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Submitted on 1 Jan 1979
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CALCULATION OF POLARIZATION IN MULTIPLET LINES EMITTED AFTER
BEAM-SURFACE INTERACTION.
H. Schröder
To cite this version:
H. Schröder. CALCULATION OF POLARIZATION IN MULTIPLET LINES EMITTED AFTER
BEAM-SURFACE INTERACTION.. Journal de Physique Colloques, 1979, 40 (C1), pp.C1-318-C1-
320. �10.1051/jphyscol:1979167�. �jpa-00218447�
JOURNAL DE PHYSIQUE Colloque C1, suppltlment au n o 2, Tome 40, fkvrier 1979, page C1-318
CALCULATION OF POLARIZATION IN WTIPLET LINES EMITTkD AFTER BEAM-SURFACE INTF3ACTION.
H. Schriider
Institut Eiir Atom- und Festkiirperphysik, Freie Universitat Berlin
Abstract.- The polarization in multiplet lines is calculated by coupling an aniso- tropic ensity operator p, of an excited electron to the density operator ;,,,p of an unpo:arized or core. For pel a pure angular momentum state is tested, whereas different assumptions are tried for pCorG. It is demonstrated, that the time delay .rlbetween the successive beam-projectile interactions, which create
pcore and pet, has a considerable effect on the relative Stokes parameter M/I.
R6sum'e.- La distribution de la polarisation entre des raies diff'erentes du m h e mltiplet est calcul6e par le couplage de la matrice densit6 anisotrope p , ~ dlun electron exit6 avec la matrice densite ,,,,p Cpolaris6e ou isotrope) des electrons interieurs. Un &tat pur de moment angulaire est 'eprouv'e pour pd, tandis que des cas diff6rents.sont consid61-6s pour .,,,,p I1 est montr6, que la dur'ee du temps T'
entre les interactions cons'ecutives, qui produisent ,,,,p et p e t , a un effet consid6rable sur le param6tre de Stokes M/I.
Introduction.- Anisotropic excitation of fast ion -Contributions to the polarization may arise from beams has been considerably improved by the grazing core electron polarization, caused by projectile- incidence technique [I ,2]
.
The understanding of the target interaction before the capture of the optical interaction mechanism between projectile and target, electron.hcnuever, has made only little progress.
gr
measure- -The main source for the polarization of the excited ments of the orientation distribution in multiplet ion is the strongly selective population of the mag- lines the spin independence of the exitation process netic substates of the optical electron by the elec- could be confirmed by Andrti et al, [3]. A separate tron capture process.theoretical treatment of the excited electron and We shall now follow the time development of a pro- the core electrons of the projectile led to good jectile ion.
fits of the distribution of circular polarization in At time to-At an interaction of the ion core with lines of supennultiplets[4]. Even the orientation of the target is assumed, creating an anisotropic den- ,states with the total orbital angular momentum L sity operator for the orbital .angular momentum Lo,
equal to zero could be explained, if not only the but leaving the total spin isotropic:
active electron but also the core electrons were core
I
to = PC, aniso(Lo) pc,iso(so) ('1 assumed to become oriented. This model will be dis-cussed here for varying times between the successive This density operator develops with the free ion interactions, which cause the polarization of core hamiltonian. Therefore p core(t) may be calculated electrons and optical electron respectively. Conse- in the base of the dyadic Operators
I
(LoSo)Jo>quences are discussed especially for the linear po- <(LoSo)JLI whose time dependence is known:
larization of the emitted light.
Model
.-
The following assumptions are made:-LS-couplkg and parentage approximation are appli- A
cable to the projectile. where $2 is the time evolution operator and h uJd;
interaction is limited to single is the energy splitting of the finestructure level events (capture, loss or exitation of electrons) of mJd0 ' = ( E - E , ) / h = A ( J o ( J o + l l - J i ( J 2 1 ) ) (3) short duration At (as compared to LS-coupling Jo JO
tines), and free ion behaviour is applicable for the tl -At an electron with isotropic spin s1 and
other times. anisotropically distributed angular momentum l1 is
-Proj ectile-target interaction is spin independent.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979167
captured: f i t s with an adjustable parameter T cannot extract (S ) (4) significant new infomation from the available data:
~ ( ~ 1 ) ' pcore(tl) 'Pel,aniso('l)Pel, i s o 1 The time evolution of eq. (4) i s treated a s i n eq.
(2) but includes an exponential decay. The time tl- tn between the interactions i s averaged over an
& e m 1 [o,T], where T i s used as parameter.
The r e s u l t f o r the irreducible tensor component pel k of the density operator P ( t ) in the subspace of t & a l angular momentum J i s given by
*
where I' is the decay constant of the level J. The appearance of j l comes from mathematical transfor- mations and does not mean that j j coupling is ap- plied. Eq. (5) i s different from t h e r e s u l t i n [4]
by t h e time average over the time between the in- teractions.
Hermiticity and symetry of reflection a t the scattering plane reduce the number of independent components of the density operators i n (5). For a geometry withthe reflected beam i n the z-direction, the normal of the target i n the z-y-plane, and the optical detection in the x-direction only the fol- lawing irreducible tensor components with k 5 2 are independent parameters f o r pc,-Lo (L 0' L o )
0 1 2 2 2 2
and ~ ~ ~, I l ) : ,P,, p1, ~ P,, ~p2, p l . ~ p1 and ~ ~ ( l ~ tensor componehts with
.
k>2 w i l l be negle2ted, be-cause they are considered t o be small.
