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The structure of the secondary electron energy spectra
Volume 26A, number 12
THE
STRUCTURE
PHYSICS LETTERS
OF
THE
SECONDARY
6 May 1968
ELECTRON
ENERGY
SPECTRA
I. N. EVDOKIMOV and V. A. MOLCHANOV Scientific Institut of Nuclear Physics, Moscow State University, Moscow, USSR Received 3 April 1968
The low-energy part of the energy distribution of secondary electrons ejected from metal targets by fast noble gas ions. showed a fine structure, represented by a number of narrow maxima and minima.
The study of e n e r g y s p e c t r a of s e c o n d a r y e l e c t r o n s ejected f r o m s o l i d s by fast ions can p r o v i d e valuable i n f o r m a t i o n about e l e m e n t a r y a c t s of i o n - a t o m c o l l i s i o n s and about the e l e c t r o n i c s t r u c t u r e of solids. However, the a v a i l a b l e e x p e r i m e n tal data a r e few and c o n t r a d i c t o r y . Only the fact that m o s t e l e c t r o n s a r e e m i t t e d with e n e r g i e s l e s s than s e v e r a l t e n s of eV may be r e g a r d e d a s soundly e s t a b l i s h e d . It is a l s o u s u a l l y b e l i e v e d that the whole energy d i s t r i b u t i o n of t h e s e e l e c t r o n s c o n s i s t s of smooth a s y m m e t r i c a l peaks [1]. Meanwhile as f a r back a s 1930 Oliphant [2] studying the l o w - e n e r g y p a r t of s e c o n d a r y e l e c t r o n e n e r g y s p e c t r a , m e n t i o n e d the e x i s t e n c e of a "fine s t r u c t u r e " r e p r e s e n t e d by two or t h r e e s m a l l m a x i m a below 20 eV in the case of He + b o m b a r d m e n t of molybdenum. U n f o r t u n a t e l y all a t t e m p t s to r e p r o d u c e such s t r u c t u r e failed until r e c e n t l y . Only not long ago some new evidence of the fine s t r u c t u r e has b e e n d i s c o v e r e d : two "steps" at 4.5 and 7.5 eV for high e n e r g y p r o t o n s i n c i d e n t on Cu, by K a m i n s k y [3] and a wide m a x i m u m at s e v e r a l t e n s of eV for ion b o m b a r d m e n t of A1, Mg and Si, by Hennequin et al. [4]. The a i m of this work was the d e t a i l e d study of the l o w - e n e r g y p a r t of s e c o n d a r y e l e c t r o n e n e r g y s p e c t r a for m e t a l s . The t a r g e t s were b o m b a r d e d with 30 keV noble gas ions. The e n e r gy s p e c t r a were obtained f r o m the r e t a r d i n g field c u r v e s by m e a n s of g r a p h i c a l d i f f e r e n t i a t i o n and also by c o m p u t e r d i f f e r e n t i a t i o n u s i n g T i k h o n o v ' s r e g u l a r i s a t i o n method [5]. The s t a b i l i t y of the r e s u l t s with r e s p e c t to a v a r i a t i o n of the r e g u l a r i sation p a r a m e t e r , c o n f i r m e d the r e l i a b i l i t y of the fine s t r u c t u r e in the e n e r g y s p e c t r a , d e s c r i b e d below. The s e c o n d a r y e l e c t r o n e n e r g y s p e c t r a for all the i o n - t a r g e t c o m b i n a t i o n s used, could be r e garded, in f i r s t a p p r o x i m a t i o n , as c o m p a r a t i v e l y wide a s y m m e t r i c a l peaks. They had a m a x i m u m 636
I/)
4
t-
"£'3 P, I..
