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The Compton effect on relativistic electrons and the possibility of obtaining high energy beams
Volume 4, number 3
PHYSICS
1) R.Rabinowitz et al., Proc. Inst. Radio Engrs. ( c o r r e spondence) 50 (1962) 2365. 2) A. Javan, E.A. Ballik and W. L. Bond, J. Opt. Soe. Am. 52 (1962) 96. 3) S. Jacobs and P.Rabinowitz, Proc. of the 3rd Quantum Electronics Conf., Paris, 1963 (to be published).
THE COMPTON EFFECT THE POSSIBILITY OF
LETTERS
1 A p r i l 1963
4) K.D. Froome and R. H. Bradsell, J. Sci. Instr. 38 0961) 458. 5) J . T e r r i e n , J. phys. radium 19 (1958) 390. 6) G.R.Hanes, Can. J. Phys. 37 (1959) 1283. 7) C. F. Bruce and R. M. Hill, Australian J. Phys. 14 (1961) 64; 15 (1962) 152. 8) R.M.Hill and C.F.Bruce, Australian J. Phys. 15 (1962)194.
ON RELATIVISTIC OBTAINING HIGH
ELECTRONS AND ENERGY BEAMS
F. R. A R U T Y U N I A N and V. A. T U M A N I A N Physical Institute of the State Committee of the Council of Ministers of the USSR for the Use of Atomic Energy Received 20 February 1963
A c h a r a c t e r i s t i c f e a t u r e of the C o m p t o n e f f e c t on r e l a t i v i s t i c e l e c t r o n s is the a p p e a r a n c e of p h o t o n s with e n e r g i e s e x c e e d i n g t h o s e of the p r i m a r y p h o t o n s . As a r e s u l t , e v e n when l ig h t p h o t o n s a r e s c a t t e r e d on e x t r e m e l y r e l a t i v i s t i c e l e c t r o n s , the e n e r g i e s of the s c a t t e r e d p h o t o n s will be of the s a m e o r d e r of m a g n i t u d e as t h o s e of the e l e c t r o n s . T h i s f e a t u r e ma y p o s s i b l y be e x p l o i t e d f o r o b t a i n i n g high e n e r g y y - r a y b e a m s in e l e c t r o n a c c e l e r a t o r s . An i m p o r t a n t point to be m e n t i o n e d is that the c h a r a c t e r i s t i c s of s u c h y - b e a m s will s i g n i f i c a n t l y d i f f e r f r o m t h o s e o b t a i n e d by b r e m s s t a h l u n g . In the C o m p t o n e f f e c t i n v o l v i n g m o v i n g e l e c t r o n s the e n e r g y of the s c a t t e r e d q u a n t u m ~2 is r e l a t e d to the e n e r g y of the p r i m a r y photon ~cI by the w e l l known e q u a t i o n (h = c = 1) 1 - v 1 c o s 01 w2 = ~ 1 1 - v 1 c o s e 2 + ( ~ l / e 1) (1 - c o s 0) '
(1)
w h e r e v 1 and el a r e r e s p e c t i v e l y the e l e c t r o n v e l o c ity and e n e r g y , 01 and ~2 a r e the a n g l e s b e t w e e n the d i r e c t i o n of m o t i o n of the e l e c t r o n s and i n c i d e n t and s c a t t e r e d q u a n t a and 0 is the a n g le b e t w e e n the i n c i dent and s c a t t e r e d quanta. T h e e n e r g y of the s c a t t e r e d y - q u a n t a is m a x i m a l (w2 max.) when the p r i m a r y e l e c t r o n and photon m o v e in o p p o s i t e d i r e c t i o n s (01 = ~r) and the s c a t t e r e d photon m o v e s in the d i r e c t i o n of the e l e c t r o n . T h e n (Vl = 1) 2w I ~c2 max. = ½ ( m / ~ l ) 2 + 2 : ~ l / e 1
,
(2)
w h e r e m is the e l e c t r o n r e s t e n e r g y . T h e h i g h e s t e n e r g y to a t t a i n p o s s i b l y in e l e c t r o n a c c e l e r a t o r s in the n e a r f u t u r e should be --6 GeV.
