# Atomic Physics

### Electron correlation in helium studied by the Compton double-to-single ionisation ratio at 58 keV

The process of double ionisation in helium has been the focus of many experimental and theoretical investigations and continues to be a subject of fundamental interest in atomic physics.

Understanding the correlation phenomena in helium, which is the simplest neutral atomic system exhibiting correlation effects, is basic to our understanding of the more general cases of many-electron atoms and molecules.

Photoabsorption and Compton scattering are the two fundamental ionising interactions of a photon with an atom. Both interactions are described by a single particle operator, hence the simultaneous ejection of two electrons is beyond this process and must be due to electron correlation in the atom. Determining the ratio of double to single ionisation (R = He^{++}/He^{+}) by Compton scattering (R_{c}) and by photoabsorption (R_{ph}) is one of the most challenging tests of our understanding of these electron-electron correlation effects. According to the theory the ratio R should approach an asymptotic value in the limit of high photon energies which depends very sensitively on an accurate representation of the highly correlated initial state.

Whereas the theoretically predicted asymptotic value for R_{ph} = 1.68 % has been confirmed by several independent experimental studies, the predictions of the asymptotic ratio R_{c} for Compton scattering, which becomes the dominating process for double ionisation at energies above several keV, have not converged (at h = 58 keV the contribution of photoabsorption is suppressed by roughly 1/6000). There are two general non-relativistic predictions varying by a factor of two (R_{c1} = 1.68 % and R_{c2} = 0.8 %) which as well significantly differ in their spectral behaviour. The X-ray energy of 20 keV (the highest used so far) however has proved to still not be high enough to resolve the large theoretical differences at high photon energies.

As a consequence the two experiments recently performed on ID15B were designed to determine the ratio R_{c} at significantly higher photon energies. The measurements were performed by Wehlitz et al. and Spielberger et al. at photon energies of about 58 keV using ion counting time-of-flight spectrometry and a modified technique, namely cold target ion recoil ion momentum spectroscopy, respectively (Figure 81). Such experiments only become feasible at third generation synchrotron radiation facilities which can deliver sufficient flux of high-energy photons to overcome the low Compton double ionisation cross-section in this energy range.

Despite the fact that the experimentally derived values of the ratio of double to single ionisation by Compton scattering differ by 30 % ( Spielberger et al.: R_{c} = (0.84 +0.08 / -0.11) % ; Wehlitz et al.: R_{c}= (1.25 ± 0.3) %) the conclusions from the two data sets are similar.

Both experiments clearly rule out theories which predict the asymptotic value of Compton scattering to be equal to that of photoionisation (Figure 82).

Concerning the answer to the outstanding question of the exact value of R_{c} in the limit of high photon energies, the experimentalists point out the necessity to extend the studies to even higher energies, although the details of their argumentation show some differences.

Wehlitz et al. concluded on a still steadily decreasing value of R_{c} with increasing photon energies. Their data show that the applied energy is still not high enough to prove the high energy behaviour and to distinguish decisively among different theoretical predictions.

The result obtained by Spielberger et al. supports the theories which predict R_{c} = 0.8 %. Because of the high energy photons of 58 keV used in this experiment which amounts to 11% of the electron mass the question of the necessity of a fully relativistic treatment has to be raised. The currently available theoretical calculations refer to an asymptotically high, but non-relativistic limit. Relativistic calculations of R_{c} will certainly be required because of the need to extend experimental studies to even higher energies.

On the High Energy beamline (ID15A)

**Publications**

*[1] L. Spielberger (a), O. Jagutzki (a), B. Krässig (b), U. Meyer (a), K. Kayyat (a), V. Mergel (a), T. Tschentscher (c), T. Buslaps (c), H. Bräuning (a), R. Dörner (a), T. Vogt (a), M. Achler (a), J. Ullrich (d), D.S. Gemmell (b), H. Schmidt-Böcking (a), Phys. Rev. Lett. 76, 4685 (1996).*

*(a) Institut für Kernphysik, Frankfurt (Germany)*

*(b) Argonne National Laboratory, Argonne (USA)*

*(c) ESRF*

*(d) Gesellschaft für Schwerionenforschung, Darmstadt, (Germany)*

*[2] R. Wehlitz (a), R. Hentges (b), G. Prümper (b), A. Farhat (c), T. Buslaps (d), N. Berrah (c), J.C. Levin (a), I.A. Sellin (a), U. Becker (b), Compton Double-to-Single Ionization Ration of Helium at 57 keV, Phys. Rev A 53, 3720 (1996).*

*(a) Department of Physics and Astronomy, Univ. of Texas (USA)*

*(b) Fritz-Haber-Institut der Max-Planck-Gesellschaft, Berlin (Germany)*

*(c) Department of Physics, Western Michigan University (USA)*

*(d) ESRF*