Electromagnetic transition probabilities between the low-lying states of 203Tl, 205Tl and 209Bi

I.E.4:2.H]

Nuclear Physics A201 (1973) 179--192; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

ELECTROMAGNETIC

TRANSITION PROBABILITIES

BETWEEN THE LOW-LYING STATES

OF 2°3T1, 2°STl AND 2°9Bi W. KRATSCHMER t, H. V. KLAPDOR and E. GROSSE

Max-Planck-lnstitut fiir Kernphysik, Heidelberg, Germany Received 2 August 1972

Abstract: A high-accuracy investigation of absolute ?'-ray yields and angular distributions after Coulomb excitation of 2°3T1, 2°ST1 and 2°9Bi allowed the determination of B(E2) and B(M1) values in these nuclei. Some of the data obtained are compared with direct lifetime measurements and internal conversion data. The influence of deorientation effects on our results is discussed. A comparison is made between the experimental transition matrix elements and shell-model and core-coupling-model calculations. The "/-forbidden" M1 transitions, which are caused by core-polarization effects, have strengths of ~ 10 -3 W.u. In 2°9Bi the strength of the fg=-~- h~r E2 transition is equivalent to a surprisingly large proton polarization charge of (2.8 +0.2)e. NUCLEAR REACTIONS 2°3"2°5T1, 2°9Bi(oc, o(~'), E = 15 MeV; measured Ey,

1~,(0) for 7 transitions. 2°3"2°sT1 and 2°9Bi deduced B(E2), y-mixing, B(MI), lifetimes, effective charges and y-factors. Natural targets.

1. Introduction The e l e c t r o m a g n e t i c p r o p e r t i e s o f low-lying states in nuclei near the d o u b l y magic nucleus 2 ° a p b have been shown in several investigations t - 5) to be very sensitive to the c o u p l i n g between single-particle a n d collective nuclear excitations. This coupling is the origin o f the so-called c o r e - p o l a r i z a t i o n effect. T h e i n t e r m e d i a t e c o u p l i n g unified m o d e l 6) is a useful basis for the investigation o f these effects. T o p r o v i d e a c c u r a t e e x p e r i m e n t a l i n f o r m a t i o n o n e l e c t r o m a g n e t i c t r a n s i t i o n m a t r i x elements we e x t e n d e d o u r p r e v i o u s w o r k o n the l e a d isotopes 5, 7) by C o u l o m b exciting the low-lying states o f 2°3TI, 2°5T1 a n d 2°9Bi. T h e g r o u n d a n d first excited states o f 2°9Bi have been s h o w n by transfer reactions to be the h~ a n d f~ single-particle orbits [refs. 8, 9)]. I n 2°aT1 a n d 2°5T1 the three lowest levels c o n t a i n at least a large p a r t o f the s~, d~ a n d d~ s i n g l e - p r o t o n - h o l e strength to). C o u l o m b excitation o f TI isotopes has been carried o u t by M c G o w a n a n d Stelson 11). This e x p e r i m e n t suffers f r o m the p o o r energy r e s o l u t i o n o f the N a [ d e t e c t o r s used, a n d the analysis has been d o n e using s t a n d a r d c o n v e r s i o n d a t a n o t * Now at the Institut ffir Theoretische Physik, Abteilung Kernphysik, Universit~it Heidelberg, Germany. 179

180

W. KRATSCHMER

et al.

taking into account penetration effects. The nucleide 209Bi has been Coulomb excited with ~-particles 2, 4) and heavy ions 12.13). Absolute transition rates between singleparticle states and radiation mixing ratios are only deduced from an experiment performed with a 19 MeV ~-beam 4). Since this energy is too high to produce pure Coulomb excitation, the transition elements obtained might be doubtful. The decay of the first excited states of the two T1 isotopes has also been investigated following fl-decay, but only in the case of 2°3T1 have both B(E2) and B(M1) values been obtained 14-1a). For some time there have existed very detailed calculations dealing with the corecoupling effect in 203, 20STl and 2°9Bi and its consequences on electromagnetic properties 19-22). They cannot be comprehensively tested with previously existing data because of large experimental errors and uncertainties. Therefore, an experimental re-investigation was performed using "safe" Coulomb excitation with 15 MeV ~-particles for the determination of B(E2) values and analysis of de-excitation )'-ray angular distributions for mixing ratio determinations. A similar experiment has been performed on two levels in 2°Tpb [refs. 5, 7)], where several checks of the methods used have been made.