176
Of c o u r s e in o r d e r to obtain y - b e a m s by the m e t h o d c o n s i d e r e d h e r e high photon f l u x e s will be r e q u i r e d . A high i n t e n s i t y photon s o u r c e that should be f e a s i ble is the l a s e r . At p r e s e n t r u b y l a s e r s s e e m to be the m o s t r e l i a b l e . F o r ruby l a s e r p h o t o n s (k= 6943 /~) s c a t t e r e d on 6 GeV e l e c t r o n s one g e t s ~ 2 m a x , = 848 MeV. T h i s e f f e c t r a p i d l y g r o w s with i n c r e a s e of the e l e c t r o n e n e r g y . T h u s f o r the s a m e r u b y l a s e r s and ~ 1 = 40 and 500 GeV the m a x i m a l e n e r g y is c o r r e s p o n d i n g l y ~2 m a x . ~ 21 and 497 GeV. Of c o u r s e if l a s e r s e m i t t i n g s h o r t e r wave l e n g t h s o r o t h e r s o u r c e s of high e n e r g y p h o t o n s be e m p l o y e d : the e n e r g i e s of the s c a t t e r e d p h o t o n s m a y c l o s e l y a p p r o a c h t h o s e of the e l e c t r o n s . The differential c r o s s section for Compton scatt e r i n g on m o v i n g e l e c t r o n s is 1)
(3) w h e r e r o is the c l a s s i c a l e l e c t r o n r a d i u s and 2a~1 Xl . . . . . ~ 2 ( e l + P1)
2~ 2 x2 =-(El -PI m
2
cos e2)
w h e r e P1 is the e l e c t r o n m o m e n t u m . T h e e n e r g y e n e r g y s p e c t r u m of the s c a t t e r e d p h o t o n s can be d e r i v e d f r o m e x p r e s s i o n s (3) and (1). N e g l e c t i n g s m a l l t e r m s in (3) we o b t a i n
Volume 4, number 3
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r~r2
m2
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PHYSICS LETTERS
I rn~
1April1963
d i c a t e d m a n n e r . The b e a m s p r o d u c e d in this way will a p p a r e n t l y be p a r t i a l l y p o l a r i z e d , a fact which is of i n t e r e s t in i t s e l f .
o~2 ,2 ( ~ 1 - w2)
257
m2
(¢¢2)¢1-u~2 +
~1
I
w h e r e ~2 v a r i e s b e t w e e n cc1 and co2 max. The e n e r g y s p e c t r u m of the s c a t t e r e d p h o t o n s d e r i v e d in the i n d i c a t e d m a n n e r s i g n i f i c a n t l y d i f f e r s f r o m that due to b r e m s s t r a h l u n g which h a s the f o r m d ~ ~dcc/~_,. If the p r i m a r y p h o t o n s b e l o n g to the o p t i cal p a r t of the s p e c t r u m and ¢1 = 6 GeV, the d i s t r i b u t i o n in the range ~c2 >i 0.5 _ 0.6 w2 max. will roughly be ~2d¢¢2 and most of the radiation flux will be in the vicinity of w2 max. (fig. I). ~0
q.O
(4)
-09 ~.0
"0.8
-Q7
I ~
-0.6
~Z
.o~
40 05.
.0.2
~QJ
.0.9 --
.
-0!
