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Direct measurement of nuclear reaction times by the use of the blocking effect in single crystals
Volume29B, number 7
DIRECT
PHYSICS LETTERS
MEASUREMENT OF NUCLEAR OF THE BLOCKING EFFECT
23 June 1969
REACTION IN SINGLE
TIMES BY THE CRYSTALS
USE
M. MARUYAMA, K. TSUKADA and K. OZAWA
Japan Atomic Energy Research Institute, Tokai-mura, Ibaraki-ken, Japan F. FUJIMOTO and K. KOMAKI
Institute of Physics, College of General Education, University of Tokyo, Tokyo, Japan M. MANNAMI a n d T. SAKURAI
Department of Physics, Kyoto University, Kyoto, Japan Received 16 May 1969 A new method to measure reaction times by the use of the blockin~ effect of energetic particles in single crystals was applied to the 28Si(p,p')28Si*, 70Ge(p,p')70Ge* and72Ge(p,p')72Ge* reactions. For germanium, reaction times of the order of 10-~" s were observed.
G e m m e l l and Holland [1] and T u l i n o v [2] s u g g e s t e d the p o s s i b i l i t y of m e a s u r i n g s h o r t l i f e t i m e s a r o u n d 10 -17 s in n u c l e a r r e a c t i o n s by the u s e of the blocking effect in single c r y s t a l s . In the p r e s e n t p a p e r a d i r e c t m e a s u r e m e n t of n u c l e a r r e a c tion t i m e s i s d e s c r i b e d for the 28Si(p, p')28Si*.. ( l s t excited state, 1.78MeV, 2+), VtrGe(p, p')'lUGe~ 71st excited state, 1.04 MeV, 2+) and 2Ge(p,p')72Ge*(2nd excited state, 0.835 MeV, 2+) r e a c t i o n s . Charged particles scatteres or emitted from
500
n u c l e i at l a t t i c e s i t e s a r e p r o h i b i t e d f r o m l e a v ing the c r y s t a l along a c r y s t a l axis o r plane, and t h e i r a n g u l a r d i s t r i b u t i o n shows a dip in this d i r e c t i o n . If a s h o r t - l i v e d n u c l e a r state i s p r o duced as the r e s u l t of a n u c l e a r r e a c t i o n at an i n c i d e n t n u c l e o n e n e r g y of s e v e r a l MeV, the n u c l e u s m o v e s out of the l a t t i c e site at a velocity of the o r d e r of 108 c m / s . H the n u c l e u s has a l i f e t i m e a r o u n d 10 -17 s, it t r a v e l s on the a v e r a g e about 0.1 ~ before it decays. A s i z e a b l e f r a c tion of the s e c o n d a r y c h a r g e d p a r t i c l e s a r e then
Ge(p.p)Ge[~i '~(Pg6)r~e'X" i l
_o) 400
25crn
Ta Aperture p (O~mm~) Ep
2OO
too
./ 4
i-!
SiorGe
i
/,Quartz
T
J
p'
5
Ep.i
~
Position SensitiveDetector (2cm xO.4crn)
5
Scattered Proton Energy Ep. ( MeV )
Fig. 1. The experimental arrangement and the energy spectrum of protons scattered from germanium at an incident energy of 5.42 MeV. 414
Volume 29B, number 7
PHYSICS LETTERS
23 June 1969
Table 1 Reaction times T for the inelastic scattering of protons by germanium.
