47 Massive Transfer Reactions and the Structure of Transitional A ~ 100 Nuclei D. R. Haenni, H. Dejbakhsh, and R. P. Schmitt Cyclotron Institute, Texas A&M University, College Station, TX 77834 Band crossings and other features of the mass 100 transitional nuclei have been studied with massive transfer and fusion reaction based γ-ray spectroscopy.
Experimental blocking
argument results and calculations agree that υh 2 alignment is responsible for the band crossing in Ru. 11/2
102
soft core of
The
103
Rh is influenced by the configuration of the
odd proton; however, the mechanism for this is not clear. High-spin features of the t r a n s i t i o n a l ( Z < 5 0 , N>50) a r e i n t e r e s t i n g
but not well
change between 58 and 60 n e u t r o n s . three d i f f e r e n t
closed o r b i t a l
B a c k b e n d i n g i s known f o r w i t h cranked s h e l l
model
present discussion w i l l
1
0
4
,
1
0
configurations 6
pd
T h e r e i s an a b r u p t
c e n t e r around
1 0 2
comparisons
have been made [ S T A 8 4 ] .
R u and
1 0 3
The
R h w h i c h bave N=58 and a r e
closures.
Most o f t h e n u c l e i
The i n v e s t i g a t i o n o f h i g h - s p i n
v i a in-beam γ - r a y spectroscopy w i t h the usual h i n d e r e d by t h e l a c k o f s u i t a b l e
to
( Z = 4 0 , Z = 5 0 , and N = 5 0 ) .
t o s t u d y s i n c e t h e y l i e on t h e n e u t r o n
side o f the v a l l e y o f s t a b i l i t y .
shape
are a l s o t r a n s i t i o n a l
[GRA76] b u t o n l y s c h e m a t i c
midway between t h e 40 and 50 p r o t o n o r b i t a l
i n general
i n t h e mass 100 r e g i o n
studied.
These n u c l e i
(CSM) p r e d i c t i o n s
t h i s mass r e g i o n a r e d i f f i c u l t
nuclei
(ΗΙ,χηγ)
in
rich
phenomenon
fusion reactions
is
targets.
P a r t o f t h e s p e c t r o s c o p y program a t TAMU i s t h e d e v e l o p m e n t o f t h e so c a l l e d massive t r a n s f e r structure
studies.
of a projectile
(MT) o r b r e a k - u p f u s i o n r e a c t i o n s f o r
B a s i c a l l y these heavy-ion r e a c t i o n s
discrete-line
involve the
transfer
fragment t o the t a r g e t w i t h the remaining energetic
fragment
being emitted i n the forward d i r e c t i o n .
W i t h MT r e a c t i o n s one t e n d s
to
o b s e r v e a b e t t e r p o p u l a t i o n o f h i g h - s p i n s t a t e s when compared t o t h e corresponding fusion r e a c t i o n . also provide a sort of e x i t the study o f nuclei
D e t e c t i o n o f t h e e m i t t e d l i g h t f r a g m e n t can
channel
filter.
These f e a t u r e s can be u s e f u l
in
w h i c h a r e more n e u t r o n r i c h t h a n n o r m a l l y a c c e s s i b l e by 0097-6156/86/0324-0311$06.00/ 0 © 1986 American Chemical Society
312
NUCLEI OFF THE LINE OF STABILITY
( H I , χηγ) r e a c t i o n s , , Further d e t a i l s concerning γ-ray spectroscopy MT r e a c t i o n s can be f o u n d e l s e w h e r e [HAE82] .
with
E x p e r i m e n t a l l y p a r t i c l e - γ and p a r t i c l e - γ - γ c o i n c i d e n c e s a r e m e a s u r e d . W i t h beams h e a v i e r t h a n L i a γ - r a y m u l t i p l i c i t y select high-multiplicity energetic particles measurement i t
filter
i s needed t o
MT e v e n t s f r o m o t h e r r e a c t i o n s w h i c h r e s u l t
b u t low m u l t i p l i c i t i e s .
in
From a s i n g l e MT s p e c t r o s c o p y
i s p o s s i b l e t o s i m u l t a n e o u s l y o b t a i n much o f t h e
usual
4803 4052 -(25/2*)
3431
3214
3109
2704
21/2* 19/2*
2318
1874-
1554
2
4
1
8
1716-
1400 1332 642 590
2802
-
*
2680-
-23/2*
2804
-17/2*
2132-
-19/2*
2 I / 2
2
93 - L - L 9/2*
^
3 / 2
1
774 -
i /2-
2
9/2* Τ 772*
-
5
1.
