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Evidence for a four-quasiparticle state in the deformed nucleus 164Dy
Volume
34]3, number
1
EVIDENCE
PHYSICS
FOR
LETTERS
A FOUR-QUASIPARTICLE DEFORMED NUCLEUS
18 January 1971
STATE
IN
THE
164Dy
N. KAFFRELL and G. HERRMANN Inst~tut f u r Anorganlsche Chemic und Kernchern~e der Untt'ers~tat, D-65 Maznz, W.-Gerrnany
Received 2 December 1970
An allowed-unhindered f l - r a y t r a n s i t i o n was o b s e r v e d in the decay of 3 O min 164Tb to a level of 164Dy at 2206 keV energy Thin level ~s i n t e r p r e t e d as a r a t h e r pure f o u r - q u a s t p a r h c l e conhguration
In the framework of the superfluld nuclear model moderately excited, non-rotational states of even-even deformed nuclei can be described as two-quasIpartIcle conflgurations with two extreme cases: pure two-quasipartlcle states conslsting of a single component, and collective states whose wave functions are a snperposition of many two-quaslparhcle configurations Such collective states may also be treated as onephonon excltahons. Direct experimental evidence for a pure twoquasipartlcle structure ts obtained from Its populatIon by a very fast H-ray transition of the type 'allowed-unhindered (au)' with a logfl value of about 4.5 - 5.0 [I]. In the region of deformed nuclei the selection rules for such 'au'-transitions require the same asymptotic quantum numbers [NnzA ] In the initial and the final state. Hence, the structure of the hnal state in the even-even nucleus can be deduced from that of the odd-odd initial nucleus. At higher excltatlon energies, four-quasiparticle states should occur which may superpose to collective states of two-phonon character. Whereas such two-phonon excitations are well known in spherical nuclei, there is only scanty ewdence for their occurence in deformed nucle L and pure four-quampartIcle states have not yet been reported. Again, populatmn of a level by an 'au' H-ray transition should be the most dlrect experimental indication for a pure four-quasiparticle structure provided that a two-quasiparticle structure can be excluded. Normally, pure four-quasipartIcle states are e x p e c t e d at a b o u t 3 M e V e x c i t a t i o n e n e r g y , b u t t h e s p i n s p l i t t i n g e f f e c t m a y l o w e r t h e e n e r g y of p a r t of t h e s t a t e s w h i c h r e s u l t f r o m d i f f e r e n t c o u p l i n g of t h e f o u r q u a s i p a r t i e l e s [2]. T w o 46
phonon excitations should occur at energies corresponding to the sum of the energies of the onephonon excitations involved. We have obtained evidence for four-quasipartIcle and two-phonon states In the deformed nucleus 164Dy when we studied the fi--decay of 164Tb, a nuclide of 3.0 ± 0.I mln half-hfe and 3.5± 0.i MeV decay energy, whose decay properties have not yet been reported in detail. The nuclide 164Tb was produced by bombarding 400 mg samples of DY203 enriched in 164Dy to 92.7% with a 14 MeV neutron flux of about i0 I I cm-2s -I. Under these condltlons, a 3.0 rain. component predominates in the H-ray decay curves and y-ray spectra. It is assigned [3, 4] to the most probable reaction product, 164Tb from 164Dy(n,p) reaction, taking into account that other probable reactions - 164Dy(n, 2n), (n, pn), (n.~) and (n,y) - lead either to stable isotopes (163Dy) or to well-mveshgated nuclides hke 19 rain 163Tb, 3.6 mln 161Gd and 1.3 min 165mDy which are indeed observed as minor components. The asmgnment of the 3.0 rain actlvity to 164Tb is further supported by its decay to already known excited states of 164Dy. With I0 and 30 cm 3 Ge(LI) diodes, v-ray energies were measured to ±0.2 keY for strong and ±0.5 keV for weak v-rays In singles and y-y comcldence spectra. To record fi-ray spectra in the singles and ~-y coincidence mode, a Si(Li) dlode or a plastic scintillator was used. Whenever necessary, the spectra were accumulated by adding the results of many runs. Altogether, 109 y-ray transitions were observed. From the v-ray spectra recorded in coincidence with 17 y-rays and from the fl-y coincidence data, a decay scheme containing 88 transitmns was deduced which comprlses 98~o of
