The decay scheme of Pb211

1.E.I : ]

Nuclear Physics 41 (1963) 482--496; (~) North-Holland Publishing Co., Amslerdam

I.E.4

Not to be reproduced by photoprhat or microtilm without written permission from the publisher

J

THE

DECAY

SCHEME

OF Pb 2u

S. E. VANDENBOSCH, C. V. K. BABA t p. R. CHRISTENSEN, O. B. NIELSEN and H. NORDBY Institute for Theoretical Physics, Umversity of Copenhagen, Denmark Received 22 August 1962 Abstract: The disintegration scheme of the 36.1 min fl- emitter Pb m has been studied by means of a six-gap fl-ray spectrometer, scintillation spectrometers, coincidence techniques, directional correlation measurements and lifetime measurements. The fl- spectrum of Pb zu has four components with endpoint energies: 1355 keV (92.4 %), 951 keV (1.4 ~), 525 keV (5.5 ,~/o) and 251 keV (0.7 %). The following transitions in Bim were observed: 404 keV (55 Yo MI and 45 E2), 426 keV (MI), 700 keV (M1), 830 keV (MI) and 1104 keV. A decay scheme is proposed with levels in Bim at 0 keV (~-), 404 keV (~r-), 830 keV (.~-) and 1104 keV. The transition energy between Pb m and Bi2u is 1355 keV. The half life of the 404 keV level is (3.15-i-0.20)× 10-1° sec. The E2 lifetime of the 404 keV level is compared with theoretical estimates. The half life of the 830 keV level is less than 0.9 × 10 q° see. In addition it was possible to set an upper limit of 0.6 × 10-l° see on the half life of the 351 keV level in TI2°7. The levels of Bi'zx~are discussed in terms of single-proton states or states involving the single proton and two neutrons outside the doubly closed shell. 1. I n t r o d u c t i o n A l t h o u g h s2-,,t29pk2 t i is a m e m b e r o f the n a t u r a l l y o c c u r r i n g a c t i n i u m (4n + 3) r a d i o a c t i v e series, v e r y little d e t a i l e d i n f o r m a t i o n has b e e n a v a i l a b l e a b o u t t h e levels in n.211 p o p u l a t e d b y t h e fl-decay o f Pb 211 A s u m m a r y l) o f p r e v i o u s s c i n t i l l a t i o n 83]Dl128 a n d f l - s p e c t r o m e t e r m e a s u r e m e n t s s h o w s five levels in Bi 211 b e l o w 900 keV. N o spin a n d p a r i t y a s s i g n m e n t s are m a d e . T h i s level d e n s i t y s e e m s h i g h f o r a n u c l e i d e w h i c h has o n l y t w o n e u t t o n s a n d o n e p r o t o n o u t s i d e o f a d o u b l e d o s e d shell a n d also is n o t in a g r e e m e n t w i t h m o r e r e c e n t ?- a n d fl-scintillation s p e c t r o m e t e r m e a s u r e m e n t s 2). T h e levels o f Bi 2t ~ a r e o f i n t e r e s t b e c a u s e o f t h e p r o x i m i t y t o a d o u b l y c l o s e d shell. It is e x p e c t e d t h a t t h e e n e r g y levels in this n u c l e i d e c a n b e a s c r i b e d t o s i n g l e - p a r t i c l e states o f the p r o t o n o r t o t h r e e - p a r t i c l e states o f the t w o n e u t r o n s a n d t h e p r o t o n o u t s i d e the d o u b l y c l o s e d shell. I n t h e w o r k r e p o r t e d here, t h e levels o f Bi 211 p o p u l a t e d by the fl-decay o f P b 21 t w e r e s t u d i e d b y m e a n s o f y-scintillation s p e c t r o m e t e r , f l - s p e c t r o m e t e r , fl-y c o i n c i d e n c e , d i r e c t i o n a l a n g u l a r - c o r r e l a t i o n a n d l i f e t i m e m e a s u r e m e n t s . I t was t h e n p o s s i b l e t o assign m u l t i p o l a r i t i e s to m o s t o f the t r a n s i t i o n s a n d to suggest spin a n d p a r i t y assignm e n t s f o r the levels in Bi 2x 1 w h i c h a r e c o n s i s t e n t w i t h the shell m o d e l states a v a i l a b l e . F r o m these m e a s u r e m e n t s w e h a v e c a l c u l a t e d the B ( E 2 ) v a l u e for t h e first e x c i t e d state in Bi 211. A d e c a y s c h e m e for P b 211 is p r o p o s e d , i n c l u d i n g a level in Bi 211 at 1104 k e V w h i c h h a d n o t p r e v i o u s l y b e e n o b s e r v e d . * Permanent address: Atomic Energy -Establishment Trombay, Bombay, India. 482

