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Mössbauer effect following coulomb excitation measurements of electric quadrupole moment ratios in the first excited 2+ states of 182,4,6W
Volume 30B, n u m b e r 3
PHYSICS
LETTERS
MCISSBAUER EFFECT FOLLOWING MEASUREMENTS OF ELECTRIC+QUADRUPOLE FIRST EXCITED 2 STATES
29 September 1969
COULOMB EXCITATION MOMENT RATIOS OF 182,4,6W*
IN
THE
Y. W. CHOW,
E. S. GREENBAUM, R. H. HOWES, F. H. H. HSU P. H. SWERDLOW and C. S. WU Depa~'tment of Physics, Columbia University, New York, N. Y. 10027, USA Received 12 August 1969 The following ratios of quadrupole m o m e n t s in the f i r s t excited 2 + state of 182'4,6W have been m e a s u r e d simultaneously using the M~bssbauer effect following Coulomb excitation: 1 : (0. 930 ± 0.016) : (0.908 ± 0.024). Single c r y s t a l s of WS2 have been used as the a b s o r b e r s . These r e s u l t s are c o m p a r e d with the rotational model and the calculations of Kumar and B a r a n g e r . T h e M S s s b a u e r s p e c t r u m of a n u c l e u s s i t u a t e d in a n e l e c t r i c f i e l d g r a d i e n t e x h i b i t s a h y p e r f i n e s t r u c t u r e ( h . f . s . ) p a t t e r n d u e to t h e i n t e r a c t i o n of the nuclear quadrupole moment with the field grad i e n t . In o r d e r to d e t e r m i n e t h e v a l u e of t h e q u a d r u p o l e m o m e n t of t h e h . f . s s p e c t r u m , b o t h t h e m a g n i t u d e a n d s i g n of t h e f i e l d g r a d i e n t m u s t be known accurately. This data are usually not a v a i l a b l e . H o w e v e r , a d i r e c t t e s t of t h e t h e o r y of r o t a t i o n a l n u c l e i h a s b e e n p r o p o s e d w h i c h d e p e n d s s e n s i t i v e l y o n t h e b e h a v i o r of t h e r a t i o s of q u a d r u p o l e m o m e n t s of t h e e x c i t e d s t a t e s in s e v e r a l i s o t o p e s of a r o t a t i o n a l n u c l i d e . T h e r a t i o s of q u a d r u p o l e m o m e n t s c a n b e d e t e r m i n e d p r e * Work partially supported by the U. S. Atomic Energy Commission
c i s e l y if t h e f i e l d g r a d i e n t s of t h e h o s t l a t t i c e , in a l l c a s e s i n v e s t i g a t e d , a r e i d e u t i c a l s o t h a t t h e y e x a c t l y c a n c e l o u t in t h e r a t i o s . F o r t h i s p u r p o s e , w e r e c e n t l y i n v e s t i g a t e d t h e r a t i o s of t h e q u a d r u p o l e m o m e n t s of t h e f i r s t 2 + e x c i t e d s t a t e s in 1 8 2 , 4 , 6 W by M S s s b a u e r e f f e c t f o l l o w i n g C o u l o m b e x c i t a t i o n o n a m e t a l l i c m i x t u r e of e n riched W isotopes. For this Coulomb excited s o u r c e e a c h W a t o m r e s i d e s in a c u b i c l a t t i c e . T h e r e f o r e , t h e r e i s no h y p e r f i n e i n t e r a c t i o n in t h e s o u r c e . T h i s i s u n l i k e t h e c a s e of e a r l i e r M O s s b a u e r s t u d i e s in 184W a n d 186W u s i n g 1 8 4 R e a n d 186He r a d i o a c t i v e s o u r c e s , r e s p e c t i v e l y . T h e c r y s t a l s t r u c t u r e of r h e n i u m i s h e x a g o n a l c l o s e - p a c k e d . F o r t h i s t y p e of c r y s t a l structure an axially symmetric field gradient
