Home Search Collections Journals About Contact us My IOPscience A scaling law of cross sections for multiple electron transfer in slow collisions between highly charged ions and atoms This content has been downloaded from IOPscience Please scroll down to see the full text 1995 J Phys B: At Mol Opt Phys 28 L643 (http://iopscience.iop.org/0953-4075/28/20/003) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 130.237.165.40 This content was downloaded on 23/08/2015 at 09:32 Please note that terms and conditions apply I Phys B: At Mol Opt Phys 28 (1995) L64SL647 Printed in the UK LETTER TO THE EDITOR A scaling law of cross sections for multiple electron transfer in slow collisions between highly charged ions and atoms M Kimurat, N Nakamurat, H Watanabe$, I Yamada, A Danjog, K Hosaka, A Matsumotoll, S Ohtanit, H A Sakaue, M Sakwaill, H T a w m and M Yoshino+ National Institute for Fusion Science Nagoya 464.01, Japan Received 13 June 1995 Abstract A simple scaling relation is derived for the pmisl and total multiple-electron capture cross sections in slow collisions of highly chwged ions with atoms based on the extended classical over-banier model If is shown that the currently available experimental cross sections are reproduced quite satisfactorily by this relation In single collisions between slow, highly charged ions Aq+ and multi-electron target atoms B a number of electrons are transferred into excited levels of A The multiply excited states thus formed are unstable and decay by emitting Auger electron(s) or photon($ or both and are finally stabilized These processes are expressed as follows: Aq+ + B -+ A@-j)+* + Bj+ -+ A'9"'+ + Bj+ + ( j - i)e- + (hu) (U;) (1) (uq+-,) j (2) The cross section in equation (1) for j-electron removal from the target is equivalent to the cross section for the formation of intermediate excited states A(q-j)+* ions, while ui,q-i corresponds to the partial cross section for i-electron capture by projectile and j-electron removal from the target It is known from theories and many experiments that electron capture cross sections for multiply charged ions not significantly depend on the impact velocities in the range below au (e.g Raphaelian el al 1995) and, furthermore, are nearly independent of the projectile species but depend only on the initial charge state q (Janev and Winter 1985, Janev et al 1987) Though one-electron capture processes can now well be predicted by using sophisticated quantum mechanical calculations (Fritsch and Lin 1991), accurate theoretical treatments for the capture of multiple electrons are still hindered due to the participation of dense levels of multiply excited states and their inherently complicated electron correlation It is thus useful to find a simple scaling law which can be used to estimate the cross sections for multiple electron capture processes t Permanent address: Department of Physics, Osaka University Toyonaka Osaka 560 Japan $ Permanent address: Institute fur Laser Science University of Elenro-Comunication, Chofu, Tokyo 182, Japan P e m e n t address: 11 P e m e n t address: P e m e n t address: Department of Physics Niigata University, Niigata 950-21, Japan Hiroshima Institute of Technology, Hiroshima 731-51, Japan Deparlment of Physics, Kobe University, Kobe 657, Japan + P e m e n f address: Shibaura Institute of Technology, Ohmiya 330, Japan 0953475/95i200643f.OS$l9.50 @ 1995 IOP Publi;hing Ltd L643 L644 Letter to the Editor Recently we have measured the dependence of the multiple-electron capture cross sections and the decay of the multiply excited states both on projectile charge states and on target species in order to obtain some systematic trends in these processes Our measurements have included coincidence detection of charge-selected collision partners in collisions of I’’+ and I”+ on rare gas atoms (Yamada el al 1995) as well as absolute measurements of total and one-electron capture cross sections in P - r a r e gas atoms in the range of < q 30 (Nakamura et al 1995a, b, and unpublished data) From these data we have obtained U; as well as U& Multiple-electron capture processes in slow collisions of highly charged ions and atoms have been recently described by Barat and Roncin (1992) Some scaling laws have been proposed by several authors (Muller and Salzborn 1977, Muller el ~l 1979, Sakisaka el al 1983) but are applicable only to the cross sections for the processes of producing the final charge states ( u ~ , ~ - In , ) the present work we focus on a scaling law which can be applied to the