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ATOMIC COLLISIONS OF CHANNELED IONS : RESONANT COHERENT EXCITATION
S. Datz
To cite this version:
S. Datz. ATOMIC COLLISIONS OF CHANNELED IONS : RESONANT COHERENT EXCITA- TION. Journal de Physique Colloques, 1979, 40 (C1), pp.C1-327-C1-334. �10.1051/jphyscol:1979170�.
�jpa-00218450�
S. Datz
Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, U.S.A.
R d s d . Les i o n s bien c a n a l i s g s n ' e n t r e n t e n c o l l i s i o n qu'avec l e s e l e c t r o n s de conductance ou de valence du c r i s t a l . Aux v i t e s s e s v i >> vo l e s processus de p e r t e ou de capture d ' e l e c t r o n s s o n t e q u i v a l e n t s d ceux s e produisant avec l e bombardement d ' e l e c t r o n s d ve = v i . Pour l e s i o n s de Z suffisamment dl6vds e t fortement ionise's, l e s s e c t i o n s e f f i c a c e s de capture; de p e r t e e t d ' e x c i t a t i o n de l ' e l e c t r o n s o n t diminuegs, s i b i e n que les d u d e s de v i e e n t r e c o l l i s i o n s s o n t s u f f i s a n t e s pour permettre des d t a t s atomiques b i e n d e f i n i s 5 l ' i n t e r i e u r du c r i s t a l . La n a t u r e periodique du r h e a u f o u r n i t une p e r t u r b a t i o n cohdrente q u i permet d ' e x c i t e r des t r a n s i t i o n s dans c e s & t a t s e t q u i donne une forme de spectroscopie, au cours de l a q u e l l e , on peut mesurer l e s d t a t s ioniques d e t a i l l d s e t l e s champs c r i s t a l l i n s s t a t i q u e s e t dynamiques.
Abstract. Well channeled i o n s c o l l i d e only with conduction o r valence e l e c t r o n s i n the c r y s t a l . A t i o n v e l o c i t i e s v i >> vo e l e c t r o n l o s s and capture processes a r e equivalent t o those occurring with e l e c t r o n bombardment a t ve = v i . For h i g h l y s t r i p p e d i o n s of s u f f i c i e n t l y high Z, e l e c t r o n c a p t u r e , l o s s , and e x c i t a t i o n c r o s s s e c t i o n s a r e lowered s o t h a t c o l l i s i o n a l l i f e t i m e s a r e long enough t o allow defined atomic s t a t e s i n s i d e t h e c r y s t a l . The p e r i o d i c n a t u r e of the l a t t i c e s u p p l i e s a coherent p e r t u r b a t i o n which can e x c i t e t r a n s i t i o n s i n t h e s e s t a t e s and a f f o r d s a form of spectroscopy with which t h e d e t a i l e d i o n i c s t a t e s and c r y s t a l f i e l d s , both s t a t i c and dynamic, may be measured.
INTRODUCTION
I n general the frequency and c h a o t i c n a t u r e of c o l l i s i o n s of f a s t i o n s p e n e t r a t i n g s o l i d s precludes an e x a c t d e s c r i p t i o n of t h e t o t a l i o n i c s t a t e . However, the process of channeling r e s t r i c t s t h e range of impact parameters a v a i l a b l e , l i m i t s i t s c o l l i s i o n s t o conduc- t i o n and valence e l e c t r o n s , and, under c e r t a i n condi- t i o n s permits t h e e x i s t e n c e of d i s c r e t e s t a t e s f o r long enough p e r i o d s t o allow a meaningful measurement of t h e i o n i c s t a t e i n i t s milieu. I n any form of spectroscopy energy l e v e l d i f f e r e n c e s a r e measured by absorption o r emission; i n t h e case t o be discussed h e r e the coherent p e r t u r b a t i o n caused by t h e p e r i a d i c - i t y of t h e c r y s t a l l a t t i c e s u p p l i e s the frequency necessary t o perform absorption $pectroscopy between s t a t e s .
p o t e n t i a l of t h e f i r s t atom, again by t h e second, and s o f o r t h . The f i n a l c o l l i s i o n w i l l thereby be con- s i d e r a b l y softened, and, depending upon the angle, $, with r e s p e c t t o the atomic row, i t may nor " c o l l i d e "
a t a l l with the o r i g i n a l t a r g e t atom. This i s the b a s i s of channeling; i . e . , w i t h i n a small c r i t i c a l angle, J,, with r e s p e c t t o an atomic row o r plane, determined by t h e i n t e r a t o m i c p o t e n t i a l and spacing, d , of atoms, t h e p a r t i c l e w i l l be d e f l e c t e d by a continuum p o t e n t i a l made by properly summing the atomic p o t e n t i a l s .
