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Magnetic properties of K = 12 rotational band in Tm171
Volume 14, number 3
PHYSICS LETTERS
1 F eb r u ar y 1965
References 1. S.J.Hall, W.R.Gibson, A.R.Johnston, R . J . G r i f fiths, E.A. McClatchie, K.M. Knight, Comptes Rendus du Congres international de physique nucl~aire, Paris (1964) to be published. 2. H.E. Conzett, G. Igo, W.J. Knox, Phys. Rev. Letters 12 (1964) 222. 3. G.H.Stafford, J.M.Diekson, D.C.Salter, M.K. Craddock, Nucl.Inst. and Methods 15 (1962) 146. 4. W.H.Evans and S.J. HaI1, Nucl. Inst. and Method.s 24 (1963) 345. 5. R.C.Hanna, private communication.
MAGNETIC
PROPERTIES
OF
6. H.E. Conzett, H.S. Goldberg, E. Shield, R . J . Slobodrian and S.Ys.mabe, Physics Letters 11 (1964) 68. 7. L. Castillejo and L.S.Singh, Nuovo Cimento 11 (1959) 131. 8. K.L.Kowalski and D. Feldman, Phys.Rev. 130 (1963) 276. 9. N.M.Queen, Nuclear Phys.55 (1964) 177. 10. J.H. Williams and M. K. Brussel, Phys. Rev. 110 (1958) 136. 11. N.M.Queen, private communication.
K = ½ ROTATIONAL
BAND
IN T m 171
Y. K. AGARWAL, C . V . K . BABA * and S. K. B H A T T A C H E R J E E
Tara Institute of Fundamental Research, Bombay, India Received 28 December 1964
Magnetic m o m e n t s of s t a t e s within a K = ½ r o tational band and r e d u c e d t r a n s i t i o n p r o b a b i l i t i e s B(M1) of M1 t r a n s i t i o n s within the band can be e x p r e s s e d in t e r m s of t h r e e p a r a m e t e r s GO, g R and b0 [1]. Th es e t h r e e p a r a m e t e r s can be d e t e r m i n e d if any t h r e e of the m a g n e t i c p r o p e r t i e s of m e m b e r s of the r o t a t i o n a l band a r e known. The o t h e r m a g n e t i c p r o p e r t i e s of the s t a t e s in the band can be then c a l c u l a t e d and c o m p a r e d with e x p e r i m e n t a l v a l u e s . This c o m p a r i s o n cons t i t u t e s a t e s t of the model. The m a g n e t i c m o m e n t P(D of a s t at e with spin I in a K = ½ r o t a tional bkfid is g i v en by 1 ~(I) : 4 ( / ~ G 0 [ 1
l - (-)I--~(2I+l)bo] + gR I . (1)
Also B(M1, I + 1 4 1 )
3
=~-
[ e~ ~ 2 2 r 1 + t ~I-½b 12
\ ~ - - ] ~'OL
~-~
O' (2)
with
GO : (gk-gR)
= (gs-gl)~l
(a20-aff1) + gl-gR(3)
and
%G0= -[(gs -gl) ~l a20+ (gl- gR)a]
"
(4)
Equa t i o n s (3) and (4) give the r e l a t i o n between the q u a n t i t i e s GO, b0, the decoupling p a r a m e t e r * Member, Atomic Energy Establishment, Trombay. 214
a and the spin g f a c t o r gs" The c o e f f i c i e n t s a depend on the d e f o r m a t i o n and have been tabulated [1]. Such an a n a l y s i s was m a d e f o r the (411½) ground state r o t a t i o n a l band in T m 169 [2, 3]. In Tm 169 t h r e e v a l u e s of B(M1) and f o u r v a l u e s of m a g n e t i c m o m e n t s a r e known. Bo eh m et ai. [2] u s e d ~/!~, ~¢-h and B(M1, ~5 + . _ , ~3 + ) to e v a l u a t e the t h r e e q u a n t i t i e s GO, b 0 a n d g R. Sundstr(im et al. [3] made use of all known q u a n t i t i e s and obtained a set of v a l u e s GO, b 0 and g R that fit the data best. The low lying s t a t e s of T m 171 populated by f l - d e c a y of E r 171 (T~ = 7.5 hr) a l s o f o r m a (411) K = ½ r o t a t i o n a l band. The m a g n e t i c m o m e n t of the ground state (½+) has been m e a s u r e d r e c e n t l y by Budick et a i . [4] to be - 0.227:~ 0.005 nm. The l i f e t i m e of the ~+ and ½+ s t a t e s and B(M1, ~+ -~ I+) have been m e a s u r e d by SundstrGm et al. [5]. The v a l u e s obtained by t h e m a r e T(~ +) = 80 ~: 19 ps, T(zI+) = 523 ~- 21 ps and B(M1, ~5+ ~ ~3+ ) = 0 . 