Volume 34B, number 1
PHYSICS
LETTERS
t h e t o t a l ) , - r a y i n t e n s i t y . T h e p o p u l a t i o n of t h e l e v e l s by f l - d e c a y w a s o b t a m e d f r o m i n t e n s i t y b a l a n c e c o n s t d e r a t i o n s a f t e r tt had b e e n p r o v e d t h a t no s t r o n g / % r a y b r a n c h to the g r o u n d s t a t e e x t s t s . A p a r t t a l d e c a y s c h e m e s h o w i n g o n l y the l e v e l s and t r a n s t t t o n s r e l e v a n t to the f o l l o w i n g d t s c u s s t o n t s g t v e n m ftg. 1. About 33% of the f i - r a y t r a n s ~ t t o n s l e a d to l e v e l s not m d t c a t e d m the ftgure. Up to 1225 keV e x c t t a t t o n e n e r g y , the w e l l k n o w n r o t a t t o n a l b a n d s [5] b m l t upon t h e g r o u n d s t a t e , upon the K;r= 2 + g a m m a v t b r a t m n at 762 k e V and upon a K rr = 2- o c t u p o l e v t b r a t t o n at 977 keV are o b s e r v e d For both vtbrattonal s t a t e s , t h e t h e o r e t t c a l l y p r e d t c t e d c o n t r t b u t t o n s [6] of two-quas,parttcle states are gtven as mserts m fig. 1. The m o s t m t e r e s t m g f e a t u r e of t h t s d e c a y s c h e m e t s the s t r o n g p o p u l a t t o n - 44% of all ~ r a y t r a n s i t i o n s - of a l e v e l at 2206 k e V e n e r g y . T h e l o g f l v a l u e of 4.8 f o r t h t s f l - r a y t r a n m t i o n i n d t c a t e s an ' a u ' - t r a n s , t t o n f r o m the g r o u n d s t a t e of 164Tb to t h a t s t a t e m 164Dy. F u r t h e r d, s c u s -
18 January 1971
s t o n r e q u t r e s t h e k n o w l e d g e of t h e s p m and p a r t t y of b o t h s t a t e s r e v o l v e d . S m c e t e c h m q u e s f o r d ~ r e c t d e t e r m m a t m n of t h e q u a n t u m n u m b e r s c a n not b e a p p h e d m the p r e s e n t c a s e , s e v e r a l m d t r e c t a r g u m e n t s h a v e to b e c o m b i n e d . F t r s t , f o r the 2206 keV l e v e l , I ~ = 3 + o r 4 + f o l l o w s l r o m the o b s e r v a t t o n that t h e d e p o p u l a t i n g y - r a y s f e e d k n o w n l e v e l s w t t h I ~ - 2 + to 5 + and 3-. S e c o n d , c o n c e r n i n g the g r o u n d s t a t e of 164Tb 65 99 , m s p e c t t o n of the N f l s s o n o r b t t a l s o c c u p t e d by t h e 65th p r o t o n and 99th n e u t r o n m n e t g h b o u r m g n u c l e t and t h e t r a d j a c e n t o r b t t a l s [7] r e v e a l s only two s t r u c t u r e s w h t e h w o u l d d e c a y by an a l l o w e d f l - t r a n s i t t o n to an I rr = 3 + o r 4 + s t a t e : the s t r u c t u r e p~+[411t] + n } ~ [ 6 3 3 t ] c o u p h n g [8] to I r' : 5 + but e x c l u d l n g I rr = 3 + f o r t h e f m a l s t a t e , and t h e s t r u c t u r e I rr = 3 + , p ~ - [ 5 2 3 ~ ] - n~-[5215] e x p e c t e d f o r t h e 67th p r o t o n and 101th n e u t r o n and, h e n c e , m u c h l e s s h k e l y t h a n the f o r m e r s t r u c t u r e . In the l a t t e r c a s e , s t r o n g / 3 - r a y t r a n s t t m n s to t h e K r; = 2 + r o t a t t o n a l b a n d s h o u l d o c c u r w h i c h a r e not o b s e r v e d e x p e r i m e n t a l l y . T h t s g i v e s f u r t h e r s u p p o r t f o r the f o r m e r s t r u c -
16~,. 9g 30ram
65TD 5+
pl411~] n[633#]
Qp:35~01MeV
(53).
04 I~.
(4g)-
11
(55)
,, ,,
,,
.] (C5'6+)
30055
(&+,5+)
,,
3001 4
], , (4*)
2752 7
. ~ ~.~ _=~. _~.~ i'~ 31 44 11
(58) (¢8).
7
~
Is4, . . . . . . . . .
