Dong, C. Z.

Fritzsche, S.

Kabachnik, N. M.

Surzhykov, A.

Wu, Z. W.

GSI Repository

Proposed determination of small level splittings in highly charged ionsZ. W. Wu1, N. M. Kabachnik2, A. Surzhykov1, C. Z. Dong3, and S. Fritzsche1,41Helmholtz Institute Jena, Germany; 2European XFEL, Hamburg, Germany; 3Northwest University Lanzhou, China;4University of Jena, GermanyHighly charged ions (HCI) are known as a unique toolfor exploring the interaction of strong electromagneticfields with matter. In particular the x-ray emission fromthese ions has been investigated for many years and helpedreveal many details about the structure and dynamics ofHCI [1]. Moreover, recent studies on the angular distri-bution and linear polarization of these x-rays provided notonly insight into the electron-electron and electron-photoninteractions but also showed a rather strong influence ofthe hyperfine interaction upon the angular x-ray emissionof HCI, even if the fine and hyperfine structure of theselines cannot be resolved in detail [2].Until the present, however, almost all experimental andtheoretical investigations on the angular distribution of x-rays have dealt with the photon emission from well-isolatedfine-structure levels. In contrast, little attention was paid tocascade emissions that proceed via two (or more) overlap-ping intermediate resonances. For such cascades, we havetherefore explored, by using the density matrix theory, boththe photon-photon correlation function as well as the an-gular distribution of the second photon (if the first photonremains unobserved). General expressions were derivedfor these distributions, independent of the particular shellstructure of the HCI [3]. For the sake of simplicity, let usconsider the two-step cascade1s2p2 Ji = 1/2, 3/2−→ γ1 +{1s2s2p J = 1/21s2s2p J ′ = 3/2}−→ γ1 + γ2 + 1s22s Jf = 1/2 (1)of lithium-like ions. These ions have a relatively simplelevel structure and are known to exhibit a level crossing ofthe two 1s2s2p J = 1/2, 3/2 intermediate resonances be-tween 74 ≤ Z ≤ 79. For this decay cascade, indeed, aquite remarkable effect of the level splitting and the align-ment of the initial 1s2p2 Ji = 3/2 resonance is foundfor the angular distribution of the emitted x-ray photons.For lithium-like W71+ ions, for example, Fig. 1 displaysthe angular distribution of the second-step photon emissionfor an initially aligned 1s2p2 Ji = 3/2 resonance with(alignment parameter) A2 = −1.0 and for four differentsplittings of the intermediate J = 1/2 and 3/2 levels (allin a.u.).When compared with the photon emission of isolatedlevels, the x-ray emission via overlapping resonances is af-fected also by spin-spin and spin-orbit interactions that giverise to a depolarization (in time) of these intermediate lev-els. This effect of partially overlapping resonances uponFigure 1: Angular distribution of the second-step photonemission for the cascade (1). See text for further discus-sions.the emission of photons and electrons has been termedlifetime-induced depolarization in the literature. If no fur-ther details are known about the exact time interval betweenthe subsequent emission processes in some cascade, thisdepolarization can be characterized by means of so-calleddepolarization factors that just depend on the energy split-ting and the natural width of the intermediate resonances.Owing to the strong dependence of the photon-photoncorrelation and angular distribution functions upon the en-ergy splitting of the intermediate levels, we conclude thataccurate measurements of the angular x-ray emission mayserve also as a tool for determining small level splittings inhighly charged ions [3]. Such measurements of the pho-ton angular distributions will be feasible with present-dayx-ray detectors and could be carried out at both, heavy-ionstorage rings and electron beam ion trap facilities.References[1] S. Fritzsche, P. Indelicato and T. Sto¨hlker, J. Phys. B38, S707(2005).[2] Z. W. Wu, A. Surzhykov and S. Fritzsche, Phys. Rev. A89,022513 (2014).[3] Z. W. Wu et al., Phys. Rev. A90, 052515 (2014).GSI SCIENTIFIC REPORT 2014 APPA-MML-AP-16DOI:10.15120/GR-2015-1-APPA-MML-AP-16 231

Proposed determination of small level splittings in highly charged ions

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Proposed determination of small level splittings in highly charged ions

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