2. Experimental procedure The experiments were carried out at the Heidelberg EN tandem accelerator using a 15 MeV e-beam, which was stopped in thick metallic targets of natural bismuth and thallium, and also isotopically enriched 2°6pb(97.4 ~o) and 2°7Pb(92.4 ~). The )'-rays following Coulomb excitation were detected by two Ge(Li) detectors with energy resolutions of 2.5 and 4 keV, respectively, for )'-rays of 1200 keV. The 7-ray yields and angular distributions for the transitions shown in fig. 1 were measured. To perform the yield measurement one detector was placed at 55 ° relative to the beam, while the other detector, at 90 ° was used to determine the dead-time o f the electronics, as described elsewhere 7). In order to be independent of an absolute beam-charge measurement and the absolute efficiency of the detectors, with the same experimental set-up, the ),-ray intensities of the transitions ~- ~ ½- g.s. in 2°7pb and 2 + ~ 0 + g.s. in 2°6pb, whose B(E2)values are very well known from earlier measurements 5.23), were measured. Electric insulation of the target chamber and part o f the beam tube allowed very accurate relative beam-charge measurements. To obtain the )'-ray angular distributions, spectra were taken with one detector at angles of 0 °, +__35°, -t-55 ° and +90 °. The second detector was held at a fixed position for dead-time determination and to normalize the beam charge at the different angles. Detectors and target were optically adjusted to the beam axis. The beam was focussed to a beam spot not larger than 1 mm in diameter. The relative efficiency of the detectors was determined using 133Ba, 75Se, s a y and 228Th y-ray sources 24-26) with energies between 120 keV and 2600 keV. To do the calibration for the angular distribution measurement, the sources were fixed at the target in such a way as to take into account the y-ray absorption in the thick targets at the different angles, which

203. 205TI ' 209Bi T R A N S I T I O N P R O B A B I L I T I E S

181

2 1 i ,52

E2 ~: ~

3/2+

E2 2°~T[

~ ~

~

3/2 ÷

l/2+gs.

1/2+g.s. 2°~Tt

Fig. 1. Level and decay scheme of the three lowest states in Z°3Tl and Z°STl. I

I

natTI + 4He

6000

15 MeV @'v = O°

2O5Ti 5/2"T312"

p 4ooo

203TI

W

m 2000

J

S

3/2+~I/2 + 205TI

0

2O3TI

I

0

200

t

4OO

i

'1

300C

I

3o0

natTI

+

r~

I

4He

15 MeV IE

Oy = 0 °

~x~c E lxl

× lOO0

/

2O5TI 5/2. T.1/2 •

2°3TI 5/2"T'1/2"

?, U

o

I

I

500

600

I

I

700

800

E ~ (keV)

I

I

209Bi + 4He 15 MeV e y = O*

3OOO :r

I

I

2°9Bi 7/2--~-9/2-

~

!

2000 E

Ld × 1000 E 3 0

u

0

I

700

I

800

I

I

900

1OOO E v (keY)

Fig. 2. G a m m a - r a y spectra from the b o m b a r d i n g o f natural TI and Bi with 15 MeV ~-particles. The Ge(Li) detector was positioned at 0 ° with respect to the beam. Lines following C o u l o m b excitation are labelled.

182

et al.

W. KRATSCHMER

203T1+a

Ea=15M~

2°5T1* ot l(O)l

I l l l [ l l l l l

I(0)

~

t

,

Ee =15MeV

,

~

,

;

L

,

,

35 x I04 ~

,

20x104 16x 104 r

25xI04~

I

I

=

I

'

[

{

I

[

l l l l l l } l l J -

5 X1 0 4] ~ . . ~, . ~

~2*~3/2 *

4 x 1 0 4' I I 1 I I t I I I I ~ l ooo

10x 104~ ~ ,

8,,o,,t-

I

ooo

5/2"-~.3/2-

I ""-4 I

ooo

I

I

90*

I

60°

I

I

I

30 °

I

I

I

O* -3-

Fig. 3. G a m m a - r a y angular distributions following the C o u l o m b excitation of the ~+ and t + levels in 2°3T1 and 2o STl" The lines are Legendre polynomial fits including terms of zero and second order.

[

IIIIIIl

I

I

I Ililll

I

I iiiillr

I

I t li)lll[

i

IIJll~l

2O9Bi

O8 Q4 ,2 0.0 -04 -08

I

I I*lllil

001

0.1

i

i iiilll[

1.0

~ 11111

10.0 ~(E2/M1)

12x 103

I

I

I

I

I

I

I

I

1

I /

" ~ ~

7/2----"912- ~

10x102

8 xlO-"

I 90 °

I

I

I 60 °

I

r

I

30°

I[ - " ~

0°

8

Fig. 4. Upper part: angular correlation coefficient for a mixed E2/M1 transition ~ -+ .] as a function o f the mixing ratio 6. Lower part: angular distribution ofT-rays following excitation of the ~ - level in 2°9Bi with 15 M e V s-particles. The A2 as determined from a Legendre fit (drawn line) to the angular distribution is shown in the upper part of the figure with its error bars.

was necessary since the detector was on the far side o f the beam. The v-ray yields o f the transitions ~ ~ ~2 in 2°9Bi relative to 2°vpb and { ~ k, ~ ~ and ~ ~ k in 2°3,2°5T1 relative to 2°6pb can be found in table 1. Fig. 2 shows the spectra o f z 0 9Bi and ""tT1 taken at 0 °. The angular distributions obtained f r o m o u r experiments for the transitions ~2 ~ 3, ~2 ~ k in 2°3'1°5T1 and ~ ~ ~ in 2°9Bi are shown in figs. 3 and 4. The error bars at the data points are m u c h bigger than the p u r e statistical errors o f the yields owing to the fact that a large C o m p t o n b a c k g r o u n d in