~
~--- ~
08
(70) ~7--7~2:
,,
++1 I+ III
37
(651
lilt
[P[°/°],(Iogft) l
[:
I 1 4,':
1523tl o[411lJ nn 1633#] *15211I I~11II p141Ii ] 16131] n[521#] pp
K. t~
I II I
1, ii
4.5 +
IIII
AI
II +
'+ '+
III
+
I
}I
22060 23127
2194 6
4 5 - - -
4,4-__
1588;
4
I154 I122 8103g 3
_/tK~2:I
Z ~-+6° 8z82
~--
t
1686 7
~I024 8 975 8
pp[4111] 152]#]75% -- ?~18 [nn [6]],, 15,1,~
501 3 24Z Z 73~, K'! 0+ [
16&_ 98
E [keY]
56UY Ftg 1. Partial decay s c h e m e of 164Tb
Energy levels, fl- a n d ) , - r a y transtttons not relevant to the p r e s e n t discussion have been left out 47
Volume 34B, n u m b e r 1
PHYSICS
ture for which such translt,ons are K-forbidden. T h u s , we c o n c l u d e to t h e s t r u c t u r e p[411~] + n[633~] f o r t h e g r o u n d s t a t e of 1 6 4 T b a n d I ~ =4 + f o r t h e 2206 k e V l e v e l o f 164Dy. T h e r e a r e two I ~ - 4+ two-quamparticle eonflguratmns theoretic a l l y p r e d m t e d [6] in 164Dy at e x c i t a t i o n e n e r g i e s b e t w e e n 1 4 a n d 2 9 M e V , a s s h o w n r a t a b l e 1. N o n e of t h e s e s t a t e s c a n b e fed, h o w e v e r , f r o m t h e g r o u n d s t a t e of 1 6 4 T b by a B - r a y t r a n s i t i o n of the type 'au'. T h e r e f o r e , t h e 2206 k e V s t a t e i s s u g g e s t e d to b e a r a t h e r p u r e f o u r - q u a m p a r t m l e s t a t e of t h e k i n d 2 p , 2 n , b e c a u s e B - r a y t r a n s i t i o n s to 4 n - o r 4 p - s t a t e s a r e F - f o r b i d d e n [9]. A c c o r d i n g to t h e o r e t i c a l c a l c u l a t i o n s ~6], t h e l o w e s t t w o - q u a s i p a r t i c l e s t a t e s in 16"~Dy a r e pp[411~] - [523~] a n d nn[523~] + [ 6 3 3 t l . T h e i r c o m b i n a t i o n p[4111] - p[5231] + n[523 H + n[633~] is p r o p o s e d for t h e 2206 k e V l e v e l . T h e B - d e c a y o c c u r s b e t w e e n t h e orbitals n~-[523~] ~ p7-[523~] while the compon e n t p[411~] + n[633#], r e p r e s e n t i n g t h e c o n f i g u r a t i o n of t h e i n i t i a l s t a t e , r e m a i n s u n c h a n g e d . If t h e 2206 k e V l e v e l i s of p u r e f o u r - q u a s i particle character, electromagnetic single-particle transitions from this level are strmtly forbidden. Thus, either this state should have a rather long lifetime or the deexcltatlon should o c c u r t h r o u g h s m a l l a d m i x t u r e s of o t h e r c o n h g u rattans like the two-phonon gamma vibration or t h e t w o - q u a m p a r t l c l e s t a t e s h s t e d in t a b l e 1. F r o m o u r f i - y c o i n c i d e n c e e x p e r i m e n t s it f o l l o w s that the hfetlme is less than 200ns. Even a m u c h s h o r t e r v a l u e , l e s s t h a n 0.1 n s , w a s r e ported for a rather pure three-quam-particle s t a t e in 1 7 5 y b [10]. It i s i n t e r e s t i n g t h a t t h e b r a n c h i n g r a t i o s f r o m t h e 2206 k e V l e v e l into t h e gamma vibrational band calculated assuming pure E2 t r a n m t i o n s a r e in d i s a g r e e m e n t w i t h t h e o r e t i c a l p r e d i c t i o n s [11]. T h e low f t v a l u e s of t h e B - r a y t r a n s i t i o n s to t h e l e v e l s at 2195, 2753, 3001 a n d 3005 k e V energy indicate that the four-quasiparticle comp o n e n t f o r m i n g t h e 2206 k e V l e v e l i s d i s t r i b u t e d o v e r s e v e r a l l e v e l s , e s p e c i a l l y t h e fir=4+ l e v e l at 2195 k e V w h i c h p o p u l a t e s t h e s a m e l e v e l s a s t h e 2206 k e V l e v e l d o e s but w i t h d