I n Fig. 1 we show some cases of low index axes and planes i n the face-centered cubic c r y s t a l . For p a r t i c l e s e n t e r i n g i n a c l o s e t o a x i a l d i r e c t i o n a t high v e l o c i t y , Lindhard [ I ] showed t h a t t h e c l o s e c o l l i s i o n s with t h e r e s u l t a n t rows o r " s t r i n g s " of
CHANNELING AND IONIC CHARGE STATES atoms a r e avoided f o r incidence angle $c i f
Consider a p r o j e c t i l e i o n aimed f o r a hard c o l l i s i o n with a n atom contained in a c l o s e l y packed
( i . e . , -low index) atomic row i n a c r y s t a l . Because For p l a n a r channeling, i . e . , confinement of of t h e pre-set arrangement of t h e atoms with r e s p e c t t h e i o n ' s motion between s h e e t s of p l a n a r d e n s i t y n- t o i t s path the p r o j e c t i l e w i l l undergo a set of
c o r r e l a t e d c o l l i s i o n s with t h e e q u a l l y spaced row
(atoms t h e c r i t i c a l angle J, i s P
*
- -
atoms. I t w i l l be s l i g h t l y d e f l e c t e d by t h e r e p u l s i v e 2 J, = ( 2 r n Z Z e a
P P 1 2
!Research sponsored bv t h e Division of Chemical where a, is t h e Thomas Fermi screening l e n g t h . Sciences, b f f i c e of Basic Energy Sciences, U. S.
Department of Energy under c o n t r a c t W-7405-eng-26
I C
The primary r e s u l t of channeling is t o pre- w i t h Union Carbide Corporation. v e n t small impact parameter c o l l i s i o n s from occurring.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979170
JOURNAL DE PHYSIQUE
I
Face Centered Cubic Crystal '\I Viewed Along the [OM] Axls )
I
I[lw] Axis, Rotation [ t l 0 ] Axis lRotatian
( 9 0 0 ) Planar Channel ( t 4 0 ) Planar Channel
[01i] Channel till] Channel
FIG. 1.
-
I l l u s t r a t i o n of some a x i a l and p l a n a r chan- n e l s i n a f a c e c e n t e r e d cubic c r y s t a l .Hence, such e f f e c t s a s t h e e l i m i n a t i o n of Rutherford s c a t t e r i n g and n u c l e a r s t o p p i n g and t h e r e d u c t i o n of xiray and n u c l e a r s t o p p i n g and t h e r e d u c t i o n of x-ray and n u c l e a r r e a c t i o n y i e l d s a r e observed [2].
Of g r e a t e s t importance t o t h e s u b j e c t i n q u e s t i o n h e r e i s t h a t f o r channeled i o n s of vi >> vo c l o s e e l e c t r o n i c i n t e r a c t i o n s a r e l i m i t e d t o valence and/or conduction e l e c t r o n s , a l l of which have v e l o c i - ties lower t h a n t h e p e n e t r a t i n g i o n . Thus, f o r e l e c - t r o n c a p t u r e and l o s s from t h e i o n , we can view t h e p e n e t r a t i n g i o n a s s t a t i o n a r y and being bombarded by e l e c t r o n s of energy 112 mevi. 2 For example, a n i o n moving i n a channel w i t h a n energy of 2 MeVIamu maX be viewed a s being bombarded with e l e c t r o n s w i t h 1 keV of engrgy.
The r e s u l t of t h i s can be s e e n i n Fig. 2 where we show t h e eFergent charge s t a t e f r a c t i o n s , $i, f o r 40 MeV oxygen i o n s which have been i n j e c t e d i n t o a t h i n Au c r y s t a l [3]. When t h e beam i s d i r e c t e d i n a
"random" (non-channeled) d i r e c t i o n t h e observed
110 MeV 0 IONS
INTO A Au CRYSTAL I
0.8
i, EMERGING ION CHARGE
I
8+in
[llO] AXIS PATHLENGTH 033um
FIG. 2.
-
F r a c t i o n a l p o p u l a t i o n s of charge s t a t e s of 40 MeV oxygen i o n s emerging from a n Au c r y s t a l when a l i g n e d i n a random and [I101 channeled d i r e c t i o n a s a f u n c t i o n of i n c i d e n t i o n charge s t a t e .emergent d i s t r i b u t i o n i s independent of t h e i n i t i a l charge on t h e oxygen i o n (6+, 7+, o r 8
+
) and a l s o independent of t h e c r y s t a l t h i c k n e s s over t h e range 0.143 t o 0.663 pm. This i s t o be a n t i c i p a t e d s i n c e"normal" e l e c t r o n c a p t u r e and l o s s c r o s s s e c t i o n s f o r i o n s of t h i s v e l o c i t y i n g a s e s (2
5
8) a r e i n t h e o r d e r 10'17 cm 2.
