Solving coupled equations by iteration for heavy-ion multiple Coulomb-nuclear excitation

Journal Article · Thu Jan 01 04:00:00 EST 1987 · Phys. Rev. C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.35.177· OSTI ID:7016552

Tolsma, L D

To describe quantum mechanically multiple Coulomb-nuclear excitation in heavy-ion reactions, the set of coupled differential equations of the partial-wave radial solutions is rewritten in integral form. Decomposing these solutions into two basis functions, the corresponding amplitudes of these functions satisfy a set of coupled integral equations. Expressing the basis functions in terms of appropriately chosen piecewise analytic reference solutions, the integrals appearing in this set can be evaluated analytically. The coupled set of amplitude equations is solved iteratively. The efficiency of two iteration methods, the inward-outward and the sequential one, has been investigated for test cases dealing with multiple Coulomb and nuclear excitation of /sup 238/U by 286 MeV /sup 40/Ar and 718 MeV /sup 84/Kr up to high spin states of the ground-state rotational band. Pade approximants to the S-matrix elements were also included in both of the iteration methods. It turns out that the inward-outward iteration method converges much faster than the sequential one. In many cases, the inward-outward method does not need Pade acceleration at all, while the sequential method does. It happens that convergent cases in the inward-outward method diverge in the sequential method aided by Pade approximants. Numerical studies of the excitation probabilities as a function of the scattering angle for the aforementioned heavy-ion reactions show that the probability functions of the members of the ground-state rotational band satisfy a general rule at near-grazing angles, previously formulated for the excitation probability as a function of the energy near the Coulomb barrier for backward scattering from a deformed rotor.

• Research Organization: Department of Physics, Eindhoven University of Technology, Eindhoven, The Netherlands
• OSTI ID: 7016552
• Journal Information: Phys. Rev. C; (United States), Journal Name: Phys. Rev. C; (United States) Vol. 35:1; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

653001 -- Nuclear Theory-- Nuclear Structure
Moments
Spin
& Models
653003* -- Nuclear Theory-- Nuclear Reactions & Scattering
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
AIRY FUNCTIONS
ARGON 40 REACTIONS
BASIC INTERACTIONS
CHARGED-PARTICLE REACTIONS
COULOMB EXCITATION
COULOMB SCATTERING
DEFORMED NUCLEI
DIFFERENTIAL EQUATIONS
ELASTIC SCATTERING
ELECTROMAGNETIC INTERACTIONS
ENERGY LEVELS
ENERGY RANGE
ENERGY-LEVEL TRANSITIONS
EQUATIONS
EXCITATION
EXCITED STATES
FUNCTIONS
HEAVY ION REACTIONS
HIGH SPIN STATES
INTERACTIONS
ITERATIVE METHODS
KRYPTON 84 REACTIONS
MATRICES
MECHANICS
MEV RANGE
MEV RANGE 100-1000
MULTIPLE SCATTERING
NUCLEAR REACTIONS
NUCLEI
PADE APPROXIMATION
PARTIAL DIFFERENTIAL EQUATIONS
PROBABILITY
QUANTUM MECHANICS
ROTATIONAL STATES
S MATRIX
SCATTERING
SCHROEDINGER EQUATION
TARGETS
URANIUM 238 TARGET
WAVE EQUATIONS