No abstract

The dynamic dipole polarizabilities for the Li atom and the Be + ion in the 2 2 S and 2 2 P states are calculated using the variational method with a Hylleraas basis. The present polarizabilities represent the definitive values in the non-relativistic limit. Corrections due to relativistic effects are also estimated. Analytic representations of the polarizabilities for frequency ranges encompassing the n = 3 excitations are presented. The recommended polarizabilities for 7 Li and 9 Be + were 164.11 ± 0.03 a 3 0 and 24.489 ± 0.004 a 3 0 .

We present the first measurement for helium atoms of the tune-out wavelength at which the atomic polarizability vanishes. We utilise a novel, highly sensitive technique for precisely measuring the effect of variations in the trapping potential of confined metastable (2 3 S1) helium atoms illuminated by a perturbing laser light field. The measured tune-out wavelength of 413.0938(9Stat.)(20Syst.) nm compares well with the value predicted by a theoretical calculation (413.02(9) nm) which is sensitive to finite nuclear mass, relativistic, and quantum electro-dynamic (QED) effects. This provides motivation for more detailed theoretical investigations to test QED. 11 level with differences of several standard deviations.Of much lower precision are the experimental and theoretical determinations of transition rates, which are both inherently difficult to measure and predict respectively. Nevertheless, theory and experiment appear to be in good agreement within the (typically of order a few per cent) uncertainty. In helium, we have previously verified theoretical QED predictions in a series of measurements of the transition rates to the ground state for the 2 3 P manifold [5,6] and the 2 3 S 1 metastable level [7]. Recently, QED has been challenged by experiments that determine the proton radius via spectroscopy of muonic hydrogen [8,9], whose values differ by seven standard deviations (7σ) from those measured by precision hydrogen spectroscopy (combined with QED theory [10]), and by proton-electron scattering experiments [11]. This has created the so-called proton radius puzzle [12]. More stringent tests of QED using different experiments are therefore important to provide independent validation or otherwise of QED.One such example is the precision measurement of tune-out (or magic-zero [13]) wavelengths that can provide independent verification of QED predictions for transition rate ratios. At excitation energies above the lowest excited state, the contribution to the dynamic polarizability from the lowest excited state is negative. There will then occur a series of wavelengths, each associated with a further excited state, where positive contributions to the polarizability from other states will exactly cancel the negative polarizability contributions, thereby creating so-called tune-out wavelengths.Mitroy and Tang [14] have estimated theoretically the tune-out wavelengths for transitions from the helium 2 3 S 1 metastable state (He*) to near the 2 3 P , 3 3 P and 4 3 P triplet manifolds (at 1083, 389 and 319 nm respectively). These approximate calculations (at around the 0.02% level) were designed to provide guidance for the first experimental measurements which we present here. Their calculations were based on a composite theory utilizing state-of-the-art transition rate data by Morton and Drake [15] for the low lying transitions, and model potential oscillator strengths for higher excitations. From a theoretical perspective, it should be noted that the same QED contributions to the dynamic polarizability are als...