Choice of parameters and results.- As there does not exist much new systematic experimental material on polarization i n surface exited multiplets, and a s f i t s with the upper and lower l i m i t of the pa- rameter T i n eq. (5) already gave agreement of ex- periment and theory within experimental errors,
the problems with a l l these f i t s are that only the circular polarization, characterized by the Stokes parameter S/I, has been extensively measured, where-
a s data on the linear polarization (respectively the Stokes parameters M / I and C/I) have been reported only occasionally. A s S/I depends only weakly on
2 2 2 2
po
( t ), p
( t ),
the uncertainty i n the o,,
values a r e correspondingly large.
Instead of making a new f i t we prefer t o make some reasonable guesses of the parameters P ~ , ~ ( L ~ L ~ ) , k
(1 1 ) and T and show the consequences of the Pq,el 1 1
variations i n the parameters f o r S/I a s well as f o r M/I; C/I tends t o be very small in f a s t ion beams and has been excluded already by choosing pZ = 0.
1 For the density operator of the optical elec- tron a pure s t a t e of angular momentum l1 quantized along the x-axis is taken pel, (11
,
11) = ,11,3(11m
(dl
,-m which gives f o r 1,=1 and w i t h normalization' ?:=I/Jv
:This i s the simplest choice which gives strong ori- entation. I t is further motivated by the low M / I values*, which it produces, similar a s the complete polarization measurements of Berry e t a l . [2] on one
2 2
ArII l i n e , which gave considerable po(L,L) and p2 (L,L) components and a low M / I value. These results were interpreted i n
[z]
i n terms of a s t a t e of max- imum orientation f o r the t o t a l angular momentum.However, a s the density operator' of the optical electron is considered i n eq.(6), the choice i n eq. ( 6 ) i s preferable here, because it leaves p a r t of the orientation f o r the core, see 141.
A) The influence of the core polarization is seen best, i f the different examples are compared with the case of an isotropic core, which means
D~,c(Lo,Lo) = 0 f o r k>O. (7) Applying formula (5) and the above given parameters
t o some ArII multiplets gives S/I values (see fig.
I ) , which reproduce the qualitative behaviour of the c i r c u l a r polarization measured by Andra e t a l .
(33, but gives somewhat too low absolute values.
The M/I values a r e practically zero, whereas the few available measurements of M/I give small but nonzero values C1
,
21.
B) As second example a core polarization is consid-
C1-320 JOURNAL DE PHYSIQUE
ered i n analogy t o the polarization of the optical electron but weakened by a factor of 5, say,
(L L ) =
.zpk
(1 , I l ),
L , , = l = IOq,c o 7 o q , e l 1 1 (8)
with p k (1 ,1 ) from eq. (6).
q l l
This case could occur i f the interaction of the ion core with the target i s e i t h e r l e s s effective i n producing polarization or i s l e s s probable than the f i n a l electron capture.
The results for S/I (fig. 1) agree better with ex- periment, because the values a r e generally increa- sed by the core orientation. The variation with the time delay T between core polarization and optical electron capture i s rather small. The M/I values a r e again almost zero, as could be expected from case (A)
.
C) If some of the projectiles enter into the target [5] before being reflected, the core can be polari- zed symmetrically around t h e beam axis. Therefore the following core polarization is chosen: a l l pq(Lo,Lo)= k 0 with exception of
(9) A s no core orientation is adopted, the S/I values
Fig. I
.
Comparison of - S/I values f o r ArII multipletsi n f i g . 1 do not d i f f e r much from case (A)
.
TheM/I r e s u l t s , however, a r e markedly different from' zero i n t h i s case and they show a strong variation with (see fig. 2)
.
Fig.2. Comparison of M / I values f o r ArII multiplets, (symbols as i n f i g
.
1 ).
For case (A),
(B) M/Id.Large values of M/I can of course also be produced by a change of the density operator components of the optical electron. But the strong dependence on
T seems to indicate that systematic measurements of M/I could answer the question of the validity of the core polarization model, and i n any case would give more reliable values of a l l components of the density operator. This would a t the same time cla- r i f y , i f pel is a nearly pure s t a t e .
A s byproduct of the calculations we found multi- p l e t s with same upper level (third and fourth mul- t i p l e t i n f i g
.
l ,2),
which gave identical polari- zation. This r e s u l t can be used t o look f o r system- a t i c errors o r cascade effects in experiments.This work i s supported by the Deutsche Forschungs- gemeinschaf t
.
Many valuable discussions with D r . Kupfer, Prof.
Gabriel, Prof. Andra and R. Frohling a r e grateful- l y acknowledged.
References
€11 H.J. Andra, Phys. Lett.
s,
31 5 (1975) [2] H.G. Berry, G.Gabrielse, A.E. Livingston,Phys. Rev. A
16,
1915 (1977)[3] H.J. Andra, R.Frohling, H.J. PlCjkn, in:
Inelastic Ion Surface Collisions, eds. N.H.
Tolk e t a l . , N.Y., Academic Press (1977) with plrent 3 ~ - The centers of the s ~ b o l s
h#
[4] H. Schrsder, I . Physik A284,
125 (1978) correspond totA=.4, whereas the v e r t i c a l l i n e s in [5] R. Schiffner, K. Goltz, C. Varelas, Vakuum-$give the range of polarization f o r .o56tAL- 25
