D.L. MOORES
Department of Physics and Astronomy, University College London,
London,
United Kingdom
ABSTRACT. The best available data on electron impact ionization cross-sections of B and Be ions have been selected and are presented in simple parametric form. Tables of the fitting parameters are included.
1. INTRODUCTION
Data on cross-sections for ionization of atomic systems by electron impact can be derived from three principal sources: semi-empirical methods and for-mulas, ab initio theory and experimental measurements.
In the first category we have the Seaton formula [1]
(which is only valid near threshold), the exchange classical impact parameter method [2], the infinite-z scaling method of Golden and Sampson (applicable to highly charged ions) [3], the formula of Percival [4]
(for hydrogenic ions), and the formulas of Lotz [5]
(probably the most widely used) and of Burgess and Chidichimo [6] (including an estimate of the excitation-autoionization contribution).
Ab initio theoretical methods include the Coulomb-Born and the distorted wave methods with exchange, which are me most elaborate and become increasingly accurate with increasing charge on the ion, as well as the Born and Bethe-Born approximations (which should be valid at very high impact energies, provided accurate target wave functions have been used), and a range of classical [7] and semi-classical methods.
For complex ions it may be necessary to include not just inner-shell processes but also contributions from
indirect processes such as excitation-autoionization and resonant excitation-double autoionization.
It should be pointed out that no reliable theoretical method capable of yielding accurate data for ions of low charge at low energies has been developed.
On the experimental side, the crossed beam technique is capable of producing accurate results.
Methods based on plasma spectroscopy measure rate coefficients rather than cross-sections, but in many cases they yield data of uncertain precision. For
very highly charged systems, electron beam ion trap methods are beginning to be used.
Estimates of unknown cross-sections can be obtained by making use of the fact that for a given isoelectronic sequence the reduced cross-section
QR(X) ^ I2Q(X) (1)
(where I is the ionization energy, Q(X) is the«.ioniza-tion cross-secthe«.ioniza-tion in cm2, and X is the incident energy divided by I) varies slowly as a function of Z. This technique is referred to as scaling.
The high energy behaviour of the cross-section can be fixed by making use of the fact that, for large X,
XQ(X) = A lnX + B (2) where
= 4 f " * *
Ji de « (3)
with df/de being the differential dipole continuum oscillator strength of die ion, and B is independent of X.
In mis report, the cross-sections have been para-metrized ekher in the form
XQ(X) = A lnX +
or in the form XQ(X) = A lnX +
_9L X lnX +
i = 1
1 - —
X1
(4)
(5) where Q and a{ are constants with no special physical interpretation, merely having the role of fitting para-meters. We now discuss the recommended data for each isoelectronic sequence in turn.
MOORES
TABLE I. PARAMETERS OF Eq. (4) FOR ELECTRON IMPACT IONIZATION OF Be"+ AND B"+ IONS
Species
2. RECOMMENDED IONIZATION CROSS-SECTIONS
H-like ions B V and Be IV
Bell et al. [8] recommended results based on a scaling of Younger's [9] distorted wave exchange cal-culations for C VI. The scaled curve agreed well with Younger's calculation for Ne X. The formulas of Lotz [5], Golden and Sampson [3] and Percival [4] gave results roughly 10% higher. New calculations [10]
using a relativistic distorted wave method (relativistic effects were in fact negligible) were carried out speci-fically for B V and Be IV. Similar calculations for Ne X were in close agreement with those by Younger.
These calculations for X < 5 were merged with the Born calculation of Peach [11] above X = 150 and fitted to Eq. (4), and these results provide the recom-mended data. The parameters are given in Table I. The accuracy of these cross-sections should be better than 12%.
For ionization from states other than the ground state the formulas of Golden and Sampson [3] should be used.
He-like ions Be III, BIV
For ground state ionization of B IV, Bell et al. [8]
point out the good agreement between a crossed beam experiment, distorted wave exchange calculations and a semi-empirical formula. We recommend a cross-section
based on these data for X < 5, merged with Peach's calculation [11] above X = 150. Be HI data are to be obtained by scaling the B TV data using Eq. (1).
Parameters obtained from fitting to Eq. (4) are given in Table I; the estimated accuracy is 12%.
