Helium atom and helium-like ions - where are we today?
- Special MP Department Seminar
- Date: Nov 27, 2024
- Time: 09:30 AM - 10:30 AM (Local Time Germany)
- Speaker: Dr. Alexander Turbiner
- Instituto de Ciencias Nucleares, Universidad Autonoma de Mexico, Mexico & Department of Physics and Astronomy, Stony Brook University, USA
- Location: Building C, Room C1.13
- Room: Communication Room
- Host: Department of Molecular Physics
- Contact: friedrich@fhi-berlin.mpg.de
The Z-Helium atom is Nature's simplest atomic, 3-body system. As a result of enormous computational efforts during the last 90 years (∼150 calculations), unprecedented accuracy of 35-44 figures has been achieved for non-relativistic ground state energies (in the static approximation). It looks like we approached the moment to ask Lev Landau’s famous question: “...and so what!?” (i.e., what have we learned from all of that, what is the physics behind it?).
After a brief review of the present situation, it will be shown that the physics extracted from perturbation theory at small and large nuclear charges Z allows us to easily get 12-13 figures in energy for Z ≤ 20. Furthermore, the domain of applicability of non-relativistic Quantum Mechanics of Coulomb Charges (no photons; no relativistic, QED, or mass corrections) of 4-5 figures is described by a 2nd-degree polynomial in Z (it comes from a recently recovered formula by Ettore Majorana, from about 1930). The first 3 figures of the sum of mass, relativistic, and QED corrections vs. Z contribute to 5, 6, and 7 figures of the ground state energy: they are described by a 4th-degree polynomial in Z (!) for Z ≤ 20. A similar result obtains for excited states of helium-like and lithium-like ions.
Generalizing the Hylleraas-Kinoshita-Harris approach, an ultra-compact, 7-parametric trial function leading to 5 figures in energy will be presented.