Second-order contributions to the fine structure of helium from all intermediate states
For the theoretical assessment of the 2 /sup 3/P helium fine structure to become comparable to the precision measurements that have been made, it is necessary that the theory be calculated through order ..cap alpha../sup 6/mc/sup 2/. In particular, the second-order contribution from the Breit and mass-polarization operators must be evaluated to an accuracy of 1% or so. In this work, for each of five possible intermediate state symmetries the Dalgarno-Lewis method is used to obtain the first-order perturbed wave function, from which the second-order energy follows by integration. Both the perturbed and unperturbed wave functions are expanded in Hylleraas-type series with a progressively larger number of terms, the second-order energies being computed at each stage; up to 455 terms are used for /sup 3/P intermediate states and up to 286 for /sup 1/P, /sup 3/D, /sup 1/D, and /sup 3/F. The sequence of second-order energy results for each symmetry is extrapolated to the limit of an infinite number of basis functions to arrive at a final result. The /sup 3/P, /sup 1/P, and /sup 3/D states will contribute to both the larger and the smaller fine-structure intervals ..nu../sub 01/ and ..nu../sub 12/, respectively, while /sup 3/F and /sup 1/D states affect only ..nu../sub 12/. The total theoretical result, up to order ..cap alpha../sup 6/mc/sup 2/, for ..nu../sub 01/ is much more accurate than that for ..nu../sub 12/, allowing the fine-structure constant ..cap alpha.. to be determined very precisely by comparison of theory to experiment, with the result ..cap alpha../sup -1/ = 137.036 08(13), good to 0.94 ppm.
- Research Organization:
- Gibbs Laboratory, Physics Department, Yale University, New Haven, Connecticut 06520
- OSTI ID:
- 6672854
- Journal Information:
- Phys. Rev., A; (United States), Vol. 18:3
- Country of Publication:
- United States
- Language:
- English
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