i f f e r e n t b r a n c h i n g s a n d p o p u l a t i o n b y a B - r a y t r a n s i t i o n of h i g h e r l o g ft v a l u e . T h e s t a t e at 2313 k e V e n e r g y i s m o s t l i k e l y t h e f i r s t r o t a t m n a l l e v e l to e i t h e r t h e 2206 o r t h e 2195 k e V l e v e l . A n o t h e r 2p, 2n f o u r - q u a m p a r t i c l e c o n f i g u r a t i o n , n a m e l y p [ 4 1 1 t ] + p [ 4 1 1 ; ] + n[633~] - n[5211] m a y c o n t r i b u t e to t h e / 7 r = 4 - l e v e l at 1588 k e V e n e r g y a n d to t h e r o t a t i o n a l b a n d b u i l t upon t h i s s t a t e . T h e 1588 k e V l e v e l c a n a l s o b e i n t e r p r e t e d [12] a s a t w o - p h o n o n s t a t e ' q u a d r u p o l e 2 + (762 keV) 48
LETTERS
18 J a n u a r y 1971
Table 1 Theoretically predmted high-energy I~= 4 + levels in 164Dy and expected log f t values for H-ray t r a n s i t i o n s of 164Tb to these states Configuration
Ene rgy [MeV]
B--decay of 164Tb type log f t
p[413~] +p[411~]
2.1a)
n[521~'] + n[523~]
2.9 a)
ah(AN=2) aF
6
high
7
p[411~] - p [ 5 2 3 ~ ] + 3 0b) n[523~] + n[633~]
au
4.5-5 O
a) F r o m r e f [6]. b) From r e f [2] p l u s o c t u p o l e 2- (977 keV) e x c i t a t i o n s e x p e c t e d to l e a d to a l e v e l at a b o u t 1700 k e V e n e r g y . T h e l o g f l v a l u e of 6.5 f o r t h e f l - r a y b r a n c h to t h i s l e v e l i s in a g r e e m e n t w i t h t h l ~ i n t e r p r e t a t i o n , s i n c e t h e d e c a y to s u c h a t w o - p h o n o n c o n h g u r a t l o n s h o u l d b e h i n d e r e d [12] by a f a c t o r of 5 c o m p a r e d to t h e s i n g l e - p a r t i c l e t r a n s i t , o n n[521~] ~ p[4111 ]. In a d d i t i o n , t h e t w o - q u a s i p a r t l c l e c o n f i g u r a t i o n s [6] pp[523~] -~ [411~] and nn[633~] + [521~] m a y also contribute. The reduced branching ratios f o r E2 t r a n s i t i o n s f r o m t h e l e v e l s of t h i s K n = 4h a n d to t h o s e of t h e K ~ = 2- b a n d a r e in good a g r e e m e n t w i t h t h e o r e t i c a l p r e d i c t i o n s [11]. W e a r e i n d e b t e d to P r o f e s s o r A. F a e s s l e r f o r v e r y v a l u a b l e d i s c u s s i o n s a n d to P r o f e s s o r s W. G r e m e r a n d V. G. S o l o v l e v f o r t h e i r c o m m e n t s , to H. H e r t e r f o r p r o v i d i n g a h i g h flux of 14 M e V n e u t r o n s , a n d to K. H. Gl~isel a n d U. T h a r u n f o r t h e i r a s s i s t a n c e . W e w i s h to t h a n k t h e B u n d e s m i m s t e rium fur Bildung und Wissenschaft for financial support.
References [1] J. Z y h c z , P. G. Hansen, H. L Nielsen and K. Wilsky, Arklv Fymk 36 (1967) 643 [2] V G. Soloviev, private commumcation. [3] N. Kaffrell and G. H e r r m a n n , Verh. Dtsch Physik Ges., 5 (1967) 368 [4] E Monnand and A. Moussa, J Physique 29 (1968) 545. [5] O. W. B. Schult, U Gruber, B. P. Maier and F. W. Stanek, Z. Phymk 180 (1964) 298. [6] N I Pyatov and V. G. Soloviev, Izv. Akad. Nauk SSSR (Ser. flz.) 28 (1964) 321. [7] O. Nathan and S. G. Nllsson, m: Alpha-, beta- and g a m m a - r a y spectroscopy, ed K. Smgbahn (NorthHolland, A m s t e r d a m , 1965) p. 664-672. [81 C. J. Gallagher and S. A. Moszkowski, Phys Rev. 111 (1958) 1282. [9] V G. Soloviev, Soviet Physics J E T P 43 (1962) 246. [1oj L Funke et al., Nuel. Phys A130 (1969) 333. [ii] G. Alaga, K. Alder, A. Bohr and B R. Mottelson, Mat. Fys Dan Vld. Selsk. 29, No. 9 (1955). [121 V. G Soloviev, Yadern. Flz. 10 (1969) 297.