S o l i d d e n s i t i e s a r e i n t h e o r d e r $5 x 10 22 atomslcm 3.
A mean f r e e p a t h f o r charge exchange i s only a . 0 2 pm s o t h a t a s t e a d y s t a t e ("equilibrium") w i l l be reached independent of t h e i n i t i a l charge s t a t e .The same s i t u a t i o n does n o t o b t a i n i f we i n s t e a d i n j e c t t h e beam i n a channeled d i r e c t i o n , i n t h i s c a s e t h e 4 1 0 7 a x i a l d i r e c t i o n . The emergent charge f r a c t i o n s a r e a s t r o n g f u n c t i o n of t h e i n p u t charge. Equilibrium i s n o t a t t a i n e d and t h e r e l e v a n t charge changing c r o s s s e c t i o n s must be much reduced.
From t h e m a t r i x of v a l u e s of emergent charge d i s t r i b u - t i o n s f o r d i f f e r e n t i n p u t charges ( o r from t h e v a r i a - t i o n of charge f r a c t i o n w i t h t h i c k n e s s [3] we can d e r i v e t h e r e l e v a n t e l e c t r o n c a p t u r e and l o s s c r o s s s e c t i o n s f o r channeled i o n s .
Taking a c a s e i n p o i n t we have found an e l e c - t r o n c r o s s s e c t i o n f o r 0 7+ ,a7,) = 3 x 10-l9 a t 28 MeV
p e r e l e c t r o n of 3 x
loe2'
o r a b o u t 2 times a s h i g h a s one would c a l c u l a t e from Sampson and Golden's [5]method f o r %900 eV e l e c t r o n s on 07+(1s). An i m p o r t a n t p o i n t h e r e , however, i s t h a t i n t h e c r y s t a l channel any c o l l i s i o n l e a d i n g t o e x c i t a t i o n soon l e a d s t o ion- i z a t i o n , e . g . , t h e i o n i z a t i o n c r o s s s e c t i o n f o r 0 (2p) 7+ i s $10 times t h a t f o r 1s [5]. I n s o f a r a s t h e e x c i t a t i o n c r o s s s e c t i o n f o r t h e 1s e l e c t r o n i s e q u a l t o i t s d i r e c t i o n i z a t i o n c r o s s s e c t i o n , t h e e f f e c t i v e i o n i z a t i o n c r o s s s e c t i o n i n a channel c a n be a s much a s twice t h a t f o r a s i n g l e e l e c t r o n c o l l i s i o n .
The e l e c t r o n c a p t u r e (recombination) c r o s s s e c t i o n s i n t h e channel f o r 07+ and 08+ were even lower [ I ] ( o = 9 x 07,6 = 6 x s o t h a t
897
f o r c r y s t a l t h i c k n e s s e s of t h e o r d e r 0 . 1 t o 1 um an a p p r e c i a b l e f r a c t i o n of 07+ i o n s can p a s s through w i t h no charge changing c o l l i s i o n s and t h e s e which a r e i o n i z e d have o n l y a v e r y s m a l l chance of r e c a p t u r i n g a n e l e c t r o n .
F u r t h e r evidence f o r tie. absence of charge changing c o l l i s i o n s was shown i n measurement of energy l o s s s p e c t r a of i o n s emerging i n a given charge s t a t e a s a f u n c t i o n o f t h e i n p u t charge. F i g u r e 3 shows such s p e c t r a f o r 0 i o n s i n c i d e n t a t 27.5 MeV p a s s i n g
( 54178, THICK )
FIG. 3.
-
Emergent energy s p e c t r a of 27.5 MeV 07+ and 08+. i o n s i n c i d e n t on (111) p l a n a r channel of4 .
The s p e c t r a shown are f d r t h e i o n s having t h e same"charge a s t h e i n c i d e n t beam.-
through a 5400
%
Ag c r y s t a l [6]. The energy l o s s f o r f i x e d charge i o n s is c l o s e l y p r o p o r t i o n a l t o q2 [71.I n f a c t , d e t a i l e d s t u d i e s
[a]
of t h i s type have enabled u s t o measure t h e e f f e c t of s c r e e n i n g by bound 1s e l e c t r o n s upon e l e c t r o n i c energy l o s s . For i o n s of lower Z ( e .g.,
and C 5+ ) t h e r e l e v a n te n a b l e s u s t o p i c k o u t t h o s e i o n s which have n o t under- gone charge exchange [8].