"Q? - } "Q$ =% .~0
"O~ -O.k
'
20"
O,z max
Fig. 2. Energy distribution of scattered photons. 1. ¢1 = 6 GeV, w1 = 35.6 eV, ~2 max. = 4.58 GeV. 2. ¢I = 6 G e V , ~1 = 178 eV, w2 m a x . =5"64GeV. 2' is the spectral distribution of the intensity for case 2. t~ f3'
I0
,
OI
,
Q2
-
,
Q5
-
,
,
04
Q5
•
Q6
-
•
0,7
-
•
0.~
-
,
till
0
12'
tO
Ll"
Fig. 1. Energy distribution of scattered photons. 1. ¢1 = 6 GeV, ~1 = 1.78 eV, ~2 max. = 848 MeV. 2. ¢1 6 GeV, ~1 = 3.56 eV, ~2 max. = 1.48 GeV. 1' is the spectral distribution of the intensity in case 1. A n o t h e r , no l e s s i n t e r e s t i n g , f e a t u r e of the d i s t r i b u t i o n u n d e r c o n s i d e r a t i o n a p p e a r s when ¢~2 max. "~ ¢1" In t h i s c a s e the r e l a t i v e n u m b e r of p h o t o n s in the v i c i n i t y of ~2 max. i n c r e a s e s . F o r w 2 max. ~ ~1 the ~ - q u a n t a a r e r a t h e r m o n o e n e r g e t i c . The h i g h e s t ~,-quantum e n e r g y ¢¢2 m a x . ~ ¢1 m a y be a t t a i n e d e i t h e r by i n c r e a s i n g Wl o r i n c r e a s i n g (1. F o r e x a m p l e , it can be s e e n in figs.2 and 3 that a l r e a d y f o r u~1 = 178 eV the b e a m will be s u f f i c i e n t ly m o n o e n e r g e t i c and for ¢¢1 = 1.78 keV the h a l f width at ~2 m a x . ~ 6 GeV i s of the o r d e r of 1%. M o n o e n e r g e t i c q u a n t a will a l s o be p r o d u c e d when r e d l i g h t is s c a t t e r e d on e l e c t r o n s with ~1 = 500 GeV (fig. 3, c u r v e 2). The c h a r a c t e r i s t i c s c a t t e r i n g a n g l e f o r y - q u a n t a with e n e r g i e s w2 ~ e 1 a r e 0 2 ~ m/~ 1 and for w 1 << u:2 << e I 0~ = 2 ( u : l / w O ~ . T h e e x a c t e x p r e s s i o n fo~ the a n g u l a r f f i s t r i b u ~ i o n - c a n be o b t a i n e d f r o m (3) and (1). It should a l s o be noted that photon b e a m s in any p r e s c r i b e d f r e q u e n c y r a n g e f r o m u:2 m i n . = U:l (1 - /~)/(1 + /~) to w 2 max. can be o b t a i n e d in the i n -
LP"
X~I6-
04"
02IDo
o'~ o12
~h " ~.,
d5
o:6 o'7 " ~'~ Q'9 ~o
e'"~z,"nQx
Fig. 3. Energy distribution of scattered photons. 1. ¢1= 6GeV, Wl= 1.78keV, w2max.=5.98 GeV 2. el = 5 0 0 G e V ' ~ l = 1.78 eV, w2max.= 497 GeY 3. e l = 6 G e V , ~ l = 1 2 7 . 8 keV, w2max.=5.9995GeV The C o m p t o n effect c r o s s s e c t i o n ~ is of o r d e r 6 x 10 -25 c m 2. T h e n u m b e r of p h o t o n s f r o m a p o w e r f u l l a s e r p u l s e of 10- 8 s e c d u r a t i o n is 1020 - 1022. When this n u m b e r of p h o t o n s is s c a t t e r e d on an e l e c t r o n b u n c h c o n s i s t i n g of about 10° e l e c t r o n s and a l i f e t i m e of about the s a m e d u r a t i o n a p p r o x i m a t e l y 105 - 107 high e n e r g y p h o t o n s should 177
Volume 4, number 3
PHYSICS
be p r o d u c e d in the r a n g e d¢c2/~ 2 = 0.05. T h i s n u m b e r of y - q u a n t a i s c o m p a r a b l e to p h o t o n flux in the s a m e f r e q u e n c y r a n g e due to b r e m s s t r a h l u n g of a s i m i l a r e l e c t r o n bunch p e r unit r a d i a t i o n l e n g t h . It s h o u l d be e m p h a s i z e d t h a t the y - q u a n t u m b e a m s c o n s i d e r e d h e r e a r e p r o d u c e d a s a r e s u l t of i n t r o d u c i n g t h e l i g h t in the a c c e l e r a t o r c h a m b e r and the e n c o u n t e r b e t w e e n the e l e c t r o n s and nlight t a r g e t " m a y be m a d e to o c c u r a t any p e r i o d of the a c c e l e r a t i n g c y c l e , t h a t i s , at v a r i o u s e l e c t r o n e n e r g i e s . Of c o u r s e t h e r e w i l l be no b a c k g r o u n d when s u c h a nlight target ~ is employed. A s m e n t i o n e d a b o v e , with i n c r e a s e of w 1 the v a l ue of ¢c2 m a x . a l s o i n c r e a s e s a s w e l l a s the d e g r e e of m o n o e n e r g e t i c i t y of the y - q u a n t a p r o d u c e d . W i t h i n c r e a s e of 4,1 the d i f f e r e n t i a l c r o s s s e c t i o n in the
PARAMAGNETIC
RESONANCE
LETTERS
1April1963
vicinity of w2 max. decreases rather slowly compared to the value of the total cross section. Thus it may be expected that by using powerful sources of photons possessing energies exceeding those of light photons, sufficiently high fluxes of monoenergetic y-quanta may be attained. Such y-ray beams should undoubtedly be useful in solving a large number of physical problems. T h e a u t h o r s a r e t h a n k f u l to P r o f . A. I. A l i k h a n i a n f o r i n t e r e s t in t h i s w o r k and to V. M. A r u t y u n i a n f o r valuable suggestions.