1.0
0.5
5.42
E p = 4.84 MeV i
3
I
Incident energy (Env)M~
7"(s) 70Ge (p' pw)70Ge, 72Ge (p, pv)72Ge. 1.04 MeV, 2+ 0.835 MeV, 2+
4.84
(3.4 ±2.1) x l 0 -17 (4.1-1.8) x l 0 -17
5.42
(3.1-1.3) x l 0 -17 (2.3:~0.9) x l 0 -17 (3.7~-1.8) x l 0 -17 (2.3~-1.0) x l 0 -17
5.91
(2.2 ±1.3) x l 0 -17
<0.5×10 -17
5.9! ,
I
,
4
5 Scotfered Proton Energy Irp. (MeV)
Fig. 2. The value of Mobserved for the (111) plane of a germanium single crystal. The quantity En is the incident proton energy. Closed circles, ov~n 8ircles and crosses show the value for Ge (p+~p)Ge, 7°Ge (p, p~70Ge* (lst excited state, 1.04 MeV, 2 !+and "~Ge(p,p')'~Ge* (2rid excited state, 0.835 MeV, 2 ), respectively. The vertical bars show the statistical e r r o r s . e m i t t e d in a r e g i o n r e m o v e d f r o m l a t t i c e s i t e s by a d i s t a n c e g r e a t e r than the T h o m a s - F e r m i s c r e e n i n g d i s t a n c e and the t h e r m a l v i b r a t i o n a m p l i t u d e of the l a t t i c e , and they w i l l r e d u c e the b l o c k i n g dip a r e a and e m p h a s i z e the c h a n n e l ing peak. On the o t h e r hand, if the l i f e t i m e i s much s h o r t e r , one e x p e c t s to o b s e r v e the n o r m a l b l o c k i n g dip. T h e r e f o r e , one can e s t i m a t e the r e a c t i o n t i m e b y c o m p a r i n g the blocking p a t t e r n of the c h a r g e d p a r t i c l e s e m i t t e d in the r e a c t i o n with that of the p a r t i c l e s p r o m p t l y s c a t t e r e d a t the l a t t i c e s i t e s , e . g . by R u t h e r f o r d scattering. The a n g u l a r d i s t r i b u t i o n of p r o t o n s s c a t t e r e d f r o m thin s i n g l e c r y s t a l s a t s c a t t e r i n g a n g l e s of 88 ° to 92 ° w a s m e a s u r e d a t i n c i d e n t e n e r g i e s of 1.79, 3.61, 4.02, 4.21, 4.56, 5.45 and 5.86 MeV f o r s i U c o n and of 3.36, 3.77, 4.36, 4.84, 5.42 and 5.91 MeV f o r g e r m a n i u m . Silicon and g e r m a n i u m s i n g l e c r y s t a l s with a t h i c k n e s s of about 10/~m w e r e p r e p a r e d with the s u r f a c e n e a r l y p a r a l l e l to the (441) p l a n e by m e c h a n i c a l and c h e m i c a l polishing. T h e y w e r e o r i e n t e d with the [111] a x i s in the b e a m d i r e c t i o n and with the [11]] a x i s in the d e t e c t o r d i r e c t i o n n o r real to the i n c i d e n t b e a m . A s a r e s u l t , the c e n t e r - o f - m a s s m o t i o n w a s n o r m a l to the (111) p l a n e and the b l o c k i n g dip b y the (111) p l a n e w a s o b s e r v e d at about 90 ° to the i n c i d e n t b e a m . T w o p a r a m e t e r p u l s e - h i g h t a n a l y s i s of both the e n e r g i e s and the d i r e c t i o n s of p r o t o n s s c a t t e r e d a r o u n d the d i r e c t i o n p a r a l l e l to the (111) p l a n e w a s p e r f o r m e d by the u s e of a p o s i t i o n - s e n s i t i v e