Partial
102
level
10 - (A) 1 0 4
Pd GSB
Τ
l04
Ru
0 "
l 0 2
l 0 0
excita
t i o n f u n c t i o n , c r o s s bombardment,
angular
lcÎ2
R u GSB
its
Ru
" ^ " ^
( ίι,χηγ) 7
Rh9/2*
1 0 1
R u GSB 0.2
03 0.4 0.5 h ω (MeV)
These
Each
results
MT r e a c t i o n s 1 0 0
Mo
t a r g e t a t 49
and 77 MeV, r e s p e c t i v e l y and c o n v e n t i o n a l
T c 9/2*
, 0 2
and
i n d u c e d on a m e t a l l i c
l 0 l
l 0 3
Ru and
neighbors are given i n F i g . 1 .
Institute with \ i
s
5 - RuH/2l0l
schemes f o r
were o b t a i n e d a t t h e TAMU C y c l o t r o n
I T ^ R u 7/2* Ru5/2* _ l0,
l 0 3
level
band c o n t a i n s new l e v e l s .
2
' (C)
several
channels. 102
Partial
Ru7/ **V
Rhi/2>^
for
R u GSB"
\
5 l03
2.
nuclei.
G S B / ^
'
l 0 3
Fig.
-15/2-
' -
experimental γ - r a y data ( s i n g l e s ,
RuGSB"V^
10
0
-I9/2"
4
Ru and n e i g h b o r i n g
adjacent e x i t
0 10
-23/2"
d i s t r i b u t i o n , and c o i n c i d e n c e )
5
M
-27/2"
2132
,443-
i — l 9/ «
Fig.
3080-
0.6
P a r t i c l e alignment
vs
r o t a t i o n a l f r e q u e n c y f o r bands 102 Ru and n e i g h b o r i n g n u c l e i .
s p e c t r o s c o p y a t 45 MeV.
For
R u o t h e r bands were a l s o p o p u l a t e d
but
t h e y c o u l d n o t be e x t e n d e d t o h i g h e r s p i n s than p r e v i o u s l y r e p o r t e d [KLA82]. The 104 Ru l e v e l
scheme a g r e e s w i t h
Coulomb e x c i t a t i o n work
recent
[STA84].
Massive Transfer Reactions
47. HAENNI ET AL.
313 102
The y r a s t cascade i n ι
π—
1
backbend w i t h a c r o s s i n g f r e q u e n c y o f
1
l 0 2
Ο.370ω and an a l i g n m e n t g a i n o f 9 . 5 t f . The u s u a l a l i g n m e n t p l o t s [BEN79] i n F i g . 2a 102 compare Ru w i t h a d j a c e n t e v e n - e v e n 104 nuclei. Except f o r Pd t h e r e f e r e n c e 102 band f o r Ru i s used t o g e n e r a t e t h e s e plots. Both R u [VOI76] and R u show upbends w i t h t h e f o r m e r a t a h i g h e r 102 frequency than Ru. The e x p e r i m e n t a l in?
Ru
w V\ v\ V
\\
\
^ \* \
Ii_ _y_ Neutron
-0.5
0°
B
0.14
10°
C
0.20
-10°
D
\
2
0.17
Proton ~
i/hn, ll/
A
\
Y
-
1 0 0
wai 0.05
w
-60°
A
\ -
04 ticu
1 0 4
R o u t h i a n [BEN79] f o r
(MeV)
w i t h CSM p r e d i c t i o n s Fig.
3. in?
for
Experimental
Ru shows a
routhian
u
Ru i s compared
(triaxial
version)
[FRA83] i n F i g . 3 assuming e i t h e r t h e vh or ïïg alignment. From t h e s e LL/ά via 1 0 2 1
Ru compared w i t h CSM.