References 1) A. I. Akhiezer and V. B. Berestetsky, Quantum E l e c t r o dynamics. (Izd. Fiz. Mat. L i t . , Moscow, 1959) § 28.
OF
Gd 3+ I N S r F 2 A N D
BaF2*
J. S I E R R O Institute of experimental physics, University of Geneva, Geneva, Switzerland
Received 1 March 1963
E l e c t r o n p a r a m a g n e t i c r e s o n a n c e s p e c t r a of Gd 3+ i o n s h a v e b e e n o b s e r v e d in s i n g l e c r y s t a l s of s t r o n t i u m and b a r i u m f l u o r i d e . T h e e f f e c t s of t h e r m a l t r e a t m e n t and h y d r o l y s i s a t high t e m p e r a t u r e s on the e l e c t r o n p a r a m a g n e t i c r e s o n a n c e s p e c t r a have b e e n s t u d i e d . W e h a v e u s e d two s y n t h e t i c s i n g l e c r y s t a l s f r o m s e m i - e l e m e n t s d o p e d in the m e l t with 0.02% G d F 3 b y w e i g h t . T h e r o o m t e m p e r a t u r e e l e c tron paramaguetic resonance spectrum was measu r e d b y m e a n s of a high s e n s i t i v i t y X - b a n d s p e c t r o m e t e r 1 ) . T h e o r i e n t a t i o n of t h e s a m p l e s w a s a c h i e v e d by c l e a v a g e a l o n g the [ 111] d i r e c t i o n s and t h e s t a t i c m a g n e t i c f i e l d w a s r o t a t e d in a (110) p l a n e . A s g r o w n , the c r y s t a l of S r F 2 : Gd s h o w e d a c o m plicated electron paramagnetic resonance spectrum. T h e a n g u l a r v a r i a t i o n of t h e l i n e s i n d i c a t e d the p r e s e n c e of t h r e e s p e c t r a h a v i n g c u b i c , t e t r a g o n a l , o r trigonal symmetry. After the samples were heated to 1000 ° C in an i n e r t a t m o s p h e r e o r in v a c u u m and r a p i d l y q u e n c h e d to r o o m t e m p e r a t u r e , t h e y s h o w e d only the c u b i c s p e c t r u m . If, on the o t h e r hand, the s a m p l e s w e r e c o o l e d to r o o m t e m p e r a t u r e v e r y s l o w l y ( 1 0 ° C / h r ) the c u b i c and t r i g o n a l s p e c t r a d e c r e a s e d in i n t e n s i t y while the t e t r a g o n a l s p e c t r a i n c r e a s e d . W h e n t h e s a m p l e s w e r e h e a t e d in an a t m o s p h e r e c o n t a i n i n g a s m a l l a m o u n t of w a t e r v a p o u r , h y d r o l y s i s took p l a c e . At the b e g i n n i n g of the reaction the spectra previously present decreased 178
in intensity and several other lines with trigonal symmetry appeared. The former disappeared completely after a few hours of treatment and only the new trigonal spectra remained while an isotropic weak line with g = 1.992 +_ 0.001 appeared. The crystal of BaF 2 : Gd showed at first a less complicated electron paramagnetic resonance spectrum. The angular variation of the lines indicated that there were two sets of spectra having cubic and trigonal symmetry. Quenching of the samples from 1000°C to room temperature resulted in the conversion of all the trigonal spectra into the cubic spectrum. But in contrast to the SrF~ crystal, z a slow cooling to room temperature did not change the initial spectra. After hydrolysis at high temperature, all the Gd 3+ spectra disappeared entirely and a very weak line with g = 1.992 ± 0.001 appeared. The ground state of Gd 3+ which results from a 4f 7 configuration is 8S7/2. The perturbation by an axial crystal field splits the ground level into four doublets. The interaction of the ion ground state with the crystal field and the effective magnetic field H may be described phenomenologically by a spin Hamiltonian of the form 2) * This work was supported by the Swiss National Foundation for the Scientific Research.
