340 Nuclear Instruments and Methods in Physics Research B40/41 (1989) 340-344 North-Holland. Amsterdam zyxwvutsrq SIMPLE CORRELATION IN ATOMIC COLLISIONS J.H. McGUIRE, N.C. DEB and O.L. WEAVER Department of Physics, Kansas State University, Manhattan, KS 66502, USA T. ISHIHARA Department of Applied Physics, Tsukuba University, Tsukuba, Ibaraki 30.5, Japan L. KOCBACH Department of Physics, University of Bergen, N-5007 Bergen, No~ay T. MUKOYAMA Laboratory of Nuclear Radiation, Institute for Chemical Research, Kyoto University, Kyoto, Japan Corrections to the independent electron approximation in atomic scattering incorporate correlation. At very high collision velocities, correlation often dominates for multiple electron transitions. Generalized shake probabilities depend on correlation in static asymptotic wavefunctions. Various shake contributions are considered including shakeoff, shakeup, and shakeover. Some overall stalling relations of these shake probabilities with target and projectile charges and collision velocities is discussed. A distinction between shake and two-step electron-electron collision mechanisms is made. Recent observations indicating that shake-off probabilities are dependent on projectile parameters is discussed. Further experimental and theoretical studies are recommended. 1. Introduction zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA Two of the simplest examples of correlation in atomic collisions are shake effects and a direct interaction of an outgoing electron with another electron in the collision system. Both of these correlation effects can give rise to multiple excitation and io~zation, i.e., expe~mentally observable effects. Of course not ail multiple electron transitions are caused by correlation. Multiple transi- tions may occur, for example, when various target elec- trons interact directly and independently with a pro- jectile. Thus, it is not always clear how a multiple transition occurs. Furthermore, even if correlation can be identified as a dominant cause for a particular transi- tion, it is not always clear what correlation mechanism, e.g., shake or direct interaction, dominates. The purpose of this paper is to give an overview of the simplest mechanisms for multiple electron transi- tions in atomic collisions, and to begin to define and differentiate simple correlation mechanisms. Since the number of experimental studies have been completed on helium and helium-me targets, we shall concentrate on two electron transitions corresponding to Projectile + He --) Projectile * + He * * where * indicates the possibility of a change of elec- tronic state on the projectile and He. 0168-583X/ 89/ $03.50 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) 2. Fo~ uIation The scattering probability, P(B), may be expressed as the square of the quantum probability, a(B), given at a given impact parameter, B, by [I], a={+,/ ~-Il#i)- (I) Here & and rpi are the asymptotic initial and final states and U is the evolution operator which may be expressed in terms of the scattering potential, u, as U= T exp( - if V dt), where T is the time ordering operator. In the independent electron approximation cp= “G, and U = TU, so that a = ‘rraj. Thus the wavefunctions, evolution operators and probabilities are all uncorrelated. The scattering probability is correlated [l], i.e., P f nPj, if either 9 # “ 3 or U+ rtU,. Correlation occurs when the electrons interact with one another so that the electrons are interdependent, i.e., they affect one another. Correlation in the asymptotic wavefunctions is referred to as static correlation and correlation in the evolution operator is called scattering correlation. The boundary between the static and scattering terms de- pends on the choice of the boundary between the asymptotic zone and the scattering zone and is not yet well established. For example, terms with direct interac-