1 3 9 + 0.033 in units of (e~/2Mc) 2. We have m e a s u r e d the m a g n e t i c m o ment of the ½+ state. A p a r t i a l l e v e l s c h e m e of T m 171 as given by A r t n a and Johns [6], who a l s o d e t e r m i n e d the m u l t i p o l a r i t i e s and m i x i n g r a t i o s of t h e s e t r a n s i t i o n s v e r y p r e c i s e l y , is shown in fig. 1. We have m e a s u r e d a Y-7 d i r e c t i o n a l c o r r e l a t i o n a c cepting the c o m p o s i t e 120 keV and the c o m p o s i t e 300 keV peaks of the V - s p e c t r u m . The o b s e r v e d c o r r e l a t i o n is due to the c a s c a d e s i) 296-124 keV,
Volume 14, number 3
PHYSICS
I
LETTERS
'T1"
(keY)
(n m ]
O
26#s
425.1
65
0.94
362 p=
129.1
~" (~
\ N 116.7 \ - - - -
°°" 3.8 n =
'Irl 6
~"
V
°12
(41H) ZI
5.1 o
-0.227
~.
--
69
29
x-½ 3/2
|
i
69Tin 171
Fig. 1. A partial l e v e l s c h e m e of Tm 171 taken from ref. 6. The half lives of the 116.7 keY and 129.1 keV levels are taken f r o m r e f . 5. The magnetic moment of the ground state is taken from ref. 4. The magnetic moment of the 129.1 keY state is obtained from the p r e s e n t work.
1 February 1965
ii) 3 0 8 - 1 1 2 k e V , iii) 308-117 keV. C a s c a d e s (ii) and (iii) c o n s t i t u t e 76~o of the t o t a l n u m b e r of obs e r v e d c o i n c i d e n c e s , but the d i r e c t i o n a l c o r r e l a tion c o e f f i c i e n t s of t h e s e two c a s c a d e s a r e s m a l l c o m p a r e d w i t h t h a t of the 296-124 k e V c a s c a d e . The c o e f f i c i e n t s c a n be c a l c u l a t e d f r o m the known b r a n c h i n g r a t i o s , m u l t i p o l a r i t i e s and m i x i n g r a t i o s of the v a r i o u s y - r a y s . The r e s u l t a n t d i r e c tional correlation coefficients were measured u s i n g both a s o l i d p o l y c r y s t a l l i n e s o u r c e of ErC13 and a l i q u i d s o u r c e of ErC13 d i s s o l v e d in w a t e r . Both m e a s u r e m e n t s g a v e the s a m e r e s u l t A 2 = 0.083 =~ 0.003. T h i s a g r e e s w i t h the c a l c u l a t e d v a l u e . A l s o the s i g n of the M 1 / E 2 m i x i n g r a t i o 5 f o r the 112 k e V y - r a y d e m a n d e d by t h e ' o b s e r v e d A 2 i s c o n s i s t e n t w i t h the s i g n of 5 c a l c u l a t e d [7] f r o m v a l u e s of gk, g R and b 0 o b t a i n e d b e l o w . The m a g n e t i c m o m e n t w a s m e a s u r e d by an i n t e g r a l m e t h o d u s i n g the a p p a r a t u s a l r e a d y d e s c r i b e d [8]. The o b s e r v e d v a l u e of R, a s d e f i n e d in eq. (5) i s m a i n l y due to the ~+ s t a t e s i n c e the ~+ s t a t e h a s a m u c h s m a l l e r l i f e t i m e and the dir e c t i o n a l c o r r e l a t i o n c o e f f i c i e n t s of c a s c a d e s t h r o u g h that s t a t e a r e a l s o m u c h s m a l l e r . The v a l u e of the m a g n e t i c f i e l d u s e d w a s 21.47 kG. A p a r a m a g n e t i c c o r r e c t i o n f a c t o r ~ = 5.08 [9] at 3 0 0 ° K w a s u s e d . T h e v a l u e of R d e f i n e d a s W(0,/-/) - W(0, -H) R(O) = 2 W(O,H) + W(O,-H)
(5)
(W(0, H) and W ( 0 , - / / ) a r e the c o i n c i d e n c e c o u n t -
Table 1 Summary of the magnetic properties of the (411) K = ½ rotational bands in Tm 169 and Tm 171. References for the experimental values for Tm 169 can be found in ref. 3. Tm 169
Tm~171
Quantity Experimental value
ud I (n m) ~(~-) /
-0.229 + 0.003
-
-0.228
0.553 + 0.010
-
0.522
0.54 ± 0.10
0.74
0.93
1.11 ± 0.14
1.45
1.58
32 ~ ½)
0.18 + 0.02
B(M1; ~ ~ ~) 2
0.13 + 0.01
B(MI;½ ~.~)
0.12 ± 0.02
B(M1;
GO
ga bo
gs, e f f / g s , free
ref.Calculated 2 ref. 3
0.055 + 0 . 0 1 4 -
-1.98
+ 0.12
0.41 ± 0.02 -0.16
+ 0.03
0.75
Calculated
-0.227 + 0.005
0.94 + 0.18
0.105 0.163
0.071 +_0 . 0 1 4
Experimental value
0.139 + 0.033
0.134 -2.45
-2.5
+ 0.6
0.47
0.32 + 0.06
-0.066
0.04 + 0.14 0.95 + 0.15
215
Volume 14, number 3
PHYSICS LETTERS
ing r a t e s at angle ~ in an e x t e r n a l m a g n e t i c field +H and -H, r e s p e c t i v e l y ) is r e l a t e d to the L a r m o r p r e c e s s i o n f r e q u e n c y ~o by the r e l a t i o n
3A2w~R
= 1 + 0 . 2 5 A 2"
Substituting the values for A 2 and the l i f e t i m e s of the ~+ and ~+ s t a t e s with p r o p e r weights we obtain R(135 °) = [(0.94± 0.08) p(~+) + + (0.13±0.03) ~(~+)] × 10 -2 .
(6)
The e x p e r i m e n t gave a value of R = (0.97 + 0.10) × 10 -2. In o r d e r to c o r r e c t for any a s y m m e t r y in the e x p e r i m e n t a l set up each of the y - r a y s of the cascade was accepted in t u r n in either of the c o u n t e r s and the a v e r a g e value of R was obtained. F u r t h e r , m e a s u r e m e n t s were made by shifting the 120 keV channel to accept the K X - r a y peak. The value of R obtained in this case, with the s a m e s t r e n g t h of the m a g n e t i c field as in the m a i n e x p e r i m e n t , was l e s s than 0.1%. In the case of T m 169 the m a g n e t i c m o m e n t of the ~+ state was c a l c u l a t e d [3] to be between 0.4 n m and 1.0 n m for any r e a s o n a b l e set of p a r a m e t e r s GO, KR and b 0. Using the s a m e l i m i t s for ~(~) in T m 171 also and the m e a s u r e d value of R, we get ~(~+) = 0.94 i 0.18 nm from eq. (6). Using the values of ~(½), ~(½) and B(M1; ~+ ~ ~+) the values of the paramegers GO, b0 and gR can be calculated. However one can also express gt_7+~ and gt!+~ in terms of these three p a r a m e t e r s and s u b s t i t u t e in eq. (6) to give a r e l a t i o n between the t h r e e p a r a m e t e r s GO, g R and b 0. U(½) a n d B ( M 1 ; ~ + ~ ~+) give two m o r e r e l a t i o n s so that the t h r e e p a r a m e t e r s can be c a l c u l a t e d without any a s s u m p t i o n about the value of ~t-~+~. The values so obtained a r e given in %.2 / table 1 along with the values for T m 169, for c o m p a r i s o n . The value of gcT_~c a l c u l a t e d f r o m these t h r e e p a r a m e t e r s is 0 . ~ n m in the case of T m 171.
216
1February 1965
The spin g factor gs of a nucleon in a nucleus is known to be less than that for a free nucleon, in several nuclei [I0]. One can obtain the effective spin g factor gh eff from the values of G O and gR using eq. (3~'above. The values of gs eff/gs, free so obtained are also given in the talkie. A value of gs eff/gs free can also be obtained from b0, G O and the decoupling factor a (see eq. 4). The value of gs, eff/gs, free so obtained agrees with that obtained from G O and gR. It may be mentioned that Bowman et al. [ii] observed an attenuation of the directional correlation coefficient of the 177 keV - 131 keV ¥-y cascade through the ½+ state in Tm 169 using an aqueous solution of YbCI 3. They found an attenuation coefficient G 2 = 0.84. In the above analysis of our Tm 171 results we have not assumed such an attenuation since its nature is not clear. The inclusion of such an attenuation would change the value of /z tT_~ and consequently that of gR to gR = 0.36 ± 0.0~.ZIThe other two parameters do not change significantly.
RCfCYCnCCS 1 S.G.Nilsson, Dan. Mad. Fys.Medd.29 No.16 (1955). 2 F. Boehm, J.De Boer and D.Bowman, in Perturbed angular correlations (ed. E. Karlsson, E.Matthias and K. Siegbab_n, North-Holland Publishing Company, Amsterdam 1964) p. 213. 3 T.Sundst-rt~m, J.Lindskog, J.O.Lindstr~m and P. Sparrman, Ark. Fys.26 (1964) 361. 4. B. Budick, I. Maleh and R. Marrus, Phys. Rev. 135 (1964) B 1281. 5. T.Sundstrt~m, J.O.Lindstr(~m, P.Sparrman and J. Lindskog, Ark. Fys. 26 (1964) 397. 6. A. Artna and M. W. Johns, Can. J. Phys. 39 (1961) 1817. 7. K. Alder, A.Bohr, T.Huus, B.R.Mottelson and A. Winther, Rev.Mod.Phys.28 (1956) 432. C.V.K.Baba and S.K.Bhattaehcrjee, 8. Y.K.Agarwal, Nuclear Phys. 58 (1964) 651. 9. C. Gffnther and I. Lindgren, in Perturbed angular correlations loe. eit. p. 357. 1O. J.De Boer and J.D.Rogers, Physics Letters 3 (1963) 304. J.De Boer and F.Boehm, Bull. Am. II. D.Bowman, Phys. Soe. 8 (1963) 596.
PHYSICS LETTERS
1 F eb r u ar y 1965
References 1. S.J.Hall, W.R.Gibson, A.R.Johnston, R . J . G r i f fiths, E.A. McClatchie, K.M. Knight, Comptes Rendus du Congres international de physique nucl~aire, Paris (1964) to be published. 2. H.E. Conzett, G. Igo, W.J. Knox, Phys. Rev. Letters 12 (1964) 222. 3. G.H.Stafford, J.M.Diekson, D.C.Salter, M.K. Craddock, Nucl.Inst. and Methods 15 (1962) 146. 4. W.H.Evans and S.J. HaI1, Nucl. Inst. and Method.s 24 (1963) 345. 5. R.C.Hanna, private communication.
MAGNETIC
PROPERTIES
OF
6. H.E. Conzett, H.S. Goldberg, E. Shield, R . J . Slobodrian and S.Ys.mabe, Physics Letters 11 (1964) 68. 7. L. Castillejo and L.S.Singh, Nuovo Cimento 11 (1959) 131. 8. K.L.Kowalski and D. Feldman, Phys.Rev. 130 (1963) 276. 9. N.M.Queen, Nuclear Phys.55 (1964) 177. 10. J.H. Williams and M. K. Brussel, Phys. Rev. 110 (1958) 136. 11. N.M.Queen, private communication.
K = ½ ROTATIONAL
BAND
IN T m 171
Y. K. AGARWAL, C . V . K . BABA * and S. K. B H A T T A C H E R J E E
Tara Institute of Fundamental Research, Bombay, India Received 28 December 1964
Magnetic m o m e n t s of s t a t e s within a K = ½ r o tational band and r e d u c e d t r a n s i t i o n p r o b a b i l i t i e s B(M1) of M1 t r a n s i t i o n s within the band can be e x p r e s s e d in t e r m s of t h r e e p a r a m e t e r s GO, g R and b0 [1]. Th es e t h r e e p a r a m e t e r s can be d e t e r m i n e d if any t h r e e of the m a g n e t i c p r o p e r t i e s of m e m b e r s of the r o t a t i o n a l band a r e known. The o t h e r m a g n e t i c p r o p e r t i e s of the s t a t e s in the band can be then c a l c u l a t e d and c o m p a r e d with e x p e r i m e n t a l v a l u e s . This c o m p a r i s o n cons t i t u t e s a t e s t of the model. The m a g n e t i c m o m e n t P(D of a s t at e with spin I in a K = ½ r o t a tional bkfid is g i v en by 1 ~(I) : 4 ( / ~ G 0 [ 1
l - (-)I--~(2I+l)bo] + gR I . (1)
Also B(M1, I + 1 4 1 )
3
=~-
[ e~ ~ 2 2 r 1 + t ~I-½b 12
\ ~ - - ] ~'OL
~-~
O' (2)
with
GO : (gk-gR)
= (gs-gl)~l
(a20-aff1) + gl-gR(3)
and
%G0= -[(gs -gl) ~l a20+ (gl- gR)a]
"
(4)
Equa t i o n s (3) and (4) give the r e l a t i o n between the q u a n t i t i e s GO, b0, the decoupling p a r a m e t e r * Member, Atomic Energy Establishment, Trombay. 214
a and the spin g f a c t o r gs" The c o e f f i c i e n t s a depend on the d e f o r m a t i o n and have been tabulated [1]. Such an a n a l y s i s was m a d e f o r the (411½) ground state r o t a t i o n a l band in T m 169 [2, 3]. In Tm 169 t h r e e v a l u e s of B(M1) and f o u r v a l u e s of m a g n e t i c m o m e n t s a r e known. Bo eh m et ai. [2] u s e d ~/!~, ~¢-h and B(M1, ~5 + . _ , ~3 + ) to e v a l u a t e the t h r e e q u a n t i t i e s GO, b 0 a n d g R. Sundstr(im et al. [3] made use of all known q u a n t i t i e s and obtained a set of v a l u e s GO, b 0 and g R that fit the data best. The low lying s t a t e s of T m 171 populated by f l - d e c a y of E r 171 (T~ = 7.5 hr) a l s o f o r m a (411) K = ½ r o t a t i o n a l band. The m a g n e t i c m o m e n t of the ground state (½+) has been m e a s u r e d r e c e n t l y by Budick et a i . [4] to be - 0.227:~ 0.005 nm. The l i f e t i m e of the ~+ and ½+ s t a t e s and B(M1, ~+ -~ I+) have been m e a s u r e d by SundstrGm et al. [5]. The v a l u e s obtained by t h e m a r e T(~ +) = 80 ~: 19 ps, T(zI+) = 523 ~- 21 ps and B(M1, ~5+ ~ ~3+ ) = 0 . 1 3 9 + 0.033 in units of (e~/2Mc) 2. We have m e a s u r e d the m a g n e t i c m o ment of the ½+ state. A p a r t i a l l e v e l s c h e m e of T m 171 as given by A r t n a and Johns [6], who a l s o d e t e r m i n e d the m u l t i p o l a r i t i e s and m i x i n g r a t i o s of t h e s e t r a n s i t i o n s v e r y p r e c i s e l y , is shown in fig. 1. We have m e a s u r e d a Y-7 d i r e c t i o n a l c o r r e l a t i o n a c cepting the c o m p o s i t e 120 keV and the c o m p o s i t e 300 keV peaks of the V - s p e c t r u m . The o b s e r v e d c o r r e l a t i o n is due to the c a s c a d e s i) 296-124 keV,
Volume 14, number 3
PHYSICS
I
LETTERS
'T1"
(keY)
(n m ]
O
26#s
425.1
65
0.94
362 p=
129.1
~" (~
\ N 116.7 \ - - - -
°°" 3.8 n =
'Irl 6
~"
V
°12
(41H) ZI
5.1 o
-0.227
~.
--
69
29
x-½ 3/2
|
i
69Tin 171
Fig. 1. A partial l e v e l s c h e m e of Tm 171 taken from ref. 6. The half lives of the 116.7 keY and 129.1 keV levels are taken f r o m r e f . 5. The magnetic moment of the ground state is taken from ref. 4. The magnetic moment of the 129.1 keY state is obtained from the p r e s e n t work.
1 February 1965
ii) 3 0 8 - 1 1 2 k e V , iii) 308-117 keV. C a s c a d e s (ii) and (iii) c o n s t i t u t e 76~o of the t o t a l n u m b e r of obs e r v e d c o i n c i d e n c e s , but the d i r e c t i o n a l c o r r e l a tion c o e f f i c i e n t s of t h e s e two c a s c a d e s a r e s m a l l c o m p a r e d w i t h t h a t of the 296-124 k e V c a s c a d e . The c o e f f i c i e n t s c a n be c a l c u l a t e d f r o m the known b r a n c h i n g r a t i o s , m u l t i p o l a r i t i e s and m i x i n g r a t i o s of the v a r i o u s y - r a y s . The r e s u l t a n t d i r e c tional correlation coefficients were measured u s i n g both a s o l i d p o l y c r y s t a l l i n e s o u r c e of ErC13 and a l i q u i d s o u r c e of ErC13 d i s s o l v e d in w a t e r . Both m e a s u r e m e n t s g a v e the s a m e r e s u l t A 2 = 0.083 =~ 0.003. T h i s a g r e e s w i t h the c a l c u l a t e d v a l u e . A l s o the s i g n of the M 1 / E 2 m i x i n g r a t i o 5 f o r the 112 k e V y - r a y d e m a n d e d by t h e ' o b s e r v e d A 2 i s c o n s i s t e n t w i t h the s i g n of 5 c a l c u l a t e d [7] f r o m v a l u e s of gk, g R and b 0 o b t a i n e d b e l o w . The m a g n e t i c m o m e n t w a s m e a s u r e d by an i n t e g r a l m e t h o d u s i n g the a p p a r a t u s a l r e a d y d e s c r i b e d [8]. The o b s e r v e d v a l u e of R, a s d e f i n e d in eq. (5) i s m a i n l y due to the ~+ s t a t e s i n c e the ~+ s t a t e h a s a m u c h s m a l l e r l i f e t i m e and the dir e c t i o n a l c o r r e l a t i o n c o e f f i c i e n t s of c a s c a d e s t h r o u g h that s t a t e a r e a l s o m u c h s m a l l e r . The v a l u e of the m a g n e t i c f i e l d u s e d w a s 21.47 kG. A p a r a m a g n e t i c c o r r e c t i o n f a c t o r ~ = 5.08 [9] at 3 0 0 ° K w a s u s e d . T h e v a l u e of R d e f i n e d a s W(0,/-/) - W(0, -H) R(O) = 2 W(O,H) + W(O,-H)
(5)
(W(0, H) and W ( 0 , - / / ) a r e the c o i n c i d e n c e c o u n t -
Table 1 Summary of the magnetic properties of the (411) K = ½ rotational bands in Tm 169 and Tm 171. References for the experimental values for Tm 169 can be found in ref. 3. Tm 169
Tm~171
Quantity Experimental value
ud I (n m) ~(~-) /
-0.229 + 0.003
-
-0.228
0.553 + 0.010
-
0.522
0.54 ± 0.10
0.74
0.93
1.11 ± 0.14
1.45
1.58
32 ~ ½)
0.18 + 0.02
B(M1; ~ ~ ~) 2
0.13 + 0.01
B(MI;½ ~.~)
0.12 ± 0.02
B(M1;
GO
ga bo
gs, e f f / g s , free
ref.Calculated 2 ref. 3
0.055 + 0 . 0 1 4 -
-1.98
+ 0.12
0.41 ± 0.02 -0.16
+ 0.03
0.75
Calculated
-0.227 + 0.005
0.94 + 0.18
0.105 0.163
0.071 +_0 . 0 1 4
Experimental value
0.139 + 0.033
0.134 -2.45
-2.5
+ 0.6
0.47
0.32 + 0.06
-0.066
0.04 + 0.14 0.95 + 0.15
215
Volume 14, number 3
PHYSICS LETTERS
ing r a t e s at angle ~ in an e x t e r n a l m a g n e t i c field +H and -H, r e s p e c t i v e l y ) is r e l a t e d to the L a r m o r p r e c e s s i o n f r e q u e n c y ~o by the r e l a t i o n
3A2w~R
= 1 + 0 . 2 5 A 2"
Substituting the values for A 2 and the l i f e t i m e s of the ~+ and ~+ s t a t e s with p r o p e r weights we obtain R(135 °) = [(0.94± 0.08) p(~+) + + (0.13±0.03) ~(~+)] × 10 -2 .
(6)
The e x p e r i m e n t gave a value of R = (0.97 + 0.10) × 10 -2. In o r d e r to c o r r e c t for any a s y m m e t r y in the e x p e r i m e n t a l set up each of the y - r a y s of the cascade was accepted in t u r n in either of the c o u n t e r s and the a v e r a g e value of R was obtained. F u r t h e r , m e a s u r e m e n t s were made by shifting the 120 keV channel to accept the K X - r a y peak. The value of R obtained in this case, with the s a m e s t r e n g t h of the m a g n e t i c field as in the m a i n e x p e r i m e n t , was l e s s than 0.1%. In the case of T m 169 the m a g n e t i c m o m e n t of the ~+ state was c a l c u l a t e d [3] to be between 0.4 n m and 1.0 n m for any r e a s o n a b l e set of p a r a m e t e r s GO, KR and b 0. Using the s a m e l i m i t s for ~(~) in T m 171 also and the m e a s u r e d value of R, we get ~(~+) = 0.94 i 0.18 nm from eq. (6). Using the values of ~(½), ~(½) and B(M1; ~+ ~ ~+) the values of the paramegers GO, b0 and gR can be calculated. However one can also express gt_7+~ and gt!+~ in terms of these three p a r a m e t e r s and s u b s t i t u t e in eq. (6) to give a r e l a t i o n between the t h r e e p a r a m e t e r s GO, g R and b 0. U(½) a n d B ( M 1 ; ~ + ~ ~+) give two m o r e r e l a t i o n s so that the t h r e e p a r a m e t e r s can be c a l c u l a t e d without any a s s u m p t i o n about the value of ~t-~+~. The values so obtained a r e given in %.2 / table 1 along with the values for T m 169, for c o m p a r i s o n . The value of gcT_~c a l c u l a t e d f r o m these t h r e e p a r a m e t e r s is 0 . ~ n m in the case of T m 171.
216
1February 1965
The spin g factor gs of a nucleon in a nucleus is known to be less than that for a free nucleon, in several nuclei [I0]. One can obtain the effective spin g factor gh eff from the values of G O and gR using eq. (3~'above. The values of gs eff/gs, free so obtained are also given in the talkie. A value of gs eff/gs free can also be obtained from b0, G O and the decoupling factor a (see eq. 4). The value of gs, eff/gs, free so obtained agrees with that obtained from G O and gR. It may be mentioned that Bowman et al. [ii] observed an attenuation of the directional correlation coefficient of the 177 keV - 131 keV ¥-y cascade through the ½+ state in Tm 169 using an aqueous solution of YbCI 3. They found an attenuation coefficient G 2 = 0.84. In the above analysis of our Tm 171 results we have not assumed such an attenuation since its nature is not clear. The inclusion of such an attenuation would change the value of /z tT_~ and consequently that of gR to gR = 0.36 ± 0.0~.ZIThe other two parameters do not change significantly.
RCfCYCnCCS 1 S.G.Nilsson, Dan. Mad. Fys.Medd.29 No.16 (1955). 2 F. Boehm, J.De Boer and D.Bowman, in Perturbed angular correlations (ed. E. Karlsson, E.Matthias and K. Siegbab_n, North-Holland Publishing Company, Amsterdam 1964) p. 213. 3 T.Sundst-rt~m, J.Lindskog, J.O.Lindstr~m and P. Sparrman, Ark. Fys.26 (1964) 361. 4. B. Budick, I. Maleh and R. Marrus, Phys. Rev. 135 (1964) B 1281. 5. T.Sundstrt~m, J.O.Lindstr(~m, P.Sparrman and J. Lindskog, Ark. Fys. 26 (1964) 397. 6. A. Artna and M. W. Johns, Can. J. Phys. 39 (1961) 1817. 7. K. Alder, A.Bohr, T.Huus, B.R.Mottelson and A. Winther, Rev.Mod.Phys.28 (1956) 432. C.V.K.Baba and S.K.Bhattaehcrjee, 8. Y.K.Agarwal, Nuclear Phys. 58 (1964) 651. 9. C. Gffnther and I. Lindgren, in Perturbed angular correlations loe. eit. p. 357. 1O. J.De Boer and J.D.Rogers, Physics Letters 3 (1963) 304. J.De Boer and F.Boehm, Bull. Am. II. D.Bowman, Phys. Soe. 8 (1963) 596.