PHYSICS
1) R.Rabinowitz et al., Proc. Inst. Radio Engrs. ( c o r r e spondence) 50 (1962) 2365. 2) A. Javan, E.A. Ballik and W. L. Bond, J. Opt. Soe. Am. 52 (1962) 96. 3) S. Jacobs and P.Rabinowitz, Proc. of the 3rd Quantum Electronics Conf., Paris, 1963 (to be published).
THE COMPTON EFFECT THE POSSIBILITY OF
LETTERS
1 A p r i l 1963
4) K.D. Froome and R. H. Bradsell, J. Sci. Instr. 38 0961) 458. 5) J . T e r r i e n , J. phys. radium 19 (1958) 390. 6) G.R.Hanes, Can. J. Phys. 37 (1959) 1283. 7) C. F. Bruce and R. M. Hill, Australian J. Phys. 14 (1961) 64; 15 (1962) 152. 8) R.M.Hill and C.F.Bruce, Australian J. Phys. 15 (1962)194.
ON RELATIVISTIC OBTAINING HIGH
ELECTRONS AND ENERGY BEAMS
F. R. A R U T Y U N I A N and V. A. T U M A N I A N Physical Institute of the State Committee of the Council of Ministers of the USSR for the Use of Atomic Energy Received 20 February 1963
A c h a r a c t e r i s t i c f e a t u r e of the C o m p t o n e f f e c t on r e l a t i v i s t i c e l e c t r o n s is the a p p e a r a n c e of p h o t o n s with e n e r g i e s e x c e e d i n g t h o s e of the p r i m a r y p h o t o n s . As a r e s u l t , e v e n when l ig h t p h o t o n s a r e s c a t t e r e d on e x t r e m e l y r e l a t i v i s t i c e l e c t r o n s , the e n e r g i e s of the s c a t t e r e d p h o t o n s will be of the s a m e o r d e r of m a g n i t u d e as t h o s e of the e l e c t r o n s . T h i s f e a t u r e ma y p o s s i b l y be e x p l o i t e d f o r o b t a i n i n g high e n e r g y y - r a y b e a m s in e l e c t r o n a c c e l e r a t o r s . An i m p o r t a n t point to be m e n t i o n e d is that the c h a r a c t e r i s t i c s of s u c h y - b e a m s will s i g n i f i c a n t l y d i f f e r f r o m t h o s e o b t a i n e d by b r e m s s t a h l u n g . In the C o m p t o n e f f e c t i n v o l v i n g m o v i n g e l e c t r o n s the e n e r g y of the s c a t t e r e d q u a n t u m ~2 is r e l a t e d to the e n e r g y of the p r i m a r y photon ~cI by the w e l l known e q u a t i o n (h = c = 1) 1 - v 1 c o s 01 w2 = ~ 1 1 - v 1 c o s e 2 + ( ~ l / e 1) (1 - c o s 0) '
(1)
w h e r e v 1 and el a r e r e s p e c t i v e l y the e l e c t r o n v e l o c ity and e n e r g y , 01 and ~2 a r e the a n g l e s b e t w e e n the d i r e c t i o n of m o t i o n of the e l e c t r o n s and i n c i d e n t and s c a t t e r e d q u a n t a and 0 is the a n g le b e t w e e n the i n c i dent and s c a t t e r e d quanta. T h e e n e r g y of the s c a t t e r e d y - q u a n t a is m a x i m a l (w2 max.) when the p r i m a r y e l e c t r o n and photon m o v e in o p p o s i t e d i r e c t i o n s (01 = ~r) and the s c a t t e r e d photon m o v e s in the d i r e c t i o n of the e l e c t r o n . T h e n (Vl = 1) 2w I ~c2 max. = ½ ( m / ~ l ) 2 + 2 : ~ l / e 1
,
(2)
w h e r e m is the e l e c t r o n r e s t e n e r g y . T h e h i g h e s t e n e r g y to a t t a i n p o s s i b l y in e l e c t r o n a c c e l e r a t o r s in the n e a r f u t u r e should be --6 GeV.
