Measured multipole moments of continuum electron transfer angular distributions

Abstract The velocity space distribution of electrons emitted near the forward direction from collisions involving fast, highly stripped oxygen ions with gaseous and solid targets is presented and described in terms of multipole moments of the ejected charge distribution, which permits direct comparison with recent theory. The measurements are produced by employing position-sensitive electron detection to combine emission angle definition with conventional electrostatic spectrometry. Agreement obtained between theory and distributions observed for binary continuum electron loss processes coupled with a similar multipole content observed with solid targets suggests a model of convoy electron production dominated by electron loss from the projectile within the bulk of the target. Further, the connection between multipoles of the projectile electron emission distribution in single collisions and the state of excitation of that projectile excited states may provide the basis for a probe of the state of ions traversing bulk solid matter.

(ELC), produce a transversly emitted charge distribution characterized by even-order raultipole moments (monopole, quadrupole, hexadecapole, etc.) and maximum multipolarity k = 2n determined by the principal quantum number n of the contributing projectile orbital [3,1]. The so-called 'convoy' cusp produced by swift charged particles passing through solid materials has been observed to possess the transverse signature of the projectile loss mechanism and to become enriched in higher-order multipoles with increasing projectile speed [5]. This latter observation can be interpeted as reflecting steadystate excitation of high n-and 1-states during passage through the bulk material, followed by electron loss processes which populate the cusp region of the spectrum. If this interpetation is correct, detailed measurements of the convoy electron cusp can, under appropriate circumstances, provide a probe of the state of excitation of charged particles penetrating condensed matter.
The history underlying this current state of understanding of cusp formation is too lengthy to detail here; several reviews of relevant theoretical and experimental work, which pertain to the domain of high velocity, high-Z projectiles, have appeared [1]. The existence of the cusp is seen as merely a consequence of the Coulomb final state interaction, the details of the shape of the cusp, however, reflect the entire history of the collision: anisotropies arise in the doubly differential cross section (DDCS) which are collision mechanism-dependent. It is important to appreciate that detailed comparison between measurements and most existing theory often requires collision velocities large compared to the characteristic oribtal velocities of any electrons that can contribute to the cusp, usually so that the first and at most second-order Born approximations can be made with some confidence. Joachim BurgdCrfer [3] has developed a density matrix descrip-tion of the ELC process which exploits smooth continuation of projectile excitation across the ionization limit to show that a set of dynamical multipoles originally introduced to describe bound-state coherences are suited for the description of continuum-state coherences as well. Consequently, the anisotropies in the DDCS for ELC can be expressed as expectation values of the dynamical multipoles. BurgdOrfer has shown this method to be extensible to other electron transfer to continuum (ETC) processes and to collisionally excited Rydberg manifolds [6]. A unified approach thus emerges in which the same fundamental parameters describe the populations of cusp and Rydberg final states.
In the framework of the method advanced by BurgdOrfer, the DDCS for ETC processes is expanded in the zero-velocity limit as 00 -- where v is the electron emission velocity in the projectile rest frame (PRF), Pk are the Legendre polynomials, and gk are the asymmetry parameters derivable from the theory. Contact can also be made with the double-series expansion of the DDCS introduced by Meckbach, Garibotti, and co-workers [7] and employed in previous work in our laboratory [8] by expanding the f$i< to account for finite-velocity corrections to the cross section: 00 --(7) I B v J P k (cose) . [2] dv k,j*O J

II. Method
Much experimental data on ETC processes to date have been singly differential (in electron energy or longitudinal velocity component), even though in most cases a small range of collection angles have been employed.
As a result, much of the collision-dependent information contained in the above DDCS expansions is lost in apparatus-dependent averaging over emission angles interior-to the spectrometer collection cone. We employ an apparatus developed in our laboratory which subdivides a forward-oriented collection cone of about 5 degrees half-angle into differential angular elements of about one-third degree full angle. These elements are sized so that the effective angular resolution in the PRF corresponds to a differential slice in transverse electron emission velocity v^ of a size comparable to that of the slice in longitudinal emission velocity v^ determined by the electron spectrometer employed. The apparatus collects data simultaneously from all elements within this forward cone by means of position-sensitive detection techniques and thereby permits efficient data acquisition, eliminates mechanical scanning linkages, and automatically determines the zero-degree direction.
The major elements of the electron spectrometric apparatus are diagrammed in Figure 1. The target region, which is a -0.5 cm thick cell for gaseous targets and a self-supporting foil for solid target measurements, is  verse projectile frame emission velocity v t . As expected from earlier singly differential work [10], the distributions are dominated by ELC from the loosely bound n = 2 levels by an order of magnitude over ECC and ELC from n -1. The immediate appearance of these data are of strongly transverse emission, as predicted by Burgdo'rf er's calculation [3,6], and in striking contrast to the strong dipole character of the ECC distribution obtained from a v p -15.4 au collision in Ne, shown in part f of Figure 2. Also shown is the theoretical angular distribution calculated by Burgdo'rf er, convoluted with the spectrometer acceptance function.