Table 1. The quadrupole i n t e r a c t i o n e n e r g i e s for 2 + s t a t e s of 182, 4, 6 w in WS2 and the i s o m e r shifts of these states. C eQVzz ~ - (mm/sec)
IAE I S I(mm/sec) u~ in'g eQVzz (keV) f r o m WS 2 ± WS2 3_ WS~powder WS2tl (neglectAEi.s.) WSe 2 powder WSe 2 ir(neglectAEi.s) 182W 100.1 10.08 ±0.08 10.03±0.11 0.015±0.067 10.19 ~-0.06 0.01 ±0.07 184W 111.1 8.36±0.11 8.42 =e0.12 8.38±0.09 0.03 ±0.09 186W 122.5 7.47±0.17 7.49 ±0.19 7.22±0.13 Ey
182Ta 100.1 10.25±0.10 10.11±0.11 186Re 122.5
7.32±0.18
7.33±0.20
Results of p r e s e n t e x p e r i m e n t K u m a r and B a r a n g e r [3] Rotational model *
10.06±0.06 7.25± 0.15
9.19±0.10
9.26±0.15
6.74±0.23 Q~o Q22 184Q22: 182Q22 186Q22 : 182Q22 ~--~?02(184) : ~-~2 (182)w02 0.930 • 0.016 0.946 0.946 • 0.009
6.88±0.18
0.013±0.06 0.02 ±0.08 Q22 ~ (186) r~-~,~02(182)
0.908 ± 0.024
0.983 ± 0.020
1.007 ± 0.028
0.862
0.981
0.925
0.902 ±0.009
1.00
1.00
• B (E2) values from ref. 5 171
Volume 30B, n u m b e r 3
PHYSICS
LETTERS
29 September 1969
1,010 ~.m= 0 a)
w * e 2 - wS 2 POWDER
1.000 ~
0.990
(RANDOM)
0.980
~
0.970 1.005
1=~
I
\
~/1
I
)
I
u) Z
Am=_+Z + I
DIRECTIONOF ~ FIELD GRADIENT
0.990
I"ml = I --
0,980 1.005
\~
1~1=2
b) w ~82-WS2 SINGLE CRYSTAL PERPENDICULAR $~r 1.0OO ~1~ }
.J t.=J OC
= 4-_I
DIRF'CTI~I OF F,E,D GR,D,ENT
Z C' u')
~
'
m
~
=
I~ml = z
I
I
~
I
.
C) WIsz- WS2 PARALLEL
,oooL, , ,'~m= 4"1 0.995l DIRECTtONOF ~ I~IELDGRADIENT
1
~
o.99o t
0"985t
,ml=I
0.980/ 5
I 0
0.5 VELOCITY (ram/sec)
Fig. 1. M b s s b a u e r h.f.s, s p e c t r a of the f i r s t rotational v - r a y s of 182W in WS 2 powder and W S 2 s i n g l e crystal. e x i s t s a t t h e s i t e of e a c h e m i t t i n g n u c l e u s . T h i s q u a d r u p o l e s p l i t t i n g in t h e s o u r c e m u s t b e i n c l u d e d in t h e a n a l y s i s of t h e q u a d r u p o l e s p l i t t i n g in t h e a b s o r b e r . The nuclear quadrupole interaction was s t u d i e d in WS 2 w h i c h h a s a h e x a g o n a l c l o s e p a c k e d c r y s t a l s t r u c t u r e . F o r t h i s t y p e of c r y s tal structure, as stated above, the electric field g r a d i e n t at the s i t e of e a c h t u n g s t e n n u c l e u s i s a x i a l l y s y m m e t r i c . We h a v e s t u d i e d t h e 172
