Recent Experimental Investigations and Interacting Boson Model

34 Recent Experimental Investigations and Interacting Boson Model Calculations of Even Te Isotopes 1

1

1

2

J. Rikovska, N. J. Stone, V. R. Green , and P. M. Walker 1

Clarendon Laboratory, OX1 3PU, Oxford, United Kingdom Daresbury Laboratory, WA4 4AD, Warrington, United Kingdom

Downloaded by UNIV LAVAL on July 11, 2016 | http://pubs.acs.org Publication Date: November 14, 1986 | doi: 10.1021/bk-1986-0324.ch034

2

The most interesting question occurring in studies of low excitations in even-even Te isotopes (Z = 52, Ν = 62-72) is the problem of existence of "intruder" states. These states have their origin in excitation of a pair of particles across a closed shell gap and have been observed in nuclei near to both neutron and proton closed shells (or subshells) [HEY83]. There are several main features of these states: - considerable deformation due to residual proton-neutron interaction amongst the increased number of valence particles outside a closed shell as compared with "normal" vibrational-like configuration, which implies that the proton (neutron)intruder configuration should be lowest in energy in the middle of neutron (proton) shell, increasing rapidly as one moves away from the centre, - a rotational band built on the intruder O state, - enhanced EO transition probability between intruder and normal O states and EO admixtures in transitions between the intruder and normal states of the same spin because of the difference in shape of the two configurations, - increased excitation cross section in specific ew nucleon transfer reactions as compared with the cross section to the ground state. In even-even nuclei around Ζ = 50, the intruder configurations, although somewhat mixed with the normal ones have been identified in Cd (Z = 48) (4h - 2p states) [HEY82, MHE84] and Sn (Z = 50) (2p - 2h states) [WEN8l] Recent nuclear orientation experiments at the Daresbury DOLIS facility (j>HA85a, GRE85] together with preliminary results from electron con version measurement [GRE853 , ( He, n) reactions [FIE78] and thermal neutron capture reactions [ROB83] provide a possible experimental basis for identi fication of these states in even Te isotopes. All data available on lowlying 0 , 2 and 4"[ and 42 state energies for even Cd and Te isotopes are shown in Fig. 1, to stress similarities and differences between these two isotopic chains, where the intruder configurations should be of related structure, proton 4h - 2p in Cd and 4p - 2h in Te. Experimental data suggests that there are three different kinds of excited 0 states in Te isotopes. The second 0 state, simply considered as a two-phonon vibrational state, shows rapidly increasing energy with increasing neutron number, particularly between Ν = 68 and 70. The same change is observed in Cd between Ν = 60 and 62. The behaviour can be accounted for by increasing γ-softness of the nuc lei [MEY77]. Intruder configuration admixture can explain the relatively low energy of the 0"J state in T e (see below) but otherwise those states are almost pure normal con figuration. As a second type of 0 state, in Cd mixed intruder 0% states have been identified in the closed vicinity of the two-phonon triplet, however in Te they appear to be found close to the three-phonon quintuplet and are probably strongly mixed with states belonging to this vibrational excitation The evidence for this is rather incomplete at this stage. In Te there are two candidates for higher 0 states (at 1517 and 1845 keV) and one 0 state (at 1710 keV) has been identified in T e in ( He, n) reactions [jIE78]. We tentatively assign the 1517 keV state in T e and the +

+

0

3

+

+

+

+

118

+

0

118

+

+

120

3

118

0097-6156/86/0324-0227$06.00/0 © 1986 American Chemical Society Meyer and Brenner; Nuclei Off the Line of Stability ACS Symposium Series; American Chemical Society: Washington, DC, 1986.


228

NUCLEI OFF THE LINE OF STABILITY

Fig.

1.

S y s t e m a t i c s o f p o s i t i v e p a r i t y s t a t e s i n e v e n Cd The l i n e s c o n n e c t s t a t e s d i s c u s s e d i n the t e x t .

and

Te

isotopes.

