# High-Precision Atomic Calculations

High-precision atomic calculations combined with experiments of matching accuracy provide an excellent opportunity to improve our understanding of atomic structure as well as to test atomic theory. One very appealing and challenging application of such calculations is the study of parity nonconservation (PNC) in atoms and ions. It requires a systematic study and accuracy estimates of the PNC amplitude and other atomic parity conserving quantities.

*Why is high precision important?*

Quantum Electrodynamic effects calculated for hydrogen resulted in the Lamb shift of only 1057.70 MHz. Thus, the study of PNC requires a theory with precision < 1% in order to to impact the development of unified quantum field theories for elementary particle physics.

High-precision calculations of atomic properties of systems with one valence electron outside of a closed core can be carried out using a relativistic all-order method, such as a linearized version of coupled-cluster method which sums infinite sets of many- body perturbation theory terms. This allow to calculate energy levels for the ground state and five excited states of sodium and sodium-like ions with nuclear charges Z in the range 12-16 in precise agreement with experimental values (to 0.002%-0.01%). The resulting fine structures are also in excellent agreement with experiment. By computing systematically atomic properties of alkali-metal atoms from sodium to francium (which includes the calculations of energy levels, fine structures, electricdipole matrix elements, hyperfine constants, static polarizabilities of the ground states and first excites s states, scalar transition polarizabilities, and vector transition polarizabilities), we can provides benchmark values for a large number of yet unmeasured properties.

While the implementation of the relativistic all-order method that completely includes single and double excitations yielded very accurate data for some atomic properties, the results for a number of atomic properties where the correlation was very large were much less accurate. The partial inclusion of the triple excitations, where only energy and single excitation coefficient equations were modified, provided improved accuracy for certain cases where specific contributions were dominant but produced inconsistent results in other cases. Our research recently has aimed at the consistent inclusion of the triple excitations. We evaluate computational challenges involved in the efficient implementation of the all-order method with triple excitations balancing the need for accurate calculation and computational difficulties associated with an extremely large number of the corresponding triple excitation coefficients.

**Research Projects:**

- Atomic PNC theory: Current status and future prospect (Safronova)
- High precision calculations are performed on the He atom, a benchmark system for both theory and experiment (Szalewicz).

M. S. Safronova, R. Pal, D. Jiang, M. G. Kozlov, W. R. Johnson, and U. I. Safronova, *New directions in atomic PNC*, submitted to Nuclear Physics A (2009). [PDF]

E. Gomez, S. Aubin, L. A. Orozco, G. D. Sprouse, E. Iskrenova-Tchoukova, and M. S. Safronova, *The nuclear magnetic moment of ^{210}Fr: a combined theoretical and experimental approach*, Phys. Rev. Lett.

**78**, 172502 (2008). [PDF]

M. S. Safronova and W. R. Johnson, *All-order methods for relativistic atomic structure calculations*, in "Advances in Atomic, Molecular, and Optical Physics," Vol. 55, Eds. E. Arimondo, P. R. Berman, and C. C. Lin, (Academic Press, San Diego, 2008). [PDF]

G. Lach, B. Jeziorski, and K. Szalewicz, *Radiative corrections to the polarizability of helium*, Phys. Rev. Lett. **92**, 233001 (2004). [PDF]