M O s s b a u e r e f f e c t in s i n g l e c r y s t a l s of WS2, w i t h t h e c - a x i s of t h e c r y s t a l o r i e n t e d b o t h p a r a l l e l a n d p e r p e n d i c u l a r to t h e d i r e c t i o n of o b s e r v a t i o n , a s w e l l a s in p o w d e r e d WS 2 w h i c h i s c o m p o s e d of r a n d o m l y o r i e n t e d c r y s t a l l i t e s . T h e r e a s o n f o r t h e u s e of s i n g l e - c r y s t a l a b s o r b e r s i s t h a t t h e y s e r v e to s i m p l i f y t h e i n t e r p r e t a t i o n of t h e s p e c t r a in a b e a u t i f u l a n d e l e g a n t way. This may be seen as follows. Consider f i r s t a n a b s o r b e r of r a n d o m l y o r i e n t e d c r y s t a l -
Volume 30B, number 3
PHYSICS
LETTERS
29 September ]969
(a) 1.02 ,
I.OC
~
ROTATIONALMODEL
2 0.96 0"~ ~
0.96 0.94
z~ RESULTS OF PERSSON, et
ol
PRESENT EXPERIMENT
0.92
~,~ %1"
I
I
182
184
I
186
1.00
t~ + (3r
OO
0.75 PRESENT EXPERIMENT ROTATIONAL MODEL + KUMAR AND BARANGER
(b) o.5o
I
I
182
164 A
I
166
-
Fig. 2. Comparisons between the theoretically predicted and experimental determined ratios of Q22 Q22 ~ 0 2 (,4)/~0~2 (182) and V (,4)/0(182) . l i t e s . T h e t r a n s m i s s i o n s p e c t r u m c o n s i s t s of t h r e e p e a k s c o r r e s p o n d i n g to the t r a n s i t i o n s A re=O, ± 1, + 2 , the f i r s t two of w h i c h a r e u n r e s o l v e d . T h i s is i l l u s t r a t e d by the d a t a in fig. l a . A d j a c e n t to fig. l a is shown the a n g u l a r d i s t r i bution of y r a d i a t i o n f o r a p u r e m u l t i p o l e t r a n s i t i o n of o r d e r l =2. T h i s c a s e c o r r e s p o n d s to WS 2 p o w d e r . All c o m p o n e n t s of the t r a n s i t i o n a r e p r e s e n t and the y - r a y e m i s s i o n is i s o t r o p i c . In fig. l b , the d a t a for a s i n g l e - c r y s t a l a b s o r b e r with the c - a x i s and f i e l d g r a d i e n t p e r p e n d i c u l a r to the d i r e c t i o n of o b s e r v a t i o n is shown. F r o m a study of the a n g u l a r d i s t r i b u t i o n of e a c h c o m p o n e n t we s e e that only Am = ± 1, ± 2 h a v e n o n - z e r o c o n t r i b u t i o n s p e r p e n d i c u l a r to the
a x i s of q u a n t i z a t i o n . T h e r e f o r e , the M 6 s s b a u e r s p e c t r u m for t h i s c a s e c o r r e s p o n d s to two p e a k s of e q u a l i n t e n s i t y . A s i m i l a r a r g u m e n t h o l d s f o r the p a r a l l e l c o n f i g u r a t i o n e x c e p t that in this c a s e A m = + 1 is the only n o n - v a n i s h i n g c o m p o n e n t . S i m i l a r s t u d i e s w e r e c a r r i e d out w i t h 1 8 2 T a and 186Re r a d i o a c t i v e s o u r c e s inc l u d i n g WSe 2 ( p o w d e r ) and WSe 2 s i n g l e - c r y s t a l (parallel) absorbers. T h e m e a s u r e m e n t s w e r e p e r f o r m e d at 25 ° K with the u s e of a c l o s e d c y c l e h e l i u m r e f r i g e r a t o r a s d e s c r i b e d e l s e w h e r e [1]. T h e e x p e r i m e n t w a s c a r r i e d out with the 8 MeV He ++ b e a m of the C o l u m b i a U n i v e r s i t y Van de G r a a f f a c c e l e r a t o r , and a thin window Ge ( L i ) d e t e c t o r w a s u s e d to 173