203.20STI ' 209Bi TRANSITION PROBABILITIES

183

TABLE I De-excitation ~'-ray intensities observed at 55 ° in 2°9Bi relative to 2°Tpb(~- ~ t - ) and in 2o3.2O5T1 relative to 2°6Pb(2+ ~ 0+), and the internal conversion coefficients used in the analysis of the experiments Nucleus

Transition jf -->jff

Energy (keV)

2°9Bi 2°7pb

~~-

~½-

2°3T1

,~+

1+

~÷ {+

~+ t+

2°5T1

~+

½+

2°6pb

25+ ~+ 2+

~+ ½+ 0+

896.3 ±0.3 569.7 --0.3 ~) 279.16--0.02 b) 401.27--0.05 680.43--0.06 203.7 --0.1 ~) 415.7 --0.2 619.4 --0.4 803.3 --0.3 ~)

Rel. ~,-yields l}I(Jr ~ Jff)

Internal conversion coefficients d)

56± 3 1000 5030±330 20305_140 568-- 55 4200--290 1660_+_120 128-- 11 1000

0.0176 0.0204 0.2262~0.0019 ~) 0.1760 0.0142 0.4400 0.1718 0.0175 0.0097

~tot

") Ref. s). b) Energies for 2°3T1 from ref. ~6). ~) Energies for 2°ST1 were determined by a least-squares fit using the energies of 2°3T1 as a reference. a) All conversion coefficients except one *) were calculated with the computer program MONICA 27) using the mixing ratios of table 3. Errors are estimated to be of the order of < 4 ~. e) Experimental value ~s). TABLE 2 Parameters ~2E2 for Coulomb excitation with 15 MeV c~-particles on thick targets Nucleus Jr -->Jfr

B2exp

a2 E2

2°9Bi 2°3TI 2°5T1

~ ~ --0.129--0.019 0.762 ~ 23 --0.185___0.018 0.662 ~ ~ --0.168--0.009 0.630

2°3T1

~

2°5T1

t ~ I

0.164i0.002 0.366 0.166--0.001 0.284

/:2(2, 2 , j l , j r )

K2 a)

0.296 --0.535 --0.535

0.226 --0.354 --0.337

K)~3,a)

R2 a)

A2

B,*¢alc

--0.5754-0.085 --5.5 x 10-'* 0.520--0.051 4.5×10 -5 0.497±0.025 2.0;< 10- s

0.533--0.030 --0.214--0.010 --0.767±0.044 0.394--0.035 --0.175--0.009 --0.949--0.050

0 0

Experimentally obtained Legendre coefficients B2 and angular correlation coefficients A2 of the 7-angular distribution after Coulomb excitation. The coefficients Be were calculated from the mixing ratios to show that they may be neglected in the analysis. a) These coefficients are defined in sect. 5. t h e s p e c t r a h a d t o b e s u b t r a c t e d . E r r o r b a r s w e r e f u r t h e r i n c r e a s e d b y c o u n t i n g statistics in t h e m o n i t o r d e t e c t o r at fixed angle. T h e solid lines are fits to a L e g e n d r e p o l y n o m i a l e x p a n s i o n i n c l u d i n g the t e r m s o f z e r o a n d s e c o n d o r d e r . T h e c o r r e s p o n d i n g e x p a n s i o n coefficients B2 a r e listed in t a b l e 2 w i t h t h e i r s t a n d a r d d e v i a t i o n s as o b t a i n e d f r o m t h e fit.

3. Determination of the B (E2) values T h e 7-ray yields w e r e c o r r e c t e d f o r i n t e r n a l c o n v e r s i o n . I n t h e case o f t h e h i g h e r e n e r g y t r a n s i t i o n s (3 ~ ~, { -* ½ in 203, 2O5T1 a n d { ~ ~ in 2 ° 9 B i ) i n t e r n a l c o n v e r s i o n

184

W. KRATSCHMER et al.

coefficients as calculated with the c o m p u t e r p r o g r a m M O N I C A 27) could be used without introducing any serious errors, because o f the smallness o f those coefficients for higher energies. They can be f o u n d in table 1. F o r the low-energy ½ ~ ½ transitions the conversion corrections are appreciable. These transitions are treated separately in sect. 4. As will be shown below, the coefficient o f the Legendre polynomial P4(cos 0) is either zero or insignificant within our accuracy (see table 2). Therefore, the fact that the ) + state decays via the two transitions ~ ~ ½ and { ~ ½ could be taken into a c c o u n t by adding the y-rates observed at 55 ° after correction for conversion. Using the quantum-mechanical first-order C o u l o m b excitation formalism 2s, 2 9) and empirical energy-loss data ao, 31) the B(E2) values were then determined from these experimental relative excitation rates and the k n o w n B(E2) values for 2°6pb (2 + ~ 0 +) [ref. 5)] and 2 ° 7 p b ( ~ - ~ ½-) [ref. 23)]. The B(E2) values for the {+ ~ ½+ transitions in the TI isotopes were derived f r o m the branching ratios o f the decay o f the ~r+ states as observed at 55 ° . Since the transitions in question are mixed, the mixing ratios had to be considered. These were obtained from the y-ray angular distributions as shown in sect. 5. The results are listed in table 3. TABLE3 The B(E2) values and mixing ratios 6 as obtained from ),-ray yields and angular distributions following Coulomb excitation with 15 MeV u-particles J,

