Solving coupled equations by iteration for heavy ion multiple Coulomb excitation

Journal Article · Wed Aug 01 04:00:00 EDT 1979 · Phys. Rev., C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.20.592· OSTI ID:6245410

Tolsma, L D

The set of coupled linear second-order differential equations which has to be solved for quantum-mechanical calculations of inelastic scattering processes with multiple excitation can be rewritten as an equivalent set of coupled first-order integral equations. When Airy functions are used as piecewise analytic reference solutions, it makes it possible to evaluate analytically the integrals that arise in the set of integral equations. This set can be solved iteratively with a considerable reduction of computation time in cases of heavy ion scattering, when compared to quantum-mechanical coupled-channel calculations of the conventional type. The efficiency of two iteration schemes, an inward-outward and a perturbative one, has been investigated for some test cases dealing with multiple Coulomb excitation of /sup 238/U by Kr and Pb. It turns out that, for heavy ion scattering, only the inward-outward iteration scheme has a practical importance. Finally, the excitation probabilities for /sup 238/U, Coulomb excited by 385 MeV Kr up to I = 24h, are shown for a reduced E2 transition matrix element of 3.5 eb and they are compared with the excitation probabilities calculated according to the semiclassical theory.

• Research Organization: Department of Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
• OSTI ID: 6245410
• Journal Information: Phys. Rev., C; (United States), Journal Name: Phys. Rev., C; (United States) Vol. 20:2; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

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73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ACTINIDE ISOTOPES
ACTINIDE NUCLEI
ALPHA DECAY RADIOISOTOPES
CHARGED-PARTICLE REACTIONS
COULOMB EXCITATION
COUPLED CHANNEL THEORY
DIFFERENTIAL EQUATIONS
E2-TRANSITIONS
ELEMENTS
ENERGY RANGE
ENERGY-LEVEL TRANSITIONS
EQUATIONS
EVEN-EVEN NUCLEI
EXCITATION
HEAVY ION REACTIONS
HEAVY NUCLEI
INELASTIC SCATTERING
INTEGRAL EQUATIONS
ISOTOPES
ITERATIVE METHODS
KRYPTON
LEAD
MATRIX ELEMENTS
MECHANICS
METALS
MEV RANGE
MEV RANGE 100-1000
MULTIPOLE TRANSITIONS
NONMETALS
NUCLEAR REACTIONS
NUCLEI
PROBABILITY
QUANTUM MECHANICS
RADIOISOTOPES
RARE GASES
SCATTERING
TARGETS
URANIUM 238
URANIUM 238 TARGET
URANIUM ISOTOPES
YEARS LIVING RADIOISOTOPES