RESONANT COHERENT EXCITATION
What we have demonstrated t h u s f a r is t h a t t h e s t a t e s of c e r t a i n c o n d i t i o n s i s a meaningful con- c e p t , i . e . , t h e y a r e n o t c o l l i s i o n broadened s o t h a t d i s c r e t e e i g e n s t a t e s a r e n o t u s e f u l concepts i n t h e i r d e s c r i p t i o n . I n t h i s c a s e i t i s a l s o meaningful t o d i s c u s s t r a n s i t i o n s between t h e s e e i g e n s t a t e s ( i . e . , t o perform a type of spectroscopy t o b e t t e r d e s c r i b e t h e s e s t a t e s ) . I n t h i s t h e l a t t i c e p e r i o d i c i t y sup- p l i e s r e q u i s i t e e x c i t i n g f r e q u e n c i e s and t h e presence of an e x c i t e d s t a t e i s s i g n a l e d by an i n c r e a s e d i o n i z a t i o n p r o b a b i l i t y [9
1.
Although t h e p o t e n t i a l c o n t r o l l i n g t h e d e t a i l e d t r a j e c t o r y of a channeled i o n can b e w e l l r e p r e s e n t e d a s a continuum, t h e i o n p a s s i n g between o r d e r e d rows of atoms w i t h v e l o c i t y vi e x p e r i e n c e s a c o h e r e n t p e r i o d i c p e r t u r b a t i o n of f r e q u e n c i e s
v = K(vi/d), K = 1, 2, 3
...,
where d i s t h e d i s t a n c e between atoms i n t h e row (Fig. 4 ) . When one of t h e s e f r e q u e n c i e s c o i n c i d e s w i t h v = AE / h where AE i sr i j i j
t h e e n e r g y d i f f e r e n c e between s t a t e s i and j of t h e i o n a r e e o n a n t c o h e r e n t e x c i t a t i o n might o c c u r . I f t h e e x c i t a t i o n does occur an enhanced i o n i z a t i o n prob- a b i l i t y i n t h e t r a n s m i t t e d f i x e d charge f r a c t i o n should be observed.
FIG. 4.
-
Schematic showing t h e i n f l u e n c e of t h e symmetry of t h e p e r t u r b a t i o n s on an i o n p e n e t r a t i n g i n a<loo>
d i r e c t i o n of a f a c e c e n t e r e d c u b i c l a t t i c e .I n Fig. 5 f o r i n c i d e n t N ~ + we d i s p l a y t h e t o t a l p o p u l a t i o n f r a c t i o n of N ~ + emerging from an 850-&thick Au c r y s t a l a s a f u n c t i o n of t h e i n c i d e n t . energy [9]. The s p a c i n g a l o n g a <Ill> raw i s 7.064
i.
Resonances a r e s e e n f o r n = 1 t o n = 2 t r a n s i t i o n s w i t h K = 4 , 5 , and 6 , and f o r n = 1 t o n = 3, K = 5 . The a d d i t i o n a l s c a l e s shown a r e g i v e n i n terms of v / v where vr i s t h e r e s o n a n t v e l o c i t y c a l c u l a t e d f o r t h e n = 1 t o n = 2 vacuum s t a t e s of t h e i o n .
Although t h e t o t a l (2-1) i f r a c t i o n is
JOURNAL DE PHYSIQUE
I I I I I
NITROGEN ( 6 9 <Ill> AXIS AIJ
6th WWJNK: (n-I1 D
i:h
3 (74) - --
51h WRMONC (n-1) TO:
''''
0 9 5 1.00 1.05 (n121-
(n-31 (11-41
a 6 5 I I I -
qrn HARMONIC E,=33.03 MeV 5' HARMONIC Er-21.19 MeV 6M HARMONIC E,- 1472 MeV
ION ENERGY (MeV1
FIG. 5.
-
Ratio, R, of N ~ + Counts t o the sum of N 6+and ~ 7 + counts a s a f u n c t i o n of i n i t i a l energy f o r
<Ill> a x i a l channeling. The i n c i d e n t beam i s
N6+.
The a d d i t i o n a l s c a l e s a r e i n terms of the resonant v e l o c i t y c a l c u l a t e d f o r t h e vacuum s t a t e of ~ 6 + .
p l o t t e d , the energy l o s s s p e c t r a f o r one-electron ions c o n s i s t of two p a r t s : (1) f ixed-charge-state i o n s which appear a s a low-energy l o s s peak, and (2) p a r t i a l l y charge e q u i l i b r a t e d ions which have passed c l o s e r t o atom rows and appear a s a separable peak towards higher energy l o s s e s . By deconvolution we can show t h a t the resonance a f f e c t s only t h e fixed- charge peak. Hence, the a c t u a l dips a r e deeper than shown.
The Oak Ridge group has observed almost 50 n = 1 t o n = 2 resonances ( a x i a l and planar) with hydrogen-like ions of Z = 5-9 i n t h e energy range 1 5 E 5 3.5 MeV/amu. For a l l t h e simpler f e a t u r e s of the resozances, some g e n e r a l i z a t i o n s can be made: (1) narrower channels give s t r o n g e r resonances, (2) higher harmonic resonances a r e weaker, (3) t h e r e a r e s l i g h t s h i f t s i n the resonance peaks t o lower (v/vr), and (4) the peaks a r e asymmetric towards lower (v/vr).