176
Of c o u r s e in o r d e r to obtain y - b e a m s by the m e t h o d c o n s i d e r e d h e r e high photon f l u x e s will be r e q u i r e d . A high i n t e n s i t y photon s o u r c e that should be f e a s i ble is the l a s e r . At p r e s e n t r u b y l a s e r s s e e m to be the m o s t r e l i a b l e . F o r ruby l a s e r p h o t o n s (k= 6943 /~) s c a t t e r e d on 6 GeV e l e c t r o n s one g e t s ~ 2 m a x , = 848 MeV. T h i s e f f e c t r a p i d l y g r o w s with i n c r e a s e of the e l e c t r o n e n e r g y . T h u s f o r the s a m e r u b y l a s e r s and ~ 1 = 40 and 500 GeV the m a x i m a l e n e r g y is c o r r e s p o n d i n g l y ~2 m a x . ~ 21 and 497 GeV. Of c o u r s e if l a s e r s e m i t t i n g s h o r t e r wave l e n g t h s o r o t h e r s o u r c e s of high e n e r g y p h o t o n s be e m p l o y e d : the e n e r g i e s of the s c a t t e r e d p h o t o n s m a y c l o s e l y a p p r o a c h t h o s e of the e l e c t r o n s . The differential c r o s s section for Compton scatt e r i n g on m o v i n g e l e c t r o n s is 1)
(3) w h e r e r o is the c l a s s i c a l e l e c t r o n r a d i u s and 2a~1 Xl . . . . . ~ 2 ( e l + P1)
2~ 2 x2 =-(El -PI m
2
cos e2)
w h e r e P1 is the e l e c t r o n m o m e n t u m . T h e e n e r g y e n e r g y s p e c t r u m of the s c a t t e r e d p h o t o n s can be d e r i v e d f r o m e x p r e s s i o n s (3) and (1). N e g l e c t i n g s m a l l t e r m s in (3) we o b t a i n
Volume 4, number 3
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I rn~
1April1963
d i c a t e d m a n n e r . The b e a m s p r o d u c e d in this way will a p p a r e n t l y be p a r t i a l l y p o l a r i z e d , a fact which is of i n t e r e s t in i t s e l f .
o~2 ,2 ( ~ 1 - w2)
257
m2
(¢¢2)¢1-u~2 +
~1
I
w h e r e ~2 v a r i e s b e t w e e n cc1 and co2 max. The e n e r g y s p e c t r u m of the s c a t t e r e d p h o t o n s d e r i v e d in the i n d i c a t e d m a n n e r s i g n i f i c a n t l y d i f f e r s f r o m that due to b r e m s s t r a h l u n g which h a s the f o r m d ~ ~dcc/~_,. If the p r i m a r y p h o t o n s b e l o n g to the o p t i cal p a r t of the s p e c t r u m and ¢1 = 6 GeV, the d i s t r i b u t i o n in the range ~c2 >i 0.5 _ 0.6 w2 max. will roughly be ~2d¢¢2 and most of the radiation flux will be in the vicinity of w2 max. (fig. I). ~0
q.O
(4)
-09 ~.0
"0.8
-Q7
I ~
-0.6
~Z
.o~
40 05.
.0.2
~QJ
.0.9 --
.
-0!
"Q? - } "Q$ =% .~0
"O~ -O.k
'
20"
O,z max
Fig. 2. Energy distribution of scattered photons. 1. ¢1 = 6 GeV, w1 = 35.6 eV, ~2 max. = 4.58 GeV. 2. ¢I = 6 G e V , ~1 = 178 eV, w2 m a x . =5"64GeV. 2' is the spectral distribution of the intensity for case 2. t~ f3'
I0
,
OI
,
Q2
-
,
Q5
-
,
,
04
Q5
•
Q6
-
•
0,7
-
•
0.~
-
,
till
0
12'
tO
Ll"
Fig. 1. Energy distribution of scattered photons. 1. ¢1 = 6 GeV, ~1 = 1.78 eV, ~2 max. = 848 MeV. 2. ¢1 6 GeV, ~1 = 3.56 eV, ~2 max. = 1.48 GeV. 1' is the spectral distribution of the intensity in case 1. A n o t h e r , no l e s s i n t e r e s t i n g , f e a t u r e of the d i s t r i b u t i o n u n d e r c o n s i d e r a t i o n a p p e a r s when ¢~2 max. "~ ¢1" In t h i s c a s e the r e l a t i v e n u m b e r of p h o t o n s in the v i c i n i t y of ~2 max. i n c r e a s e s . F o r w 2 max. ~ ~1 the ~ - q u a n t a a r e r a t h e r m o n o e n e r g e t i c . The h i g h e s t ~,-quantum e n e r g y ¢¢2 m a x . ~ ¢1 m a y be a t t a i n e d e i t h e r by i n c r e a s i n g Wl o r i n