2°3T1

2°STl

2°9Bi

J2

This work

Other experiments

B(E2;A ---~J2) (e2" fro4)

~(E2/MI) J2 -+A

B(E2;jt --->J2) 6(E2/M1) (e 2" fm 4)

1.16 4-0.07 a) 1240 4-140

½

~

1106 ± 77

~-

~ ~

2 1 1 2 +188 ~ 333 4-150 b) --0.079±0.029

½ ½ ~-

~ ~ ~

1060 4- 80 1.56 4-0.15 ~) 1000 4-100 1.465:0.16 1284 4- 96 oo 1140 4-120 264 -4-152b) --0.066-t-0.014 90 --0.05

~

~

27.54-1.4

--0.95 4-0.25

2100 4-270 180

1.504-0.08 1.204-0.20 0.05

18 4-6 12.3 4q'.46 --!.0 4-0.3 24 4-2 4-0.6 ~)

Ref.

ll) 44) ll) 11) ,t) 11)

11) la) 4) aT) 45)

a) Determined by using the results from refs. 14. 15. ~a), as described in sect. 4. b) Derived from branching and mixing ratios (see sect. 3). c) Derived from conversion data without accounting for penetration effect.

4. The 3 ..4. ~ transitions in 2°3'2°ST1 In 2°3T1 the total internal conversion coefficient has been very precisely measured [ref. 15)]. This value was used in the determination o f the B(E2) value f r o m the

20a,2OSTl ' 2O9Bi T R A N S I T I O N

PROBABILITIES

185

experimental ~-ray yield. The feeding of the ½+ state from the {+ decay was taken into account by subtracting the observed yields after correction for internal conversion. The B(E2) value obtained is given in table 3. The transition rates T(E2) and T(M1) are related to the reduced transition possibilities B(E2) and B ( M 1 ) a s described in ch. 3C-2 of ref. 3). The T(M1) value was calculated from our B(E2) value, the electronically measured total mean lifetime "ttot = 0.405___0.008 nsec [ref. 1,)] and the total internal conversion coefficient CXtot [ref. 15)] using the relation Ztot

= ET(M1) + T(E2)]- 1(1 --~~,ot)- 1.

(1)

For the mixing ratio fi = + [T(E2)/T(M1)] ~ we thus obtain fi = 1.15+0.10. An exact measurement of partial conversion coefficients, especially of those of the L-subshells, allows a simultaneous investigation of the mixing ratio 6 and the socalled penetration effect which can be parametrized by a parameter 2 as described elsewhere 32. 33). We re-analysed the old conversion data of ref. 16) using the code MONICA and got the results 6 = 1.17+0.09 and 2 = 7.2-t-1.5. Combining the two results for 6 we adopt a value of 6 = 1.16+0.07 and calculate from that the B(M1) and "[totvalues as given in table 4. TABLE 4 Experimentally d e t e r m i n e d transition m a t r i x elements in c o m p a r i s o n to calculated values a n d m e a n lifetimes

J2 J,

~.

(2j2-+1) B ( E , M,Tt;j2 .->j~) : exp

2°aTl

.{

~ { ½

2°5T1

~

~ { ½

2°9Bi

a) b) c) d)

~

~-

•29

~

II2 ")

shell m o d e l

corepolarization model

ref.

20)

M1 E2

(8.8 :kl.6) X 10 - 3 2212 i 1 5 6

0 206

2.9>(10-3 2880

20)

MI E2 E2

4.14i0.66 1332 :k600 4224 i378

11.82 112 342

3.24 720 4980

2o) 2o) 20)

M1 E2

(2.524-0.36) × 10- 3 2120 ±160

0 206

2.48 × I0 - a 1880

20) 2o)

M1 E2 E2

2.94±0.42 1056 ±606 2568 4-192

11.82 112 342

2.82 420 3120

20) 2o)

MI E2 E2

(17 275 2620

! 1 0 ) X10 - 3 5:14 ± 2 0 0 c)

0 18.4 1169

7X10-3 143 4101

r,o~ ( h ) (nsec)

0.41-4-0.04 (1.5 4-0.2) < l0 - 3

2.164-0.14 b)

2o) ( 1 . 3 i 0 . 2 ) ; < l0 - a

22) a) a)

(19

Jz9)×10 -3

In units o f e 2 • f m 4 or p 2 . Electronically m e a s u r e d value 1 s) which was used in the analysis o f o u r data in sect. 4. Ref. as). Calculational m e t h o d described in sect. 8 a n d in ref. 5).

