Solving coupled equations by iteration for heavy-ion multiple Coulomb-nuclear excitation
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), Vol. 35:1
- Country of Publication:
- United States
- Language:
- English
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ARGON 40 REACTIONS
COULOMB SCATTERING
KRYPTON 84 REACTIONS
URANIUM 238 TARGET
AIRY FUNCTIONS
COULOMB EXCITATION
DEFORMED NUCLEI
DIFFERENTIAL EQUATIONS
HEAVY ION REACTIONS
HIGH SPIN STATES
ITERATIVE METHODS
MEV RANGE 100-1000
MULTIPLE SCATTERING
PADE APPROXIMATION
PROBABILITY
QUANTUM MECHANICS
ROTATIONAL STATES
S MATRIX
SCHROEDINGER EQUATION
BASIC INTERACTIONS
CHARGED-PARTICLE REACTIONS
ELASTIC SCATTERING
ELECTROMAGNETIC INTERACTIONS
ENERGY LEVELS
ENERGY RANGE
ENERGY-LEVEL TRANSITIONS
EQUATIONS
EXCITATION
EXCITED STATES
FUNCTIONS
INTERACTIONS
MATRICES
MECHANICS
MEV RANGE
NUCLEAR REACTIONS
NUCLEI
PARTIAL DIFFERENTIAL EQUATIONS
SCATTERING
TARGETS
WAVE EQUATIONS
653003* - Nuclear Theory- Nuclear Reactions & Scattering
653001 - Nuclear Theory- Nuclear Structure
Moments
Spin
& Models