To understand these and o t h e r f e a t u r e s l e t us concentrate on a s i n g l e channel, the
<loo>
a x i a l chan- n e l . The configuration of t h i s channel, i . e . , a l t e r - nating p a i r s of atoms a c t i n g on t h e ion, i s i l l u s -t r a t e d i n Fig. 4. The e l e c t r i c p o t e n t i a l i n t h i s a x i s can be shown t o have t h e following form [ 9 ] :
even
V =
1
VkRm cos(2nkzIa) cos(2n&x/a) cos(2my/a) kRmodd
+ 1
VkRm sin(2nkzIa) sin(2n!Lx/a) sin(2mny/a) kRmwhere t h e z a x i s is centered on the d i r e c t i o n of motion
<loo>
and x and y a r e centered on t h e orthogonal <010>and <011> channels. The term a denotes the u n i t c e l l l e n g t h ; f o r t h e
<loo>
a x i s , a = d.Using a Moliere p o t e n t i a l t o describe the Au atom, t h e Fourier components of t h e e l e c t r i c f i e l d can be c a l c u l a t e d [ l o ] and a r e shown f o r K = 2, 3, and 4
i n Fig. 6. The value a t t h e c e n t e r l i n e i s f o r those i o n s which pass e x a c t l y down t h e center of t h e channel.
The A and B d i r e c t i o n s denote the f i e l d experienced along paths which take t h e ion toward atomic rows and i n a d i r e c t i o n between atomic rows r e s p e c t i v e l y . The explanation of two of the f e a t u r e s mentioned above a r e
" 1.8 t.4 1.0 0.6 0 . 2 6 0 . 2 0.6 1.0 1.4 1.8.
DISTANCE FROM AXIS (A)
ALONG A DIRECTION+ALONG 8 DIRECTION
FIG. 6.
-
Fourier c o e f f i c i e n t s of t h e l o n g i t u d i n a l and t r a n s v e r s e components of t h e e l e c t r i c f i e l d f o r t r a j e c - t o r i e s p a r a l l e l t o t h e<loo>
a x i s v s displacement from t h e channel c e n t e r l i n e ; toward an atomic row (A) and between atomic rows (B).t o atomic rows have stronger Fourier components.
More s i g n i f i c a n t l y t h e q u a l i t a t i v e d i f f e r e n c e between even and odd harmonics i s demonstrated. For c e n t e r l i n e t r a j e c t o r i e s even harmonics only t h e
I I
component i s present where i n odd harmonics only the
1
component i s present. Thus, f o r example, i n the Is t o 2p t r a n s i t i o n only 1s -c 2pZ e x c i t a t i o n i s possible i n even harmonics, and only 1s t o 2p is possibleX,Y
i n odd harmonics.
Other f e a t u r e s appear i f one considers i n j e c t - ing an i o n a t a s l i g h t angle t o t h e c e n t e r l i n e ( i . e . , the ion has transverse v e l o c i t y i n t h e B d i r e c t i o n of Fig. 6. Then i n addition t o t h e high frequency (vi/d) a lower frequency component corresponding t o t h e r a t e a t which atomic rows a r e crossed i s introduced and here again d i f f e r e n c e s between odd and even harmonics e n t e r .
For odd harmonics the f i e l d contains the frequencies (v/a)(kcose _+ RsinB); R = 1, 3, 5
.. . .
The 2p and 2p (degenerate) s t a t e s a r e t h e s t r o n g e s t
X Y
and only the sideband frequencies vo
+
v,,/KtanB appear.The c e n t r a l frequency vo i s missing because f o r odd K the f i e l d changes phase one cycle a s t h e t r a j e c t o r y moves along d i r e c t i o n B a distance a. For even har- monics t h e f i e l d contains frequencies (tr/a)(kcosi3 f
a s i n e ) ;
a
= 0, 2 , 4... .
The c e n t r a l component is mainly i n the z d i r e c t i o n s o t h a t the c e n t r a l frequen- cy vO i s maintained.The p r e d i c t i o n s of t h i s model a r e amply borne o u t i n Figs. 7 and 8. Figure 8 shows an odd (K = 3) harmonic resonance f o r 07+ ions. For t i l t s i n the B d i r e c t i o n t h e c e n t r a l frequency disappears and only sidebands a r e seen. For example, a t i l t of 0 . 7 ' causes an ion t o s t e p over a distance a once every 80 atoms of i t s passage i n the Z d i r e c t i o n (thus once per 240 cycles of t h e t h i r d harmonic) giving sidebands 0.4 above and below t h e frequency vo K(v/a) (lt0.4%
i n v/vr). Figure 8 shows an equivalent t i l t i n g exper- iment but this time f o r an even (K = 2) harmonic f o r
ions. The c e n t r a l f e a t u r e i s seen t o be main- tained but note t h a t t h e c e n t r a l f e a t u r e here is a doubtet.