483

D E C A Y SCHEME OF Pb 21t

2. Source Preparation Pb 211 is a descendent o f 22 y AC 227. The decay chain is shown in fig. 1. A l m C u r sample of mc 227 in equilibrium with its daughters was obtained from The Radiochemical Centre, Amersham, England. The sample also contained about 1 mg of stable Fe +3. Since the numerous gamma-ray transitions in Th 227 and Ra 22a would interfere with the study of the Pb 21Ldecay scheme, it was necessary to develop a procedure which would separate pb214 from these elements. T h 227 was separated from Fe, Ac z27 and daughters by absorption on a Dowex-1 anion exchange resin column (free column volume about 3 ml) from 7N H N O 3 (ref. 3)). Ra223 was allowed to

(22y',Ac ;:) (IB.2d) Th ;~7

(i L 6 d ) Ro 2~3 (3.92 s) Em 2!9 (0.0018 s) PO215

(235rain) B i

p" 03"/,

(4.78rnin) Tt 13-

Po ct

s t o n e Pb

Fig. 1. The actinium ~ decay chain.

grow into equilibrium for 22 days. Radium was then removed from the colunm with 7N H N O 3 and this solution was evaporated. The radium was dissolved in water and absorbed on a Dowex 50 cation resin micro column 4) (free column volume 10/zl). Pb 211 could now be "milked" from the Ra 22s with a solution of 0.025M a m m o n i u m ethylene diamine tetra-acetic acid (pH 5.7) (ref. 5)). The activity was placed on 150/~g/cm 2 AI foil wlfich was heated to destroy organic material. The sources were just visible on the foil. Using this procedure it was possible to separate 36 min Pb 2~ J from the Ra 223 and mount the activity for fl-spectrometer measurements in 30 minutes. About 50 sources were made for scintillation spectrometer, fl-spectromcter, lifetime- and angular-correlation measurements. After completing the Pb 2~ t measurements, sources of Ra 22s were made for some of the lifetime measurements. Ra 22s was removed from the cation column with 7N HNO3.

484

s . E . VANDENBOSCH e t al.

3. The ~,-Scintillation Measurements 3.1. E Q U I P M E N T

Gamma-ray-singles measurements were made using a 7.6 cm x 7.6 cm thallium activated sodium iodide crystal. The counting was done in a standard position for which the efficiency and geometry have been determined for photons ranging in energy from 50 keV to 2000 keV. For the Y-7 coincidence work a 3.8 cm x 3.8 cm thallium activated sodium iodide crystal was also used. 3.2. M E A S U R E M E N T S

The singles y-ray spectra of Pb u 11 is shown in fig. 2. The peak at 90 keV is due to KX-rays. The 351 keV peak is due to the decay of the 351 keV level in T12o7 populated

K X-RAYS

351

10000 +425

000

100

1

I

200

I

I

400

I

I

l

600 800 ENERGY (keY)

I

/

I

1000

Fig. 2. The singles g a m m a ray spectrum o f Pb ttl and Bi txx

in the a-decay of Bi 2t 1. The other y-rays observed in this spectrum are assigned to transitions between levels in Bi 211 populated by the fl-decay of Pb 211. Gamma-ray intensities relative to the 351 keV 7 transition in TI 2°7 are listed in table 1. Energies are obtained from conversion electron work. The relative y-ray intensities of the 351 keV plus 415 keV complex and the 830 keV complex are in agreement with the values reported by PiStzelberger 2). The intensity of the 700 keV 7-ray as well as the relative intensities of the 400 keV and 426 keV y-rays were determined by fl-y-coincidence measurements which will be described later.

