Scaling laws for single and double electron ... - APS Link Manager

PHYSICAL REVIEW A

VOLUME 57, NUMBER 6

JUNE 1998

Scaling laws for single and double electron capture in A q1 1He collisions „q>Z A 22… at low impact velocities F. Fre´mont, C. Bedouet, and X. Husson Laboratoire de Spectroscopie Atomique, Institut des Sciences de la Matie`re et du Rayonnement, 6 Boulevard Mare´chal, Juin, F-14050 Caen Cedex, France

J.-Y. Chesnel Hahn-Meitner Institut, Bereich Festko¨rperphysik, Glienicker Strasse 100, D-14109 Berlin, Germany ~Received 24 November 1997; revised manuscript received 27 January 1998! We present empirical scaling laws, as a function of the projectile charge state, for single and double electron capture in slow collisions between highly charged ions and He atoms at impact velocities of 0.1 and 0.5 a.u. The fitting parameters are shown to be suitable for predicting the populated states in single and double electron capture. The scaling law for single capture is found to be nearly independent of the projectile velocity in the range 0.1–0.5 a.u. The same fitting procedure is followed for double electron capture at the velocity of 0.5 a.u. since independent monoelectronic transitions, due to electron-nucleus interactions, are dominant. At this velocity, the scaling law for the projectile charge dependence of double electron capture cross sections is found to be similar to that for single electron capture. At the lower velocity of 0.1 a.u., where dielectronic processes caused by the electron-electron interaction gain importance, the charge dependence of double capture cross sections is strongly modified. @S1050-2947~98!01706-5# PACS number~s!: 32.80.Hd, 34.10.1x

I. INTRODUCTION

Electron capture processes involving highly charged ions are of great interest in many fields of physics such as controlled-thermonuclear fusion @1# and astrophysical plasmas @2#. The main directions of these charge-exchange studies have been oriented towards understanding the basic physical mechanisms governing the capture process @3–8#. Theoretical @3,4# and experimental @5–7# methods were developed to determine cross sections for total electron capture and cross sections for producing specific states ~partial cross sections!. Particular attention has been devoted to the study of atomic collisions at low impact velocities v ~smaller than the classical velocity of the target electrons involved in the capture!. For single electron capture in collisions of highly charged ions on atomic targets, energy gain spectroscopy and photon spectroscopy ~see, for example, @9–12#! have been used extensively to measure with good accuracy the corresponding total and partial cross sections. In parallel, theoretical methods, such as the classical trajectory Monte Carlo model @13#, the classical over-barrier model @14#, the Landau-Zener model @15#, and molecular expansion closecoupling methods @16#, have been developed. From such experimental and theoretical works, the main features for single charge exchange ~total and partial cross sections! have been explained over a large range of impact velocities @9#. The situation is quite different for multiple electron capture. This is partly due to the fact that the number of active electrons involved is larger, leading to a more complex, many-body problem. The second difficulty lies in the high number of molecular states necessary to describe the collision. In order to reduce these difficulties, experiments @7,17,18# and calculations @16# were devoted to double electron capture from a helium target ~two active electrons!. The 1050-2947/98/57~6!/4379~8!/$15.00

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helium atom is an interesting target because it is easily prepared in collision experiments and its electronic structure is the simplest one for a theoretical treatment of double capture. Nevertheless, it should be emphasized that a collision system involving two active electrons forms a complex fourbody system whose analysis is still a challenge for the following two reasons. ~i! The mechanisms that are responsible for capture are still under debate @17,19#. Typically, two kinds of interactions are invoked to describe double charge transfer. These mechanisms are illustrated in Fig. 1, which shows the orbital energies for the C611He system. First, the electron-nucleus interaction causes a two-step mechanism involving monoelectronic processes. For the example of C611He collisions, crossings occur between the He 1s orbital and a few orbitals of carbon, where the electrons from He can be transferred independently of each other. Then configurations of near equivalent electrons nln 8 l 8 ~n and n 8 ranging from 2 to 4! are produced ~Fig. 1!. The electron-nucleus interaction is found to be dominant at velocities around 0.5 a.u. @8#. Second, the small residual electron-electron interaction that is not incorporated in the independent particle model produces dynamic electron-correlation effects referred to as dielectronic processes @8#. As illustrated in Fig. 1 for C611He collisions, this dynamic electron correlation is likely to create configurations of nonequivalent electrons nln 8 l 8 (n 8 @n) where one electron is transferred into the 2l orbital of carbon, while the second electron is excited into a high-lying Rydberg orbital ~e.g., 6l 8 ! @17,20#. These dielectronic processes were found to play a decisive role at very low velocities @21,22#. ~ii! Agreement between different theories is quite poor @3,4#. Discrepancies occur also between theory and experi4379