A t t h i s p o i n t we have demonatrated the mechanics of t h e ' e x c i t a t i o n process w e l l enough. The c e n t r a l now i s what can be learned about the c r y s t a l f i e l d and the d e t a i l e d s t a t e of the i o n i t i t s e l e c t r o n i c milieu.
Two p r i n c i p a l e f f e c t s occur which p e r t u r b the energy l e v e l s of an i o n moving i n a c r y s t a l channel
formed by bounding atomic rows o r planes. Simply put, t h e p o t e n t i a l becomes more p o s i t i v e moving away from t h e center of t h e channel so t h a t l a r g e r o r b i t s on the
O X W N (~*)<Iw>u(Is Au
a64 tn-tl m 111-21
E,
-
38.22 MeVRERUN Ui AXIS
FIG. 7.
-
E f f e c t of a small t i l t i n the (B) d i r e c t i o n upon an (odd) t h i r d harmonic resonance.TILT 0.7' TILT 1.4.
0.30 -
I
0.95 1.00 I.05
'!.
'"r
FIG. 8.
-
E f f e c t of a small tilt i n the (B) d i r e c t i o n upon an (even) second harmonic resonance.c1-332 JOURNAL DE PHYSIQUE
channeled i o n a r e more weakly bound than i n n e r ones compared t o t h e vacuum s t a t e . The r e s u l t is, e.g., a r e d u c t i o n i n t h e n = 1 t o n = 2 s p a c i n g , and a c c o u n t s f o r t h e g e n e r a l o b s e r v a t i o n of lowered r e s o n a n t v e l o c i - t i e s . I o n s moving on p a t h s which a r e o f f t h e c e n t e r of t h e channel e x p e r i e n c e s h a r p e r f i e l d g r a d i e n t s and t h i s probably accounts f o r t h e asymmetric broadening t o lower v e l o c i t i e s .
The second e f f e c t i s caused by t h e presence of a n e l e c t r o n "wake"; e l e c t r o n s s c a t t e r e d from t h e i o n ( v i > > v o ) c r e a t e an enhanced e l e c t r o n d e n s i t y wave which f o l l o w s t h e i o n ; t h e d i s t a n c e t o t h e f i r s t node i n t h e wave being %2&v /w i s t h e plasmon frequency
1. P
and t h e i n t e g r a t e d enhanced charge d e n s i t y i n t h i s p a r t of t h e wake i s e q u a l t o -q, t h e charge on t h e moving i o n . Thus t h e i o n e x p e r i e n c e s a v e l o c i t y dependent DC f i e l d which can a c t t o S t a r k mix t h e i o n i c s t a t e s . Since t h e f i e l d a c t s always i n t h e z d i r e c t i o n t h e mix- i n g o c c u r s between t h e 2p and 2s s t a t e s and t h e d o u b l e t s observed i n even harmonics a r e due t o t h e s e s p l i t t i n g s .
It f o l l o w s t h a t t h e s e p a r a t i o n between t h e minima i n F i g . 8 'is a measure of t h e wake f i e l d i n t h e v i c i n i t y of t h e moving i o n . I f we assume a uniform f i e l d 5, t h e f i r s t - o r d e r S t a r k s p l i t t i n g i s 6ecao/Z.
The d a t a of Fig. 9 g i v e a v a l u e of 0.10e a. 2 f o r t h i s s p l i t t i n g , from which we deduce = 0.12e/ao2 which i s of t h e expected o r d e r of magnitude [ I l l .
Crawford and R i t c h i e [ I 2 1 have c a l c u l a t e d t h e d e t a i l s of t h e a n t i c i p a t e d e f f e c t s of t h e s e p e r t u r b a - t i o n s u s i n g Hartree-Fock r e l a t i v i s t i c wave f u n c t i o n s f o r t h e Au atoms w i t h Wigner-Seitz boundary c o n d i t i o n s . The r e s u l t f o r 44.1 MeV N ~ + i o n s i n t h e < l o o > a x i a l c h a n n e l of Au is shown i n F i g . 9. S i n c e t h e 2p
X Y Y
ENERGY LEVELS N'+ CHANNELING IN GOLD (001) axas, VELOCITY
-
1q.3 v0I S
I
1,sI
i 1-18.4
VACUUM STATIC STATIC
+
POLARIZATION
FIG. 9.