DECAY SCHEME OF Pb2u

485

The results of y-y-coincidence measurements are shown in table 2. No y-rays were observed to be in coincidence with 830 keV y-lays. TABLE 1 Bi ~at gamma-ray intensities relative to the 351-keV gamma-ray transition in TI-207 Transition energy (keV)

Intensity

351 4044-426 404 a) 426 a) 700 a) 830 1104

1.000 0.3834-0.057 0.258 4- 0.052 0.125 4- 0.025 0.038-t-0.011 0.248-4-0.025 0.01074-0.0016

a) Intensity determined by coincidence measurements. TABLE 2 Coincident gamma-ray transitions Gate

Gammas in coincidence

351 4044-426 700 830

KX-rays KX-rays, 4044-426, 700 KX-rays, 404 no gammas in coincidence

4. The p-Spectrometer Me~tsarements 4.1. EQUIPMENT

A 6-gap fl-ray spectrometer was used to study the conversion-electron spectrum. In general, the measurements were made at a setting corresponding to 1.2% resolution and I0% transmission. In a few experiments the baffles and counter slit were adjusted so that the spectrometer was operated at 0.5 ~o resolution with I ~o transmission. Coincidences between conversion electrons or fl-rays focused in the spectrometer and y-rays were measured by means of a 7.6 x 7.6 cm NaI crystal placed behind the source. Coincidence resolving times 2z = 2-5x 10 -a see could be used. In some cases, the y-ray spectra in coincidence with certain conversion lines were recorded on a 512-channel analyser. Endpoints and intensities of relatively weak fl-groups were determined by counting coincidences with individual y-rays selected by a single channel. Finally, some K-conversion lines were measured by the recording of events in coincidence with KX-rays. 4.2. MEASUREMENTS

4.2.1. The fl-groups. A Kurie plot of the fl-spectrum shown in fig. 3 gives an end point energy of 1400__+20 keV. Most of the Pb 211 fl-decay goes to the ground state,

486

s . E . VANDENBO$CH et aL

but this end point cannot be taken as the decay energy of Pb 211 since half of the /Y-rays that are recorded are due to the decay of TI 2°7. The decay energy of Pb 2tl (1355 keV) was determined from the Kurie plot of/Y-rays coincident with 830 keV I

i

I

I

I

;

I

8.0 32 ~ o o o K U R i E PLOT pb211*T1207 p SINGLES

KURIE PLOT Pb211 B COINCIDENT WITH 830keV GAMMAS . £o : 525 ~ 25 keV

~-o Eo = 1/.00 ~-20 key

o

6.0

+1f

2.0

+

r

400

I

L

i

I

200

800 1200 ENERGY (keV)

Fig. 3. Kurie plot o f the Pb ~1 and T P 7 beta spectrum. I

8.0 ~ 6.0

,

400 600 ENERGY (keV~

I

Fig. 4. Kurie plot of Pb =it beta rays coincident with 830 keV gamma rays.

l

[

i

KURIE PLOT pJll 13 COINCIDENT WITH 404 AND 426 keY GAMMAS

"~

4.0-

2.o

- ~ 200

, 400 600 ENERGY {keY)

B00

Fig. 5. Kurie plot o f P b 2t~ beta rays coincident with the complex 404-426 keV gamma ray peak.