cross sections (U;) for the formation of intermediate excited statcs of projectiles As a guiding principle we use the extended classical over-barrier model (ECBM) proposed by Niehaus (1986), which has been proved to account satisfactorily for some features of multiple-electron capture processes for all its simplicity In the ECBM the collision processes are divided into two parts: the ‘way in’ and the ‘way out’ At large nuclear separation R before the collision the Coulomb barrier between the collision partners isolates the electrons of target B from the strong attractive potential around A4+ On the ‘way in’ this Coulomb barrier is depressed with decreasing R until the closest approaching point is reached When a bound electron surmounts the barrier this electron becomes ‘molecular’, meaning that the electron is shared by the projectile and the target The larger the original ionization potential energy Pk of the kth electron on B, the smaller the distance Rk where the barrier ceases to be effective Rk is expressed as follows in atomic units (Niehaus 1986) < Rk = [q(l/ffr - 1) + k / ( l - f f k ) l / P k (3) + where o l p = I/[] (k/~)]p and ] (k - 1) elcctrons are assumed not to screen the charge q effectively On the ‘way out’, the potential barrier between A and B increases again with increasing R The ‘molecular’ electron which stays around both A and B has finite probabilities of being captured by either A or B Niehaus assumed that the probability of being captured into projectile A is determined by the degrees of degeneracy of the quantum states to be occupied by the electron after the collision on A and B We have further simplified his model for the case that the projectile charge q is much larger than the number k of transferred electrons In such cases the probability that the electron is found around A is almost unity, so that the electron is finally transferred to A when the particles A and B are separated again This leads to an approximation that the collisions where the impact parameters are between Rk and Rk+, result in the k-electron transfer, i.e U,“ = RR: - r ~ : + , (4) From this equation the effective cross section Q, = Z R ,2 (5) represents the cross section for the transfer of more than j electrons; Q, = R R , ~= + J + l4 + U¶i+z + (6) Letter to the Editor L645 Equation (4) implies that only a few partial cross sections o p , those with small values of m ,contribute significantly to Q, in (6) It is seen furthermore that Q I corresponds to total charge transfer and Q, can be expressed in another form, Q, = Ql - (U: +U:+ (7) ,+U:-‘) When j is much smaller than q the distance follows, Rj in ( ) can be further approximated as R, = ( j q ) ’ / ’ / P j (8) and the following relation is finally obtained: Qj = 4rrjq/P; When Qj is expressed in A’ (9) and Pj in eV units, Q, = 2.6 x IC? jq/P; (10) In order to test this scaling law the reduced cross sections Q, should be known Currently, however, very few measured data are available from which Qj can be derived In the following, the proposed scaling formula (IO) is compared with experimental data (i) IIo+ and I’”-Ne, AI, Kr and Xe In our first measurement partial cross sections U ; as well as total capture cross sections in collisions of I]’+ and I”+ with Ne, Ar, Kr and Xe were obtained at the energy of 1.Sq keV The details of the measurements have been described elsewhere (Yamada er a/ 1995, Nakamura er a/ 199Sa) Here, the recoil ion charge state ( j ) is assumed to be equal to the number of electrons initially transferred to the projectile, implying that the target autoionization process can be neglected According to the measurements made by Ali er nl (1994) this effect was, in fact, found to be very small for small j In figure the reduced cross section Q , is plotted against qjjP,’ The data points are seen to lie well on a single straight line which represents the relation (IO) 0.1 0.2 q j /:P (ev2) Figure Reduced partial and total cross sections in collisions of 1‘” and on Ne (0) Ar ( ) Kr ( )and Xe (M) at 1.59 keV energy (Nakamuraeial 1995a) The full line represents relorion (IO) The parameter j ranges from I Io < < (ii) Is+ (6 q 30)-Ne, Ar, KI and Xe In our next experiment absolute total charge transfer cross sections Ql were measured for Iq+ (6 q 30) colliding on Ne, Ar, Kr and Xe atoms at the energy of 1.Sq keV (Nakamura er al 1995b, and unpublished results) In figure the cross sections Ql are plotted The full straight line represents relation (10) < < L646 Letter to the Editor Iq+ (6 q 30) 400 N - 09 O-200 0.1 