Tests of quantum electrodynamics with EBIT (1).(electron beam ion trap)(Report)

Abstract: A Feynman-diagram-based approach to calculating the spectra of highly charged ions is described and applied to lithiumlike and sodiumlike ions. Discrepancies between calculations excluding the two-loop Lamb shift and experiment allow that shift to be determined, as the accuracy of EBIT experiments is well below the size of the effect. The present status of the theory of hyperfine splitting is described, where a large quantum electrodynamics (QED) effect is made difficult to observe because of nuclear physics uncertainties. The importance of a correct treatment of nuclear recoil at present levels of accuracy is stressed, and prospects for a full QED treatment of copperlike ions are discussed.

PACS Nos.: 31.30.Jv, 32.30.Rj, 31.25.-v, 31.15.Ar

Resume : Nous decrivons et utilisons une methode basee sur des diagrammes de Feynman pour calculer les spectres d'ions hautement charges et l'appliquons a des ions de type Li et Na. Les differences entre les calculs qui excluent le deplacement de Lamb a deux boucles et les resultats experimentaux EBIT (piege ionique a faisceau d'electrons) permettent d'evaluer ce deplacement, parce que la precision de EBIT est nettement sous la grandeur de cet effet. Nous decrivons l'etat actuel de la theorie des effets hyperfins o il est difficile d'observer un effet QED a cause d'imprecisions sur les proprietes nucleaires. Nous insistons sur la necessite de calculer correctement le recul nucleaire a un niveau de precision contemporain et nous evaluons les possibilites d'un calcul QED complet dans des ions de type Cu.

[Traduit par la Redaction]

1. Introduction

Progress in physics comes in different forms, most commonly incrementally, with known physics being applied to explain an ever widening set of experiments. Occasionally, however, an anomaly is found, and sometimes this can lead to the discovery of new physics. One of the most famous examples of the latter case, the explanation of the anomaly in the precession of Mercury by general relativity, has an interesting parallel with the recent discovery of the two-loop Lamb shift at the Electron Beam Ion Trap (EBIT) facility at the Lawrence Livermore National Laboratory (LLNL) achieved through the combination of theory that will be described in this talk and the incredibly precise experiments on highly charged ions carried out at LLNL. Because we will refer to this parallel frequently in the following, we begin with a brief history of Mercury's precession.

A single planet orbiting the Sun does not of course precess at all in Newtonian gravity, a characteristic feature of the 1/[r.sup.2] force. However, there is a lowest order effect that observers based on the Earth must take into account that leads to the largest contribution to the observed precession. This is the fact that the axis of the Earth rotates with a period of roughly 26 000 years. This effect was discovered in another context by the ancient Greeks. Specifically, Hipparchus, comparing astronomical observations with those made by Timocharis 170 years earlier, found the positions of the stars had apparently shifted. Even if Mercury did not precess at all, this same effect gives rise to a precession of 5025 arcsec per century. It accounts for the great bulk of the actual measurement of 5600, but to learn more physics, the difference of 575 arcsec per century must be explained.

At this point the issue of accuracy arises: because the lowest order effect is large, it must be understood with precision. Were it difficult to account for the rotation of the axis of the Earth, the 575 arcsec per century (which, it should be emphasized, is a tiny effect) could perhaps be attributed to ones lack of understanding of this effect. Of course that is not the case, but once one goes to finer levels the issue becomes central. Similarly, were the precession too difficult to determine at the 575 arcsec per century level, no conclusions could be drawn.

Because of the closeness of the planet to the Sun, accurate measurements, for example made by observing the transit of the planet across the Sun, an event that occurred recently, in fact are difficult. However, by the time of the next stage of this historical analogy, around 1845, the precession was sufficiently well-known that it was clearly necessary to explain the difference. At this point, the story intersects with the famous discovery of Neptune from observed anomalies in the orbit of Uranus. Both Adams in England and Le Verrier in France developed methods to calculate the relatively small effect the presence of other planets has on the orbit of a given planet. While Le Verrier is generally given most credit for the discovery [1], Adams is of interest because one of the numerical methods he developed, named after him, is used in the solution of differential equations, and in fact the quantum electrodynamics (QED) calculations that will be described here use that method heavily. Once the methods were in place, they could also be applied to the precession of Mercury's orbit, and indeed were …