34]3, number
1
EVIDENCE
PHYSICS
FOR
LETTERS
A FOUR-QUASIPARTICLE DEFORMED NUCLEUS
18 January 1971
STATE
IN
THE
164Dy
N. KAFFRELL and G. HERRMANN Inst~tut f u r Anorganlsche Chemic und Kernchern~e der Untt'ers~tat, D-65 Maznz, W.-Gerrnany
Received 2 December 1970
An allowed-unhindered f l - r a y t r a n s i t i o n was o b s e r v e d in the decay of 3 O min 164Tb to a level of 164Dy at 2206 keV energy Thin level ~s i n t e r p r e t e d as a r a t h e r pure f o u r - q u a s t p a r h c l e conhguration
In the framework of the superfluld nuclear model moderately excited, non-rotational states of even-even deformed nuclei can be described as two-quasIpartIcle conflgurations with two extreme cases: pure two-quasipartlcle states conslsting of a single component, and collective states whose wave functions are a snperposition of many two-quaslparhcle configurations Such collective states may also be treated as onephonon excltahons. Direct experimental evidence for a pure twoquasipartlcle structure ts obtained from Its populatIon by a very fast H-ray transition of the type 'allowed-unhindered (au)' with a logfl value of about 4.5 - 5.0 [I]. In the region of deformed nuclei the selection rules for such 'au'-transitions require the same asymptotic quantum numbers [NnzA ] In the initial and the final state. Hence, the structure of the hnal state in the even-even nucleus can be deduced from that of the odd-odd initial nucleus. At higher excltatlon energies, four-quasiparticle states should occur which may superpose to collective states of two-phonon character. Whereas such two-phonon excitations are well known in spherical nuclei, there is only scanty ewdence for their occurence in deformed nucle L and pure four-quampartIcle states have not yet been reported. Again, populatmn of a level by an 'au' H-ray transition should be the most dlrect experimental indication for a pure four-quasiparticle structure provided that a two-quasiparticle structure can be excluded. Normally, pure four-quasipartIcle states are e x p e c t e d at a b o u t 3 M e V e x c i t a t i o n e n e r g y , b u t t h e s p i n s p l i t t i n g e f f e c t m a y l o w e r t h e e n e r g y of p a r t of t h e s t a t e s w h i c h r e s u l t f r o m d i f f e r e n t c o u p l i n g of t h e f o u r q u a s i p a r t i e l e s [2]. T w o 46
phonon excitations should occur at energies corresponding to the sum of the energies of the onephonon excitations involved. We have obtained evidence for four-quasipartIcle and two-phonon states In the deformed nucleus 164Dy when we studied the fi--decay of 164Tb, a nuclide of 3.0 ± 0.I mln half-hfe and 3.5± 0.i MeV decay energy, whose decay properties have not yet been reported in detail. The nuclide 164Tb was produced by bombarding 400 mg samples of DY203 enriched in 164Dy to 92.7% with a 14 MeV neutron flux of about i0 I I cm-2s -I. Under these condltlons, a 3.0 rain. component predominates in the H-ray decay curves and y-ray spectra. It is assigned [3, 4] to the most probable reaction product, 164Tb from 164Dy(n,p) reaction, taking into account that other probable reactions - 164Dy(n, 2n), (n, pn), (n.~) and (n,y) - lead either to stable isotopes (163Dy) or to well-mveshgated nuclides hke 19 rain 163Tb, 3.6 mln 161Gd and 1.3 min 165mDy which are indeed observed as minor components. The asmgnment of the 3.0 rain actlvity to 164Tb is further supported by its decay to already known excited states of 164Dy. With I0 and 30 cm 3 Ge(LI) diodes, v-ray energies were measured to ±0.2 keY for strong and ±0.5 keV for weak v-rays In singles and y-y comcldence spectra. To record fi-ray spectra in the singles and ~-y coincidence mode, a Si(Li) dlode or a plastic scintillator was used. Whenever necessary, the spectra were accumulated by adding the results of many runs. Altogether, 109 y-ray transitions were observed. From the v-ray spectra recorded in coincidence with 17 y-rays and from the fl-y coincidence data, a decay scheme containing 88 transitmns was deduced which comprlses 98~o of
