Magnetic sublevel population in 1s 2p excitation of helium by fast electrons and protons

Transcription

1 INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS B: ATOMIC, MOLECULAR AND OPTICAL PHYSICS J. Phys. B: At. Mol. Opt. Phys. 34 (1) PII: S (01) Magnetic sublevel population in 1s 2p excitation of helium by fast electrons and protons A L Godunov 1, H Merabet 2, J H McGuire 1, R Bruch 2, J Hanni 2 and V S Schipakov 3 1 Department of Physics, Tulane University, New Orleans, LA , USA 2 Department of Physics, University of Nevada Reno, Reno, NV 89557, USA 3 Troitsk Institute for Innovation and Fusion Research, Troitsk, , Russia Received 30 January 1, in final form 30 April 1 Abstract We report experimental and theoretical results for the magnetic sublevel population of the helium atom in collisions with fast (v i = 3 9 au) electrons and protons. Cross sections for excitation of magnetic sublevels with M = 0 and ±1 have been obtained using polarization measurements of emitted radiation in combination with differential cross sections. Calculations have been carried out using the expansion of the transition amplitude in the Born series over the projectile target interaction through the second order. Results of calculations are in agreement with experimental data. We find that the particle antiparticle Z ± difference exceeds the statistical error of measurement up to collision velocities v i 6 au for excitation of sublevels with M = 0. It is commonly accepted that the more differential cross sections there are, the more can be determined about the driving mechanisms of atomic collisions and the role of atomic correlation. For single-electron excitation, it is possible to measure not only total and differential cross sections, but also cross sections for different quantum numbers of initial and final states, in particular, populations of individual magnetic sublevels. The degree of polarization of radiation emitted by atoms and ions following particle impact contains information on the excitation of magnetic sublevels with a different M (Persival and Seaton 1958, Blum 1981). Recently Godunov et al (0) demonstrated how to determine the magnetic sublevel population of autoionizing states of helium, excited by the charged particle impact, from the shape of autoionizing resonances distorted by dynamic electrical fields. But then the question is: what kind of new information about collision dynamics can be obtained from populations of individual magnetic sublevels? Another question is whether the effects of projectile charge and mass are stronger for excitation to atomic states with different projections M of orbital momentum. Surprisingly little has been done in this direction either in theory or experiment (see Merabet et al (1999) and references therein). The purpose of this paper is to present new experimental and theoretical results on excitation of the (1s2p) 1 P state to magnetic sublevels with M = 0, ±1 by fast electron and proton impact /01/ $ IOP Publishing Ltd Printed in the UK 2575

2 2576 A L Godunov et al The experiment has been performed at the University of Nevada, Reno. The H + ions are provided by a2mvvandegraaf accelerator. The experimental apparatus used in this paper has been described in detail before (Merabet et al 1999, 1). An optically characterized Mo/Si multilayer mirror (MLM) polarimeter has been exploited to measure the degree of linear polarization in the extreme ultraviolet region. Cross sections of excitation to individual magnetic sublevels have been derived using the common equation for the linear polarization (Blum 1981): σ(0) σ(1) P = (1) σ(0) + σ(1) together with σ = σ(0) +2σ(1). (2) We calculated the cross sections for single-electron excitation of helium using expansion of the transition amplitude in the Born series over the projectile target interaction through the second order. The explicit equations can be found elsewhere (Godunov et al 1997). We separate the second-order amplitude f b2 into off-energy-shell and on-energy-shell terms using 1 the identity E E+iɛ = P E E iπδ(e E). Then the transition amplitude can be written as f ex = f b1 + fb2 off on iπfb2. (3) The fb2 off term corresponds to the off-shell scattering amplitude (the principal value part) and the fb2 on term is the on-shell part of the scattering amplitudes. The analysis of the matrix elements has shown that the on-shell (pole) and off-shell (principal value) parts of the amplitudes in equation (3) are purely real to within a common phase factor. There are arguments for splitting the second-order amplitude into off- and on-shell parts. First, the interference of the secondorder off-shell term with the first-order amplitude results in particle antiparticle, or Z ±, effects in the same way for single-electron transitions as for double-electron transitions (McGuire 1997). Second, a term responsible for time ordering of interactions in time-dependent collision theory is directly related to the off-shell term in the stationary collision theory (McGuire et al 1999, 1). If the off-shell term is neglected then one obtains an independent time approximation (Godunov and McGuire 1) when the interactions may be taken in any time order. Consequently the magnitude of the Z ± effects indicates the strength of time ordering. Effects of time ordering in atomic collisions has been previously considered (Stolterfoht 1993, Nagy et al 1997, McGuire 1997). The measured and calculated cross sections for excitation of individual magnetic sublevels of the (1s2p) 1 P state with M = 0 and ±1 are presented in figures 1 and 2 for electron impact. Figures 3 and 4 display similar cross sections for excitation by proton impact. We find that cross sections for excitation of the sublevels with M = 0, both for electron and proton impact, are comparable in magnitude to those with M =±1for the collision velocities considered here. As the collision energy increases, the relative populations of sublevels with M =±1 increases slightly compared to M = 0. It is worth noting that the asymptotic region where excitation to M = 0 dominates M =±1, i.e. σ(0) σ(1), starts at relativistic v i. That is far from our present conditions. Our second Born calculations for electron impact are in good agreement with the experimental data, although the second Born term plays a more important role in the excitation of M = 0 sublevels than in M =±1. Indeed, we find numerically that f b2 f b1 for the excitation of M =±1sublevels. In figures 1 and 2 we also present calculations for positron impact to study the effects of particle antiparticle excitation. It was noticed before that Z ± effects are expected to be very small for single-electron excitation of optically allowed transitions by fast charged particles

