A GENERALIZED OPTICAL-POTRNTIAL METHOD AND ITS APPLICATION TO THE SCATTERING OF ELECTRONS BY ATOMIC HYDROGEN. (thesis)

Technical Report · Tue Jun 18 04:00:00 EDT 1963

OSTI ID:4633788

Pu, R T

A generalized optical-model-potential method for calculation of the scattering of charged particles by atoms is described. The method is shown to combine, in practical applications, the advantages of two conventional approaches, the eigenfunction expansion method and the optical-potential method, and to contain these two approaches as linaiting cases. With certain modification to allow for the Pauli exclusion principle explicitly, the method is applied to the elastic scattering of the electrons by hydrogen atoms for energies below the excitation of the second quantum level (10.2 ev), with 1s, 2s, 2p hydrogen atomic states used in the close-coupling scheme. The resulting coupled set of integro-differential equations, with appropriately approximated generalized optical potentials, was integrated numerically on an IBM 7090 computer, yielding phase shifts in various total spin and total angular momentum states. Results from this calculation are compared with other theoretical predictions and available experimental data. The short-range interelectron correlation effect is found to be of major importance for S-wave scattering in the entire energy range except very near zero energy. The influences of the long- range polarization potential and the short-range effect become comparable for P- waves. For D-waves, the long-range polarization potential begins to assume a major role in the scattering, and for F and higher waves it becomes singularly dominant throughout. Extremely narrow resonance-type effects in phase shifts of various spin and angular momentum states are found at energies slightly below the second quantum level. The resonance in singlet S-state is analyzed in detail, by a BreitWigner type fit, and is found to be centered at 9.51 ev with a narrow full width of 0.067 ev. For the scattering length of singlet S-wave, a value of 6.520 (in unit of Bohr radius) is obtained. The method is less successful in singlet lowangular-momentum waves where short-range oorrelation effect is important. A modified trial wave-function form is suggested for these cases, to take better account of the mutual repulsion between electrons. 33 references. (auth)

• Research Organization: California. Univ., Berkeley. Lawrence Radiation Lab.
• DOE Contract Number: W-7405-ENG-48
• NSA Number: NSA-17-036456
• OSTI ID: 4633788
• Report Number(s): UCRL-10878
• Country of Publication: United States
• Language: English

Related Subjects

ANGULAR MOMENTUM
ATOMIC MODELS
ATOMS
BIBLIOGRAPHY
CHARGED PARTICLES
COMPUTERS
D-WAVE
DIFFERENTIAL EQUATIONS
EIGENFUNCTIONS
ELECTRONS
ENERGY
ENERGY LEVELS
ENERGY RANGE
EXCITATION
F-WAVE
FERMIONS
HYDROGEN
IBM 7090
INTERACTIONS
MATHEMATICS
MEASURED VALUES
MOMENTUM
NUCLEAR MODELS
NUMERICALS
OPTICAL MODEL
P-WAVE
PAULI PRINCIPLE
PHYSICS
POLARIZATION
QUANTUM MECHANICS
RESONANCE
S-WAVE
SCATTERING
SPECTRAL SHIFT
SPIN