TABLE 3 Energy

and

intensity

of

the

Pb =it beta groups

Beta energy (keV)

Intensity (~)

log ft

1355--25 951 --25 525~E25 251 =t=-25

92.4± 1.5 1.4±0.5 5.5±0.8 0.7±0.2

5.9 7.3 5.9 5.9

DECAY

SCHEME

OF

P b 211

487

T-rays (fig. 4). A Kurie plot of the two fl-groups coincident with the complex 404426 keV T-ray peak is shown in fig. 5. By correcting for efficiency, conversion coefficient, and random coincidences it was possible to determine the relative intensity of the fl-groups. The relative intensities and l o g f t values of the beta groups are listed in table 3. 4.2.2. Conversion electrons. Both the energy and the intensity of the conversion electrons were determined relative to the 351 K line in TI 2°7. The singles conversion electron spectrum of the 351 K, 404 K, 426 K + 3 5 1 L, 700 K and 830 K lines are shown in fig. 6 and in fig. 7(a). It was not possible to resolve the 351 L line and the 426 K line. Not even measurements with 0.5~o resolution showed any detectable broadening of the line. The intensity of the 426 K line relative to the 404 K line was determined by measuring both of these lines in coincidence with KX-rays. This measurement eliminated the 351 L line. The 700 K and 830 K lines were too weak to be measured on the fl-ray background (fig. 7(a)). The signal-to-noise ratio was improved by about a factor of 10 by recording only events in coincidence with KX-rays (fig. 7(b)). With a total counting rate in the T-ray channel of about 50 000 sec-1 and a coincidence resolving time 2~ = 3 × 10 - s sec, the background, which at this energy is not coincident with any T-ray, was reduced about 10 000 times, whereas the conversion electron counting rate was only reduced corresponding to the efficiency of the N a I crystal for X-rays 8 ~o. The 404, 426 and 700 K lines were coincident with other transitions and a correction was made for the KX-rays arising from conversion of these transitions. The relative K conversion electron intensities are listed in table 4. By gating the T-crystal with the 404 K line a value of 3.32 for the intensity ratio of the 426 keV g a m m a ray to the 700 keV g a m m a ray was obtained. TABLE 4 Relative K conversion electron intensities

Transition energy (keV)

Intensity

.............................................

351±1 404±1 4264- I 700 ~ 2 83012

1.000 0.119 4-0.006 0.082 ~0.012 0.0057 ~ 0.0009 0.028 ~ 0.003

5. Conversion Coefficients 5.1. THE ?,-INTENSITIES The intensities of the 415 keV complex (404+426 keV), 830 keV and 1104 keV peaks have been determined relative to the 351 keV T, as described in sect. 3. With this information and the results of fl-T-coincidence measurements one obtains the relative intensity values of 0.258 for the 404 keV T-ray and 0.125 for the 426 keV T-ray.

488

VANDm,mOSCHet aL

s.z.

351K

+

ulooo00

L

80000

426K+ 351L / , 351M.N

40~K

60000 z 40 000 o u

20000 . . . .

t

. . . .

280(

I

. . . .

r

. . . .

r

,

,

.:

. . . .

!

,

.

i

,

,

,

3000

3200 3400 3600 mA Fig. 6. The singles conversion electron spectrum o f the 351 K, 404 K and the 426 K+351 L lines.

I

I

700K ..J %, %% %

30 000

I

I

I

Pb211 13 SINGLES (NOT DECAY CORRECTED)

.E E ,:5

.% Ooo%

2000O

830K

-..,,

z 0 u

"%. 0°%°~%a,o

I0 000 o)

I

I

5.0

~

5.2

5.4

I

I

5.6

5.8

A lOO

(NOT DECAY CORRECTED)

"E 80

z 40

•

•

• e

b) ©o

°

20

,•

700K

"~ 6o 0

83O K

Pb211 CONVERSION ELECTRONS COINCIDENT WITH K X-RAYS

-

~m

I

5.0

I

5.2

i

A

5.4

t

5.6

i 5.8

Fig. 7(a). The singles conversion eloctron spectrum o f the 700 K and 830 K lines. (b). The conversion electron spoctrum o f the 700 K and 830 K lines coincident with KX-rays.