Volume 34B, number 1
PHYSICS
LETTERS
t h e t o t a l ) , - r a y i n t e n s i t y . T h e p o p u l a t i o n of t h e l e v e l s by f l - d e c a y w a s o b t a m e d f r o m i n t e n s i t y b a l a n c e c o n s t d e r a t i o n s a f t e r tt had b e e n p r o v e d t h a t no s t r o n g / % r a y b r a n c h to the g r o u n d s t a t e e x t s t s . A p a r t t a l d e c a y s c h e m e s h o w i n g o n l y the l e v e l s and t r a n s t t t o n s r e l e v a n t to the f o l l o w i n g d t s c u s s t o n t s g t v e n m ftg. 1. About 33% of the f i - r a y t r a n s ~ t t o n s l e a d to l e v e l s not m d t c a t e d m the ftgure. Up to 1225 keV e x c t t a t t o n e n e r g y , the w e l l k n o w n r o t a t t o n a l b a n d s [5] b m l t upon t h e g r o u n d s t a t e , upon the K;r= 2 + g a m m a v t b r a t m n at 762 k e V and upon a K rr = 2- o c t u p o l e v t b r a t t o n at 977 keV are o b s e r v e d For both vtbrattonal s t a t e s , t h e t h e o r e t t c a l l y p r e d t c t e d c o n t r t b u t t o n s [6] of two-quas,parttcle states are gtven as mserts m fig. 1. The m o s t m t e r e s t m g f e a t u r e of t h t s d e c a y s c h e m e t s the s t r o n g p o p u l a t t o n - 44% of all ~ r a y t r a n s i t i o n s - of a l e v e l at 2206 k e V e n e r g y . T h e l o g f l v a l u e of 4.8 f o r t h t s f l - r a y t r a n m t i o n i n d t c a t e s an ' a u ' - t r a n s , t t o n f r o m the g r o u n d s t a t e of 164Tb to t h a t s t a t e m 164Dy. F u r t h e r d, s c u s -
18 January 1971
s t o n r e q u t r e s t h e k n o w l e d g e of t h e s p m and p a r t t y of b o t h s t a t e s r e v o l v e d . S m c e t e c h m q u e s f o r d ~ r e c t d e t e r m m a t m n of t h e q u a n t u m n u m b e r s c a n not b e a p p h e d m the p r e s e n t c a s e , s e v e r a l m d t r e c t a r g u m e n t s h a v e to b e c o m b i n e d . F t r s t , f o r the 2206 keV l e v e l , I ~ = 3 + o r 4 + f o l l o w s l r o m the o b s e r v a t t o n that t h e d e p o p u l a t i n g y - r a y s f e e d k n o w n l e v e l s w t t h I ~ - 2 + to 5 + and 3-. S e c o n d , c o n c e r n i n g the g r o u n d s t a t e of 164Tb 65 99 , m s p e c t t o n of the N f l s s o n o r b t t a l s o c c u p t e d by t h e 65th p r o t o n and 99th n e u t r o n m n e t g h b o u r m g n u c l e t and t h e t r a d j a c e n t o r b t t a l s [7] r e v e a l s only two s t r u c t u r e s w h t e h w o u l d d e c a y by an a l l o w e d f l - t r a n s i t t o n to an I rr = 3 + o r 4 + s t a t e : the s t r u c t u r e p~+[411t] + n } ~ [ 6 3 3 t ] c o u p h n g [8] to I r' : 5 + but e x c l u d l n g I rr = 3 + f o r t h e f m a l s t a t e , and t h e s t r u c t u r e I rr = 3 + , p ~ - [ 5 2 3 ~ ] - n~-[5215] e x p e c t e d f o r t h e 67th p r o t o n and 101th n e u t r o n and, h e n c e , m u c h l e s s h k e l y t h a n the f o r m e r s t r u c t u r e . In the l a t t e r c a s e , s t r o n g / 3 - r a y t r a n s t t m n s to t h e K r; = 2 + r o t a t t o n a l b a n d s h o u l d o c c u r w h i c h a r e not o b s e r v e d e x p e r i m e n t a l l y . T h t s g i v e s f u r t h e r s u p p o r t f o r the f o r m e r s t r u c -
16~,. 9g 30ram
65TD 5+
pl411~] n[633#]
Qp:35~01MeV
(53).
04 I~.
(4g)-
11
(55)
,, ,,
,,
.] (C5'6+)
30055
(&+,5+)
,,
3001 4
], , (4*)
2752 7
. ~ ~.~ _=~. _~.~ i'~ 31 44 11
(58) (¢8).
7
~
Is4, . . . . . . . . .
