scattering of a structureless charged particle through E2 excitation of a point nucleus. It is assumed that all nuclear effects can be ignored.
* Research supported in part by the National Science Foundation and the Army Research Office (Durham). ** Present address: Davidson County Community College, Lexington, North Carolina, USA. *** Work done at Duke Univexsity.
Method o f solution The numerical calculation closely follows the well-known quantum-mechanical theory of Coulomb excitation [1, 2] in the distorted wave Born approximation. The target and projectile axe assumed to be point particles. Radical integrals are calculated in the long wavelength (of the transferred photon) limit. Restrictions on the complexity o f the problem The calculation is non-relativistic and in the center of mass coordinates. In spite of the program's capability to consider up to 300 partial waves, even that may not provide good resuits with a combination of very small energy loss and small scattering angles.
(2-130 S. M. Lea et al., Differential cross sections for electric quadrupole Coulomb excitation I Unusual features o f the program The capacity for considering up to 300 partial waves is necessaxy to get reliable results for small angle scattering. The spherical harmonics are calculated by a recursion relation that is very stable for high angular momenta [3], as are the techniques for computing the Clebsch-Gordan and Racah coefficients. The finite-sum method [4] is used for calculating the radial integrals. This methods is remarkably fast and stable with respect to errors; at present there axe no available codes for Coulomb excitation that incorporate this method. Typical running time In the IBM 360/75 the program takes about 52 seconds to compile and the running time depends on the number of pax-
119
tial waves used. Typically for about 60 partial waves it takes about 2 minutes to calculate the radial integrals and an extra 15 seconds for each angle. Running time increases significantly with increase in the number of partial waves used. References [ 1 ] K. Alder, A. Bohr, T. Huus, B. Mottelson and A. Winther, Rev. Mod. Phys. 28 (1956) 432. [2] L. C. Biedenharn and P. J. Brussaard, Coulomb excitation (Clarendon Press, Oxford, 1965). [3] S. L. Belousov, Tables of normalized associated Legendre polynomials (MacMillan, New York, 1962). [4] M. Goldstein, R. M. Thaler and L. C. Biedenharn, A tabulation of the radial Coulomb integrals (n, m,/), LASL Report LA-2106 (1957).