Volume 30B, number 3
P H Y S I C S LETTERS
d e t e c t the Coulomb e x c i te d n u c l e a r ~ r a y s . The r e g i o n of i n t e r e s t in the Coulomb e x c i t e d pulse height s p e c t r u m was c o m p o s e d of t h r e e peaks of e n e r g i e s 100.1 keV, 111.2 keV and 122.5 keV which c o r r e s p o n d s to the lowest 2 + - . 0 + t r a n s i tion of the i s o t o p e s 182W, 184W and 186W, r e s p e c t i v e l y . T h e s e peaks a r e well r e s o l v e d and can be s e p a r a t e l y s e l e c t e d by t h r e e s i n g l e channel a n a l y z e r s . The v e l o c i t y o r timing s p e c t r u m is r o u t e d to t h r e e m u l t i - c h a n n e l a n a l y z e r s by the outputs of the t h r e e s i n g l e - c h a n n e l anal y z e r s . Thus the h y p e r f i n e i n t e r a c t i o n s in all the i s o t o p e s may be studied s i m u l t a n e o u s l y : The h a l f - a n g l e subtended by the c o l l i m a t o r is 4 ° . T h e r e f o r e , the contribution, in s i n g l e - c r y s t a l s t u d i e s , f r o m c o m p o n e n t s which a r e not s t r i c t l y z e r o is n e g l i g i b l e when c o m p a r e d to the total r a d i a t i o n in that d i r e c t i o n . The Compton c o n t r i bution in the p h o t o - p e a k due to the h i g h e r e n e r g y line o r l i n e s is taken c a r e of in the a n a l y s i s . Data f o r the t h r e e i s o t o p e s 182,4,6W w e r e taken with powder, p e r p e n d i c u l a r and p a r a l l e l a b s o r b e r s . It is b e l i e v e d that the data obtained with the p e r p e n d i c u l a r a x i s c o n f ig u r a ti o n is the m o s t r e l i a b l e s i n ce the l e a s t - s q u a r e s fit r e q u i r e s only two lines. T h e s e r e s u l t s a r e in good a g r e e m e n t with the r e s u l t s of P e r s s o n et al. [2] who u s e d r a d i o a c t i v e s o u r c e s and WS2 powder absorbers.
174
29 September 1969
In fig. 2a the e x p e r i m e n t a l data a r e c o m p a r e d with t h e o r e t i c a l p r e d i c t i o n s . In fig. 2b the r a t i o s V ( 1 8 4 ) / Q ( 1 8 2 ) and Q ( 1 8 6 ) / Q (182) a r e plotted. F i n a l l y , no e v i d e n c e f o r an i s o m e r i c shift has been found in the m e a s u r e m e n t s r e p o r t e d h e r e ( u p p e r l i m i t 0.09 m m / s in 182W). T h e s e r e s u l t s a r e c o n s i s t e n t with muonic X - r a y m e a s u r e m e n t s [4] and with the r e c e n t M h s s b a u e r effect m e a s u r e m e n t s u si n g r a d i o a c t i v e s o u r c e s [6]. Th e single c r y s t a l s of WS 2 w e r e supplied by D r s . H. J. Heinen and M. M. Wong of the U.S. B u r e a u of Mines. T h e a u t h o r s would like to thank them for t h e i r v a l u a b l e c o n t r i b u t i o n of this experiment.