186

W. KRATSCHMER et aL

According to Church and Weneser 32) and other authors 33, 34), ~, is related to a reduced transition probability Bpen, which describes the penetration effect, by the equation ,l

.

(2)

B(MI) Contrary to the normal M 1 transition there is no 1 selection rule for the penetrationinduced M1 conversion. This leads to the importance of the penetration effect in the case of forbidden M1 transitions. To get an estimate for the penetration effect in 2°5T1 we assume the "allowed" penetration matrix elements to be equal in both TI isotopes, i.e. R2°5= R 203 = 115+52p~. --pen --pen In 2°STl the internal conversion coefficients for the ~ -* ½ transition are not measured. A calculated total conversion coefficient had to be used introducing a dependence of B(E2) on the two parameters c5 and 2, which are, however, dependent on B(E2) and B ( M I ) . To overcome this problem we proceeded in the following way to determine B(E2), B(M1) and 2 from the experimental y-ray yields, the penetration transition probability Bpe,, as given above, and the total mean lifetime ztot = 2.16_+0.14 nsec [ref. 18)]. Adopting a series of input values for 6 and 2, ~,ot was calculated. Together with the y-ray yields for the 3 ._. ½ and ~ ~ ~ transitions the B(E2) value was determined as in the 2°3T1 case. Using relations (1) and (2) B(M1), 6 and 2 were calculated from "Ctot and Bpen- Input and output values for 6 and 2 were the same for 6 = 1.56+0.15 and 2 = 13.5-+2.5 which were taken to be the self-consistent solutions. The corresponding B(E2) and B(M1) are listed in tables 3 and 4.

5. Gamma-ray angular distributions The angular distribution of ~,-rays following Coulomb excitation can be expanded in Legendre polynomials of even order 2s)

W(O) = 1 + B 2 P2(cos 0) + B4 P4(cos 0).

(3)

Higher-order terms are vanishing in our case. As can be seen in table 2 even t h e / ' 4 terms are negligible. The Legendre coefficients can be written

B2 = AzKz,

(4)

where the angular correlation coefficients Az contain the dependence on the mixing ratio 6(E2/M1): A2 = F2(l' 1, jff, jf) + 26Fz(1, 2, jff, jr) + 62F2(2, 2, jff, jr)

(5)

l+fi2

where jr and jfr are the spins of the initial and final state of the decay, F2(L, L ' , j , ] ' )

2oa.2O5T1 ' 2O9Bi T R A N S I T I O N

PROBABILITIES

187

are the F-coefficients, as defined and tabulated in refs. 35, 36), and L and L' are the multipolarities of the ~-rays. For the transitions ~z ~ { in 203, 205T1 and { ~ ~ in 2°9Bi, where the upper level is populated only by E2 Coulomb excitation, the coefficient K2 is given by " . \aE2 Kz(ji , jf) = F2(2, 2,ji,jr) 2 ,

(6) Ez where Ji and jf are the spins of the initial and final state for the excitation. The a 2 are Coulomb excitation parameters which are functions of the energy of the projectile, the excitation energy and the mass and charge numbers of the target nucleus and the projectile 28). To correct for the slowing down of the beam in the thick target, t h e a2 E2 were averaged taking into account the decrease of the excitation cross section for decreasing projectile energies. The angular correlation coefficients extracted from the Legendre fits to the angular distributions are given in table 2 together with B2, the averaged ~E2 2 , K 2 and B 4. The values for the corresponding mixing ratios are listed in table 3. The angular distributions of the { ~ ½ transitions in 203,205T1 are more complicated to analyze, since the ~ state is not only populated directly by Coulomb excitation but also by the z} ~ { transition. The angular distribution consists, therefore, of three parts:

W(O) = W~,(O)-]-Ky~,[W77(O)-Jc-0~We~,(0)],

(7)

where W~(O) arises from the direct Coulomb excitation, and Wry and Wet from the 7-decay and the internal conversion of the ~ to the ½ state, respectively. The weighting factor K~r can be calculated from the measured decay intensities I v of the { ~ ½ and ~ ~ ½ transitions taking into account the total conversion coefficients ~tot~and O~tot

•

(s) I v (l+CXtot)--l~,

(I+(Xtot)

Eq.(7) can be written in terms of eqs.(3)-(5) by introducing the normalized coefficient K"2 :

"[-~tot 1 + ~ e _]

K2(½~)+K2(½~)tc~ [_ 1 ~ - ~ Kz =

(9)

The two terms in the square brackets containing C2 take into account the part of the angular distribution which arises from the feeding of the { state by the upper transition; C2 is defined in ref. 35). The symbols 61 and 61e are the E2-M1 mixing ratios of the ~-rays and the internal conversion for the upper transition: ~2e __ Zv ~E2 612 Ev

v 0~M1

'

V = K, L, L2, L 3 M, '

~

....

(10)

188

W. KRATSCHMER

et al.

