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SYSTEMATICS OF ELECTRON, PROTON AND PHOTON IONIZATION CROSS SECTIONS
E. Mcguire
To cite this version:
E. Mcguire. SYSTEMATICS OF ELECTRON, PROTON AND PHOTON IONIZA- TION CROSS SECTIONS. Journal de Physique Colloques, 1971, 32 (C4), pp.C4-37-C4-39.
�10.1051/jphyscol:1971407�. �jpa-00214608�
JOURNAL DE PHYSIQUE Colloque C4, supplkment au no 10, Tome 32, Octobre 1971, page C4-37
SYSTEMATICS OF ELECTRON, PROTON AND PHOTON IONIZATION CROSS SECTIONS (*)
E. J. McGUIRE
Sandia Laboratories, Albuquerque, N. Mex. 871 15
Resumb. - Nous prksentons des rksultats concernant les calculations des sections, en utilisant un modkle mono-Hectronique noyau non relaxk, a h de calculer des forces d'oscillateur gknkra- liskes. Nous avons trouvi: que les sections d'ionisation pour l'electron et le proton peuvent etre exprimks en une forme rkduite et possiblement universelle. Ensuite, nous discutons la possibilite d'exprimer les sections de photo-ionisation par une forme rkduite.
Abstract. - We present results on cross section calculations using a one-electron, unrelaxed core model to compute generalized oscillator strengths. It is found that the electron and proton ioniza- tion cross sections can be put in a reduced, and possibly universal, form. The possibility of putting photoionization cross sections in a reduced form is then discussed.
I. Introduction. - We have used the approach where M, and E, are the mass and energy of the inci- discussed in the paper on Auger transitions t o compute dent projectile. I n addition to the ionization cross the generalized oscillator strength (GOS) for He-Ar. section we have computed dolds, the excitation cross In a one-electron model with an unrelaxed core the section and the stopping power [l]. In figures 1-3 GOS per nl electron per &l' hole is given by we show some results of these calculations.
2 l
%(&, K , 1 ) = 3 l < nl l l > / z
dE lC2
where A& = E $ I Enl 1, - Enl is the ionization thres- hold, K Z is the momentum transfer, and we use atomic units. The ionization cross section is given by
4 za2, a = M , E,/M, X
" ds ( E , K ~ , E') ~d~
dE
FIG. 1. - EP ~ E P ) for ionization of He. Ne and Ar. The dashed Fm. Z. - Cross section in secondary electron curves labelled A are Peach's hydrogenic calculations. The energy for proton ionization of He. The dashed curves are
solid curves are our total cross section calculations. experimental measurements of Rudd and Jorgensen 191 and the
(*) This work was supported by the U. S . Atomic Energy individual points are taken from the calculations of Bell and
Commission. Kingston [10].
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1971407
E. J. McGUIRE
l 0 20 40 10 100 200 400 700 WOO
EIKeVl
FIG. 3. - The total stopping power of N, 0, and Ne for inci- dent protons. The solid lines are our direct calculations, the dashed lines are calculated from the Bethe formula using our computed mean excitation energies. The experimental values
are from ReynoIds et al. [l l].
11. Systematics. - The proton and electron ioniza- tion cross sections and the stopping power due to ionization are similar in shape for a particular shell.
In figure 4 we plot the peak ionization cross section
FIG. 4. - Computed peak cross section for ionization by incident electrons vs ionization energy.
for incident electrons as a function of the ionization energy. All cross sections are plotted as though the shells were full. The slope is in general not an integer.
We then used the computed cross sections to deter- mine a least squares fit of the form.
FIG. 5. - Scaled cross section for ionization of the l S shell by incident electrons. The experimental values are from Ref. 2-7.
We found that all the computed cross sections could be fitted to such a curve with no cross section value deviating from the least squares fit by more than 10 %. In figure 5 we compare the least squares fit cross section for ionization of the K shell by electrons for He [2], [3], A1 141, Ni [5] and Ag [6], and for C , N, 0, and Ne [7] at E,/ I E,, I = 4. The experimental
FIG. 6. - Photoionization cross section for the l s shell vs ionization energy for hvl I EIS I = 1.01, 21 and 51.
SYSTEMATICS OF ELECTRON, PROTON A N D PHOTON IONIZATION C4-39 points are for electrons with E,, 100 key. It should
be mentioned that we have no free parameter (inter- nal screening parameter) to fit the data as is the case
r
FIG. 7. - Photoionization cross section for the 3 s vs ionization energy for hv/ I E3s I = 1.01, 21, and 51.
in hydrogenic calculations. Similarly least square fits have been made for the 2 S, 2 p and 3 S shells, but there is little data with which one can compare the calculations.
The photoionization cross section is related to the K Z = 0 limit of the GOS. The electron and proton ionization cross sections involve a double integral over a region of the GOS in ( E , KZ) space. The photo- ionization cross section directly measures a section of the GOS. We are examining the possibility that atomic photoionization cross sections can be reduced to a form similar to Eq. 3. However, this is as yet an open question. In figures 6 and 7 we show the calculated photoionization cross section for the 1 S and 3 S shells, plotted as a function of I E,,, I with hv/ l E,,, I fixed at 1.01,21 and 51. For the 1 S case it appears a reduced cross section depending on hv/ IE,, I only can be found.
However, the possibility of doing so for the 3 S cross section is not apparent.
111. Conclusions. - Our calculations indicate that while one can compute electron, proton and photon ionization cross sections in a reasonably accurate way for a particular element, and reduced cross sec- tions for proton and electron ionization, the possibility of doing so for photoionization is still an open question.
Another question, which we have not yet examined, is the possibility of finding reduced expressions for da/ds. One could then predict the secondary elec- tron spectrum, including Auger and Coster-Kronig electrons, arising from an initial inner shell ioniza- tion event.
References
[l] MCGUIRE (E. J.), Phys. Rev. (to be published). [7] GLUPE (G.) and MEHLHORN (W.), Phys. Letters, 1967 [2] RAPP (D.) and ENGLANDER-GOLDEN (P.), J. Chem. 25A, 274.
Phys., 1965, 43, 1464. [g] PEACH (G.), Proc. Phys. Soc. (London), 1965,85,709 ; [3] SCHRAM (B. L.), DE HEER (F. J.), VAN DER WIEL (M. J.) 1966, 87, 375 ; and J. Phys. B, 1969, 2, 1125.
and KISTEMAKER (J.), Physica, 1965, 31, 94. [9] RUDD (M. E.) and JORGENSEN Jr (T.), Phys. Rev., 1963, [41 HINK (W.) and ZIELER (A.), 2. Phys., 1969,226, 222. 131, 666.
[5] POCKMAN (L. T.), WEBSTER (D. L.), KIRKPATRICK (P.) [l01 BELL (K. L.) and KINGSTON (A. E.), J. Phys. B, 1969, and HARWORTH (K.), Phys. Rev., 1947, 71, 330. 2, 653 ; 1969, 2, 1125.
[6] WEBSTER (D. L.), HANSEN (W. W.) and DUVENECK [l11 REYNOLDS (H. K.), DUNBAR (D. N. F.), WENZEL (W.
(F. B.), Phys. Rev., 1933, 43, 851. A.) and WHALING (W.), Phys. Rev., 1953,92,742.