References 1. Y.w. Chow et al., Nucl. Instr. and Meth. 66 (1968) 177. 2. B. Persson, H. Blumberg and D. Agresti, Phys. Rev. 170 (1968) 1066. 3. K. Kumar and M. Baranger, Phys. Rev. Letters 17 (1966) 1146. 4. S. Bernow et aL, Phys. Rev. Letters 21 {1968) 457. 5. R. G. Stokstad and B. Persson, Phys. Rev. 170 (1968) 1072. 6. P. Kienle et al. ,Contrib. ,Intern. Conf. on Nuclear structure, 1967 Tokyo, Japan, p. 195.
PHYSICS
LETTERS
MCISSBAUER EFFECT FOLLOWING MEASUREMENTS OF ELECTRIC+QUADRUPOLE FIRST EXCITED 2 STATES
29 September 1969
COULOMB EXCITATION MOMENT RATIOS OF 182,4,6W*
IN
THE
Y. W. CHOW,
E. S. GREENBAUM, R. H. HOWES, F. H. H. HSU P. H. SWERDLOW and C. S. WU Depa~'tment of Physics, Columbia University, New York, N. Y. 10027, USA Received 12 August 1969 The following ratios of quadrupole m o m e n t s in the f i r s t excited 2 + state of 182'4,6W have been m e a s u r e d simultaneously using the M~bssbauer effect following Coulomb excitation: 1 : (0. 930 ± 0.016) : (0.908 ± 0.024). Single c r y s t a l s of WS2 have been used as the a b s o r b e r s . These r e s u l t s are c o m p a r e d with the rotational model and the calculations of Kumar and B a r a n g e r . T h e M S s s b a u e r s p e c t r u m of a n u c l e u s s i t u a t e d in a n e l e c t r i c f i e l d g r a d i e n t e x h i b i t s a h y p e r f i n e s t r u c t u r e ( h . f . s . ) p a t t e r n d u e to t h e i n t e r a c t i o n of the nuclear quadrupole moment with the field grad i e n t . In o r d e r to d e t e r m i n e t h e v a l u e of t h e q u a d r u p o l e m o m e n t of t h e h . f . s s p e c t r u m , b o t h t h e m a g n i t u d e a n d s i g n of t h e f i e l d g r a d i e n t m u s t be known accurately. This data are usually not a v a i l a b l e . H o w e v e r , a d i r e c t t e s t of t h e t h e o r y of r o t a t i o n a l n u c l e i h a s b e e n p r o p o s e d w h i c h d e p e n d s s e n s i t i v e l y o n t h e b e h a v i o r of t h e r a t i o s of q u a d r u p o l e m o m e n t s of t h e e x c i t e d s t a t e s in s e v e r a l i s o t o p e s of a r o t a t i o n a l n u c l i d e . T h e r a t i o s of q u a d r u p o l e m o m e n t s c a n b e d e t e r m i n e d p r e * Work partially supported by the U. S. Atomic Energy Commission
c i s e l y if t h e f i e l d g r a d i e n t s of t h e h o s t l a t t i c e , in a l l c a s e s i n v e s t i g a t e d , a r e i d e u t i c a l s o t h a t t h e y e x a c t l y c a n c e l o u t in t h e r a t i o s . F o r t h i s p u r p o s e , w e r e c e n t l y i n v e s t i g a t e d t h e r a t i o s of t h e q u a d r u p o l e m o m e n t s of t h e f i r s t 2 + e x c i t e d s t a t e s in 1 8 2 , 4 , 6 W by M S s s b a u e r e f f e c t f o l l o w i n g C o u l o m b e x c i t a t i o n o n a m e t a l l i c m i x t u r e of e n riched W isotopes. For this Coulomb excited s o u r c e e a c h W a t o m r e s i d e s in a c u b i c l a t t i c e . T h e r e f o r e , t h e r e i s no h y p e r f i n e i n t e r a c t i o n in t h e s o u r c e . T h i s i s u n l i k e t h e c a s e of e a r l i e r M O s s b a u e r s t u d i e s in 184W a n d 186W u s i n g 1 8 4 R e a n d 186He r a d i o a c t i v e s o u r c e s , r e s p e c t i v e l y . T h e c r y s t a l s t r u c t u r e of r h e n i u m i s h e x a g o n a l c l o s e - p a c k e d . F o r t h i s t y p e of c r y s t a l structure an axially symmetric field gradient