A+ 30 keV-Cu
#
~2 Z
,~, 10
20
30
40
50
E(eV) Fig. 1.
in the r e g i o n of 1-4 eV and a half-width of about 3-4 eV, while some e l e c t r o n s had e n e r g i e s as high as s e v e r a l h u n d r e d s of eV. No s i g n i f i c a n t dependence of the shape of these s p e c t r a on the kind of b o m b a r d i n g ions was observed. It was found that these s p e c t r a have a d e v e loped fine s t r u c t u r e r e p r e s e n t e d by a l a r g e n u m b e r of n a r r o w m a x i m a and m i n i m a . T h i s s t r u c t u r e is m o r e p r o n o u n c e d than that in [2-4] where only one or two wide m a x i m a , or even a c e r t a i n "flattening" of the s p e c t r a have b e e n observed. As an example, the e n e r g y d i s t r i b u t i o n of s e c o n d a r y e l e c t r o n s for a copper t a r g e t b o m b a r d e d with a r g o n ions is shown in fig. 1. It has a m a x i m u m at 2.5 eV and a half-width of about 4 eV. The p r e s e n c e of the o b s e r v e d m a x i m a and m i n i m a could be a t t r i b u t e d to the influence of the density of t a r g e t e l e c t r o n s t a t e s N(E). This f u n c tion m u s t d e t e r m i n e the final s t a t e s of the excited e l e c t r o n s and is known to p o s s e s s some s t r u c t u r e [6,7]. Let us r e m e m b e r that the inf l u e n c e of the N(~) s t r u c t u r e is noticeable also in
Volume 26A, number 12
PHYSICS LETTERS
o t h e r p h y s i c a l p h e n o m e n a in s o l i d s , such as p h o t o e m i s s i o n [8], r e f l e c t i o n and a b s o r p t i o n of l i ght [9], X - r a y a b s o r p t i o n [10] and c h a r a c t e r i s t i c e n e r g y l o s s e s of e l e c t r o n s [11]. T h e r e is a l s o a p r o b a b i l i t y that s o m e of t h e o b s e r v e d m a x i m a , e s p e c i a l l y in the e n e r g y r e g i o n above 30-35 eV a r e due to A u g e r e l e c t r o n s f r o m c o ll id in g p a r t icles. T he a u t h o r s a r e g r e a t l y indebted to D r . Anna H. Rakhrnatulina f o r h e r v a l u a b l e a s s i s t a n c e in m a t h e m a t i c a l a n a l y s i s of the e x p e r i m e n t a l data. 1. D.B. Medved and Y. E. Strausser, Adv. in Electronics and Electron Physics v. 21 (Acad. P r e s s Inc. 1965) p. 101.
6May 1968
2. M . L . E . Oliphant, Proc. Roy. Soc. 127A (1930) 373. 3 . M.Kaminsky, Report ANL-7081 (1964/1965)p.141. 4. J. - F . Hennequin, P. Joyes and R. Castaing, Comptes Rend. B265 (1967) 312. 5. A.N. Tikhonov, Dokl. Akad. Nauk SSSR 153 (1963) 49. 6. C.N. Berglund and W. E. Spicer, Phys. Rev. 136A (1964) 1030. 7. E. Rudberg and J. C. Slater, Phys. Rev. 50 (1936) 150. 8. C. N. Berglund and W. E. Spicer, Phys. Rev. 136A (1964) 1044. 9. Optical properties and electronic structure of metals and alloys ed. F.Abeles, (North-Holland, 1965). 10. RiSntgenstrahlen, Handbuch d. Physik band 30 (Springer Verlag 1957). 11. L. Marton, J. Quant.Spectr. Radiat. Transf. 2 (1962) 671.
