The differential and total cross section for the excitation of the 3s1P10 and 3p1P1 states of neon by positron impact were calculated using a distorted-wave approximation. The results agree well with experimental conclusions

Mceachran, R. P.

Parcell, L. A.

Stauffer, A. D.

English

NASA Technical Reports Server

N90-18973
A
POSITRON EXCITATION OF NEON
L. A. Parcellt, R. P. McEachran_ and A. D. Stauffer_
Schooi_of Mathematics, Physics, Computing and Electronics, Macquarie University, Sydney, N.S.W. 2109, Australia
_Physics Department, York University, Toronto, Canada M3J 1P3
!
: ABSTRACT
The differential and total cross section for the excita-
tion of the 3s 1p_ and 3p 1P1 states of neon by positron
impact have been calculated using a distorted-wave ap-
proximation. Our results agree well with experiment.
We are continuing our earlier work on the positron
excitation of the noble gases 1'2 by calculating cross sec-
tions for the excitation of the 2p 5 (2p_/_) 3s 1p_ as well as
I
the 2p 5 (2P_'/2) 3p IP I states of neon. We use a distorted
wave approximation similar to our former calculations
on helium.
In the incident channel the distortion potential con-
sists of the static potential plus the polarized-orbital po-
larization potential used previously for elastic scattering, a
In the excited channel the distortion potential consists of
the appropriate static potential plus a polarization po-
tential determined by an extension of Stone's method. 4
In order to calculate this potential we construct the
following polarized orbital:
where the _o,zm(r ) are the unperturbed states of the
atom and r represents the coordinates of all the bound
electrons. The positron coordinate is zepresented by z
and the symbol (l'm'A'_' [ lU_'lm) is the usual vector-
coupling coefficient.
We define the adiabatic hamiltonian Had as
H_d =//_to_ + V(_, .) (2)
I
(1)
I
where//atom is the hamiltonian of the unperturbed atom
and V(r,z) represents the perturbation due to the in-
cident positron. The unknown coefficients ;3] z are then
determined from the set of equations
and
(_'.,._(,')I/'/..a- E(-)I_,.,_(,',=_)>= o
(_ _.,,,,,_,,(.)Y_,,.,,(.)(rm"r'_"Ir:_":m)l_,_-E(=,)]_,.,_(,.,,_))-o
,rn.ri_n
(3a)
(3b)
for all values of n"l" and )J' in the sum in (1). The
angle brackets indicate integration over the electron co-
ordinates only. The set of equations (3) are expanded
in spherical harmonics and the various terms in the per-
turbed energy E(z) are eliminated. Sufficient numbers
of the lowest order equations from the set (3) are re-
tained in order to solve for the unknown functions f_l.
Note that these are Mgebraic equations for the unknown
functions.
In the present work we restrict the sum in equation (1)
to a single term by taking )_' = 1 and !o_,vm, as the
3s 1p_ state when to,_ represents the 3plPl state and
l
vice versa. We note that the 2pS3p configuration gives
rise to 3 possible multiplets, viz 1D, _P and l_ so that
other choices for the polarized orbital are possible. With
our particular choice the polarization potential becomes
(4)
for both states although the value for _ differs in the two
cases.
The distorted-wave T-matrix for the excitation is then
given by
(_)
109
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where X + and X_ are the distorted-waves in the incident
and finalchannels respectively.
In the case of excitation to the 3p 1P1 state the cross
sectionfor the m = 0 magnetic sublevelis zero. This
I
means that the differential cross section for this transi-
tion is zero for a scattering angle of 0° or 180 °. The cross
section also displays a dip near 90 ° at most energies. We
show some typical results in figure 1.
N_ 10-_ FI I t i , I , t I I J I I , J J I I , , I I , I I I I I , I I J i IIs__. _
0 10 -" _ -2..
.,-, ,/ _
/ ,,'-
_ % _ _
_ 10 -4
:
10-s6)
6)
""4 _ I I I t I, I, I I I I I I I, I I R",_ I ,I0 -s
0 .30 60 go: 120. 150 so
Scattering Angle (deg)
FIG. I. Differentialcrosssectionsforthe excitationofthe 3p tPt stateof neon by positronimpact
at 20 eV,(--); 2SeV, (- - -); and 40eV, (---).
I
For the excitation of the 3s ip_ state the differential On the theoretical side, the cross sections for the exci-
cross sections decrease monotonically with angle, ration of the 3p 1]:)1 and 3p IS 1 states should also be taken
_'_te [n{egratedCrossSect_onsfort]tesetwo transitions into account when comparing with experiment. These
are shown in figure 2 along with the experimental data. 5 latter cross sections are expectea::to be:0f the same or-
The theoretical values for the excitation of the 3s tP_' der of magnitude as for the 3p xP1 state. Excitation to
state are comparable in magnitude to the experiment higher states are not very important as the higher thresh-
results. The cross sections for the 3p IP 1 state are about old energies for these states means a longer time-of-flight
a sixth of the magnitude of the ones for the 3s 1p_ state: and hence a Smaller proportion of the cross section was
In comparing the theoret]c_ an(Iexperimental results measured.
the following points sho_noted. The exper_ ....... In concluslonl whiiethc_=o_M1 magnitude of our cal-
was _based upon a time-of-flight technique which only culated cross sections agree quite well with the experi-
measured scattering in the forward direction (approxi- mental data more detailed measurements will be neces-
mateiy up to 60°). However(slnce the differential cross sary Before more quantitat!ye conclusions can be made.
sections are Peaked in th_e forwarddi_ection this does not .....
introduce an appreciableerror.It alsomeasured all the ACKNOWLEDGMENTS
positrons which arrived at the detector within the spec-
....... _<i_e_[t_me period. ThuS:_ns exciting a variety=of ...... This work was supported by the Natural sciences and
states were included and the measured Cross section is-a Engineering Research Council of Canada and by a Mac-
sum of these, quarie University Research Grant.
II0
N
o
o
.p.4
u
CD
o
0.15 I '
0.10
0.05
0.00 -_ '
20
, . l ! I , | I ' i ! , I !
J
I a I ! ' l i l I i ! i I
25 30 35
Energy (eV)
• I l I i I
4O
FIG. 2. Integratedcrosssectionsfor the excitationofneon by positronimpact: (_), excitation
ofthe 3sIp_,state;(- - -), excitationofthe 3p IPI state;(*),experiment.5
i L. A. ParceU, R. P. McEachran and A. D. Stauffer,J.
Phys. B. 16, 3125, 1983.
2 _, j.Phys. B. 20, 2307, 1987.
3 R. P. McEachran, A. G. Ryman and A. D. Stauffer,J.
Phys. B. 11,551, 1978•
4 p. M. Stone,Phys. Rev. 141, 137, 1966.
5 p. G. Colman_ 3. T. Hutton, D. R. Cook and C. A.
Chandler, Can. J.Phys. 60, 584, 1982.
111
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Positron excitation of neon

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