s u r f a c e b a r r i e r d e t e c t o r . The e x p e r i m e n t a l a r r a n g e m e n t and a t y p i c a l e n e r g y s p e c t r u m of p r o tons s c a t t e r e d by g e r m a n i u m a r e shown in fig. 1. The a n g u l a r r e s o l u t i o n w a s about 4' with this a r rangement. In the t w o - p a r a m e t e r a n a l y s i s , the b l o c k i n g d i p s w e r e o b s e r v e d on the l o w - e n e r g y s i d e of the p e a k c o r r e s p o n d i n g to a definite final s t a t e , and the channeling p e a k s w e r e g e n e r a l l y o b s e r v e d on the h i g h - e n e r g y s i d e . One can define a quantity M by M = (Nb - N c ) / N , w h e r e N b and N c a r e the a r e a s of the b l o c k i n g dips and of the c o r r e s p o n d ing channeling p e a k s , r e s p e c t i v e l y , and N i s a n o r m a l i z a t i o n f a c t o r p r o p o r t i o n a l to the d i f f e r e n t i a l s c a t t e r i n g c r o s s s e c t i o n to be o b s e r v e d if no c r y s t a l l i n e e f f e c t s would b e p r e s e n t . The q u a n t i t i e s M o b s e r v e d for g e r m a n i u m a r e p l o t t e d in fig. 2. The v a l u e s of M for the e l a s t i c s c a t t e r i n g a r e a l m o s t the s a m e at a l l i n c i d e n t p r o t o n e n e r ° g i e s , while t h o s e f o r i n e l a s t i c s c a t t e r i n g show a c l e a r / _ e d u c t i o n f r o m the e l a s t i c v a l u e s e x c e p t for the 72Ge(p, pt)72Ge* r e a c t i o n at an i n c i d e n t e n e r g y of 5.91 MeV No r e d u c t i o n of M was o b s e r v e d f o r 28Si(p, p ' ) 2 8 S i * ( l s t e x c i t e d s t a t e , 1.78 MeV, 2 +) at any e n e r g y . Since the d o m i n a n t p r o c e s s of the e l a s t i c s c a t t e r i n g in the p r e s e n t e x p e r i m e n t i s the R u t h e r f o r d s c a t t e r i n g which h a s s m a l l i m p a c t p a r a m e t e r s ( 1 0 - 4 ~ ) and an e x t r e m e l y s h o r t r e a c t i o n t i m e , i t s b l o c k i n g p a t t e r n can be u s e d a s the s t a n d a r d p a t t e r n without any r e a c t i o n t i m e effect. If one a s s u m e s a d e c a y with a c o n s t a n t r a t e , the m e a n l i f e t i m e • of the g e r m a n i u m - p l u s - p r o t o n s y s t e m i s a p p r o x i m a t e l y c a l c u l a t e d by the e q u a tion M i / M e = 1 - e x p ( - a / V ~ ) , w h e r e M i and M e a r e the v a l u e s of M o b s e r v e d f o r i n e l a s t i c and e l a s t i c s c a t t e r i n g a t the s a m e s c a t t e r e d p r o t o n e n e r g y , r e s p e c t i v e l y , and V i s the v e l o c i t y of the compound s y s t e m . The quantity a i s a c o n 415
Volume 29B. number 7
PHYSICS LETTERS
st a nt c h a r a c t e r i z i n g the c r y s t a l , of the o r d e r of the T h o m a s - F e r m i s c r e e n i n g d i s t a n c e aTF , and of the t r a n s v e r s e c o m p o n e n t of the r o o t m e a n s q u a r e a m p l i t u d e p of the t h e r m a l v i b r a t i o n s . Since a T F a n d p a r e 0 . 1 4 ~ and 0.086 ~ f o r the g e r m a n i u m c r y s t a l , r e s p e c t i v e l y , one can e x p e c t T to be of the o r d e r of 10 -17 s f o r the Ge(p, p')Ge* r e a c t i o n s . A d e t a i l e d c a l c u l a t i o n [3] to obtain r f r o m the o b s e r v e d r a t i o M i / M e has b e e n p e r f o r m e d , and the r e s u l t s a r e shown in table 1. The e r r o r s in the t ab l e a r e only of a s t a t i s t i c a l nature. If a is * * * * *
416
23 June 1969
a s s u m e d to be 0.2 ~, the l i f e t i m e s c a l c u l a t e d by the s i m p l e equation (1) a r e in good a g r e e m e n t with the t ab u l at ed v a l u e s .
R~fe~'e~ces 1. D.S. Gemrnell and R. E. Holland, Phys. Rev. Letters 14 (1965) 945. 2. A.F. Tulinov, Dokl. Akad. Nauk 162 (1965) 546; "Doklady N 10 (1965) 463. 3. K. Komaki and F. Fuj imoto, to be published.