1 2 0

1710 keV s t a t e i n T e as h a v i n g s t r o n g i n t r u d e r a d m i x t u r e . F o r h e a v i e r Te i s o t o p e s the i n t r u d e r c o n f i g u r a t i o n l i e s p r o b a b l y h i g h e r i n e n e r g y 2 MeV i n T e and ^ 3 MeV i n T e ) . The d e c a y o f the 1940 keV s t a t e i n T e has b e e n shown i n our r e c e n t n u c l e a r o r i e n t a t i o n e x p e r i m e n t t o be e n t i r e l y c o n s i s t e n t w i t h the a s s i g n m e n t 0 [ S H A 8 5 b ] . T h i s s t a t e i s p o s s i b l y a m i x t u r e of t h r e e phonon v i b r a t i o n and i n t r u d e r c o n f i g u r a t i o n s as d i s c u s s e d below. I n the t h i r d c l a s s of 0 s t a t e , the 1845 keV ( T e ) , 1883 k e V ( Te) and 1982 keV ( T e ) are v e r y l i k e l y m o s t l y of three-phonon v i b r a t i o n a l o r i g i n as seems t o be s u g g e s t e d by the mode o f t h e i r d e c a y and smooth v a r i a t i o n o f t h e i r e n e r g y w i t h n e u t r o n number. A q u e s t i o n w h i c h r e m a i n s i s the s t r e n g t h w i t h w h i c h the i n t r u d e r 0 s t a t e s w o u l d be p o p u l a t e d i n t h e d e c a y o f 118,12 0! (χπ _ 2 ) . For example, i n the s i m i l a r c a s e o f Ag (Ι = 2~) 3-decay the two Olj and 2$ i n t r u d e r spates i n Cd a r e p o p u l a t e d w i t h a l m o s t the same p r o b a b i l i t y as t h e 0$ and 22 s t a t e s . I t seems t h e r e f o r e t h a t t h e r e i s no c l e a r r e a s o n why the i n t r u d e r s t a t e s , e s p e c i a l l y 2 , s h o u l d n o t be p o p u l a t e d i n the d e c a y o f i o d i n e i s o t o p e s . C a n d i d a t e s f o r 2 i n t r u d e r s t a t e s a r e the 2% s t a t e s a t 1482 keV i n Te and 1535 keV i n Te. They show s i m i l a r decay p a t t e r n s t o t h o s e o f the 2% s t a t e s , a s s i g n e d as m i x e d i n t r u d e r , i n Cd i s o t o p e s , i . e . m o s t l y t o t h e 2t and the g r o u n d s t a t e s . The s i m p l e v i b r a t i o n a l s e l e c t i o n r u l e f o r E2 t r a n s i t i o n s (Δη = ± 1, η-number o f v i b r a t i o n a l phonons) r u l e s out t h e i r i n t e r p r e t a t i o n as t h r e e phonon s t a t e s , b e c a u s e o f t h e i r s t r o n g decay t o the one phonon 2\ s t a t e . U n f o r t u n a t e l y , v e r y l i t t l e i s known a b o u t the p o p u l a t i o n o f these s t a t e s i n n u c l e a r r e a c t i o n . No c l e a r e v i d e n c e f o r a ΔΙ = 2 r o t a t i o n a l band i n Te i s o t o p e s b u i l t on a 4p - 2h 0 s t a t e was f o u n d i n ( He, n) [FIE78], (α,χη) and ( C , 2n) r e a c t i o n s [CH082,VAN82]. P r o b a b l y a r e a c t i o n , w h i c h can p r o d u c e h o l e s t a t e s d i r e c t l y , l i k e X e ( d , L i ) w o u l d be more u s e f u l t h a n twop r o t o n t r a n s f e r i n t h e s e a r c h f o r 4p - 2h e x c i t a t i o n s . Our f i r s t m e a s u r e ments o f EO t r a n s i t i o n s t r e n g t h show EO t r a n s i t i o n s b e t w e e n O j ·> 0\ and 1 2 2

1 2 4

1 2 2

+

+

1 1 8

1 2 l +

1 2 8

+

-

1 1 2

π

1 1 2

+

+

1 1 8

1 2 0

+

3

12

6

Meyer and Brenner; Nuclei Off the Line of Stability ACS Symposium Series; American Chemical Society: Washington, DC, 1986.

