Rotational-dependent analytical solution to the dissociative state: Application to b /sup 3/. sigma. /sup +//sub u/ state of H/sub 2/
The rotational-dependent potential for a dissociative state is represented by U(r) = U/sub 0/+B/sub 1//r +B/sub 2//r/sup 2/+(N(N+1)-..lambda../sup 2/)/2Mr/sup 2/. An analytical solution psi/sub E/(r) of the Schroedinger radial equation, valid for all regions of internuclear distance r and energy E, is obtained in terms of confluent hypergeometric function of the complex arguments. The solution is evaluated by expanding the confluent hypergeometric function onto a basis set of shifted Chebyshev polynomials. The expansion coefficients are recovered by a backward recursion technique. The summation process of Chebyshev polynomials converts a slowly convergent series or a divergent asymptotic series into a rapidly convergent one. The solution thus obtained is applied to calculate the vibrational wave function of the dissociative b /sup 3/..sigma../sup +//sub u/ state of H/sub 2/ to compare with the previous semiclassical WKB wave function. The solution of the rotational-corrected Morse potential is used for the upper bound c /sup 3/Pi/sub u/ state. The bound-continuum Frank--Condon overlap amplitude is computed as a function of energy E for different rotational quantum numbers N. Its dependence on N is found to be significant for large N. The decay rate of the metastable c /sup 3/Pi/sup +//sub u/ (v = 0), via perturbative mixing with b /sup 3/..sigma../sup +//sub u/, computed here with exact wave functions, is an order of magnitude smaller than the previous semiclassical value.
- Research Organization:
- Department of Chemistry, Howard University, Washington, D. C. 20059
- OSTI ID:
- 6422346
- Journal Information:
- J. Chem. Phys.; (United States), Vol. 84:4
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
HYDROGEN
DISSOCIATION
ELECTRONIC STRUCTURE
ENERGY-LEVEL TRANSITIONS
ANALYTICAL SOLUTION
LIFETIME
POTENTIAL ENERGY
SCHROEDINGER EQUATION
DIFFERENTIAL EQUATIONS
ELEMENTS
ENERGY
EQUATIONS
NONMETALS
PARTIAL DIFFERENTIAL EQUATIONS
WAVE EQUATIONS
640302* - Atomic
Molecular & Chemical Physics- Atomic & Molecular Properties & Theory