HY1)ERFINE INTERACTION THE RACAH PARAMETER:
DE1)ENDENCE ON T H E M n ++ I O N
K. N. SHRIVASTAVA
Department of Physics, Clark University, Worcester, Massachusetts, 01610, USA Received 9 April 1968
On the basis of spin-orbit admixture from the first excited state into the ground state the hyperfine coup]hag of Mn++ ion is shown to be related to the Racah parameter. T he ground t e r m ~ ( 6 S r ) of d5 c o n f i g u r a t i o n in g e n e r a l i n v o l v e s a s m a l l a d m i x t u r e of the e x c i t e d s t a t e s ×i, t h ro u g h the o f f - d i a g o n a l m a t r i x e l e m e n t s of the s p i n - o r b i t coupling so that [1]
(6St) = N[¢(6Sr) - ~ . )tiXi $
]
where h i are the admixture coefficients. According to selection rules in the Russell-Saunders coupling, AS = 0, * 1 therefore Xi'S must be the quartets. Next, A L = 0, ± 1 so the only possible quartet is 41). Finally, A J = 0 which means that 41)_~ is the only level of d 5 configuration which has non-vanishing matrix element with 6S. The mixing of doublets for which AS = 2, directly or via the distortions of 41) would be small [2,3] even if the crystalline field is large in which case the doublets m a y lie fairly low compared to the quartets. Thus assuming the admixture from 4p alone the ground state wave function of the M n ++ ion can be written as [1] (6S r ) = N[¢ ( 6 S t ) - )~¢ ( 4 p r ) ]
w h e r e the a d m i x t u r e c o e f f i c i e n t , ~ is given by 1
1
2(s) ~
~
7(B+C)
and the n o r m a l i z a t i o n constant 1
N=(I
+~2)-~
Here ~ is the spin-orbit coupling, demonstrated by L o w [2] to be nearly 320 c m -1 in all the crystals, B and C a r e the R a c a h p a r a m e t e r s u s u a l l y m e a s u r e d in the optical absorption. T h e F e r m i - c o n t a c t h y p er f i n e i n t e r a c t i o n p a r a m e t e r , A, u s u a l l y m e a s u r e d in the p a r a m a g n e t i c r e s o n a n c e e x p e r i m e n t is A = ~8 ~g / 3 g n i 3 n l ~P(0) 12 .
_1
8~ g # g n # n [i ~( 6s0)~2, ~- ~-
-
2(5) ~ 7---~-C)
$(6S0) ~b(41)0)]
or 637
THE
STRUCTURE
PHYSICS LETTERS
OF
THE
SECONDARY
6 May 1968
ELECTRON
ENERGY
SPECTRA
I. N. EVDOKIMOV and V. A. MOLCHANOV Scientific Institut of Nuclear Physics, Moscow State University, Moscow, USSR Received 3 April 1968
The low-energy part of the energy distribution of secondary electrons ejected from metal targets by fast noble gas ions. showed a fine structure, represented by a number of narrow maxima and minima.
The study of e n e r g y s p e c t r a of s e c o n d a r y e l e c t r o n s ejected f r o m s o l i d s by fast ions can p r o v i d e valuable i n f o r m a t i o n about e l e m e n t a r y a c t s of i o n - a t o m c o l l i s i o n s and about the e l e c t r o n i c s t r u c t u r e of solids. However, the a v a i l a b l e e x p e r i m e n tal data a r e few and c o n t r a d i c t o r y . Only the fact that m o s t e l e c t r o n s a r e e m i t t e d with e n e r g i e s l e s s than s e v e r a l t e n s of eV may be r e g a r d e d a s soundly e s t a b l i s h e d . It is a l s o u s u a l l y b e l i e v e d that the whole energy d i s t r i b u t i o n of t h e s e e l e c t r o n s c o n s i s t s of smooth a s y m m e t r i c a l peaks [1]. Meanwhile as f a r back a s 1930 Oliphant [2] studying the l o w - e n e r g y p a r t of s e c o n d a r y e l e c t r o n e n e r g y s p e c t r a , m e n t i o n e d the e x i s t e n c e of a "fine s t r u c t u r e " r e p r e s e n t e d by two or t h r e e s m a l l m a x i m a below 20 eV in the case of He + b o m b a r d m e n t of molybdenum. U n f o r t u n a t e l y all a t t e m p t s to r e p r o d u c e such s t r u c t u r e failed until r e c e n t