In 2 oaT1 the coefficient K2 was calculated using the experimental cta'-t tot and the calculated ~tt~ot ~ as given in table 1. This yields an angular correlation coefficient A 2 = - 0.767 +_0.044. In 2o ST1 otto t~½, xr~, and K2 were calculated iteratively for different values of 6 in a similar way as in the case of the B (E2) determination. The influence of varying 2 as well was small, so 2 = 13.5_+2.5 was held fixed. By this procedure we got a consistent angular correlation coefficient A 2 = - 0.949_+ 0.050.

6. Deorientation effect

In an earlier experiment on 2°Tpb [ref. 7)] the method of determining the mixing ratio 6 by a measurement of the angular distribution of ~-rays following Coulomb excitation had achieved good results, which agreed with an independent lifetime measurement 5). In the case of the ~ --, ½ transitions in 203, 205TI one must be aware of the fact that the lifetimes of the ~ states are around 1 nsec, where deorientation effects are known to be important 29). By a comparison of the results of the two methods we used to determine the mixing ratios for these transitions we get an estimate for the size of the deorientation effect. Using eq. (5) the adopted mixing ratio 6 = 1.16+0.07 for 2°aTl is equivalent to an angular correlation coeffÉcient A2 = -0.942, which gives, together with our experimental value ofA 2 (cf. table 2), a reduction of the anisotropy of the angular distribution of 18 %. In the same way from A2 = - 0.996 equivalent to 6 = 1.56_ 0.15 the reduction in 2°5T1 is found to be 5 %. This result is somewhat disconcerting since the lifetime of the ½ state in 2°ST1 is about 5 times greater than in 2°aT1. It must be noted, however, that the angular correlation coefficient for 2°5T1, as determined in the way described in sect. 5, is not as well confirmed as the one in 2°aTI, due to the lack of any experimental information about the internal conversion coefficients. In the case of the other transitions investigated, i.e. the )+ ~ ~+ transitions in the TI isotopes and the ½- to ground state decay in 2°9Bi the deorientation effect can be neglected, since the lifetimes of the decaying states are shorter than 20 ps. Even in the presence of very strong fields in the lattice, deorientation times exceed this time by at least one order of magnitude.

7. Results

The resulting reducett transition matrix elements are listed in table 4. All numbers are obtained from our data except the B ( M 1 ) values for the ½+ ~ ½+ transitions in 2°3TI and E°STI where our method of mixing ratio determination may be affected by the deorientation effect, as shown in sect. 6. The B ( M 1 ) values in these cases originate from a re-analysis of previous conversion coefficients is, 16) and lifetime measurements 14. 18), taking into account the penetration effect in the internal con-

2o3.2O5T1 ' 2O9Bi T R A N S I T I O N PROBABILITIES

189

version and using the Coulomb excitation yields from our experiment, as treated in sect. 4. In the case of 2°3TI a cross check is obtained since both conversion coefficients and lifetimes were measured with high accuracy, very good agreement being obtained, shown in sect. 4. In the case of the other transitions in the T1 isotopes a comparison to the previous results of ref. 11) is difficult, since in that paper the analysis of the data was carried out neglecting deorientation and the penetration effect in the internal conversion and using inaccurate conversion coefficients. Besides that, it is not clear from the paper how the feeding from the )+ level into the ~+ level was taken into account. In 2o 9Bi the E2 transition rate between the ground and first excited states is strongly reduced by spin factors which enter into the expression for E2 transitions between single-particle states [cf. eq. (3.32) of ref. 3) for example]. The shell model predicts only 0.03 W.u. for the h~ ~ f~ E2 transition. Because of the resulting small Coulomb excitation yields all previous data for the E2 matrix elements show large statistical errors. Our value of 275_+ 14 e 2 • fm 4 agrees within these large errors to all previous measurements except the one of ref. 4) where 19 MeV e-particles have been used making the assumption of pure Coulomb excitation doubtful 29). In a very recent investigation performed during the completion of this work, a B(E2) value of 240___20 e 2" fm 4 was found 37) i n agreement with our result. The 7-___, ~2- M1 transition in 2°9Bi is hindered by the fact that it is/-forbidden connecting l = 3 and l = 5 single-particle orbits. Our value of (17 + I0) x 10-3 n.m. corresponds to about 10-3 W.u. It is in disagreement with the results of ref. 4) which is due to the doubtful B(E2) value of that work; their mixing ratio 6 agrees with our f-value in between the errors (cf. table 3). 8. Discussion

The three lowest states of 2°3T1 and 2°5T1 and their electromagnetic properties have been one of the first examples for the application of the intermediate-coupling unified model 1, 19). By coupling the s.~, d~ and d.I proton holes to the ground state and the low-lying collective states of 2°6pb and 2°4pb respectively, the observed ~transitions could be described qualitatively. Later on, rather detailed calculations in the framework of the model were performed including also higher terms in the coupling between core and extra particle 20). The core parameters are taken from the experimental properties of the even lead isotopes; the unknown 9-factor of the core is taken from the collective model. The results of this calculation agree reasonably well with our experimental data, as can be seen from table 4. The agreement is equally good for electric and magnetic transitions, and in some cases it is even quantitative. The drastic deviation of the measured E2 rate for the transition between the h~ and f~ proton single-particle states in 2°9Bi from the shell model shows that in this case the effect of core polarization is very important. The ratio of the experimental to the shell-model transition matrix element 3), often referred to as the effective nucleon