0.2 q j I P; (e+) < < Figure Reduced total cross sections for eleclron capture in collisions of lqt (6 q 30) on Ne (U) Ar (0).KI (0) and Xe (M) at 1.59 keV energy (Nakamura et 01 1995a.b and unpublished data) The full line represents relation (IO) < < (iii) Xeq+ (11 q 31)-He Anderson et01 (1988) measured U ~ ~ -uq,q9.4-I, II , uq,q9.4-l and u & - ~in Xeq+-He collisions for projectile charge states 11 q 31 at the collision , ~ Q - ~~ = ~ ~ 2,~-,+u~,,~,obtained velocityof30q eVIamu Ql = U ~ , ~ - ~ + U & ~ + U ~and from their data are plotted by full boxes in figure w ere the straight line represents relation (10) < < 0.1 0.05 q j I P: (er2) Figure Reduced total and pmial cross sections for electron capture processes: Q L and Q for collisions of Xeqt-He (I1 < q < 31) at 304 eVlamu (Andenson era/ 1988) (M); QI for Arq+-Ar and Arq'-He (8 < q < 16) 2.3q keV energy (Vancura ern/ 1993, 1994) (0); and Qi for Arq+-Ar (5 q 17) at 10 keVlamu (Ali er a1 1994) (i) < < < < (iv) A r q + (8 q 16)-Ar and He Vancura et ol (1993, 1994) measured totalelectron-transfer cross sections for A r q + ions (8 q 16) colliding on He and Ar at 2.3q keV energy Those cross sections are plotted by open circles in figure Data of oneand two-electron capture cross sections ( u ~ , ~and -, additionally obtained are not for ( I ) but for (2), and such data cannot be used to compare with our scaling law (v) Ar9+ (5 q 17)-Ar Ali er 01 (1994) also measured total-electron-transfer cross sections for Arq+ (5 q 17) colliding on AI at IO keVIamu The cross sections obtained from their figures are shown by crosses in figure < < < < < < Letter to the Editor L647 In figure all data points for (i)-(v) are plotted together The full line represents relation (IO), while the upper and lower broken ones represent the lines whose gradients are by 20% larger and smaller than 2.6 x IO3 the two boundaries & eV2 resoectivelv As seen most data points lie inside 400 N - 0-200 0 0.1 0.2 q j I:P (ev-*) Figure All data in figures 1-3 plotted together The full line represents relation (IO), while the dolled lines correspond to the gradients larger and smaller than that of the full line by 20% Experimentd data: Nalwmura et nl (1995a.b) ( ) ;Andenson er el 1988 (1); Vancura eta1 (1993, 1994) (0);and Ali er of (1994) (+) In conclusion we have shown that our scaling law based on the ECBM for multipleelectron transfer satisfactorily reproduces measured data presently available This indicates that the classical picture can well describe the multiple-electron transfer processes in slow collisions as long as the projectile charge q is very large and the number of the transferred electrons is much smaller than q This work is partially supported by a Grant-in-Aid for Scientific Research from the Ministry of Education of Japan References Ali R, Cwke C h Raphaelian M L A and Stockli M 1994 Phys Rev A 49 3586 Andersson H.Astner G and Cderquist H 1988 J Phys B: Al Mol Opt Plrys 21 LIS7 Barat M and Roncio P 1991 J, Phys B: At Mol Opt Phys 25 2205 Fritsch W and Lio C D 1991 Phys Rep 202 I Janev R K, Resnyakov P L and Shevelko V P 1987 Physic$ of Highly Ionized low (Berlin: Springer) Janev R K and Winter H P 1985 Phys Rep 117 265 Miiller A Achenbach C and Salzbom E 1979 Phys Len 70A 410 Miiller A and Salzbom E 1977 Phys Lett 62A 391 Nakamura N et a1 1995a Phys 8: At Mol Opt Phys 28 2959 Nakamura N et 01 1995b Pmc XIX Int ConJ on the Physics of Eleeironic and Atomic Colli3iow (Whistler) d J B A Mitchell J W McConkey and C E Brion Abstract3 p 284 Niehaus A 1986 J Phys B: At Mol Phys 19 2925 Raphaelian M L A, StocM M P Wu W and C o d e C L 1995 Phys Rev A 51 1304 Sakisaka M, Hanaki H Nagai N, Horiuchi T,Konomi I and Kusakabe T 1983 J, Phys Soc Japan 52 716 Vancura 1, Marchetti V 1, Perotti J I and Koslroun V 1993 Phys Rev A 47 3758 Vancura 1, Perotd I J Flidr J and KosVOun V 1994 Phys Rev A 49 2515 Yamada et nl 1995 J Phys B: At Mol Opt Phys 28 L9 ... Kimurat, N Nakamurat, H Watanabe$, I Yamada, A Danjog, K Hosaka, A Matsumotoll, S Ohtanit, H A Sakaue, M Sakwaill, H T a w m and M Yoshino+ National Institute for Fusion Science Nagoya 464.01, Japan... total and one -electron capture cross sections in P - r a r e gas atoms in the range of < q 30 (Nakamura et al 199 5a, b, and unpublished data) From these data we have obtained U; as well as U& Multiple- electron. .. B: At Mol Opt Phys 28 (1995) L64SL647 Printed in the UK LETTER TO THE EDITOR A scaling law of cross sections for multiple electron transfer in slow collisions between highly charged ions and atoms