c r e a s i n g (1. F o r e x a m p l e , it can be s e e n in figs.2 and 3 that a l r e a d y f o r u~1 = 178 eV the b e a m will be s u f f i c i e n t ly m o n o e n e r g e t i c and for ¢¢1 = 1.78 keV the h a l f width at ~2 m a x . ~ 6 GeV i s of the o r d e r of 1%. M o n o e n e r g e t i c q u a n t a will a l s o be p r o d u c e d when r e d l i g h t is s c a t t e r e d on e l e c t r o n s with ~1 = 500 GeV (fig. 3, c u r v e 2). The c h a r a c t e r i s t i c s c a t t e r i n g a n g l e f o r y - q u a n t a with e n e r g i e s w2 ~ e 1 a r e 0 2 ~ m/~ 1 and for w 1 << u:2 << e I 0~ = 2 ( u : l / w O ~ . T h e e x a c t e x p r e s s i o n fo~ the a n g u l a r f f i s t r i b u ~ i o n - c a n be o b t a i n e d f r o m (3) and (1). It should a l s o be noted that photon b e a m s in any p r e s c r i b e d f r e q u e n c y r a n g e f r o m u:2 m i n . = U:l (1 - /~)/(1 + /~) to w 2 max. can be o b t a i n e d in the i n -
LP"
X~I6-
04"
02IDo
o'~ o12
~h " ~.,
d5
o:6 o'7 " ~'~ Q'9 ~o
e'"~z,"nQx
Fig. 3. Energy distribution of scattered photons. 1. ¢1= 6GeV, Wl= 1.78keV, w2max.=5.98 GeV 2. el = 5 0 0 G e V ' ~ l = 1.78 eV, w2max.= 497 GeY 3. e l = 6 G e V , ~ l = 1 2 7 . 8 keV, w2max.=5.9995GeV The C o m p t o n effect c r o s s s e c t i o n ~ is of o r d e r 6 x 10 -25 c m 2. T h e n u m b e r of p h o t o n s f r o m a p o w e r f u l l a s e r p u l s e of 10- 8 s e c d u r a t i o n is 1020 - 1022. When this n u m b e r of p h o t o n s is s c a t t e r e d on an e l e c t r o n b u n c h c o n s i s t i n g of about 10° e l e c t r o n s and a l i f e t i m e of about the s a m e d u r a t i o n a p p r o x i m a t e l y 105 - 107 high e n e r g y p h o t o n s should 177
Volume 4, number 3
PHYSICS
be p r o d u c e d in the r a n g e d¢c2/~ 2 = 0.05. T h i s n u m b e r of y - q u a n t a i s c o m p a r a b l e to p h o t o n flux in the s a m e f r e q u e n c y r a n g e due to b r e m s s t r a h l u n g of a s i m i l a r e l e c t r o n bunch p e r unit r a d i a t i o n l e n g t h . It s h o u l d be e m p h a s i z e d t h a t the y - q u a n t u m b e a m s c o n s i d e r e d h e r e a r e p r o d u c e d a s a r e s u l t of i n t r o d u c i n g t h e l i g h t in the a c c e l e r a t o r c h a m b e r and the e n c o u n t e r b e t w e e n the e l e c t r o n s and nlight t a r g e t " m a y be m a d e to o c c u r a t any p e r i o d of the a c c e l e r a t i n g c y c l e , t h a t i s , at v a r i o u s e l e c t r o n e n e r g i e s . Of c o u r s e t h e r e w i l l be no b a c k g r o u n d when s u c h a nlight target ~ is employed. A s m e n t i o n e d a b o v e , with i n c r e a s e of w 1 the v a l ue of ¢c2 m a x . a l s o i n c r e a s e s a s w e l l a s the d e g r e e of m o n o e n e r g e t i c i t y of the y - q u a n t a p r o d u c e d . W i t h i n c r e a s e of 4,1 the d i f f e r e n t i a l c r o s s s e c t i o n in the
PARAMAGNETIC
RESONANCE
LETTERS
1April1963
vicinity of w2 max. decreases rather slowly compared to the value of the total cross section. Thus it may be expected that by using powerful sources of photons possessing energies exceeding those of light photons, sufficiently high fluxes of monoenergetic y-quanta may be attained. Such y-ray beams should undoubtedly be useful in solving a large number of physical problems. T h e a u t h o r s a r e t h a n k f u l to P r o f . A. I. A l i k h a n i a n f o r i n t e r e s t in t h i s w o r k and to V. M. A r u t y u n i a n f o r valuable suggestions.