~
~--- ~
08
(70) ~7--7~2:
,,
++1 I+ III
37
(651
lilt
[P[°/°],(Iogft) l
[:
I 1 4,':
1523tl o[411lJ nn 1633#] *15211I I~11II p141Ii ] 16131] n[521#] pp
K. t~
I II I
1, ii
4.5 +
IIII
AI
II +
'+ '+
III
+
I
}I
22060 23127
2194 6
4 5 - - -
4,4-__
1588;
4
I154 I122 8103g 3
_/tK~2:I
Z ~-+6° 8z82
~--
t
1686 7
~I024 8 975 8
pp[4111] 152]#]75% -- ?~18 [nn [6]],, 15,1,~
501 3 24Z Z 73~, K'! 0+ [
16&_ 98
E [keY]
56UY Ftg 1. Partial decay s c h e m e of 164Tb
Energy levels, fl- a n d ) , - r a y transtttons not relevant to the p r e s e n t discussion have been left out 47
Volume 34B, n u m b e r 1
PHYSICS
ture for which such translt,ons are K-forbidden. T h u s , we c o n c l u d e to t h e s t r u c t u r e p[411~] + n[633~] f o r t h e g r o u n d s t a t e of 1 6 4 T b a n d I ~ =4 + f o r t h e 2206 k e V l e v e l o f 164Dy. T h e r e a r e two I ~ - 4+ two-quamparticle eonflguratmns theoretic a l l y p r e d m t e d [6] in 164Dy at e x c i t a t i o n e n e r g i e s b e t w e e n 1 4 a n d 2 9 M e V , a s s h o w n r a t a b l e 1. N o n e of t h e s e s t a t e s c a n b e fed, h o w e v e r , f r o m t h e g r o u n d s t a t e of 1 6 4 T b by a B - r a y t r a n s i t i o n of the type 'au'. T h e r e f o r e , t h e 2206 k e V s t a t e i s s u g g e s t e d to b e a r a t h e r p u r e f o u r - q u a m p a r t m l e s t a t e of t h e k i n d 2 p , 2 n , b e c a u s e B - r a y t r a n s i t i o n s to 4 n - o r 4 p - s t a t e s a r e F - f o r b i d d e n [9]. A c c o r d i n g to t h e o r e t i c a l c a l c u l a t i o n s ~6], t h e l o w e s t t w o - q u a s i p a r t i c l e s t a t e s in 16"~Dy a r e pp[411~] - [523~] a n d nn[523~] + [ 6 3 3 t l . T h e i r c o m b i n a t i o n p[4111] - p[5231] + n[523 H + n[633~] is p r o p o s e d for t h e 2206 k e V l e v e l . T h e B - d e c a y o c c u r s b e t w e e n t h e orbitals n~-[523~] ~ p7-[523~] while the compon e n t p[411~] + n[633#], r e p r e s e n t i n g t h e c o n f i g u r a t i o n of t h e i n i t i a l s t a t e , r e m a i n s u n c h a n g e d . If t h e 2206 k e V l e v e l i s of p u r e f o u r - q u a s i particle character, electromagnetic single-particle transitions from this level are strmtly forbidden. Thus, either this state should have a rather long lifetime or the deexcltatlon should o c c u r t h r o u g h s m a l l a d m i x t u r e s of o t h e r c o n h g u rattans like the two-phonon gamma vibration or t h e t w o - q u a m p a r t l c l e s t a t e s h s t e d in t a b l e 1. F r o m o u r f i - y c o i n c i d e n c e e x p e r i m e n t s it f o l l o w s that the hfetlme is less than 200ns. Even a m u c h s h o r t e r v a l u e , l e s s t h a n 0.1 n s , w a s r e ported for a rather pure three-quam-particle s t a t e in 1 7 5 y b [10]. It i s i n t e r e s t i n g t h a t t h e b r a n c h i n g r a t i o s f r o m t h e 2206 k e V l e v e l into t h e gamma vibrational band calculated assuming pure E2 t r a n m t i o n s a r e in d i s a g r e e m e n t w i t h t h e o r e t i c a l p r e d i c t i o n s [11]. T h e low f t v a l u e s of t h e B - r a y t r a n s i t i o n s to t h e l e v e l s at 2195, 2753, 3001 a n d 3005 k e V energy indicate that the four-quasiparticle comp o n e n t f o r m i n g t h e 2206 k e V l e v e l i s d i s t r i b u t e d o v e r s e v e r a l l e v e l s , e s p e c i a l l y t h e fir=4+ l e v e l at 2195 k e V w h i c h p o p u l a t e s t h e s a m e l e v e l s a s t h e 2206 k e V l e v e l d o e s but w i t h d