3 Magnetic sublevel population of He e - + He m=0 0 Figure 1. Magnetic sublevel cross section for single-electron excitation of helium to (1s2p) 1 P state with M = 0 by electron impact. Present experimental results: full squares. Present theoretical results: full curve, full Born calculations with off-energy-shell terms; short broken curve, first Born approximation; dotted curve, calculations in Born approximation without off-energy-shell terms; chain curve, calculations for positron impact e - + He m= Figure 2. Magnetic sublevel cross section for single-electron excitation of helium to (1s2p) 1 P state with M = 1 by electron impact. Notations are the same as figure 1. (Ast et al 1988, Rodriguez and Miraglia 1992). However, it is clearly seen that, for sublevels with M = 0, the difference between electron and positron impact exceeds statistical errors of measurements for collision energies up to v i 6 au. On the other hand, for excitation of M =±1 sublevels, calculations for particles and antiparticles are closer in magnitude.

4 2578 A L Godunov et al p + + He m= Figure 3. Magnetic sublevel cross section for single-electron excitation of helium to (1s2p) 1 P state with M = 0 by proton impact. Chain curve, calculations for antiproton impact. Other notations are the same as figure p + + He m= Figure 4. Magnetic sublevel cross section for single-electron excitation of helium to (1s2p) 1 P state with M = 1 by proton impact. Notations are the same as figure 3. After the summation over M, the effect of Z ± becomes small. We mentioned above that the magnitude of the Z ± effects indicates the importance of time ordering of the interactions in atomic collisions. Thus, it may be concluded that time ordering is more important for excitation of M = 0 than ±1 sublevels. Calculations for excitation of magnetic sublevels by proton impact presented in figures 3 and 4 demonstrate a tendency similar to excitation by electron impact. Namely, the second Born

5 Magnetic sublevel population of He 2579 terms are more important for excitation of M = 0 states than for M =±1. Calculations for antiproton impact demonstrate stronger effects of projectile charge for the M = 0 sublevels. As in the case of electron impact, the time-ordering effects are stronger for excitation of sublevels with M = 0 than ±1. For excitation to specific magnetic sublevels LM it is possible to at least partially resolve collision geometry from other effects. It is known (McDowell and Coleman 1970) that in the first Born approximation the ratio for differential cross sections of hydrogenic 1s np excitation can be written as dσ 1,±1 /dσ 1,0 = tan 2 ( ˆQ)/2, where ˆQ is the direction of momentum transfer Q. Thus, the ratio of M =±1to 0 cross sections is completely determined by collision geometry. Electron correlation in multielectron atoms changes this tan 2 ( ˆQ)/2 behaviour because of the change in geometry. In the first Born approximation for total cross sections (figures 1 4) the ratio σ 1,±1 /σ 1,0 varies from 0.7 to 1.5. We have found that this result can be explained by geometric factors. In the second Born approximation the situation is more complex. Unlike the first Born term we cannot extract geometric factors because of summation and integration over intermediate states. However, it is possible to qualitatively understand why the second Born terms are more important for excitation of M = 0 sublevels. Indeed, from a mathematical point of view it can be explained by the presence of the phase factor e imφ under integration over φ. For excitation of (1s2p) 1 P state this factor partially damps the amplitude to M =±1 because other factors have a rather smooth dependence on azimuthal angle φ. The magnitude of the particle antiparticle difference (Z ± effect) in the first + second Born approximation is connected with the interference term 2f b1 fb2 off as well as relative magnitudes of the first and second Born amplitudes. As we noted above, for total excitation cross sections to (1s2p) 1 P state this effect is weak. However, the second-order terms, both fb2 on off and fb2, contribute mainly to the excitation of the M = 0 level. Therefore the Z ± effect is stronger for this level and weaker for excitation of the M =±1level. In summary, we have found that for 1s 2p single-electron excitation of helium, the effects of the sign of projectile charge Z ± are stronger for the excitation of sublevels with M = 0 than with M =±1. For electron impact, the magnitude of the Z ± difference exceeds the statistical error of measurement up to v i 6 au. For the proton impact, this effect also extends to v i 6 au. After summation over the quantum number M the particle antiparticle difference is significantly smaller. The second-order terms play a more important role for excitation of magnetic sublevel states with the quantum number M = 0 than for M =±1. We believe that experimental data, together with theoretical analysis for differential cross sections of excitation to magnetic sublevels as a function of momentum transfer, should provide a deeper insight into excitation mechanisms, including correlation both in space and time. Acknowledgments Two of us (AG and JM) acknowledge support from the Division of Chemical Sciences, Office of Basic Energy Sciences, Office of Energy Research, US Department of Energy. References Ast H, Lüdde H J and Dreizler R M 1988 J. Phys. B: At. Mol. Opt. Phys Blum K 1981 Density Matrix. Theory and Applications (New York: Plenum) Godunov A L, Ivanov P B, Schipakov V A, Moretto-Capelle P, Bordenave-Montesquieu D and Bordenave- Montesquieu A 0 J. Phys. B: At. Mol. Opt. Phys Godunov A L and McGuire J H 1 J. Phys. B: At. Mol. Opt. Phys. 34 L223 9 Godunov A L, McGuire J H and Schipakov V A 1997 J. Phys. B: At. Mol. Opt. Phys

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