DIRECT
PHYSICS LETTERS
MEASUREMENT OF NUCLEAR OF THE BLOCKING EFFECT
23 June 1969
REACTION IN SINGLE
TIMES BY THE CRYSTALS
USE
M. MARUYAMA, K. TSUKADA and K. OZAWA
Japan Atomic Energy Research Institute, Tokai-mura, Ibaraki-ken, Japan F. FUJIMOTO and K. KOMAKI
Institute of Physics, College of General Education, University of Tokyo, Tokyo, Japan M. MANNAMI a n d T. SAKURAI
Department of Physics, Kyoto University, Kyoto, Japan Received 16 May 1969 A new method to measure reaction times by the use of the blockin~ effect of energetic particles in single crystals was applied to the 28Si(p,p')28Si*, 70Ge(p,p')70Ge* and72Ge(p,p')72Ge* reactions. For germanium, reaction times of the order of 10-~" s were observed.
G e m m e l l and Holland [1] and T u l i n o v [2] s u g g e s t e d the p o s s i b i l i t y of m e a s u r i n g s h o r t l i f e t i m e s a r o u n d 10 -17 s in n u c l e a r r e a c t i o n s by the u s e of the blocking effect in single c r y s t a l s . In the p r e s e n t p a p e r a d i r e c t m e a s u r e m e n t of n u c l e a r r e a c tion t i m e s i s d e s c r i b e d for the 28Si(p, p')28Si*.. ( l s t excited state, 1.78MeV, 2+), VtrGe(p, p')'lUGe~ 71st excited state, 1.04 MeV, 2+) and 2Ge(p,p')72Ge*(2nd excited state, 0.835 MeV, 2+) r e a c t i o n s . Charged particles scatteres or emitted from
500
n u c l e i at l a t t i c e s i t e s a r e p r o h i b i t e d f r o m l e a v ing the c r y s t a l along a c r y s t a l axis o r plane, and t h e i r a n g u l a r d i s t r i b u t i o n shows a dip in this d i r e c t i o n . If a s h o r t - l i v e d n u c l e a r state i s p r o duced as the r e s u l t of a n u c l e a r r e a c t i o n at an i n c i d e n t n u c l e o n e n e r g y of s e v e r a l MeV, the n u c l e u s m o v e s out of the l a t t i c e site at a velocity of the o r d e r of 108 c m / s . H the n u c l e u s has a l i f e t i m e a r o u n d 10 -17 s, it t r a v e l s on the a v e r a g e about 0.1 ~ before it decays. A s i z e a b l e f r a c tion of the s e c o n d a r y c h a r g e d p a r t i c l e s a r e then
Ge(p.p)Ge[~i '~(Pg6)r~e'X" i l
_o) 400
25crn
Ta Aperture p (O~mm~) Ep
2OO
too
./ 4
i-!
SiorGe
i
/,Quartz
T
J
p'
5
Ep.i
~
Position SensitiveDetector (2cm xO.4crn)
5
Scattered Proton Energy Ep. ( MeV )
Fig. 1. The experimental arrangement and the energy spectrum of protons scattered from germanium at an incident energy of 5.42 MeV. 414
Volume 29B, number 7
PHYSICS LETTERS
23 June 1969
Table 1 Reaction times T for the inelastic scattering of protons by germanium.