l y . Only not long ago some new evidence of the fine s t r u c t u r e has b e e n d i s c o v e r e d : two "steps" at 4.5 and 7.5 eV for high e n e r g y p r o t o n s i n c i d e n t on Cu, by K a m i n s k y [3] and a wide m a x i m u m at s e v e r a l t e n s of eV for ion b o m b a r d m e n t of A1, Mg and Si, by Hennequin et al. [4]. The a i m of this work was the d e t a i l e d study of the l o w - e n e r g y p a r t of s e c o n d a r y e l e c t r o n e n e r g y s p e c t r a for m e t a l s . The t a r g e t s were b o m b a r d e d with 30 keV noble gas ions. The e n e r gy s p e c t r a were obtained f r o m the r e t a r d i n g field c u r v e s by m e a n s of g r a p h i c a l d i f f e r e n t i a t i o n and also by c o m p u t e r d i f f e r e n t i a t i o n u s i n g T i k h o n o v ' s r e g u l a r i s a t i o n method [5]. The s t a b i l i t y of the r e s u l t s with r e s p e c t to a v a r i a t i o n of the r e g u l a r i sation p a r a m e t e r , c o n f i r m e d the r e l i a b i l i t y of the fine s t r u c t u r e in the e n e r g y s p e c t r a , d e s c r i b e d below. The s e c o n d a r y e l e c t r o n e n e r g y s p e c t r a for all the i o n - t a r g e t c o m b i n a t i o n s used, could be r e garded, in f i r s t a p p r o x i m a t i o n , as c o m p a r a t i v e l y wide a s y m m e t r i c a l peaks. They had a m a x i m u m 636
I/)
4
t-
"£'3 P, I..
A+ 30 keV-Cu
#
~2 Z
,~, 10
20
30
40
50
E(eV) Fig. 1.
in the r e g i o n of 1-4 eV and a half-width of about 3-4 eV, while some e l e c t r o n s had e n e r g i e s as high as s e v e r a l h u n d r e d s of eV. No s i g n i f i c a n t dependence of the shape of these s p e c t r a on the kind of b o m b a r d i n g ions was observed. It was found that these s p e c t r a have a d e v e loped fine s t r u c t u r e r e p r e s e n t e d by a l a r g e n u m b e r of n a r r o w m a x i m a and m i n i m a . T h i s s t r u c t u r e is m o r e p r o n o u n c e d than that in [2-4] where only one or two wide m a x i m a , or even a c e r t a i n "flattening" of the s p e c t r a have b e e n observed. As an example, the e n e r g y d i s t r i b u t i o n of s e c o n d a r y e l e c t r o n s for a copper t a r g e t b o m b a r d e d with a r g o n ions is shown in fig. 1. It has a m a x i m u m at 2.5 eV and a half-width of about 4 eV. The p r e s e n c e of the o b s e r v e d m a x i m a and m i n i m a could be a t t r i b u t e d to the influence of the density of t a r g e t e l e c t r o n s t a t e s N(E). This f u n c tion m u s t d e t e r m i n e the final s t a t e s of the excited e l e c t r o n s and is known to p o s s e s s some s t r u c t u r e [6,7]. Let us r e m e m b e r that the inf l u e n c e of the N(~) s t r u c t u r e is noticeable also in
Volume 26A, number 12
PHYSICS LETTERS
o t h e r p h y s i c a l p h e n o m e n a in s o l i d s , such as p h o t o e m i s s i o n [8], r e f l e c t i o n and a b s o r p t i o n of l i ght [9], X - r a y a b s o r p t i o n [10] and c h a r a c t e r i s t i c e n e r g y l o s s e s of e l e c t r o n s [11]. T h e r e is a l s o a p r o b a b i l i t y that s o m e of t h e o b s e r v e d m a x i m a , e s p e c i a l l y in the e n e r g y r e g i o n above 30-35 eV a r e due to A u g e r e l e c t r o n s f r o m c o ll id in g p a r t icles. T he a u t h o r s a r e g r e a t l y indebted to D r . Anna H. Rakhrnatulina f o r h e r v a l u a b l e a s s i s t a n c e in m a t h e m a t i c a l a n a l y s i s of the e x p e r i m e n t a l data. 1. D.B. Medved and Y. E. Strausser, Adv. in Electronics and Electron Physics v. 21 (Acad. P r e s s Inc. 1965) p. 101.