-
E f f e c t of s t a t i c c r y s t a l f i e l d and p o l a r i z a - t i o n (wake) f i e l d upon t h e n=2 energy l e v e l of I&+( s e e r e f . 1 2 ) .
o r b i t a l s extend toward t h e bounding atomic rows t h e y a r e more s t r o n g l y s h i f t e d by t h e s t a t i c p o t e n t i a l t h a n 2pZ o r 2s. The mixing of t h e 2 s and 2pZ by t h e p o l a r - i z a t i o n from t h e wake f i e l d i s i n d i c a t e d on t h e r i g h t s i d e of t h e f i g u r e . T r a n s i t i o n s e x c i t i n g 2p (even) e x c i t e t h e t o p and bottom s t a t e s w h i l e odd harmonics e x c i t e t h e c e n t r a l l i n e . D e t a i l s of t h e s e c a l c u l a - t i o n s w i l l b e g i v e n i n a forthcoming paper 1121. An example of t h e i r r e s u l t s is shown i n F i g . 1 0 where t h e energy l e v e l s h i f t s f o r 2px e x c i t a t i o n o b t a i n e d
9 Y
SHIFT IN AE (2p,+Is)
I
II
F I G . 10.
-
Comparison of c a l c u l a t e d c r y s t a l f i e l d w i t h v a l u e s o b t a i n e d from e x p e r i m e n t a l s h i f t s i n r e s o n a n t v e l o c i t y .from
c5+,
N ~ + , and 07+ s p e c t r a i n a x i a l<loo>
and <Ill>channels and s l i g h t p l a n a r t i l t s i n t o (100) a r e com- pared w i t h t h e i r t h e o r e t i c a l e x p e c t a t i o n s . I n p a s s i n g i t i s i n t e r e s t i n g t o n o t e t h a t a f u l l Hartree-Fock d e s c r i p t i o n of t h e p o t e n t i a l was r e q u i r e d t o b r i n g t h e
<Ill> a x i a l r e s u l t s i n t o agreement w i t h experiment.
To t h i s p o i n t we have been d i s c u s s i n g only a x i a l channeling and s l i g h t tilts i n t o t h e (100) plane
( i . e . , c o s 8 " l ) ; i n f a c t RCE should o c c u r everywhere i n t h e p l a n e and should be o b s e r v a b l e a s l o n g a s c o l l i - s i o n a l p r o c e s s e s do n o t d e s t r o y t h e i n t e g r i t y of t h e i n i t i a l and f i n a l s t a t e s . Here, however, we need two i n d i c e s t o d e s c r i b e t h e harmonic K(k,R) i n q u e s t i o n , i . e . , i n Eqn. 3 even (Stark s p l i t ) harmonics should appear a t any v a l u e of 8 f o r k and It b o t h even. Odd harmonics should appear a t k and It b o t h odd. (The f i e l d s t r e n g t h s should v a r y % ( k * + ~ ~ ) - ' . ) These expec- t a t i o n s a r e demonstrated i n Fig. 11 f o r N ~ + i o n s i n t h e (100) p l a n e of Au. The
<loo>
a x i a l channel i s a t 8=O0, t h e <110> a t 8=45O, and o t h e r h i g h e r o r d e r a x i a l0 I0 20 30 40 ('00) ANGLE IN (I001 PLANE (Pep) ("O)
FIG. 12.
-
Demonstration of resonances i n t h e (100) plane. Note S t a r k s p l i t (2,2) resonances.FIG. 11.
-
C a l c u l a t e d e n e r y i n MeV/amu f o r c o h e r e n t n=1 t o n=2 e x c i t a t i o n i n HE+ i n t h e (100) p l a n e of Au a s a f u n c t i o n of a n g l e between t h e <loo> and <110> axes.c h a ~ e l s appear i n between. The a b s c i s s a g i v e s t h e e n e r g i e s i n MeV/amu where resonances shoc.ld appear.
A x i a l < l o o > resonances f o r K=2 and 3 and have a l r e a d y been shown ( F i g s . 7 and 81, and t h e s l i g h t 0 t i l t s f o r K=2 (Fig. 8) can now be i d e n t i f i e d a s a (2,O) resonance and f o r K=3 (Fig. 7 ) the "side bands" r e f e r r e d t o above a r e r e a l l y t h e ( 3 , l ) and (3,-1) p l a n a r resonances.