For the ionization out of metastable states ls2s1,3S, Coulomb-Born exchange calculations have been per-formed by Attaourti et al. [12] for the isoelectronic C, N, O ions. Their results for O differ by 25% from the results of a calculation by Moores and Tully [13] using the code COBION [14].
The results shown in Table II have been obtained by scaling the C.V results of Attaourti et al. [12] and merging with the Burgess and Chidichimo [6] formula above X = 150. The estimated accuracy is 30%.
Li-like ions Be II and Be III
Falk and Dunn [15] have carried out a crossed beam measurement for Be II. Their fit, which includes Is ejection and a small excitation-autoionization contribu-tion, fails to match the Born approximacontribu-tion, however at very high energy.
Instead, we recommend the calculations of Younger [16] at low energies merged with those of Peach [11]
above X = 150. The combined inner-shell and excitation-autoionization contributions are less than the estimated 30% accuracy. A similar procedure was employed for B HI. The parameters of the fits are given in Table I.
ELECTRON IMPACT IONIZATION OF Be AND B ATOMS AND IONS
TABLE n . PARAMETERS OF Eq. (4) FOR ELECTRON IMPACT IONIZATION FROM METASTABLE STATES 2'S, 23SOFHe-LIKEIONS
Species B IV Be ffl B I V B e m
State 2 ' S 2 ' S 23S 23S
I(eV) 56.4 32.0 60.8 35.3
A 1.4870-17 4.6194-17 9.7412-18 2.8908-17
C0 3.0520-17 9.4808-17 -1.6292-17 -4.8347-17
c,
-3.1517-17 9.7908-17 1.4620-17 4.3384-17
C2
1.4244-17 4.4244-17 -1.2500-17 -3.7093-17
Accuracy 30%
30%
30%
30%
TABLE ffl. PARAMETERS OF Eq. (5) FOR ELECTRON IMPACT IONIZATION OF B I
Species B I
KeV) 8.30 12.93 17.40
A 4.2820-16 3.4867-16 6.4165-17
<*o 1.1049-15 1.3375-16 2.4614-17
« i . .
-2.6816-15 6.7887-16 1.0032-16
a2
8.3591-16 -8.4807-16 -1.5607-16
a3
3.4155-15 -9.3416-16 -1.7191-16
<*4
4.1763-15 2.5971-15 4.7795-16
<*5
1.5015-16 -1.3600-15 -2.5028-16
Remarks*
(a) (b) (c)
Accuracy Factor of two Factor of two Factor of two
* (a) 2s22p2P - 2s2'S; (b) 2 8 ^ 2P - 2s2p3P; (c) 2s22p2P - 2s2p'P.
/ " ~ N
1 2 logioX
FIG. 2. Electron impact ionization cross-sections for Be II versus log X. The long-dashed curve represents the data ofFalk and Dunn [15].
Neutral B
This cross-section is the least well known. For lack of anything better, we recommend a result obtained by scaling the C II calculation of Moores [18]. Parameters obtained from a fit to Eq. (5) are given in Table HI for ejection of 2s and 2p electrons. The cross-sections may be regarded as being only accurate to within about a factor of two.
I i
1 2 logio X
FIG. 1. Electron impact ionization cross-sections for B V versus log X. The full line is the recommended cross-section of the present evaluation (Eq. (4) and Table I); the dashed line represents the cross-section earlier recommended by Bell et al. [8], and the crosses are the cross-section values used in the fitting.
Be-like ions Be I and B II
The formulas given by Younger [17] for more highly charged Be-like ions cannot be extrapolated below Z = 6. However, reasonable results can be obtained by scaling Younger's C III results. This applies equally to ionization from the 2s2 and 2s2p3P states. Parameters obtained by fitting to Eq. (4) are shown in Table I. The accuracy is 30-40%.
MOORES
Figures 1 and 2 show the recommended cross-sections for B V and Be II, respectively, resulting from the present data assessment study. They are compared with the earlier recommendations of Bell et al. [8].
REFERENCES
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INDC(NDS)-254, compiled by R.K. JANEV (1991).
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INDC(NDS)-254, compiled by R.K. JANEV (1991).
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[13] MOORES, D.L., TULLY, J. (Observatoire de la Cote d'Azur, Nice), personal communication, 1987.
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