1.0
0.5
5.42
E p = 4.84 MeV i
3
I
Incident energy (Env)M~
7"(s) 70Ge (p' pw)70Ge, 72Ge (p, pv)72Ge. 1.04 MeV, 2+ 0.835 MeV, 2+
4.84
(3.4 ±2.1) x l 0 -17 (4.1-1.8) x l 0 -17
5.42
(3.1-1.3) x l 0 -17 (2.3:~0.9) x l 0 -17 (3.7~-1.8) x l 0 -17 (2.3~-1.0) x l 0 -17
5.91
(2.2 ±1.3) x l 0 -17
<0.5×10 -17
5.9! ,
I
,
4
5 Scotfered Proton Energy Irp. (MeV)
Fig. 2. The value of Mobserved for the (111) plane of a germanium single crystal. The quantity En is the incident proton energy. Closed circles, ov~n 8ircles and crosses show the value for Ge (p+~p)Ge, 7°Ge (p, p~70Ge* (lst excited state, 1.04 MeV, 2 !+and "~Ge(p,p')'~Ge* (2rid excited state, 0.835 MeV, 2 ), respectively. The vertical bars show the statistical e r r o r s . e m i t t e d in a r e g i o n r e m o v e d f r o m l a t t i c e s i t e s by a d i s t a n c e g r e a t e r than the T h o m a s - F e r m i s c r e e n i n g d i s t a n c e and the t h e r m a l v i b r a t i o n a m p l i t u d e of the l a t t i c e , and they w i l l r e d u c e the b l o c k i n g dip a r e a and e m p h a s i z e the c h a n n e l ing peak. On the o t h e r hand, if the l i f e t i m e i s much s h o r t e r , one e x p e c t s to o b s e r v e the n o r m a l b l o c k i n g dip. T h e r e f o r e , one can e s t i m a t e the r e a c t i o n t i m e b y c o m p a r i n g the blocking p a t t e r n of the c h a r g e d p a r t i c l e s e m i t t e d in the r e a c t i o n with that of the p a r t i c l e s p r o m p t l y s c a t t e r e d a t the l a t t i c e s i t e s , e . g . by R u t h e r f o r d scattering. The a n g u l a r d i s t r i b u t i o n of p r o t o n s s c a t t e r e d f r o m thin s i n g l e c r y s t a l s a t s c a t t e r i n g a n g l e s of 88 ° to 92 ° w a s m e a s u r e d a t i n c i d e n t e n e r g i e s of 1.79, 3.61, 4.02, 4.21, 4.56, 5.45 and 5.86 MeV f o r s i U c o n and of 3.36, 3.77, 4.36, 4.84, 5.42 and 5.91 MeV f o r g e r m a n i u m . Silicon and g e r m a n i u m s i n g l e c r y s t a l s with a t h i c k n e s s of about 10/~m w e r e p r e p a r e d with the s u r f a c e n e a r l y p a r a l l e l to the (441) p l a n e by m e c h a n i c a l and c h e m i c a l polishing. T h e y w e r e o r i e n t e d with the [111] a x i s in the b e a m d i r e c t i o n and with the [11]] a x i s in the d e t e c t o r d i r e c t i o n n o r real to the i n c i d e n t b e a m . A s a r e s u l t , the c e n t e r - o f - m a s s m o t i o n w a s n o r m a l to the (111) p l a n e and the b l o c k i n g dip b y the (111) p l a n e w a s o b s e r v e d at about 90 ° to the i n c i d e n t b e a m . T w o p a r a m e t e r p u l s e - h i g h t a n a l y s i s of both the e n e r g i e s and the d i r e c t i o n s of p r o t o n s s c a t t e r e d a r o u n d the d i r e c t i o n p a r a l l e l to the (111) p l a n e w a s p e r f o r m e d by the u s e of a p o s i t i o n - s e n s i t i v e
