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Physical Review A

Test of the anisotropy method for Lamb-shift measurements—theory and experiment

G. W. F. Drake, Péter Faragó, Adriaan J. van Wijngaarden

Published May 1, 1975• 30 citations

Abstract

We show that a measurement of the anisotropy in the angular distribution of the quenching radiation emitted by metastable hydrogen and deuterium atoms in an electric field can be used to determine the Lamb shift to an accuracy of at least \ifmmode\pm\else\textpm\fi{}0.1%. The method can be extended to the hydrogenic ions, where it offers several advantages over the quench-rate technique used in earlier measurements. The experiment is interpreted by means of a nonperturbative theory of the quenching process, which includes hyperfine structure and time-dependent effects. In the limit of zero field strength, the anisotropies of H and D are measured to be 0.139 01 \ifmmode\pm\else\textpm\fi{} 0.000 12 and 0.141 21 \ifmmode\pm\else\textpm\fi{} 0.000 14, while the theoretical values are 0.139 078 and 0.141 30, respectively. The corresponding Lamb shifts are 1057.3 \ifmmode\pm\else\textpm\fi{} 0.9 MHz and 1058.7 \ifmmode\pm\else\textpm\fi{} 1.1 MHz.

DOI: 10.1103/physreva.11.1621

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We show that a measurement of the anisotropy in the angular distribution of the quenching radiation emitted by metastable hydrogen and deuterium atoms in an electric field can be used to determine the Lamb shift to an accuracy of at least \ifmmode\pm\else\textpm\fi{}0.1%. The method can be extended to the hydrogenic ions, where it offers several advantages over the quench-rate technique used in earlier measurements. The experiment is interpreted by means of a nonperturbative theory of the quenching process, which includes hyperfine structure and time-dependent effects. In the limit of zero field strength, the anisotropies of H and D are measured to be 0.139 01 \ifmmode\pm\else\textpm\fi{} 0.000 12 and 0.141 21 \ifmmode\pm\else\textpm\fi{} 0.000 14, while the theoretical values are 0.139 078 and 0.141 30, respectively. The corresponding Lamb shifts are 1057.3 \ifmmode\pm\else\textpm\fi{} 0.9 MHz and 1058.7 \ifmmode\pm\else\textpm\fi{} 1.1 MHz.

A beam of unpolarized metastable He('+) 2s(, 1/2) ions, quenched by a static electric field, (')E has an anisotropy in the emitted radiation that can be used to determine the He('+) 2('2)s(, 1/2)-2('2)p(, 1/2) Lamb shift. A high precision measurement of this anisotropy for a field strength of (VBAR)(')E(VBAR) = (370.97 (+OR-) 0.06) V/cm has been made. The value of the field-free anisotropy, A('(0)), adjusted by small corrections is (0.1178082 (+OR-) 0.0000086), where the uncertainty is the statistical one standard deviation. Using much improved apparatus over Drake, Goldman and van Wijngaarden, our values for both the anisotropy A('(0)) and the Lamb shift, S = (14022.67 (+OR-) 1.06) MHz lie lower by 17 standard deviations from theirs. The great discrepancy is not understood, and may be attributed to the inherent difficulties of measuring light intensities by photon counting techniques. Source: Dissertation Abstracts International, Volume: 47-09, Section: B, page: 3817. Thesis (Ph.D.)--University of Windsor (Canada), 1986.

The Lamb shift of

{\mathrm{He}}^{+}

is derived from the measured anisotropy in the electric-field-induced quenching radiation of the metastable

2{s}_{\frac{1}{2}}

state. The results demonstrate that the anisotropy method can be applied with high precision to one-electron ion beams, as well as neutral beams. We find a Lamb shift of 14040.2\ifmmode\pm\else\textpm\fi{}2.9 MHz (1 standard deviation). The sources of error and difficulties encountered in working with ion beams are discussed in detail.

The quenching of hydrogenic metastables is formulated as a near-resonant photon-scattering problem, and a complete analysis of the polarization and angular distribution of the emitted radiation is presented. The contribution from

\mathrm{np}

states with

n>2

is calculated, and an alternative method of measuring the Lamb shift is suggested.

The strong field-induced quantum beats observed in beam-foil studies of Ly- alpha radiation are obtained in a conventional metastable-hydrogen quenching experiment. The phase relation between the Stark shifted 2s 1/2 -2p 1/2 Lamb-shift oscillations and the much more rapid 2s 1 -2p 3/2 fine-structure oscillations depends on the detailed way in which the quenching field is switched on. Apart from a phaseshift, the results agree with a non-perturbative theoretical calculation which assumes that the field is applied suddenly. Various frequency components of the time-dependent radiation intensity are identified with specific hyperfine transitions or groups of transitions. No adjustable parameters are used for the initial state amplitudes.

The interaction between a metastable H(2s) atomic hydrogen beam and an external electric field leads to the emission of the Lyman-α line. It originates in the Stark mixing of the near-degenerate 2s1/2 and 2p1/2 levels separated by the Lamb shift. The quenched radiation proportional to the square of the electric field amplitude is recovered in vacuum by using such an atomic probe beam. We observe the strong enhancement of the signal when the field is oscillating at the Lamb shift frequency. This technique is applied in a plasma, offering an alternative way to measure weak electric fields by direct and non-intrusive means.

The interaction between a metastable H(2s) atomic hydrogen beam and an external electric field leads to the emission of the Lyman-α line. It originates in the Stark mixing of the near-degenerate 2s1/2 and 2p1/2 levels separated by the Lamb shift. The quenched radiation proportional to the square of the electric field amplitude is recovered in vacuum by using such an atomic probe beam. For larger electric field, saturation is observed and related to the beam finite transit time. We also observe the strong enhancement of the signal when the field is oscillating at the Lamb shift frequency. This technique is applied in a plasma, offering an alternative way to measure weak electric fields by direct and non-intrusive means.