34.

Even Te Isotopes

RIKOVSKA ET AL.

229

O2 in T e together with EO admixtures i n the 2^ 2"[ t r a n s i t i o n s i n T e and 2$ - 2\ i n Te. Summarizing the above experimental f a c t s concerning the existence of i n t r u d e r states i n even Te isotopes i t i s c l e a r that there i s r e l a t i v e l y l i t t l e on which to base a c a l c u l a t i o n of low-lying s t a t e s of these i s o t o p e s . Nevertheless, f o l l o w i n g the s u c c e s s f u l a p p l i c a t i o n of the i n t e r a c t i n g boson model (IBM2) to even Cd isotopes [HEY82] s i m i l a r c a l c u l a t i o n s have been performed on Te. A standard IBM2 c a l c u l a t i o n , using NPBOS code was performed f o r 1 ^ - l ^ T e i n the space of one proton boson (N = 1) and corresponding number of neutron bosons N . The parameters used (see F i g . 2) were chosen to f i t energy l e v e l s , the e l e c t r i c quadrupole and magnetic d i p o l e moments of the f i r s t 2 states (where known) and some r a t i o s of reduced E2 t r a n s i t i o n probab i l i t i e s , and are i n l i n e with the systematics of the IBM2 parameters i n t h i s mass region. The same c a l c u l a t i o n was performed for the i n t r u d e r 4p - 2h 1 1 8

θΐ

1 Ï 8

1 2 0

v

+


x,

-0.5 -0.9 -13

-0.1 -0.2 11. 0.9 0.7

62 64 6 6 68 70 72 Ν

F i g . 2.

62 64 66 63 70 72 Ν

Parameters of the IBA2 Hamiltonian as a f u n c t i o n of neutron number. Χ = -0.8, ξι = ξ = -0.09, ξ = 0.12 and C^ = 0 (L = 0,2,4) were constant f o r a l l i s o t o p e s . A l l parameters are i n MeV except f o r Χ (dimensionless). π

π

3

2

v

c o n f i g u r a t i o n , i . e . Ν = 3 and the same N . A l l the parameters d e s c r i b i n g the neutron part of the IBM2 Hamiltonian were kept the same as f o r the normal c o n f i g u r a t i o n . The strength of the neutron-proton quadrupole-quadrupole i n t e r a c t i o n κ i s approximately p r o p o r t i o n a l to the product of the number of neutron and proton bosons present and thus κ f o r the i n t r u d e r c o n f i g u r a t i o n should d i f f e r from that of the normal c o n f i g u r a t i o n . Spectra of Ru (6h) and Ba (6p) isotopes served as an approximate guide f o r a d j u s t i n g parameters ε and κ f o r 4p - 2h states i n Te isotopes, s i n c e , as the IBM does not d i s t i n guish between p a r t i c l e s and holes, these should show a c e r t a i n s i m i l a r i t y with the unknown i n t r u d e r c o n f i g u r a t i o n i n Te. The values of ε(3π) = 0.50, 0.54, 0.58 and 0.58 MeV and κ(3ττ) = -0.16, -0.18, -0.20 and -0.20 MeV f o r 1 1 8 , 1 2 0 , 1 2 2 , i 2 4 ^ r e s p e c t i v e l y , were used. Wave functions obtained f o r both c o n f i g u r a t i o n s (normal and i n t r u d e r ) were then mixed using Hamiltonian [î)lJV8lJ π

v

T e

H = H

where H provided s

+

(

θ

)

( θ )

+ a(s*s + s s ) + B(dV + d d ) s ππ π π π π π π i s the usual IBM2 Hamiltonian. Η was diagonalized i n the b a s i s by the lowest eigenstates of the Ν = 1 and N^ = 3 c o n f i g u r a t i o n s . π