© 1998 The American Physical Society

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FRE´MONT, BEDOUET, HUSSON, AND CHESNEL

FIG. 1. Diagram of orbital electron energies for the (C1He) 61 system showing uncorrelated ~inclined arrows! and correlated ~vertical arrows! double electron capture. These processes produce configurations of ~quasi! equivalent and nonequivalent electrons, respectively.

ment for the velocity dependence of the cross sections @20#. Although relative cross sections were extensively measured ~see, for example, @17–20#!, absolute cross sections are missing in most of the experiments. However, attempts were made to find general trends and scaling behaviors of single and multiple capture cross sections. Mu¨ller and Salzborn @23# concentrated their effort on total single capture cross sections in a large velocity range. Hence it was possible to reveal basic features of charge transfer collisions with multielectron targets. Iwai et al. @24# reported one-electron capture cross sections for highly charged ions in collisions with helium at impact energies lower than 3q keV ( v ,0.3 a.u.) ~q is the charge of the projectile!. Absolute cross sections were measured as a function of projectile charge q and compared with a classical oneelectron model @24#. Very recently, semiempirical scaling laws were formulated for absolute cross sections for multiple electron capture from different targets ~He, Ar, and Xe! @25#. Apart from these works, there is still a considerable need for additional studies in order to understand many important features. For example, only little is known about partial cross sections for double electron capture. In the present work, we investigate double electron capture in the collisions A q1 1He~ 1s 2 ! →A ~ q22 ! 1 ~ nln 8 l 8 ! 1He21,

~1!

where q>Z22 and Z is the atomic number of the ion A q1 @26#. In this paper single electron capture is first reviewed. The main attention is devoted to partial cross sections s n for

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FIG. 2. Experimental cross sections s SC n for producing a given n SC as a state relative to the total single capture cross sections s tot q1 function of the projectile charge in A 1He collisions ~odd n, solid circles; even n, open circles!. Collision velocities of about 0.5 and 0.1 a.u. are represented in the top and bottom figures, respectively. Gaussian curves ~solid lines! are used to fit the experimental data. Calculations using a multichannel Landau-Zener model @27# for a projectile velocity of 0.5 a.u. are compared with the experimental data ~odd n, crosses; even n, pulses!. Dashed Gaussian lines extrapolate experiment for n values larger than 5. The data are taken from the following references: for v '0.5 a.u., q51 @28#, q 52 @47#, q53 @30#, q54 @32#, q55 @33#, q56 @34#, q58 @35#, q57,9,16,17 @37#, and q510,18 @36#; for v '0.1 a.u., q51 @28#, q53 @30#, q54 @32,22#, q55 @32,33#, q56 – 8 @12#, q59 @48#, and q515– 17 @49#.

populating a state of the projectile with principal quantum number n. From the experimental data, the ratios s n / s tot ( s tot is the sum of the partial cross section over n! are determined as a function of the projectile charge. A simple scaling law is deduced and compared with calculations using the Landau-Zener model @27#. Then an analogous procedure is followed for the experimental double capture data in order to obtain a similar scaling law. The present study is divided into two parts. The velocity range around 0.5 a.u. is explored, where monoelectronic processes are dominant @17#. Details of the results are discussed in conjunction with the capture mechanisms for particular systems investigated previously. Then we focus on lower velocities (;0.1 a.u.) where dielectronic processes gain importance @18#.

II. SINGLE ELECTRON CAPTURE

Figure 2 and Table I show experimental single capture SC ratios s SC n / s tot obtained at collision velocities of about 0.5 and 0.1 a.u., as a function of the projectile charge q. The quantity s SC n is the cross section for producing the singly excited states A (q21)1 (nl) during the collision A q1 1He. The quantity s SC tot is the total cross section for single electron transfer from the target onto the projectile, i.e., the sum of the cross sections s SC n over n. Many experiments were performed for charges q