s u r f a c e b a r r i e r d e t e c t o r . The e x p e r i m e n t a l a r r a n g e m e n t and a t y p i c a l e n e r g y s p e c t r u m of p r o tons s c a t t e r e d by g e r m a n i u m a r e shown in fig. 1. The a n g u l a r r e s o l u t i o n w a s about 4' with this a r rangement. In the t w o - p a r a m e t e r a n a l y s i s , the b l o c k i n g d i p s w e r e o b s e r v e d on the l o w - e n e r g y s i d e of the p e a k c o r r e s p o n d i n g to a definite final s t a t e , and the channeling p e a k s w e r e g e n e r a l l y o b s e r v e d on the h i g h - e n e r g y s i d e . One can define a quantity M by M = (Nb - N c ) / N , w h e r e N b and N c a r e the a r e a s of the b l o c k i n g dips and of the c o r r e s p o n d ing channeling p e a k s , r e s p e c t i v e l y , and N i s a n o r m a l i z a t i o n f a c t o r p r o p o r t i o n a l to the d i f f e r e n t i a l s c a t t e r i n g c r o s s s e c t i o n to be o b s e r v e d if no c r y s t a l l i n e e f f e c t s would b e p r e s e n t . The q u a n t i t i e s M o b s e r v e d for g e r m a n i u m a r e p l o t t e d in fig. 2. The v a l u e s of M for the e l a s t i c s c a t t e r i n g a r e a l m o s t the s a m e at a l l i n c i d e n t p r o t o n e n e r ° g i e s , while t h o s e f o r i n e l a s t i c s c a t t e r i n g show a c l e a r / _ e d u c t i o n f r o m the e l a s t i c v a l u e s e x c e p t for the 72Ge(p, pt)72Ge* r e a c t i o n at an i n c i d e n t e n e r g y of 5.91 MeV No r e d u c t i o n of M was o b s e r v e d f o r 28Si(p, p ' ) 2 8 S i * ( l s t e x c i t e d s t a t e , 1.78 MeV, 2 +) at any e n e r g y . Since the d o m i n a n t p r o c e s s of the e l a s t i c s c a t t e r i n g in the p r e s e n t e x p e r i m e n t i s the R u t h e r f o r d s c a t t e r i n g which h a s s m a l l i m p a c t p a r a m e t e r s ( 1 0 - 4 ~ ) and an e x t r e m e l y s h o r t r e a c t i o n t i m e , i t s b l o c k i n g p a t t e r n can be u s e d a s the s t a n d a r d p a t t e r n without any r e a c t i o n t i m e effect. If one a s s u m e s a d e c a y with a c o n s t a n t r a t e , the m e a n l i f e t i m e • of the g e r m a n i u m - p l u s - p r o t o n s y s t e m i s a p p r o x i m a t e l y c a l c u l a t e d by the e q u a tion M i / M e = 1 - e x p ( - a / V ~ ) , w h e r e M i and M e a r e the v a l u e s of M o b s e r v e d f o r i n e l a s t i c and e l a s t i c s c a t t e r i n g a t the s a m e s c a t t e r e d p r o t o n e n e r g y , r e s p e c t i v e l y , and V i s the v e l o c i t y of the compound s y s t e m . The quantity a i s a c o n 415
Volume 29B. number 7
PHYSICS LETTERS
st a nt c h a r a c t e r i z i n g the c r y s t a l , of the o r d e r of the T h o m a s - F e r m i s c r e e n i n g d i s t a n c e aTF , and of the t r a n s v e r s e c o m p o n e n t of the r o o t m e a n s q u a r e a m p l i t u d e p of the t h e r m a l v i b r a t i o n s . Since a T F a n d p a r e 0 . 1 4 ~ and 0.086 ~ f o r the g e r m a n i u m c r y s t a l , r e s p e c t i v e l y , one can e x p e c t T to be of the o r d e r of 10 -17 s f o r the Ge(p, p')Ge* r e a c t i o n s . A d e t a i l e d c a l c u l a t i o n [3] to obtain r f r o m the o b s e r v e d r a t i o M i / M e has b e e n p e r f o r m e d , and the r e s u l t s a r e shown in table 1. The e r r o r s in the t ab l e a r e only of a s t a t i s t i c a l nature. If a is * * * * *
416
23 June 1969
a s s u m e d to be 0.2 ~, the l i f e t i m e s c a l c u l a t e d by the s i m p l e equation (1) a r e in good a g r e e m e n t with the t ab u l at ed v a l u e s .
R~fe~'e~ces 1. D.S. Gemrnell and R. E. Holland, Phys. Rev. Letters 14 (1965) 945. 2. A.F. Tulinov, Dokl. Akad. Nauk 162 (1965) 546; "Doklady N 10 (1965) 463. 3. K. Komaki and F. Fuj imoto, to be published.