*ITAMP Topical Lunch Discussion*
*Date:* Friday, April 17th
*Time: *12:00-1:30 pm
Pizza will be served.
*Location:* B-106 @ Center for Astrophysics (60 Garden Street)
*Speaker:* Prof. Alexander Turbiner (Stony Brook and Mexico-City)
*Title:* Helium-like Coulomb system: two critical charges, 2nd excited
state of H− ion and all that
*Abstract: *
Reduced Coulomb problem of two electrons in the field of charged fixed
center $Z$ $(H^-, He, Li^+, \ldots)$ is discussed and its connection to
H2+-ion. Current situation with $1/Z$ expansion is reviewed, numerical
deficiencies of seemingly firmly-established results are indicated. First
nuclear critical charge (corresponding the zero ionization energy) is
recently established with high accuracy (Drake et al, 2014; Olivares-Pilon
& AT, 2014)). Second nuclear critical charge (a loss of normalizability of
ground state) predicted by Stillinger and Stillinger (1966, 1974) is
calculated as well as associated square-root branch point singularity with
exponent 3/2. It seems it implies (i) a level crossing $1S-2S$ states and
(ii) the existence of a bound state embedded to continuum. It leads to the
prediction of the spin-singlet, 2nd 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
square-root branch point with exponent 3/2 at critical charge.
--
Dr. Swati Singh
Institute for Theoretical Atomic, Molecular, and Optical Physics (ITAMP),
Harvard-Smithsonian Center for Astrophysics,
60 Garden Street, MS-14,
Cambridge, MA 02138
https://www.cfa.harvard.edu/~ssingh/