[Paper Review] Precision study of 6p 2Pj - 8s 2S1/2 relative transition matrix elements in atomic Cs

A. Sieradzan, M. D. Havey+1 more|arXiv (Cornell University)|Aug 25, 2003

Atomic and Molecular Physics4 citations

TL;DR

This study presents a precision measurement of the relative transition matrix elements for the 6p $^{2}P_{j}$ → 8s $^{2}S_{1/2}$ transition in cesium-133 using polarization-dependent two-photon spectroscopy. By combining high-precision experimental data with relativistic all-order many-body calculations, the experimental ratio of matrix elements (1.423(2)) agrees exceptionally well with the theoretical prediction (1.425(2)), validating both the experimental technique and theoretical framework for heavy alkali atoms.

ABSTRACT

A combined experimental and theoretical study of transition matrix elements of the 6p 2Pj - 8s 2S1/2 transition in atomic Cs is reported. Measurements of the polarization-dependent two-photon excitation spectrum associated with the transition were made in an approximately 200 cm-1 range on the low frequency side of the 6s 2S1/2 - 6p 2P3/2 resonance. The measurements depend parametrically on the relative transition matrix elements, but also are sensitive to far-off-resonance 6s 2S1/2 - np 2Pj - 8s 2S1/2 transitions. In the past, this dependence has yielded a generalized sum rule, the value of which is dependent on sums of relative two-photon transition matrix elements. In the present case, best available determinations from other experiments are combined with theoretical matrix elements to extract the ratio of transition matrix elements for the 6p 2Pj - 8s 2S1/2 (j = 1/2,3/2) transition. The resulting experimental value of 1.423(2) is in excellent agreement with the theoretical value, calculated using a relativistic all-order method, of 1.425(2).

Motivation & Objective

• To determine the relative transition matrix elements for the 6p $^{2}P_{j}$ → 8s $^{2}S_{1/2}$ transition in atomic cesium with high precision.
• To resolve discrepancies in parity nonconservation (PNC) measurements by improving the accuracy of matrix elements critical for PNC analysis.
• To test the reliability of relativistic all-order many-body theory in heavy alkali atoms by comparing with high-precision experimental data.
• To demonstrate the effectiveness of combining polarization-dependent two-photon spectroscopy with theoretical corrections for far-off-resonance transitions.

Proposed method

• Polarization-dependent two-photon excitation spectroscopy was performed in a 200 cm⁻¹ range below the 6s $^{2}S_{1/2}$ → 6p $^{2}P_{3/2}$ resonance in cesium.
• The experimental spectra were fitted using a generalized sum rule formalism that includes relative two-photon transition matrix elements as free parameters.
• Theoretical matrix elements for far-off-resonance 6s $^{2}S_{1/2}$ → np $^{2}P_{j}$ → 8s $^{2}S_{1/2}$ transitions were calculated using the relativistic all-order (all-order SD and SDpT) method.
• The ratio of matrix elements for j = 1/2 and j = 3/2 was extracted by combining experimental data with precisely known 6s → 6p transition matrix elements.
• Systematic uncertainties were evaluated by comparing results from different theoretical approximations (DHF, third-order MBPT, SD, SDpT) and scaled values.
• The final theoretical value was determined as 1.425(2), with uncertainty estimated from spread in approximations and contributions from higher-order terms.

Experimental results

Research questions

• RQ1 What is the precise ratio of the reduced electric-dipole matrix elements for the 6p $^{2}P_{1/2}$ → 8s $^{2}S_{1/2}$ and 6p $^{2}P_{3/2}$ → 8s $^{2}S_{1/2}$ transitions in cesium?
• RQ2 How well do relativistic all-order many-body calculations reproduce the experimentally determined matrix element ratio in heavy alkali atoms?
• RQ3 To what extent do far-off-resonance transitions contribute to the two-photon excitation spectrum and how can they be accurately modeled?
• RQ4 Can polarization-dependent two-photon spectroscopy be used to extract relative transition matrix elements with sub-0.2% precision in cesium?
• RQ5 What is the impact of electron correlation and relativistic effects on the matrix element ratio, and how are they captured in the all-order method?

Key findings

• The experimentally determined ratio of the 6p $^{2}P_{j}$ → 8s $^{2}S_{1/2}$ transition matrix elements is 1.423(2), with a precision of ±0.002.
• The theoretical prediction using the relativistic all-order method is 1.425(2), showing excellent agreement with the experimental result.
• The difference between the all-order SD and SDpT calculations is only 0.1%, indicating high stability and accuracy of the theoretical approach.
• The total correlation correction to the matrix element ratio is only 0.4%, due to strong cancellation of dominant terms.
• The third-order many-body perturbation theory results are close to the all-order values, and scaled third-order values agree well with the all-order result.
• The study confirms that relativistic all-order methods accurately describe matrix elements in heavy alkali atoms, even for transitions involving high-lying states like 8s.