Table 1. The quadrupole i n t e r a c t i o n e n e r g i e s for 2 + s t a t e s of 182, 4, 6 w in WS2 and the i s o m e r shifts of these states. C eQVzz ~ - (mm/sec)
IAE I S I(mm/sec) u~ in'g eQVzz (keV) f r o m WS 2 ± WS2 3_ WS~powder WS2tl (neglectAEi.s.) WSe 2 powder WSe 2 ir(neglectAEi.s) 182W 100.1 10.08 ±0.08 10.03±0.11 0.015±0.067 10.19 ~-0.06 0.01 ±0.07 184W 111.1 8.36±0.11 8.42 =e0.12 8.38±0.09 0.03 ±0.09 186W 122.5 7.47±0.17 7.49 ±0.19 7.22±0.13 Ey
182Ta 100.1 10.25±0.10 10.11±0.11 186Re 122.5
7.32±0.18
7.33±0.20
Results of p r e s e n t e x p e r i m e n t K u m a r and B a r a n g e r [3] Rotational model *
10.06±0.06 7.25± 0.15
9.19±0.10
9.26±0.15
6.74±0.23 Q~o Q22 184Q22: 182Q22 186Q22 : 182Q22 ~--~?02(184) : ~-~2 (182)w02 0.930 • 0.016 0.946 0.946 • 0.009
6.88±0.18
0.013±0.06 0.02 ±0.08 Q22 ~ (186) r~-~,~02(182)
0.908 ± 0.024
0.983 ± 0.020
1.007 ± 0.028
0.862
0.981
0.925
0.902 ±0.009
1.00
1.00
• B (E2) values from ref. 5 171
Volume 30B, n u m b e r 3
PHYSICS
LETTERS
29 September 1969
1,010 ~.m= 0 a)
w * e 2 - wS 2 POWDER
1.000 ~
0.990
(RANDOM)
0.980
~
0.970 1.005
1=~
I
\
~/1
I
)
I
u) Z
Am=_+Z + I
DIRECTIONOF ~ FIELD GRADIENT
0.990
I"ml = I --
0,980 1.005
\~
1~1=2
b) w ~82-WS2 SINGLE CRYSTAL PERPENDICULAR $~r 1.0OO ~1~ }
.J t.=J OC
= 4-_I
DIRF'CTI~I OF F,E,D GR,D,ENT
Z C' u')
~
'
m
~
=
I~ml = z
I
I
~
I
.
C) WIsz- WS2 PARALLEL
,oooL, , ,'~m= 4"1 0.995l DIRECTtONOF ~ I~IELDGRADIENT
1
~
o.99o t
0"985t
,ml=I
0.980/ 5
I 0
0.5 VELOCITY (ram/sec)
Fig. 1. M b s s b a u e r h.f.s, s p e c t r a of the f i r s t rotational v - r a y s of 182W in WS 2 powder and W S 2 s i n g l e crystal. e x i s t s a t t h e s i t e of e a c h e m i t t i n g n u c l e u s . T h i s q u a d r u p o l e s p l i t t i n g in t h e s o u r c e m u s t b e i n c l u d e d in t h e a n a l y s i s of t h e q u a d r u p o l e s p l i t t i n g in t h e a b s o r b e r . The nuclear quadrupole interaction was s t u d i e d in WS 2 w h i c h h a s a h e x a g o n a l c l o s e p a c k e d c r y s t a l s t r u c t u r e . F o r t h i s t y p e of c r y s tal structure, as stated above, the electric field g r a d i e n t at the s i t e of e a c h t u n g s t e n n u c l e u s i s a x i a l l y s y m m e t r i c . We h a v e s t u d i e d t h e 172