I n F i g . 1 2 we show energy s c a n s taken a t 0=6O and 0 ~ 3 8 ' i n t h e (100) p l a n e f o r N ~ + . The 6' tilt demonstrates t h e continued s p l i t t i n g of t h e ( 3 , l ) and
(3,-1) resonances i n d i c a t e d i n F i g . 7. The 3a0 t i l t , however, i n t r o d u c e s a S t a r k s p l i t '(2,2) resonance i n t o t h e p i c t u r e ( c f . , F i g . 1 1 ) . Aside from a f u r t h e r demonstration of t h e g e n e r a l i t y of RCE, p l a n a r measure- ments p r o v i d e o t h e r parameters. The S t a r k s p l i t t i n g of t h e l i n e depends t o a l a r g e e x t e n t upon t h e s t r e n g t h of t h e wake f i e l d a t t h e i o n i c c o r e which should be veloc- i t y dependent. Thus measuring t h e s p l i t t i n g of a (2,2) resonance from, e.g., 3 MeVlamu a t 0'3' t o 1 . 6 WV/amu a t 0 ~ 3 8 ' p r o v i d e s .a means f o r d e t e r m i n i n g t h e v e l o c i t y dependence i n t h e same harmonic. T i l t i n g i n t o a p l a n e a l s o i n v o l v e s a change i n t h e p r o j e c t e d p a t h l e n g t h through t h e c r y s t a l s o t h a t changes i n resonance d e p t h s
f o r t h e same harmonic a t d i f f e r e n t t i l t a n g l e s can y i e l d i n f o r m a t i o n on coherence l e n g t h s ; e.g., i n F i g . 1 2 t h e ( 3 , l ) harmonic a p p e a r s a t 1.35 MeV/amu a t 3O and a g a i n a t 38". The resonance depth should a l s o depend on i n t e r p l a n a r spacing ( i . e . , s t r o n g e r f i e l d components accompany narrower s p a c i n g s ) s o t h a t t h e s t r e n g t h s of t r a n s v e r s e g r a d i e n t s can be t e s t e d .
Numerous s p e c t r a of ,type shown h e r e have been recorded by t h e Oak Ridge group and a r e i n t h e p r o c e s s of a n a l y s i s and i t i s hoped t h a t a h i g h l y d e t a i l e d d e s c r i p t i o n of t h e s t a t e of t h e channeled i o n and i t s i n t e r a c t i o n w i t h t h e c r y s t a l f i e l d s w i l l emerge.
Although no unambiguous r e s u l t s on t h e obser- v a t i o n of r a d i a t i o n from r e s o n a n t l y e x c i t e d s t a t e s ernerging from c r y s t a l s have y e t been r e p o r t e d , a n a l y s i s of t h e r e s u l t s of o u r enhanced i o n i z a t i o n experiments should l e a d t o t h e p r o p e r d e s i g n of experiments on t h e o b s e r v a t i o n of p o s t - f o i l r a d i a t i o n ,
The work r e p o r t e d h e r e i s based mostly upon t h e e f f o r t s of t h e Oak Ridge A c c e l e r a t o r Based Atomic P h y s i c s group over t h e l a s t a 8 y e a r s . T h i s p r o d u c t i v e group of co-workers i s l i s t e d i n t h e r e f e r e n c e s and t h i s a u t h o r i s a c t i n g t o r e p r e s e n t them on t h i s occasion.
JOURNAL DE PHYSIQUE
REFERENCES
[ I ] J. Lindhard, Phys. L e t t . , l2, p. 126 (1964). 181 S. Datz, G. Gomez d e l Campo, P.F. D i t t n e r , P.D.
[2] D.S. G e m e l l , Rev. Mod. Phys.,
46,
p. 129 (1974). M i l l e r , and J.A. B i g g e r s t a f f , Phys. Rev. L e t t . , 38, p. 1145 (1977).[3] S. Datz, F.W. Martin, C.D. Moak, B.R. Appleton,
-
and L. B r i d w e l l , Radiat. E f f . ,
12,
p. 1 6 3 (1972). [9] S. Datz, C.D. Moak, O.H. Crawford, H.F. Krause, P.F. D i t t n e r , J. Gomez d e l Campo, J.A. B i g g e r s t a f f , [ 4 ] S. Datz, C.D. Moak, and J.R. B a r r e t t , unpublished P.D. Miller, P. Hvelplund, and H. Knudsen, Phys.r e s u l t s
.
Rev. L e t t . ,40,
p. 843 (1978)[5] L.B. Golden and D.H. Sampson, Astrophys. J . ,
170,
[ l o ] C.D. Moak, S. Datz, O.H. Crawford, H.F. Krause, p. 181 (1971) and J. Phys. B,10,
p . 2229 (1977). P.F. D i t t n e r , J. Gomez d e l Campo, J.A. B i g g e r s t a f f , , [ 6 ] S. Datz, Nucl. I n s t . and Meth.,132,
p. 7 (1976). P.D. M i l l e r , P. Hvelplund, and H. Knudsen, Phys.Rev. A, ( i n press).
[71 M.D. C'D' Moaky Brown, H.F. Krause, and S' Datz' B'R' Appletons T.S. Noggle, Phys. J.A' [ l l ] R.H. R i t c h i e , W. Brandt, and P.M. Echenique, Phys.
Rev. B,
10,
p. 2681 (1974). Rev. B,14,
p. 4808 (19 76).1121 O.H. Crawford and R.H. R i r c h i e ( i n p r e s s ) .