1
/
0
Q/0
c a l c u l a t i o n s t h e backbend i n
Ru s h o u l d
a r i s e from v h ^ ^ alignment w i t h a small positive ε
d e f o r m a t i o n and perhaps a
2
s l i g h t l y positive γ deformation. T h i s c o n c l u s i o n s h o u l d be t e s t e d t h r o u g h b l o c k i n g arguments based on t h e s i n g l e q u a s i p a r t i c l e bands i n t h e a d j a c e n t odd-A n u c l e i . 102 been o b t a i n e d t h r o u g h t h i s work f o r a l l t h e n e i g h b o r s o f bands based on v d ^ f r e q u e n c y as
1 0 2
2
, vg^
a 2
n
d
π
>
Ρι/2
x
n
i
D
1
t
Ru.
I n F i g . 2b
c r o s s i n g s a t a b o u t t h e same
R u and t h u s a r e n o t t h e cause o f t h e o b s e r v e d a l i g n m e n t . 1Ω2
Bands based on t h e v h ^ n
2
o r b i t a l , F i g . 2c, block the
p r e t a t i o n o f the results f o r the π g first
e
New d a t a has
Ru b a c k b e n d .
Inter
bands i s n o t as s t r a i g h t f o r w a r d . To ' 101 103 order a p l o t of the favored states f o r Tc and Rh i n d i c a t e t h a t
this orbital
Q / 9
a l s o b l o c k s t h e backbend.
In other t r a n s i t i o n a l
odd-A n u c l e i , h o w e v e r , band c r o s s i n g s a r e known
t o change t h e s i g n a t u r e s p l i t t i n g unfavored s t a t e s )
( s t a g g e r i n g between t h e f a v o r e d and
and t h e B ( M 1 ) / B ( E 2 )
ratios.
T h i s o c c u r s when t h e odd
n u c l é o n and t h e a l i g n i n g p a i r a r i s e f r o m t h e u n i q u e p a r i t y o r b i t s i n respective shells.
In both
8 1
K r [FUN83] and
1 5 9
Tm
their
[LAR84] f o r example t h e
s i g n a t u r e s p l i t t i n g i s r e d u c e d above t h e band c r o s s i n g and t h e B ( M 1 ) / B ( E 2 ) r a t i o s are enhanced.
Frauendorf
[FRA84] has e x p l a i n e d t h e s e f e a t u r e s
with
t h e a s s u m p t i o n t h a t t h e u n p a i r e d n u c l é o n s p r o d u c e c o n f i g u r a t i o n dependent γ deformations o f the s o f t t r a n s i t i o n a l
core.
For t h e mass 100 r e g i o n an odd
314
π 9
9/2
NUCLEI OFF THE LINE OF STABILITY w
o
u
l
g e n e r a t e a n e g a t i v e γ d e f o r m a t i o n and l a r g e s i g n a t u r e
d
splitting.
A l i g n i n g a v h ^ ^ p a i r w i t h i t w o u l d push γ t o n e a r 0 ° and remove t h e ^ ~ _ ~ J-. .
l ^ j - x ^
signature ïïg
Ατ
Λ
ι
ι
ι
£
ι_
j.1
1 η / o"^~
ο ι
J
/
ι
Ί _
_c
splitting Α Δ Ι = 1 band f e e d s t h e 1 9 / 2 and 2 1 / 2 l e v e l s o f t h e 103 . . 2 band i n Rh and may r e p r e s e n t such a ^ 9 / 2 ^ 1 / 2 b a n d . T h i s band Λ
D U
9/2
3Q/9
has l e v e l s a t 3 3 9 6 , 3 6 3 0 , 3 9 3 7 , 4 3 2 0 , 1
1
1
1
4 7 0 5 , 5 1 9 5 , 5 6 6 2 , and 6205 keV w i t h
I
23/2
10
^9/2 F i g . 4 . A back bend o c c u r s a t a f r e q u e n c y c o n s i s t e n t 102
π R
l 0 2
0
h
Trg9£
RuGSB
ι
O.I
ι ·1
) 0
R u GSB
0.2 0.3 Q4 Q5 *w (MeV)
-
b
with
06
a
n
d
1 S
Ru.
s
n
o
w
n
i
n
The π ς ^ 9
b
a
n
d
i
observed
s
2
above t h e band c r o s s i n g r e g i o n . Fig. 4.
P a r t i c l e a l i g n m e n t vs
rotational πg
frequency f o r the
band i n
spins
An a l i g n
+
ment p l o t f o r t h i s band c r o s s i n g w i t h t h e
V\
'x
to 37/2 , respectively.