M O s s b a u e r e f f e c t in s i n g l e c r y s t a l s of WS2, w i t h t h e c - a x i s of t h e c r y s t a l o r i e n t e d b o t h p a r a l l e l a n d p e r p e n d i c u l a r to t h e d i r e c t i o n of o b s e r v a t i o n , a s w e l l a s in p o w d e r e d WS 2 w h i c h i s c o m p o s e d of r a n d o m l y o r i e n t e d c r y s t a l l i t e s . T h e r e a s o n f o r t h e u s e of s i n g l e - c r y s t a l a b s o r b e r s i s t h a t t h e y s e r v e to s i m p l i f y t h e i n t e r p r e t a t i o n of t h e s p e c t r a in a b e a u t i f u l a n d e l e g a n t way. This may be seen as follows. Consider f i r s t a n a b s o r b e r of r a n d o m l y o r i e n t e d c r y s t a l -
Volume 30B, number 3
PHYSICS
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29 September ]969
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Fig. 2. Comparisons between the theoretically predicted and experimental determined ratios of Q22 Q22 ~ 0 2 (,4)/~0~2 (182) and V (,4)/0(182) . l i t e s . T h e t r a n s m i s s i o n s p e c t r u m c o n s i s t s of t h r e e p e a k s c o r r e s p o n d i n g to the t r a n s i t i o n s A re=O, ± 1, + 2 , the f i r s t two of w h i c h a r e u n r e s o l v e d . T h i s is i l l u s t r a t e d by the d a t a in fig. l a . A d j a c e n t to fig. l a is shown the a n g u l a r d i s t r i bution of y r a d i a t i o n f o r a p u r e m u l t i p o l e t r a n s i t i o n of o r d e r l =2. T h i s c a s e c o r r e s p o n d s to WS 2 p o w d e r . All c o m p o n e n t s of the t r a n s i t i o n a r e p r e s e n t and the y - r a y e m i s s i o n is i s o t r o p i c . In fig. l b , the d a t a for a s i n g l e - c r y s t a l a b s o r b e r with the c - a x i s and f i e l d g r a d i e n t p e r p e n d i c u l a r to the d i r e c t i o n of o b s e r v a t i o n is shown. F r o m a study of the a n g u l a r d i s t r i b u t i o n of e a c h c o m p o n e n t we s e e that only Am = ± 1, ± 2 h a v e n o n - z e r o c o n t r i b u t i o n s p e r p e n d i c u l a r to the
a x i s of q u a n t i z a t i o n . T h e r e f o r e , the M 6 s s b a u e r s p e c t r u m for t h i s c a s e c o r r e s p o n d s to two p e a k s of e q u a l i n t e n s i t y . A s i m i l a r a r g u m e n t h o l d s f o r the p a r a l l e l c o n f i g u r a t i o n e x c e p t that in this c a s e A m = + 1 is the only n o n - v a n i s h i n g c o m p o n e n t . S i m i l a r s t u d i e s w e r e c a r r i e d out w i t h 1 8 2 T a and 186Re r a d i o a c t i v e s o u r c e s inc l u d i n g WSe 2 ( p o w d e r ) and WSe 2 s i n g l e - c r y s t a l (parallel) absorbers. T h e m e a s u r e m e n t s w e r e p e r f o r m e d at 25 ° K with the u s e of a c l o s e d c y c l e h e l i u m r e f r i g e r a t o r a s d e s c r i b e d e l s e w h e r e [1]. T h e e x p e r i m e n t w a s c a r r i e d out with the 8 MeV He ++ b e a m of the C o l u m b i a U n i v e r s i t y Van de G r a a f f a c c e l e r a t o r , and a thin window Ge ( L i ) d e t e c t o r w a s u s e d to 173
Volume 30B, number 3
P H Y S I C S LETTERS
