Monday, April 27th, 2015
03:30 PM - 04:30 PM
Storrs CampusGant Science Complex, Room PB-121
Professor Alexander Turbiner
Stony Brook and Mexico City, will present:
“Helium-like Coulomb System: Two Critical Charges, 2nd Excited State of H− ion and All That”.
The reduced Coulomb problem of two electrons in the field of a charged fixed center Z (H-, He, Li+, . . . ) is discussed. The current situation with 1/Z expansion is reviewed, and numerical deficiencies of previously seemingly firmly-established results are indicated. The first nuclear critical charge (corresponding to the zero ionization energy) is recently established with high accuracy (Drake et al, 2014; Olivares-Pilon & AT, 2014)). The second nuclear critical charge predicted by Stillinger and Stillinger (1966, 1974) is calculated as well as its associated square-root branch point singularity with exponent 3/2. It seems it implies (i) the level crossing 1S-2S and (ii) the existence of a bound state embedded to continuum. It seems it leads to the existence of the spin-singlet, second excited state of negative hydrogen ion of the same symmetry as the ground state situated very close to threshold, which looks as an experimental challenge to detect.
It is conjectured that for any many-body Coulomb system (atomic or molecular type) there is a square-root branch point with exponent 3/2 at critical charge.