References 1) A. I. Akhiezer and V. B. Berestetsky, Quantum E l e c t r o dynamics. (Izd. Fiz. Mat. L i t . , Moscow, 1959) § 28.
OF
Gd 3+ I N S r F 2 A N D
BaF2*
J. S I E R R O Institute of experimental physics, University of Geneva, Geneva, Switzerland
Received 1 March 1963
E l e c t r o n p a r a m a g n e t i c r e s o n a n c e s p e c t r a of Gd 3+ i o n s h a v e b e e n o b s e r v e d in s i n g l e c r y s t a l s of s t r o n t i u m and b a r i u m f l u o r i d e . T h e e f f e c t s of t h e r m a l t r e a t m e n t and h y d r o l y s i s a t high t e m p e r a t u r e s on the e l e c t r o n p a r a m a g n e t i c r e s o n a n c e s p e c t r a have b e e n s t u d i e d . W e h a v e u s e d two s y n t h e t i c s i n g l e c r y s t a l s f r o m s e m i - e l e m e n t s d o p e d in the m e l t with 0.02% G d F 3 b y w e i g h t . T h e r o o m t e m p e r a t u r e e l e c tron paramaguetic resonance spectrum was measu r e d b y m e a n s of a high s e n s i t i v i t y X - b a n d s p e c t r o m e t e r 1 ) . T h e o r i e n t a t i o n of t h e s a m p l e s w a s a c h i e v e d by c l e a v a g e a l o n g the [ 111] d i r e c t i o n s and t h e s t a t i c m a g n e t i c f i e l d w a s r o t a t e d in a (110) p l a n e . A s g r o w n , the c r y s t a l of S r F 2 : Gd s h o w e d a c o m plicated electron paramagnetic resonance spectrum. T h e a n g u l a r v a r i a t i o n of t h e l i n e s i n d i c a t e d the p r e s e n c e of t h r e e s p e c t r a h a v i n g c u b i c , t e t r a g o n a l , o r trigonal symmetry. After the samples were heated to 1000 ° C in an i n e r t a t m o s p h e r e o r in v a c u u m and r a p i d l y q u e n c h e d to r o o m t e m p e r a t u r e , t h e y s h o w e d only the c u b i c s p e c t r u m . If, on the o t h e r hand, the s a m p l e s w e r e c o o l e d to r o o m t e m p e r a t u r e v e r y s l o w l y ( 1 0 ° C / h r ) the c u b i c and t r i g o n a l s p e c t r a d e c r e a s e d in i n t e n s i t y while the t e t r a g o n a l s p e c t r a i n c r e a s e d . W h e n t h e s a m p l e s w e r e h e a t e d in an a t m o s p h e r e c o n t a i n i n g a s m a l l a m o u n t of w a t e r v a p o u r , h y d r o l y s i s took p l a c e . At the b e g i n n i n g of the reaction the spectra previously present decreased 178
in intensity and several other lines with trigonal symmetry appeared. The former disappeared completely after a few hours of treatment and only the new trigonal spectra remained while an isotropic weak line with g = 1.992 +_ 0.001 appeared. The crystal of BaF 2 : Gd showed at first a less complicated electron paramagnetic resonance spectrum. The angular variation of the lines indicated that there were two sets of spectra having cubic and trigonal symmetry. Quenching of the samples from 1000°C to room temperature resulted in the conversion of all the trigonal spectra into the cubic spectrum. But in contrast to the SrF~ crystal, z a slow cooling to room temperature did not change the initial spectra. After hydrolysis at high temperature, all the Gd 3+ spectra disappeared entirely and a very weak line with g = 1.992 ± 0.001 appeared. The ground state of Gd 3+ which results from a 4f 7 configuration is 8S7/2. The perturbation by an axial crystal field splits the ground level into four doublets. The interaction of the ion ground state with the crystal field and the effective magnetic field H may be described phenomenologically by a spin Hamiltonian of the form 2) * This work was supported by the Swiss National Foundation for the Scientific Research.