190

w. KRATSCHMER

et aL

charge, is very large for the transition: eelf (3.8_0.2)e. From the ground state quadrupole moment as) of 2°9Bi the effective charge of the h~ proton has been determined to be a) eeff = (1.53 +0.06)e. It is obvious from these numbers that the core-polarization effect is strongly dependent on the spins and/-values of the states involved and cannot be parametrized by one effective charge. As in the case of the T1 isotopes, the intermediate-coupling model can be applied to study this state dependence of the core polarization. As has been shown [refs. 4. 5)], the 2 + state in 2°Spb at 4.08 MeV is the collective quadrupole core excitation responsible for at least a large part of the effective E2 charges. To obtain quantitative agreement between experimental E2 transition rates in 2°Tpb and intermediatecoupling calculations, the existence of further quadrupole strength at higher energies had to be assumed 5). Recent electron scattering data show strong peaks around 10 MeV which are possibly quadrupole r e s o n a n c e s 39), but transition strengths, which are needed for a coupling calculation, are not yet known. To get some better understanding of the possible effects involved in the f~ ~ h~ transition in 2 o 9Bi we did some calculations using a quadrupole core strength renormalized to fit the s½--+ d~ E2 transition 40) in 2°9pb. The same core strength was used successfully in a work 5) on 2°Tpb where an outline of the calculational details may be found. The results of the calculations are included in table 4. As can be seen, the agreement with the experimental data is much better than for the shell model, but there are still discrepancies which indicate that there are effects not taken into account. The shell model prohibits the M1 transition between the f~ and the h~ state. From our data it can be seen that this forbidden M1 transition has about the same strength as the E2 one. This gives clear evidence for the fact that spin polarization, which has been shown 41) to arise from the unsaturated spins in the closed shell of the core which are partially aligned by interaction with the spin of the extra particle, is also present. This polarization effect is in general described 42) in terms of an effective spin g-factor g~ and in special cases by a polarization g-factor #p. In the case of an lforbidden transition, only the polarization g-factor contributes. Following the formulae of ch. 3A-2 of ref. 3) we get -----

I 1 = ~3

V3(2j, + 2j~ 1)(2j~ - 1) gp.

(11)

The radial matrix element was calculated to be 0.154 assuming no radial dependence of ~ ' . Using our experimental value, gp = 2.7 +__0.8 is obtained, which is smaller by 40% compared to a best fit 43) of four parameters to five single-particle magnetic moments around Z°Spb. As already pointed out in that paper, there seem to be extra effects which influence the M1 transitions but not the magnetic moments. In table 4 we

20a. ZOSTI' 209Bi TRANSITION PROBABILITIES

191

include an M1 transition matrix element from a calculation based on Migdal theory [ref. 22)], this value is one standard deviation away from our experimental value. 9. Conclusion

It has been shown that e-particle induced Coulomb excitation is a useful means for determining electromagnetic transition probabilities. The B (22) values were obtained with high accuracy from the de-excitation y-ray yields. Careful analysis of the y-ray angular distributions allowed a determination of mixing ratios and B(M1) values. Because of the deorientation effect only the decay of levels with lifetimes shorter than 0.1 nsec can be investigated with this method. The energies of the transitions studied in the T1 nuclei were so small that internal conversion played an important role in the transition probabilities. Conversion coefficients had therefore to be calculated very accurately. In the case of the forbidden M1 transitions this required taking the penetration effect into account, which had a strong influence on the data. Our experimental transition probabilities are in good agreement with calculations performed for the T1 isotopes using the intermediate-coupling unified model 2o). In 2°9Bi, where no detailed theoretical investigations have been made up to now, our first-order calculations for the E2 matrix elements show qualitative agreement with experiment: the stronger enhancement over the shell model for the f? --* h~ transition compared to the h a quadrupole moment is also found in the calculations, but experimentally this effect is still more pronounced (cf. table 4). Our measurement of the B ( M 1 ) value in 2°9Bi is one of the first exampIes of an exact determination of an /-forbidden M 1 transition matrix element between states of well-established single-particle character. This number, therefore, contains relevant information on spin polarization effects in heavy nuclei. The authors acknowledge Prof. P. von Brentano and Prof. E. Kankeleit for stimulating discussions. We also wish to thank Dr. K. Haberkant for helpful assistance during the early part of this work and Mr. R. Schul6 for help with the internal conversion calculations. References 1) A. de-Shalit, Phys. Rev. 122 (1961) 1530 2) O. Nathan, Nucl. Phys. 30 (1962) 332 3) A. Bohr and B. R. Mottelson, Nuclear structure, vol. I (New York, Benjamin, 1969); vol. II (preprint) 4) R. A. Broglia, J. S. Lilley, P. Perazzo and W. R. Phillips, Phys. Rev. C1 (1970) 1508 5) E. Grosse, M. Dost, K. Haberkant, J. W. Hertel, If. V. Klapdor, If. J. K5rner, D. Proetel and P. yon Brentano, Nucl. Phys. A174 (1971) 525 6) A. Bohr, Mat. Fys. Medd. Dan. Vid. Selsk. 26, no. 14 (1952); A. Bohr and B. R. Mottelson, ibid. 27, no. 16 (1953) 7) H. V. Klapdor, P. yon Brentano, E. Grosse and K. Haberkant, Nucl. Phys. A152 (1970) 263 8) R. Woods, P. D. Barnes, E. R. Flynn and G. J. Igo, Phys. Rev. Lett. 19 (1967) 453 9) J. S. Lilley and S. Stein, Phys. Rev. Lett. 19 (1967) 709

