The impact parameter dependence of carbon K-shell ionization by proton and helium impact

Volume 66A, number 4

PHYSICS LETFERS

29 May 1978

THE IMPACT PARAMETER DEPENDENCE OF CARBON K-SHELL IONIZATION BY PROTON AND HELRJM IMPACT W. JANK, F. BELL and K.-H. WEBER Sektion Physik der UniversitgIt Munchen, Munich, Germany

Received 2 March 1978

The impact parameter dependence of carbon K-shell ionization by 100 KeV/amu proton or helium impact has been measured by a coincidence technique. The results are compared with theories which take the adiabatic relaxation of the K-electron due to the Coulomb field of the projectile into account.

It is common practice to test deviations from linear response theories for inner shell ionization by measuring either total or differential cross sections for different nuclear charges of the projectiles at the same projectile velocity [1—4].Therefore we have measured the impact parameter dependence of the carbon Is ionization for p and ~ impact at 100 keV/amu. This corresponds to a rather large velocity v since the central parameter of direct ionization theories ~K = rad/aK takes the value 1.09. Here the adiabatic distance is rad = flv/EB, where E 8 is the ls binding energy and

I zf

.

-

aK the K-shell radius. ~K measures the spatial exten-

sion of the ionization probability [1]. The ionization probabilities have been obtained by measuring the X-ray photons and scattered projectiles in coincidence. For experimental details see ref. [5]. The fluorescence yields w(C) which we used in order to obtain ionization probabffities were w(C) = 1.5 X l0—~for protons and w(C) = 1.3 X 10—s for alpha particles. The validity of these values was discussed in detail in ref. [5]. In this experiment the worst true-torandom coincidence ratio was 1. Fig. 1 shows experimental results in connection with theoretical curves. Curve 1 is the SCA result [6] without any correction and is therefore identical for both projectiles. Curves 2 (protons) and 3 (alpha partides) show the SCA theory corrected for the binding effect [1]. To do this we increased the is binding energy of carbon (EB = 290 eV) by Z1Z2KHa (Z2K = Z2—0.3, Ha = 27.2 eV), which is the first-order cor-

~

10

~ ;

;

~

8 b (pm)

Fig. 1. Ionization probabilities 1(b) divided by Z~,as a function of the impact parameter b. Crosses: protons; dots: alpha partides. Full drawn curves: see text.

rection for the binding energy due to the adiabatic response of the K-shell electron at zero impact parameter [11. The justification of this choice results from the fact that the measurements have been made predominantly at impact parameters which are small cornpared to the shell radius (aK = 9.3 pm). Fig. 1 shows 293

Volume 66A, number 4

PHYSICS LETTERS

that this correction overestimates the deviation from the SCA result strongly.

Next, we calculated SCA curves for a nitrogen (EB 402 eV, curve 4) and an oxygen target (EB = 532 eV, curve 5) [61. This is the united atom limit which takes into account the adiabatic relaxation of both the binding energy and the wave function. In this sense such a procedure resembles the ideas of Andersen et al. [3]. It is seen from fig. I that this calculation greatly improves the correction. It remains that the theoretical curves are 50—70% too low for both protons and alpha particles. This discrepancy cannot be removed by polarization effects which are possible for ~K ~ 1 but should be operative at impact parameters larger than the shell radius [1,7] It might be that electron capture can account for the observed deficiency: if the total cross section for electron capture into the is-shell of a He-projectile is calculated according to a prescription given by refs. [7,8], a value of 1.5 X 1019 cm2 is found. When this is =

compared with the experimental ionization cross section of 4.9 X 10—19 cm2 [9] one sees that electron capture may contribute roughly 30% to the ionization cross section. Since the corresponding adiabatic distance r~ = flu/E~,with [8,10] EEC

=

[E

2Ekifl(EB(C)+ EB(He))

1~ + + (EB(C)

294

—

EB(He))2] 1/2,

29 May 1978

is nearly identical with that for ionization at 100 key! amu, one expects the electron capture probability to have nearly the same impact parameter dependence as

for ionization. For the above expression Ekifl = 0.5 mu2 holds, where m means the electron mass. Corrections for Coulomb deflection can be neglected since the distances of closest approach in a head-on collision are 0.1 pm (p—C) and 0.06 pm(a—C) only. This investigation has received financial support from the Bundesministerium für Forschung und Technologie, Germany. References [1] G. Basbas, W. Brandt and R. Laubert, Phys. Rev. A7 (1973) 983.

[21G. Basbas, W. Brandt and R.H. Ritchie, Phys. Rev. A7 1971. E. Laegsgaard, M. Lund and C.D. Moak, [3] (1973) J.U. Andersen, Nucl. Instr. Meth. 132 (1976) 505. [4] H. Schmidt-Bocking et al., J. Phys. BlO (1977) 2663. [5] K.-H. Weber and F. Bell, Phys. Rev. A16 (1977) 1075. [6] J.M. Hansteen, O.M. Johnson and L. Kocbach, At. Data NucI. Data Tables 15 (1975) 305. [7] and R. Laubert, to be [8] G. G. Basbas, Lapicki W. andBrandt W. Losonsky, Phys. Rev. A15published. (1977) 896. [9] N. Stolterfoht and D. Schneider, Phys. Rev. All (1975) 721. [10] H.C. Brinkman and H.A. Kramers, Proc. Kon. Ned. Akad. Wet. 33 (1930) 973.