230


In the present case, four states of each spin were taken i n t o account. The procedure i s dependent upon three a d d i t i o n a l parameters, a, 3 and Δ, which represents an energy needed to e x c i t e the i n t r u d e r c o n f i g u r a t i o n and must be added to the eigenvalues of the Ν = 3 c o n f i g u r a t i o n . The parameter Δ can be expressed i n terms of the two-proton separation energies [HEY85] π

Δ = S ( Z , N ) - {S (Z+2,N) + [S (Z+2,N) - S 2p

2p

2p

2 p

(Z+4,N)] }

and i s ^ 5 MeV i n the Ζ = 50 region. In our c a l c u l a t i o n s , Δ = 4.65 - 5.0 MeV for ~ T e . The i n t e r a c t i o n strength parameters α and 3 were kept the same, α = 3 = 0.19 MeV f o r a l l n u c l e i . The value i s somewhat l a r g e r than the published values f o r Cd, (a = 3 = 0.08 MeV) but explains very w e l l a more complicated mixing of i n t r u d e r and normal states i n Te isotopes. The r e s u l t s of the mixing c a l c u l a t i o n are i l l u s t r a t e d i n F i g . 3 where s e l e c t e d experimen t a l data are added for comparison. The mixing i n T e can e x p l a i n the p o s i t i o n of 0\ state and leads to i n v e r s i o n of the i n t r u d e r l e v e l order (2$ l i e s lower than 0$). In T e , the i n t r u d e r component i s almost equally (^50%) present i n both 2"£ and 2% states and then the i n t r u d e r c o n f i g u r a t i o n r i s e s up i n energy i n heavier i s o t o p e s . This p i c t u r e of mixing, which was not observed i n other n u c l e i , could e x p l a i n , f o r example, the d i f f i c u l t y i n the search for r o t a t i o n a l bands, which would be very d i s t o r t e d by mixing and rather high i n energy. The mixed wave functions were used to c a l c u l a t e B(E2), Β(Ml) and EO t r a n s i t i o n strengths. The t r a n s i t i o n operator f o r E2 t r a n s i t i o n i s of the form 1 1 8

1 2 i +


1 1 8

1 2 0

a)

b) 3.0

(οί ο — 4

zo

i

«a—«f>—i

2*=

(2> (0,21*=

2Y

I:

1.0

t

i _ 66

Fig.

3.

or_ or_ or_ 68

70

72

;

Q^)

+

( 2 )

δ

-

(i=l,3),

1 ) +

intruder

con

g ( 3

w

for i-configuration

ν

and T(EO)


^

r e f e r s to normal and

where g^ = /30π/4 ( £ - & ) ^ i s an e f f e c t i v e g-factor Ή

Ξ

= aN^ + Md+d^)

(0)

where Ν = (sjs-jy + d+d^) counts the number of proton bosons. The term aN d i f f e r s i n a mixing c a l c u l a t i o n for each state and moreover, a and b are d i f f e r e n t i n the Ν = 1 and Ν = 3 subspaces. Thus, i n t e r p r e t a t i o n of T(E0) i n mixing c a l c u l a t i o n s depends on a number of a d d i t i o n a l constants. No data e x i s t on parameters (such as i s o t o p i c or isomeric s h i f t s ) on Te isotopes which would y i e l d these constants f o r e i t h e r mixed or unmixed s t a t e s . Con sequently a s i m p l i f i e d expression pj_f (EO) = Αχ (dp"d ) (o) + A (djd )(°) (subscript ρ = π or ν, subscripts 1,3 as before) was used with d i f f e r e n t combinations A i , A 3 for i n v e s t i g a t i o n of q u a l i t a t i v e trends. The E2/M1 mixing r a t i o s f o r 2$ -> 2* and 2j •> 2* t r a n s i t i o n s were c a l c u l a t e d using π

π

π

p

6 = 0.00832 χ E^ where Ε

(MeV)

