The theory of parity non-conservation in atoms

Thesis

In this thesis we are concerned with calculating the parity non-conserving (PNC) E1 transition matrix elements for the caesium 6s¹⁄₂ → 7s¹⁄₂ transition and the thallium 6p¹⁄₂ → 7p¹⁄₂ and 6p¹⁄₂ → 6p³⁄₂ transitions using the Equations of Motion (EOM) formalism. We add the weak interaction Hamiltonian to derive the PNC EOM. Taking a subset of the EOM terms gives the Random Phase Approximation equations and their PNC counterpart. Solving these, we obtain good agreement with similar calculations by other groups.

In order to estimate correlation effects we use a parameterised semi-empirical potential which is adjusted to give the best fit with experimental data for the valence and excited state energy levels. Including the potential in the EOM and PNC EOM gives us very accurate values for the parity conserving transitions. For the PNC transitions we obtain

Caesium	6s1⁄2 → 7s1⁄2	0.895	(1±0.03) × 10-11 (-iea0QW/N)
Thallium	6p1⁄2 → 7p1⁄2	-7.85	(1±0.05) × 10-11 (-iea0QW/N)
Thallium	6p1⁄2 → 6p3⁄2	-28.4	(1±0.07) × 10-11 (-iea0QW/N)

These are in very good agreement with the most extensive Many-Body Perturbation Theory calculations performed. Using our value for the caesium transition matrix element and the latest experimental results gives a value of Q_W = ~ 71.8 ± 1.8 ± 2.1 where the first error is experimental and the second is theoretical. This corresponds to a value of the standard model sin²Θ_W = 0.230 ± 0.009 which is to be compared with the current world average value of 0.230 ± 0.005.

We investigate the single particle EOM terms that were not included in the above calculation and find that they are concerned with the Exclusion Principle violating terms that are implicitly included in an RPA calculation. Other terms represent the valence contribution to certain two particle effects. Since the main two particle terms have not been included however, these correction terms do not lead to a significant increase in the accuracy of the calculation.

Authors: Hartley, A

• DOI: 10.5287/ora-yredwdrp6
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford