A new electric quadrupole transition in O16

Volume I, number

8

PHYSICS

LETTERS

(4 0 4) 7 / 2 +, and the 147 k e V state is identified a s (5 1 4) 9 / 2 - , w h e r e a s the u n o b s e r v e d state (4 0 2) 5 / 2 + i s expected in about the s a m e position. T h e s e p r o t o n s t a t e s can f o r m a t h r e e - p a r t i c l e c o n f i g u r a tion with spin 21/2". A n o t h e r high spin c o n f i g u r a tion can be obtained by adding the (6 2 4) 9/2 + n e u t r o n known f r o m t h e 321 k e V level in Hf177 to t h e Lu176 ground state configuration p (4 04) 7 / 2 + n (5 1 4) 7 / 2 " , r e s u l t i n g in spin 23/2"% T h r e e - p a r t i c l e c o n f i g u r a t i o n s h~ve not b e e n o b s e r v e d p r e v i o u s l y in odd d e f o r m e d nuclei. In t h e s p h e r i c a l nucleus Mo 93, an i s o m e r at 2.43 MeV with spin 21/2 is n a t u r a l l y i n t e r p r e t e d a s a t h r e e p a r t i c l e state 3,4). A s i m i l a r case has r e c e n t l y been found in Cs 135, w h e r e the high spin i s o m e r is at 1.62 MeV 5). *

A NEW

ELECTRIC

*

15 July 1962

The a u t h o r s a r e indebted to P r o f e s s o r Niels Bohr f o r e x c e l l e n t working conditions in his Institute: and to P r o f e s s o r s A. B o h r al~3 B. R. M o t t e l s o n , and D r . R. A. Yandenbosch f o r illuminating discussions.

Refe~'ence s 1) G.R. Choppin and R.I,Silva, J. Iug. Nucl. Chem. 3 (1956) lS3. 2) B.R. Mottzlson and S. G. Nilsson, Mat. Fys. Skr. Dan. Vid. Selsk. 1 (1959) 105. 3) D.E.Albu~ger and S.Thulin, Phys. Rev. 89 (1953) 1146. 4) M.Goldhaber, Phys. Rev. 89 (1953) 1186. 5) H. Waranek0 to be published.

*

*

*

QUADRUPOLE

TRANSITION

I N 0 16

G. R. BISHOP and D. B. I S A B E L L E Ecole Norma|e Sup4rieure, Laboratoire de l'Acc41$rateur Lin~aire, Orsay (S.-03, France Received 19 June 1962

The well-known s t r o n g enhancement of s i n g l e nucleon m a t r i x e l e m e n t s f o r s o m e E2 t r a n s i t i o n s in n u c l e i netghbouring 0 1 6 , has been i n t e r p r e t e d 1) as r e s u l t i n g from the v i r t u a l excitation of a c o l l e c tive 2 + s t a t e in the 016 c o r e . A s a t i s f a c t o r y account of the =lata would be r e n d e r e d by a t r a n s i t i o n of e n e r g y about 18 MeV containing a l a r g e f r a c t i o n of the T = 0 sum rule. In the c o u r s e of a study of the giant r e s o n a n c e e l e c t r i c dipole t r a n s i t i o n s by i n e l a s t i c electron s c a t t e r i n g 2) we obtained an i n t e n s e i n e l a s t i c peak at (19.2 + 0.3) MeV, with the c r o s s s e c t i o n s s u m m a r i z e d in t a b l e 1. It is c l e a r f r o m the v a l u e s of Fin 2 for m o m e n t u m t r a n s f e r s grouped about q = 1.20 =-If- that t h i s i n e l a s t i c f o r m f a c t o r is not s i m p l y a fur,~loa of q but Table 1 Experimental cross sections and the square of the inelastic form factor defined as (dc'x/dfl)/(dat)/dfl). Eo e (MeV) (t9 qi

(i_1) d~x (cm 2) ~

~ E (cm 2)

d~

Fx2

....

147.4 70 141.8 60[ 146.8 115 214.8! 70 140.6 135 157.5 120 214 80

0.667 0.805 1.183 1.200 1.237 1.311 1.346

2.32 1.30 5.38 1.35 3.48 2.91 7.13

x 10-31 x 10-31 × 10 -32 x 10-31 x 10-32 x 10-32 x 10-32

1.97 9.34 8.54 4.45 3.38 5.76 2.42

x 10-28 0.90 x 10-29 1.39 x 10-30 6.3 x 10-29 3.04 x 10-30i 10.3 x 10-301 5.05 x 10-29 2.94

x x x x x x x

10-3 10-3 10-3 10-3 10-3 10-3 10-3

also of the s c a t t e r i n g angle e. In Born approximation the total inelastic c r o s s section is given 3) as a sum of contributions f r o m both longitudinal and t r a n s v e r s e v i r t u a l photons; no i n t e r f e r e n c e t e r m s between different multipoles n e e d to be invoked for our m e a s u r e m e n t s of the s c a t t e r e d electrons only. The c r o s s section is given by: ~D

4,,.(),+1) ..q2.X[ x x"

d'-~:'~C" X[(2k+l).,,.llhi 2 ~ +

k=OA~B(Ck, qIVL(e)

[B(EX, q) + B(MX, q)]

VT(0

(t)

where f o r ( E i , E f) >>mc 2, the a n g u l a r d i s t r i b u t i o n s of longitudinal and t r a n s v e r s e photons become: cos2e/2 VL(e) = 4 s i n 4 e / 2 VT(e) :

'

1 + stn2e/2

8 sin28/2 With t h e s e e x p r e s s i o n s for the virtual photon s p e c t r a the c r o s s section can e a s i l y be put in the f o r m c h a r a c t e r i s t i c of single v i r t u a l photon ~.xchange:

323

1. ~

V ~

~ -,~

~

PHYSICS

f~c~ors B ( C t , v ) e t e . ~

are the ~

15 July i96~

LETTERS

nm-

e~-m~ts ~

to m o m m t m n ta-an~.er ..... , ~ ~ t v z e r o they tend t o w a ~ s the 1 ~ g ~'~ ~cr',-~ I L ~ R ~ t h e s L m ! ; a r m a C c i x elements ~-~ r - ~ t t ~ t r ~ n s t ~ o ~ s . IR th~s t~rn:t, f o r e x a m -

~. ~ c ~ . 0 ) d ~ to the t r ~ s m c ~ cmu~ density, ~,,~.~y ~mt~ -~ ~ B(~x, O} d ~ e to conH o w e v e r , for t h e values electron s c a t ~er~!: ~ u ~. t e r ' ~ s .c~n b e o f c o m p a r a b l e ~ • ~, ~ ~.r ~erc~t a~4~lgr ~ c e for ftv~ ~ ~ ¢ u.c~d to ~ e theix contrtbu:~,~. ~ ~r~cu:~: ~.t ~s e v ~ d m t f r o m eq. ( I ) t h a t ~ - ~ ~ t c ~ - . ~ ~ :~ ~'-~.-~ m ~ n e t i c t r a n s i t i o n should _~,~ a (l - sinUSeS) ~ d / s t r i l m t i o n , th~s

~ ~

c~ ~

~

s~

P~ ~ . , ~ c P . ~.~.~

~ ~ ~ l z ~ ~r ~.~.~P~.n¢

v-.~:ucs ~ ~, s i n c e o t h e r ~ s e

the values of F x 2 a r e

%~,er~¢ore

f a c t o r 8.~ this f o r m i s o b m t n e d the t-r-an~tion c ~ density as a

.me ~ . ~ > " c,~m,~-~m~s ,q ~nd ~ are obtained f o r a i : m r ~ . ~ ~ r r u c ~ . ~ ~vc~. *..heeL~_ctlc f o r m f a c t o r . The

: ~ ~:~ ~ ~ . ~ - ~ . ~ ~ C ~. 0~ ~ ~ ~s tJ~en easily found ",~- :~ ,.'~::~ - ~ ' ~ / 4 ¢ ) $ k R 2~. ~ ~ ' t a ,~ ~ble I a r e s~fflcte~t to establish