+
R h assuming a 9/2 change i n s i g n a t u r e s p l i t t i n g . 1 0 3
The s t a r t
o f an up-bend i s f o u n d above 0.5Ηω. present level
scheme f o r ^ T c
e x t e n d h i g h enough t o show a s i m i l i a r c r o s s i n g band. The c o m p l e x i t y o f o u r a n g u l a r t r i b u t i o n s p e c t r a do n o t p e r m i t
extraction o f mixing r a t i o s
The
does n o t
f o r the I + I - l
transitions
i n the
dis
reliable b
a
n
d
-
Assuming t h a t t h e s e a r e p u r e M l , a 10 f o l d i n c r e a s e i n t h e e x p e r i m e n t a l B(M1)/B(E2)
i s o b s e r v e d between t h e one and t h r e e q u a s i p a r t i c l e
Donau and F r a u e n d o r f
bands.
[D0N83] have s u g g e s t e d t h a t s i n c e t h e r o t a t i o n a x i s
is
n o t t h e same as t h e a l i g n m e n t a x i s i n a h i g h Κ b a n d , p a r t i c l e a l i g n m e n t can enhance Ml t r a n s i t i o n r a t e s .
T h i s o c c u r s when t h e g f a c t o r
opposite sign f o r the i n i t i a l
and t h e a l i g n i n g q u a s i p a r t i c l e s .
semi c l a s s i c a l 9
e x p r e s s i o n f o r the B(M1)/B(E2)
ratios.
r a t i o o v e r t h e same range o f
R
has an
They gave a
With a s t r o n g
9 / 2 proton (K=9/2) t h i s expression gives a f a c t o r o f 3
B(M1)/B(E2)
(g^-g )
coupled
increase i n the
spin.
The s i g n a t u r e s p l i t t i n g o b s e r v e d i n t h e g ^ g
b
a
n
d
d
o
e
s
2
n
o
t
necessarily
i m p l y c o n f i g u r a t i o n dependent γ d e f o r m a t i o n s as p r o p o s e d by F r a u e n d o r f .
A
similiar splitting in A g was r e p r o d u c e d [P0P79] w i t h a q u a s i p a r t i c l e p l u s - r o t o r (SR) model i n c l u d i n g a VMI t r e a t m e n t o f t h e s o f t c o r e . The l e v e l 103 scheme f o r Rh shows many o f t h e same f e a t u r e s as t h e Ag i s o t o p e s b u t i s 103 1 0 5 , 1 0 7
more c o m p l e t e .
To e x p l o r e t h i s f u r t h e r t h e l e v e l s
in
c a l c u l a t e d u s i n g t h e SR, IBFM-1 [ J 0 L 8 5 ] , and t r i a x i a l models.
Rh have been rotor
(AR) [MAY 7 5 ]
P a r a m e t e r s f o r t h e SR model were chosen i n a manner s i m i l i a r
to the
47.
315
Massive Transfer Reactions
HAENNI ET AL.
(A)
4.0 L 2 5 / 2 ' -
(B)
21/2'3.0
h
17/2'-
21/219/2-
15/2"-
2
ω
2.0
17/2-
11/2"
1.0
15/2-
9/2" 5/2Ί 7/2"
13/2— 11/2(o) 5 / 2 -
5/2". 3/2'" "•g9/2Bo
0.0 IBFM-I
EXR S.R. T r p i / 2 Band
Fig.
5.
parity model
EXP
Comparison o f t h e n e g a t i v e 103 "Rh w i t h d b a n
i
Fig.
6 . Comparison o f t h e p o s i t i v e 103 Rh w i t h parity '
n
n
D
calculations.
Ag i s o t o p e s
[P0P79]
model
b u t u s i n g an a v e r a g e
n
d
Ί
J
η
n
calculations.
Ru -
parameters are from a recent c a l c u l a t i o n
a
Pd c o r e .
The IBFM-1
[ J 0 L 8 5 ] f o r o d d - A Rh i s o t o p e s
assuming t h a t Rh i s a h o l e i n t h e c o r r e s p o n d i n g Pd c o r e . Parameters f o r 102 104 AR model were a g a i n based on an a v e r a g e Ru Pd c o r e . 103 R e s u l t s o f t h e s e c a l c u l a t i o n s a r e compared t o
the
Rh i n F i g s . 5 , 6 .
