11 research outputs found
The H molecular ion: a solution
Combining the WKB expansion at large distances and Perturbation Theory at
small distances it is constructed a compact uniform approximation for
eigenfunctions. For lowest states 1s\si_{g} and 2p\si_{u} this
approximation provides the relative accuracy (5 s.d.) for
any real in eigenfunctions and for total energy it gives 10-11 s.d.
for internuclear distances . Corrections to proposed
approximations are evaluated. Separation constants and the oscillator strength
for the transition 1s\si_{g} \rar 2p\si_{u} are calculated and compared with
existing data.Comment: 16 pages, 4 figures, 6 tables, typos are corrected and small
additions are inserted, to be published at JPB (fast track comm
Relativistic corrections of order m\alpha^6 to the two-center problem
Effective potentials of the relativistic m\alpha^6 order correction for the
ground state of the Coulomb two-center problem are calculated. They can be used
to evaluate the relativistic contribution of that order to the energies of
hydrogen molecular ions or metastable states of the antiprotonic helium atom,
where precision spectroscopic data are available. In our studies we use the
variational expansion based on randomly chosen exponents that permits to
achieve high numerical accuracy.Comment: 12 pages, 3 tables 2 figures; submitted to the Journal of Physics