3

p

2

χ [efm ]/(ju^]

i s the photon energy of the t r a n s i t i o n involved. Results f o r B(E2) and B(M1) p r o b a b i l i t y r a t i o s , as w e l l as the mixing r a t i o δ, i n v o l v i n g 0$ and 2* l e v e l s i n > - T e show considerably c l o s e r agreement with experiment as compared with c a l c u l a t i o n s without mixing. For the sake of s i m p l i c i t y , e i = e3 = 12.4 efm and gi = g (g = + 1.1 μ , g (N) v a r i e d with Ν w i t h i n -0.10 to -0.15 UJJ) was taken i n a l l c a l c u l a t i o n s . The lack of data i n the energy region of i n t e r e s t does not allow such comparison for » T e . Experimental information i s also rather l i m i t e d f o r l l > l l T and does not provide a s o l i d b a s i s f o r mixing c a l c u l a t i o n despite rather reasonable r e s u l t s without mixing. Examination of the two l i g h t e r Te i s o topes would be very important f o r understanding of v a r i a t i o n s i n the i n t r u d e r c o n f i g u r a t i o n e i t h e r side of the middle of the neutron 50-82 s h e l l . The present s i t u a t i o n regarding p o s s i b l e mixing i n Te isotopes high l i g h t s s e v e r a l experimental questions, e s p e c i a l l y the uncertainty about the 1517 and 1845 keV l e v e l s i n T e . More complete data on a l l l e v e l s above 2 MeV i s needed i n > Te. In T e a search f o r a l l 0 s t a t e s , and i n the other n u c l e i , for EO t r a n s i t i o n s between O 3 and 0 j s t a t e s , by e l e c t r o n conversion measurement would be valuable. The T e (η,η'γ) r e a c t i o n should be another u s e f u l source of information on excited 0 states i n Te. However even the present stage of the i n v e s t i g a t i o n shows a p o s s i b i l i t y of understanding the problem of i n t r u d e r configurations i n even Te isotopes. γ

118

L20

2

3

1 2 2

TT

Ν

1 2 1 +

v

4

6

e

1 1 8

1 2 0

1 2 2

1 2 0

+

1 2 0

+

1 2 0



232


References [CHO82] P. Chowdhury, W.F. Piel, J r . , and D.B. Fossan, Phys. Rev. C25 813 (1982). [DUV81] P. Duval and B.R. Barrett, Phys. Lett. 100B 223 (1981). [FIE78] H.W. Fielding, R.E. Anderson, P.D. Kunz, D.A. Lind, C.D. Zafiratos and W.P. Alford, Nucl. Phys. A304 520 (1978). [GRE85] V.R. Green, J . Rikovska, T.L. Shaw, N.J. Stone, I.S. Grant, P.M. Walker and K.S. Krane, Annual Report, Daresbury Laboratory, 1984/85. [HEY82] K. Heyde, P. Van Isacker, M. Waroquier, G. Wenes and M. Sambataro, Phys. Rev. C25 3160 (1982). [HEY83] K. Heyde, P. Van Isacker, M. Waroquier, J.L. Wood and R.A. Meyer, Phys. Reports, 102 291 (1983). [HEY85] K. Heyde, P. Van Isacker, R.F. Casten and J.L. Wood, Phys. Lett. 155B 303 (1985). [ΜΕΥ77] R.A. Meyer and L. Peker, Z. Phys. A283 379 (1977). [MHE84] A. Mheemeed et a l . , Nucl. Phys. A412 113 (1984). [ROB83] S.J. Robinson, W.D. Hamilton and D.M. Snelling, J . Phys. G: Nucl. Phys. 9 961 (1983). [SHA85a]T.L. Shaw, V.R. Green, N.J. Stone, J . Rikovska, P.M. Walker, S. Collins, S.A. Hamada, W.D. Hamilton and I.S. Grant, Phys. Lett. 153B 221 (1985). SHA85b]T.L. Shaw, private communication, (1985). [WEN81] G. Wenes, P. Van Isacker, M. Waroquier, K. Heyde and J. Van Maldeghem, Phys. Rev. C23 2291 (1981).

[

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Recent Experimental Investigations and Interacting Boson Model

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