6May 1968
2. M . L . E . Oliphant, Proc. Roy. Soc. 127A (1930) 373. 3 . M.Kaminsky, Report ANL-7081 (1964/1965)p.141. 4. J. - F . Hennequin, P. Joyes and R. Castaing, Comptes Rend. B265 (1967) 312. 5. A.N. Tikhonov, Dokl. Akad. Nauk SSSR 153 (1963) 49. 6. C.N. Berglund and W. E. Spicer, Phys. Rev. 136A (1964) 1030. 7. E. Rudberg and J. C. Slater, Phys. Rev. 50 (1936) 150. 8. C. N. Berglund and W. E. Spicer, Phys. Rev. 136A (1964) 1044. 9. Optical properties and electronic structure of metals and alloys ed. F.Abeles, (North-Holland, 1965). 10. RiSntgenstrahlen, Handbuch d. Physik band 30 (Springer Verlag 1957). 11. L. Marton, J. Quant.Spectr. Radiat. Transf. 2 (1962) 671.
HY1)ERFINE INTERACTION THE RACAH PARAMETER:
DE1)ENDENCE ON T H E M n ++ I O N
K. N. SHRIVASTAVA
Department of Physics, Clark University, Worcester, Massachusetts, 01610, USA Received 9 April 1968
On the basis of spin-orbit admixture from the first excited state into the ground state the hyperfine coup]hag of Mn++ ion is shown to be related to the Racah parameter. T he ground t e r m ~ ( 6 S r ) of d5 c o n f i g u r a t i o n in g e n e r a l i n v o l v e s a s m a l l a d m i x t u r e of the e x c i t e d s t a t e s ×i, t h ro u g h the o f f - d i a g o n a l m a t r i x e l e m e n t s of the s p i n - o r b i t coupling so that [1]
(6St) = N[¢(6Sr) - ~ . )tiXi $
]
where h i are the admixture coefficients. According to selection rules in the Russell-Saunders coupling, AS = 0, * 1 therefore Xi'S must be the quartets. Next, A L = 0, ± 1 so the only possible quartet is 41). Finally, A J = 0 which means that 41)_~ is the only level of d 5 configuration which has non-vanishing matrix element with 6S. The mixing of doublets for which AS = 2, directly or via the distortions of 41) would be small [2,3] even if the crystalline field is large in which case the doublets m a y lie fairly low compared to the quartets. Thus assuming the admixture from 4p alone the ground state wave function of the M n ++ ion can be written as [1] (6S r ) = N[¢ ( 6 S t ) - )~¢ ( 4 p r ) ]
w h e r e the a d m i x t u r e c o e f f i c i e n t , ~ is given by 1
1
2(s) ~
~
7(B+C)
and the n o r m a l i z a t i o n constant 1
N=(I
+~2)-~
Here ~ is the spin-orbit coupling, demonstrated by L o w [2] to be nearly 320 c m -1 in all the crystals, B and C a r e the R a c a h p a r a m e t e r s u s u a l l y m e a s u r e d in the optical absorption. T h e F e r m i - c o n t a c t h y p er f i n e i n t e r a c t i o n p a r a m e t e r , A, u s u a l l y m e a s u r e d in the p a r a m a g n e t i c r e s o n a n c e e x p e r i m e n t is A = ~8 ~g / 3 g n i 3 n l ~P(0) 12 .
_1
8~ g # g n # n [i ~( 6s0)~2, ~- ~-
-
2(5) ~ 7---~-C)
$(6S0) ~b(41)0)]
or 637