Very Precise Atomic Structure Calculations for the Determination of Atomic Parity Non-Conservation

TYPESolid State Institute Seminar
Speaker:Dr. Tereza Uhlířová
Affiliation:Faculty of Mathematics and Physics, Charles University, Institute of Plasma Physics, Czech Academy of Sciences, Czech Republic
Time:12:30 - 13:30
Location:Solid State Auditorium(Entrance)
Remark:Host: Assistant Professor Yuval Shagam

Atomic physics is still at the frontier of our exploration of fundamental physical laws. For example, the
comparison of the theoretical and experimental values of the atomic parity non-conservation (PNC) amplitude,
which, as we will show, arises from Glashow-Weinberg theory of electroweak interactions, constitutes one of the
most stringent tests of the Standard Model. By reviewing current theoretical and experimental data, we will
see, however, that the theoretical results lag behind the latter. Moreover, there are several calculations on the
cesium atom, for example, that differ at a sub-percentage level.
There are two main obstacles inherent in any precise atomic structure calculation: frst, the determination
of an optimal radial basis and a numerically stable evaluation of atomic integrals, and second, the question of
how to take into account electron correlation. We describe our solution of the former [1] and our current efforts
for solving the latter [2].
The optimal radial basis are the Sturmian functions. They are orthonormal, discrete and complete on infnite
interval. The problem of the numerical stability is solved by considering Sturmian functions not “analytically”,
i.e. through their explicit functional form, but “algebraically”, i.e. as functions satisfying certain recursion
relations. These recursion relations then imply recursion relations for the integrals of these functions.
The electron correlation in closed-shell atoms can be accurately accounted for by the coupled-cluster method.
In the case of open-shell atoms, one can use a combination of coupled-cluster and confguration interaction
methods. We describe the adaptation of these methods to the spherical symmetry of the atoms.
[1] T. Uhl
ířová, J. Zamastil, and J. Benda, Comput. Phys. Commun. 280, 108490 (2022).
[2] T. Uhl
ířová and J. Zamastil, in progress.