d e t e c t the Coulomb e x c i te d n u c l e a r ~ r a y s . The r e g i o n of i n t e r e s t in the Coulomb e x c i t e d pulse height s p e c t r u m was c o m p o s e d of t h r e e peaks of e n e r g i e s 100.1 keV, 111.2 keV and 122.5 keV which c o r r e s p o n d s to the lowest 2 + - . 0 + t r a n s i tion of the i s o t o p e s 182W, 184W and 186W, r e s p e c t i v e l y . T h e s e peaks a r e well r e s o l v e d and can be s e p a r a t e l y s e l e c t e d by t h r e e s i n g l e channel a n a l y z e r s . The v e l o c i t y o r timing s p e c t r u m is r o u t e d to t h r e e m u l t i - c h a n n e l a n a l y z e r s by the outputs of the t h r e e s i n g l e - c h a n n e l anal y z e r s . Thus the h y p e r f i n e i n t e r a c t i o n s in all the i s o t o p e s may be studied s i m u l t a n e o u s l y : The h a l f - a n g l e subtended by the c o l l i m a t o r is 4 ° . T h e r e f o r e , the contribution, in s i n g l e - c r y s t a l s t u d i e s , f r o m c o m p o n e n t s which a r e not s t r i c t l y z e r o is n e g l i g i b l e when c o m p a r e d to the total r a d i a t i o n in that d i r e c t i o n . The Compton c o n t r i bution in the p h o t o - p e a k due to the h i g h e r e n e r g y line o r l i n e s is taken c a r e of in the a n a l y s i s . Data f o r the t h r e e i s o t o p e s 182,4,6W w e r e taken with powder, p e r p e n d i c u l a r and p a r a l l e l a b s o r b e r s . It is b e l i e v e d that the data obtained with the p e r p e n d i c u l a r a x i s c o n f ig u r a ti o n is the m o s t r e l i a b l e s i n ce the l e a s t - s q u a r e s fit r e q u i r e s only two lines. T h e s e r e s u l t s a r e in good a g r e e m e n t with the r e s u l t s of P e r s s o n et al. [2] who u s e d r a d i o a c t i v e s o u r c e s and WS2 powder absorbers.
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In fig. 2a the e x p e r i m e n t a l data a r e c o m p a r e d with t h e o r e t i c a l p r e d i c t i o n s . In fig. 2b the r a t i o s V ( 1 8 4 ) / Q ( 1 8 2 ) and Q ( 1 8 6 ) / Q (182) a r e plotted. F i n a l l y , no e v i d e n c e f o r an i s o m e r i c shift has been found in the m e a s u r e m e n t s r e p o r t e d h e r e ( u p p e r l i m i t 0.09 m m / s in 182W). T h e s e r e s u l t s a r e c o n s i s t e n t with muonic X - r a y m e a s u r e m e n t s [4] and with the r e c e n t M h s s b a u e r effect m e a s u r e m e n t s u si n g r a d i o a c t i v e s o u r c e s [6]. Th e single c r y s t a l s of WS 2 w e r e supplied by D r s . H. J. Heinen and M. M. Wong of the U.S. B u r e a u of Mines. T h e a u t h o r s would like to thank them for t h e i r v a l u a b l e c o n t r i b u t i o n of this experiment.
References 1. Y.w. Chow et al., Nucl. Instr. and Meth. 66 (1968) 177. 2. B. Persson, H. Blumberg and D. Agresti, Phys. Rev. 170 (1968) 1066. 3. K. Kumar and M. Baranger, Phys. Rev. Letters 17 (1966) 1146. 4. S. Bernow et aL, Phys. Rev. Letters 21 {1968) 457. 5. R. G. Stokstad and B. Persson, Phys. Rev. 170 (1968) 1072. 6. P. Kienle et al. ,Contrib. ,Intern. Conf. on Nuclear structure, 1967 Tokyo, Japan, p. 195.