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Electron impact multiple ionization +, N+ and O+ ions. of C
J Lecointre1;5, K A Kouzakov2;3, D S Belic4, P Defrance5, Yu V Popov3, and V P Shevelko
1. Haute Ecole Namur-LiÕge-Luxembourg HENALLUX, DÈpartement IngÈnieur Industriel Pierrard, Rue d'Arlon 112, B-6760 Virton, Belgium. 2. Department of Nuclear Physics and Quantum Theory of Collisions, Faculty of Physics, Lomonosov Moscow State University, Moscow 119991, Russia. 3. Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991, Russia.

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4. University of Belgrade, Faculty of Physics, PO Box 386, 11000 Belgrade, Serbia. 5. UniversitÈ Catholique de Louvain, Institute of Condensed Matter and Nanosciences, Chemin du Cyclotron 2, B-1348 Louvain-la-Neuve, Belgium. 6. Lebedev Physical Institute, Russian Academy of Sciences, Moscow 119991, Russia.

The maximum cross sections for the multiply-charged products Cq+ (q = 2 ­ 4) is found to range from 2.3â10-20 cm² (for C4+) up to 6.3â10-17 cm² (for C2+); for Nq+ (q = 2 ­ 5) they range from 3.0â10-22 cm² (for N5+) up to 5.1â10-17 cm² (for N2+) and, lastly, for Oq+ (q = 2 ­ 5) they range from 5.5â10-22 cm² (for O5+) up to 5.2â10-17 cm² (for O2+). The corresponding threshold energies are determined to satisfactorily compare to spectroscopic values.
6

C r o s s s e c tio n ( 1 0

In the present study the animated crossed electron-ion beams method [1] is applied for measurement of absolute cross sections for electron impact single and multiple ionization of C+, N+ and O+ ions at incident electron energy values up to 2.5 keV.

6 6

(a) C

2+

(b) N

2+

cm )

2

- 17

4 4

2

2

0 10 6

100

1000

0 10

100

1000

E (eV) (c) O
2+

cm )

2

(a) C

3+

8

(b) N

3+

C r o s s s e c tio n ( 1 0

- 17

4

cm )

2

2

Cross sections for electron impact single ionization of (a) C+, (b) N+ and (c) O+: present experimental results (·), measurements of Yamada et al () and calculations based on the CB E approximation using the ATOM code (--).

C r o s s s e c tio n ( 1 0

- 19

4

6

4 2 2

0 10

100

1000

E (eV)

0 12

100

1000

0

100

1000

E (eV) (c) O
3+

C r o s s s e c tio n ( 1 0

- 19

8

4

Cross sections for electron impact double ionization of (a) C+, (b) N+ and (c) O+: present experimental results (·), measurements of Zambra et al (â), measurements of Westermann et al (), semi-empirical model of Talukder et al (- -), and semi-empirical formula (--).

The cross section values for single ionization reasonably agree with the calculations using the Coulomb-Born approximation with exchange [2]. Those for multiple ionization are found to compare well with the semi-empirical model for q = 3 [3], but they appear to be notably overestimated by a semi-empirical Bethe- Born type formula when q > 3 [4].

cm )

2

0

10
100 1000

-15

E (eV)

The Bethe-Fano plot show that for reasonably high energy of the incident electron, the quantity nEi linearly depends on lnEi, according to the Bethe formulae. The Born approximation in the interaction between a fast electron and an ion turns out to be sufficient already at impact energies of only about 1 keV.
6 C C
s.E/(4..R.a0)
2+ 3+ 4+

Cross section (cm )

10

-17

10

-19

Ne + C + N + O + C + N + O

+

10

-21

Ionization cross sections for C+, N+, O+ and Ne+ plotted as a function of the number of ejected electrons at E = 1995.1 eV: measurements of Lecointre et al (â) and present experimental results (open symbols) together with CBE calculations using the ATOM code for n = 1 and semi-empirical formulas [3] and [4] for, respectively, n = 2 and n = 3, 4 (filled symbols).

2

6 (a) (25) (250) 4 N N N N
2+ 3+ 4+ 5+

10

-23

(b) (50) (500) (1.10 )
4

0

1

2

3

4

5

Number of ejected electrons (n)

4

2

C

2

2

0

0 O O O O
2+ 3+ 4+ 5+

2 (c) (50) (500) (1.10 )
4

4

6

0

The remarkable point is that, at a given incident electron energy, the sequence of single and multiple ionization cross sections is observed to decrease exponentially with respect to the number of ejected electrons:
4 6

0

2 ln(E/R)

s n s1 exp n 1 q0
where s1 is the single ionization cross section and the fitting parameter q0 appears to be an effective charge. This peculiarity is also observable for neutral targets, and therefore seems to be a general feature common to any atomic or ionic target, but, up to now, it seems to have not receive any qualitative or quantitative theoretical treatment.

6
s.E/(4..R.a0)
2

4

2

Bethe-Fano plots for Xq+ produced by electron i ionization of (a) C+, (b) N+ and Straight lines result from the procedure.

ions mpact (c) O+: fitting

0

0

2 ln(E/R)

4

6

References [1] P. Defrance et [2] V. P. Shevelko [3] V. P. Shevelko [4] V. P. Shevelko

al 1981 J. Phys. B: At. Mol. Phys. 14 103 and L. A. Vainshtein 1993 Atomic Physics for Hot Plasmas (Bristol: Institute of Physics Publishing) et al 2005 J. Phys. B: At. Mol. Opt. Phys. 38 525 and H. Tawara 1995 J. Phys. B: At. Mol. Opt. Phys. 28 L589

Contact julien.lecointre.henallux@gmail.com kouzakov@gmail.com popov@srd.sinp.msu.ru