...... .~ c c.r m ~ - ~ o t i c c h ~ a c t e r o~ the tr'An~_:. :..... =:-e :;~,~ fc,L : ~ f.-~,m the ~rtRrvJRr d i ~ b u -

~- > ' . r : =-:: ~. . . . " '" /(~p/d~) . . . . . . . . . ='~s ..... ~.c~ ~ b ~ h t o n ~ t u d ~ l r L ' ~r-~- ~'er-~c F T for.~. ,~actors. E t h e t h e o r e t i c a l • v--r~:~ a b ~ : e ~ r e ~pp:Icable tl~n the t r ~ s i t i c n

~

~;:~ "~[':~ : { ~ ; ~ ' ~ ,]} = 8.8 ' i0 -52 c m 4 w h i c h is "-- ~t-,- t:me.~ L~r~er t_.~.n Lhe p r e ~ c t J o n c~ the single ~ ' ~ ' . ~ m : ~ e l B~', "~, n} : 4.42 iO " ~ c m 4. A r e -

, ,~..~-,. . . . .

o

of i ~ . e l ~ c

|t i s .~os~ble to m_~-__eare F x 2 o v l y

. :~ ~ . . ~

'--~.~-:~c ? ~ k ~

.

,,-(,.:,.0

c~rr~ts.

-. ~ c . ~ ~ e r ~ , s ~ c

rare s l o w e r t h ~

"~:- _~:.':mi~_ ~ r t ~ -

0

~

2

3

4

5

6

Fig. 1. Plot of Fx2(q,O) versus t a n ~ / 2 for q = 1.2 fermi "1.

s m a ~ q-values gives B L ( ~ , 0) = 6 x 10"52 cm4, which is equal to the single l~trtlcle value. This corresponds to about 2C°~ of ~ e T - 0 elececrlc quadrupole s u m rule (mtturally our m e c s u r e m e n t s do not d e t e r m i n e t h e i s o t o p i c spin of the l e v e l ) . Interpretation of the t r a n s v e r s e ec~tHb~,tton to the c r o s s section cannot be r e l a t e d so s i m p l y to the radlaClve absorption unless the wave functions f o r the ground and excited s t a t e s a r e known. It Iv also possible that the component proportlon~1 to tan28/2 m a y be s i m p l y a r e f l e c t i o n of the i n a d e quacy of the Born a p p r o x i m a t l o n , however, no p h a s e shift c ~ l c u l a t i o n s of i n e l a s t i c e l e c t r o n s c a t t e r i n g have yet been p e r f o r m e d . R s e e m s unlikely that the obs, rved strength of this transition is enough by itself to account f o r enhancement, but evidence is accumulRting of the presence of several E2 transitions between 10 and 75 M e V excitation energy which between them m a y suf~¢e. R ere

TC~tCeS

1~ S. PaiIieros and R. A. Ferrell, Phys. Hey. 116 (1959) 66G. G. Barton, D.M.Brink and L.M.Delves, Nuclear Physics 14 (1959) 256. D. H. W ~ o n , Proc. of the Int. Conf. on Kuolear Structures, Kingston 1960 (North-Holland Publ. Co. UnWersi~" of Toronto P r e s s Publ., 1960), p. 20. z~ D IsaL-eile and G. R. Bishop, J. phys. radium 22 (1961) 548.

..... c

-'=

", - L:-~:.~ e ,. e . ~., ... -

-4 " -

---~-~-"~c.

These c:r,,~:.:£r~:-,ns

~'~-'~÷ ~ . ~

"~--~-,'= . . . . .

~

-

r~C--~-i =

K. Alder, A. Bohr, T. Huus, B. Mottelson and A. Winther, Rev. Mod. Phys. 28 (1956) 432. ;~ G Von Gehlen, Phys. Rev. 118 (1960) 1455. 5~ L I.Schiff, Phys. Rev. 96 (1954) 765. g~ R Foucher and A. De Pinto, J. phys. radium 23 (1962) ~

22.