III. Results and Discussion
Excellent agreement is obtained for fitted values of the multipole strengths fi^ of the argon data at the higher two velocities; somewhat poorer agreement at 10 au is not of concern because the first Born approximation is suspected to be less accurate at lower vp [6]. A lack of agreement between helium target data and theory is of much greater concern. The simpler structure of this target and the use of more accurate scattering functions than were available for argon would at first suggest a more accurate description for helium. An experimental source of a difference between these targets is unlikely because the data sets were alternately acquired for He and Ar targets by merely switching between target gas bottles on a time scale of minutes, while the accelerator operators were instructed to leave all beam conditions (i.e. focusing and steering) unchanged. Further, although pixel-by-pixel 'gas-dump' background subtractions (see section 5) contribute more heavily to statistical and systematic errors with helium targets, the ELC to background ratio at the cusp peak was £11:1 in the worse case.
Lacking a known, sufficiently large source of experimental error that would selectively affect the helium data, we speculate that doubly inelastic collisions between the active projectile electron and target electrons may be responsible for the difference. Such processes are taken into account in the theory within the framework of a closure approximation and this contribution is fractionally more important for He because of its much smaller nuclear charge. Previous investigations [11], however, have indicated only minor errors in asymmetry parameters are induced by the closure approximation. In addition, the closure approximation cannot account for a difference in radial distribution. It is also possible, of course, that an as yet unidentified excitation or ionization process is occurring either in addition to, or in combination with simple electron loss to the forward peak.
Our recent measurements [5] of the multipole moments of the solid target convoy electron distribution, while limited in scope, are intriguing in that they suggest the feasibility of applying ' owledge gained from ELC studies such as those in the previous section and extensions of theoretical studies like those of BurgdOrfer [3,6] to probe the processes leading to convoy emission from condensed matter targets. They reveal multipole content of order well beyond the quadrupole and hexadecapole moments obtained for ELC from n = 2 orbitals and offer an opportunity to perform unique, new measurements sensitive to excitations of swift projectiles that oocur while immersed in bulk material. Figure 3 presents contoured emission distributions we have observed for convoy electron production together with corresponding data for ELC from equal velocity 05+ in argon. The targets employed (15 yg/cm2) were substantially below equilibrium thickness. The resemblence between the convoy cusps and those for ELC is striking -both are strongly transverseand the convoy data displays no evidence of the strong dipolarity which is the hallmark of ECC (see Figure 2f). We interpet this feature of the data to signify a prominent role for ELC in the convoy production process.
The displayed ELC and convoy distributions differ in one important respect, however: attempts to fit multipole moments to the convoy distributions in the same manner as was done with the ELC data produced poor results until multipoles of order up to k -10 were included in the fitting procedure. The resulting fitted values of 3^ are given in Table I for the three impact velocities studied. As can be seen from a close examination of the g^ values, the enhanced multipolarity of convoy emission skews toward higher raultipoles with increasing projectile velocity. Recalling that the maximum predicted multipolarity P k of ELC from a given n level is k -2n, the data then suggests convoy production which behaves as loss from highly changing. While it is expected that elastic and inelastic electron scattering processes which occur after convoy production and prior to or during exit from the foil surface (including the effect of the exit potential 'step') must be taken into account in any detailed examination of convoy multipole distributions, the strong Coulomb 'focusing' [13] provided by the nearby projectile ion may make these effects smaller that they would appear to free electrons of the same speed, at least for the highly charged ions studied here. Further, there are indications that the effect of the static exit surface potential step is at least partially compensated for by a dynamical screening effect [1*1]. We are therefore cautiously optimistic that the present results will provide a basis for a detailed probe of the state of excitation and ionization of ions traversing bulk condensed matter.