192

W. K R A T S C H M E R et aL

10) S. Hinds, R. Middleton, J. H. Bjerregaard, O. Hansen and O. Nathan, Nucl. Phys. 83 (1966) 17 I1) F. K. McGowan and P. H. Stelson, Phys. Rev. 109 (1958) 901 12) D. S. Andreev, J. Z. Gangrskij, I. C. Lemberg and V. A. Nabitchvritchvili, Izv. Akad. Nauk. SSSR (ser. fiz.) 29 (1965) 2231 13) J. W. Hertel, D. G. Fleming, J. P. Schiffer and H. E. Gove, Phys. Rev. Lett. 23 (1969) 488 14) A. Schwarzschild and J. V. Kane, Phys. Rev. 122 (1961) 854 15) J. G. V. Taylor, Can. J. Phys. 40 (1962) 383 16) C. J. Herrlander and R. L. Graham, Nucl. Phys. 58 (1964) 544 17) T. R. Gerholm, B. G. Petterson and Z. Grabowski, Nucl. Phys. 65 (1965) 441 18) S. G. Malmskog, Ark. Fys. 34 (1967) 109 19) A. Covello and G. Sartoris, Nucl. Phys. A93 (1967) 481 20) N. Azziz and A. Covello, Nucl. Phys. A123 (1969) 681 21) A. B. Migdal, Nuclear theory: the quasiparticle method, (New York, 1968) p. 127 22) V. Klemt and J. Speth, Nucl. Phys. A161 (1971) 273 23) H. J. KSrner, K. Auerbach, J. Braunsfurth and E. Gerdau, Nucl. Phys. 86 (1966) 395 24) Y. Gurfinkel, A. Notea, Nucl. Instr. 57 (1967) 173 25) C. M. Lederer, J. M. Hollander and I. Perlman, Table of isotopes, (Academic Press, New York, 1967) 26) T. S. Nagpal and R. E. Gaucher, Nucl. Instr. 89 (1970) 311 27) H. C. Pauli, A computer program for internal conversion coefficients and particle parameters, The Niels Bohr Institute, Copenhagen, 1969 28) K. Alder, A. Bohr, T. Huus, B. Mottelson and A. Winther, Rev. Mod. Phys. 28 (1956)432 29) J. de Boer and J. Eichler, Adv. Nucl. Phys. 1 (1968) 1 30) W. Booth and I. S. Grant, Nucl. Phys. 63 (1965) 481 31) C. F. Williamson, J. P. Boujot and J. Picard, rapport CEA-R 3042 (1966) 32) E. L. Church and J. Weneser, Ann. Rev. Nucl. Sci. 10 (1960) 193 33) H. C. Pauli, Helv. Phys. Acta 40 (1967) 713 34) R. E. Lombard, Phys. Lett. 9 (1964) 254; Contribution to the Conf. on internal conversion processes, 1966 35) L. C. Biedenharn, in Nuclear spectroscopy part B, ed. F. Ajzenberg-Selove, (New York, 1960) 36) Landoldt-BiSrnstein, Group I, vol. 3, ed. H. Appel (Springer, Berlin, 1967) 37) O. H/iusser and D. Ward, AECL progress report P86 (1970) p. 27 38) G. Eisele, I. Koniordos, G. Miiller and R. Winkler, Phys. Lett. 28B (1968) 256 39) T. Walcher, private communication 40) P. Sailing, Phys. Lett. 17 (1965) 139 41) A. Arima and I4. Horie, Progr. Theor. Phys. 11 (1954) 509; 12 (1954) 623 42) E. Bodenstedt and D. J. Rogers, Perturbed angular correlations, (Amsterdam, North-Holland, 1964) p. 93 43) K. H. Maier, N. Nakai, J. R. Leigh, R. M. Diamond and F. S. Stephens, Nucl. Phys. A182 (1972) 289 44) B. I. Deutch and F. R. Metzger, Phys. Rev. 122 (1961) 848 45) M. J. Martin, Nucl. Data Sheets 5, no. 3 (1971) 307 and private communication