For
t h e n e g a t i v e p a r i t y l e v e l s t h e SR and IBFM-1 models p r o d u c e a r e a s o n a b l e agreement w i t h t h e d a t a . sets
The f i t s
to the g
g
^
D
a
n
d
w
l
t
n
t h e same p a r a m e t e r
[ ( A ) f o r t h e SR m o d e l ] a r e n o t as good and a p p e a r t o i n d i c a t e a
core than observed.
softer
The AR model p r e d i c t s s i g n a t u r e s p l i t t i n g f o r t h e g ^ g
band as do t h e o t h e r models b u t i t s a s s u m p t i o n o f a r i g i d r o t o r c o r e i s appropriate for a transitional can be improved (B) i f parameter C i s
nucleus.
the deformation ε
The SR model f i t
i s decreased ( 0 . 2 - 0 . 1 5 )
2
increased (0.006-0.02 MeV ).
d i r e c t i o n o f a s t i f f e r more s p h e r i c a l
to the g ^
3
core.
These changes a r e i n
g
b
2
not a
n
d
2
and t h e VMI the
316
N U C L E I OFF T H E LINE OF STABILITY
With core parameters d e r i v e d from n e i g h b o r i n g even-even n u c l e i t h e SR and IBFM-1 models g e n e r a t e a s i m i l i a r p a t t e r n o f r e s u l t s . band i s more o r l e s s r e p r o d u c e d w h i l e t h e g 103 provides evidence t h a t the s o f t core i n proton.
It
results
g
i s not c l e a r .
/
9
band i s c o m p r e s s e d .
band t h a n t h e p ^
2
2
This i n t e r a c t i o n
The
perhaps
has a l r e a d y been shown
[FED79] t o be t h e d e f o r m a t i o n d r i v i n g f o r c e i n t h i s mass r e g i o n w i t h ^9g/2
a
orbital
n
d
v g
7/2
o
r
D
l
t
would l i k e l y
a
l
s
playing
show e f f e c t s
particularly
transition
transitional
odd-A n u c l e i
key r o l e s . from t h i s
r a t e s f o r the g ^ g
2
Bands based on t h e interaction.
^9g/2
More d a t a ,
b a n d / b e t t e r models f o r
a r e needed t o draw more d e f i n i t e
the
such
conclusions.
References [BEN79] R.Bengtsson and S. Frauendorf, Nucl. Phys. A327 139 (1979). [DON83] F. Dőnau and S. Frauendorf, High Angular Momentum Properties of Nuclei edited by N. R. Johnson (Harwood Academic, New York) 281 (1983). [FED79] P. Federman and S. Pittel, Phys. Rev. C 20 820 (1979). [FRA83] S. Frauendorf and F. R. May, Phys. Lett. 125B 245 (1983). [FRA84] S. Frauendorf, International Symposium on In-Beam Nuclear Spectroscopy, Debrecen, Hungary (1984). [FUN83] L. Funke et a l . , Phys. Lett. 120B 301 (1983). [GRA76] J. A. Grau et al., Phys. Rev. C 14 2297 (1976). [HAE82] D. R. Haenni et al., Phys. Rev. C 25 1699 (1982). [JOL85] J. Jolie et al., Nucl. Phys. A438 15 (1985). [KLA82] W. Klamra et al., Nucl. Phys. A376 463 (1982). [LAR84] A. J. Larabee et al., Phys. Rev. C 29 1934 (1984). [MAY75] J. Mayer-ter-Vehn, Nucl. Phys. A249 111 (1975). ibid. 141. [POP79] Rakesh Popli et al., Phys. Rev. C 20 1350 (1979). [STA84] J. Stachel et al., Nucl. Phys. A419 589 (1984). [VOI76] M. A. J. de Voight et al., Nucl. Phys. A270 141 (1976). RECEIVED July
14, 1986
1
This
band.
I t may a r i s e f r o m γ d e f o r m a t i o n o r
f r o m n-p i n t e r a c t i o n s .
p
Rh i s i n f l u e n c e d by t h e odd
i s more a p p a r e n t f o r t h e g ^
cause f o r t h i s
Q
both
The
