Classical binary approximation for ionization by proton impac

Garcia, J. D.

Gerjuoy, E.

Welker, J. E.

English

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d&i& 39.- o w -  04 5 
Classical  Approximation f o r  Ionization by Heavy Pa r t i c l e  Impact 
J. D. Garcia and E. Gerjuoy 
Deparlxhent of Physics - 
University of Pit tsburgh 
Pittsburgh, Pennsylvanfa, W.S.A. 
and 
Jean E. Welker 
MASA-Goddard Space Flight Center 
Greenbelt, Maryland, U.S .A.  
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I n  t h i s  paper, we e x d n e  the u t i l i t y  of the  c l a s s i ca l  binary ap- 
proximation proposed by Gryzinski' i n  predicting the ionization of atoms 
by h e a v y l e s ,  notably protons. 
of the c l a s s i ca l  binary approximation as an evaluation of its u t i l i t y .  
Our a i m  w a s  as much a delineation 
The method i s  based on a knowledge of t he  d i f f e ren t i a l  cross 
sect ion,  aeff(v v ), f o r  the exchange of energy AE i n  the  lab frame be- bE 1 2  
tween two charged pa r t i c l e s  of 
orientations of one pa r t i c l e  e 
impinging upon an atom is  then 
unequal mass, averaged over all velocity 
The ionization cross section fo r  protons 
given by 
(1) 
dU i i 
1 where ni is the  number of electrons having ionization energy Ui and E 
-is the  incident proton energy. The resul tant  cross section i s  then t o  
I1 
be averaged over t h e  velocity dis t r ibut ions of t he  bound electrons,  
Our spec i f ic  contributions are: (a)  the use of the exact ex- 
pressions f o r  aeff(v v ), avoiding any approximation (these have been 
recently made available2 i n  closed form, and are eas i ly  integrated t o  
AI3 1,2 
give the  t o t a l  cross sec t ion) ;  (b)  i n  the case of ionization of hydrogen 
, . '  " 
https://ntrs.nasa.gov/search.jsp?R=19680018066 2020-03-12T10:44:08+00:00Z
by proton impact, the use of the quantum 
dis t r ibu t ion  f o r  the  bound electron e 
The sens i t i v i ty  of the Gryzinski 
2 
mechanically correct velocity 
approximation f o r  i ne l a s t i c  
atomic cross sections t o  velocity dis t r ibut ions i s  dramatically illustrated 
by proton iotaization of hydrogen. This  i s  i n  contrast  with ionization by 
electron impact, where even the assumption f(v2) = J ( v 2  -p gives cross 
me 
sections at a l l  accurately measured incident energies which i n  hydrogen 
are  within a fac tor  of about 3 of experimental values o 3  For protons , t h i s  
assumption would predict  a cross section which i s  zero f o r  incident energies 
V 1 E-1 me &?+I l e s s  than ~ 7 8 € J ,  (7 g (-1- + - m 2  -1 1 o r  about 1 keV. 
2 P 
This i s  due t o  the 
r e l a t ive  i n a b i l i t y  of a heavy pa r t i c l e  t o  t r h s f e r  large energies t o  a 
l i g h t e r  one a 
Despite t h i s  s e n s i t i v i t y ,  the cross sections given by (1) even 
wi th  the 8-function d is t r ibu t ion  are  found t o  be qui te  good approximations 
t o  the  experimental values fo r  energies above E 
dicted cross sections d i f f e r  from the experimental by l e s s  than a factor  
of 2 o r  3, very similar t o  the resu l t s  found by Bauer and Bartky 
electron ionization, 
= 7 8 ~ ~ .  I n  f ac t ,  the  pre- 1 
4 for  
Ionization of the noble gases by protons and other 
assorted heavy pa r t i c l e  ionizations have been examined and comparison 
w i t h  experiment w i l l  be given where possible. Both d e l t a  function and 
hydrogenic electron velocity dis t r ibut ions have been used. A comparison 
of electron and proton ionization f o r  equal ve loc i t ies  a l so  w i l l  be given 
as well  as an examination of ionization from a sequence of excited s t a t e s .  
It is  found t h a t  f o r  a given velocity of the  bound electron,  the heavy 
pa r t i c l e  ionization cross section scales  readi ly  with ionization energy. 
Re ferenees 
1. 
2. 
3. 
M. Gryzinski, Phys. Rev. - 138A, 336 (1965). 
E. Gerjuoy, Phys. Rev. 148, 54 (1966). 
R. C. Stabler ,  Phys. Rev. 133A 1286 (1964). 
4. E. Bauer and C. D. Bartky, J. Chem. Phys. I 43, 2466 (1965). 


Classical approximation for ionization by heavy particle impact

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