i f f e r e n t b r a n c h i n g s a n d p o p u l a t i o n b y a B - r a y t r a n s i t i o n of h i g h e r l o g ft v a l u e . T h e s t a t e at 2313 k e V e n e r g y i s m o s t l i k e l y t h e f i r s t r o t a t m n a l l e v e l to e i t h e r t h e 2206 o r t h e 2195 k e V l e v e l . A n o t h e r 2p, 2n f o u r - q u a m p a r t i c l e c o n f i g u r a t i o n , n a m e l y p [ 4 1 1 t ] + p [ 4 1 1 ; ] + n[633~] - n[5211] m a y c o n t r i b u t e to t h e / 7 r = 4 - l e v e l at 1588 k e V e n e r g y a n d to t h e r o t a t i o n a l b a n d b u i l t upon t h i s s t a t e . T h e 1588 k e V l e v e l c a n a l s o b e i n t e r p r e t e d [12] a s a t w o - p h o n o n s t a t e ' q u a d r u p o l e 2 + (762 keV) 48
LETTERS
18 J a n u a r y 1971
Table 1 Theoretically predmted high-energy I~= 4 + levels in 164Dy and expected log f t values for H-ray t r a n s i t i o n s of 164Tb to these states Configuration
Ene rgy [MeV]
B--decay of 164Tb type log f t
p[413~] +p[411~]
2.1a)
n[521~'] + n[523~]
2.9 a)
ah(AN=2) aF
6
high
7
p[411~] - p [ 5 2 3 ~ ] + 3 0b) n[523~] + n[633~]
au
4.5-5 O
a) F r o m r e f [6]. b) From r e f [2] p l u s o c t u p o l e 2- (977 keV) e x c i t a t i o n s e x p e c t e d to l e a d to a l e v e l at a b o u t 1700 k e V e n e r g y . T h e l o g f l v a l u e of 6.5 f o r t h e f l - r a y b r a n c h to t h i s l e v e l i s in a g r e e m e n t w i t h t h l ~ i n t e r p r e t a t i o n , s i n c e t h e d e c a y to s u c h a t w o - p h o n o n c o n h g u r a t l o n s h o u l d b e h i n d e r e d [12] by a f a c t o r of 5 c o m p a r e d to t h e s i n g l e - p a r t i c l e t r a n s i t , o n n[521~] ~ p[4111 ]. In a d d i t i o n , t h e t w o - q u a s i p a r t l c l e c o n f i g u r a t i o n s [6] pp[523~] -~ [411~] and nn[633~] + [521~] m a y also contribute. The reduced branching ratios f o r E2 t r a n s i t i o n s f r o m t h e l e v e l s of t h i s K n = 4h a n d to t h o s e of t h e K ~ = 2- b a n d a r e in good a g r e e m e n t w i t h t h e o r e t i c a l p r e d i c t i o n s [11]. W e a r e i n d e b t e d to P r o f e s s o r A. F a e s s l e r f o r v e r y v a l u a b l e d i s c u s s i o n s a n d to P r o f e s s o r s W. G r e m e r a n d V. G. S o l o v l e v f o r t h e i r c o m m e n t s , to H. H e r t e r f o r p r o v i d i n g a h i g h flux of 14 M e V n e u t r o n s , a n d to K. H. Gl~isel a n d U. T h a r u n f o r t h e i r a s s i s t a n c e . W e w i s h to t h a n k t h e B u n d e s m i m s t e rium fur Bildung und Wissenschaft for financial support.
References [1] J. Z y h c z , P. G. Hansen, H. L Nielsen and K. Wilsky, Arklv Fymk 36 (1967) 643 [2] V G. Soloviev, private commumcation. [3] N. Kaffrell and G. H e r r m a n n , Verh. Dtsch Physik Ges., 5 (1967) 368 [4] E Monnand and A. Moussa, J Physique 29 (1968) 545. [5] O. W. B. Schult, U Gruber, B. P. Maier and F. W. Stanek, Z. Phymk 180 (1964) 298. [6] N I Pyatov and V. G. Soloviev, Izv. Akad. Nauk SSSR (Ser. flz.) 28 (1964) 321. [7] O. Nathan and S. G. Nllsson, m: Alpha-, beta- and g a m m a - r a y spectroscopy, ed K. Smgbahn (NorthHolland, A m s t e r d a m , 1965) p. 664-672. [81 C. J. Gallagher and S. A. Moszkowski, Phys Rev. 111 (1958) 1282. [9] V G. Soloviev, Soviet Physics J E T P 43 (1962) 246. [1oj L Funke et al., Nuel. Phys A130 (1969) 333. [ii] G. Alaga, K. Alder, A. Bohr and B R. Mottelson, Mat. Fys Dan Vld. Selsk. 29, No. 9 (1955). [121 V. G Soloviev, Yadern. Flz. 10 (1969) 297.