DECAY

489

SCHEME OF Pb ell

Using the value of 3.32 for the ratio of the 426 keV y to the 700 keV ?-intensity obtained in fl-?-coincidence measurements (sect. 4), we calculate a value of 0.038 for the relative intensity of the 700 keV ?-ray. 5.2. THE 351 keV

K[7 RATIO

Both the conversion electron intensities and y-ray intensities of transitions in Bi 211 were determined relative to the 351 keV K-conversion electron and y-ray intensities, and therefore it is necessary to know the 351 K/? ratio before computing conversion coefficients of these transitions. Our measurements show that there are 0.0314 351 K lines per Pb 2~ fl-decay. Combining this with the fact that the number of Pb 2 ~1 fl-decays is equal to the number of Bi 2~a 0c-decays and the information that 17 70 of the Bi 2~ or-decays populate the 351 keV level 6), a K/y ratio of 0.24 for this transition is obtained. The conversion coefficients for the Bi 2~ t transitions calculated using this value are compared with theoretical values for E2 and M1 transitions in table 5. The decay scheme of Pb 2 ~ based on these measurements is shown in fig. 8. TABLE 5 Comparison of experimental conversion coefficients with Rose's theoretical values ~)

K/7

Transition energy (keV) 351 404 426 700 830 1104

Exp. 0.239 0.108±0.022 0.154_--'.0.039 0.035 ±0.012 0.026." 0.004

Theoretical

Transition intensity

M1

E2

0.232 0.175 0.155 0.041 0.026

0.035 0.034 0.031 0.010 0.008

0.17 0.039 --0.008 0.020 -t-0.004 0.0054-L 0.0016 0.035 ~0.004 0.0014-4,-0.0002 s)

s) estimated assuming MI.

p. 21~ 82

b129

ENERGY

\ \

m ~ 1104 i700 J1104 0.0054 0.0014

-

5.5*/,

IMI I

924%

1404

i

. . . /. .

tog "tt =5.9 (J.04 / 'k

%

B3o -~o

-" 0.90x I0 sec

Jh/2 =3.15x10 "" --i---t.04 -iosec

IM 1 55'1,,wi

o .211 83BI12B

tl/2 = 2.2rain

Fig. 8. The decay scheme of Pb m~.

M1 (70) 100 55 100 82 100

490

s.E.

VANDENBOSCH et aL

6. Angular Correlation The directional correlation measurements between the 404-426 and 404-700 keV y-ray cascades were made using a four counter assembly. Liquid sources of Pb 2~ dissolved in 0.025 M E D T A were used in the experiments. The counts were collected simultaneously in all the counters and thus the decay corrections were eliminated. By taking the ratios o f the coincidence counting rates and by changing the position of the counters, efficiency corrections for the coincidence circuits are eliminated. The data were fitted to the function W(O) = 1 +A2P2(cos O)+A4P4(cos 0). The resulting A2 and A 4 coeffÉcients were then corrected for the geometry of the detectors according to the method of Rose s). These corrected coefficients are 426-404 keV cascade ,42 = -0.079___0.018, A 4 = -0.006-t-0.018, 700-404 keV cascade A 2 = - 0 . 1 4 ___0.03, A4 =

0.130 +0.04.

I f the 426 keV transition is pure M1 as indicated by the conversion coefficient and spins 9 and ]- are assumed for the ground state and 404 keV levels, respectively, only a spin assignment of 9 for the 830 keV level gives an E2 mixing of 45 4- 5 70 for the 404 keV transition in agreement with conversion coefficient data. The situation is not as clear for the 1104 keV level. From the angular correlation measurements the E2 admixture in the 700 keV transition is less than 1 70 if the spin is 9 and 45 70 if the spin is ~. The E2 admixture 18+3570calculated from the conversion coefficient is intermediate and therefore it is not possible to assign a unique spin to the 1104 keV level.

7. Half Lives of Excited States The half life of the 404 keV level in Bi 211 was measured by the delayed coincidence method. The apparatus was the same as that described previously 9). Measurements of the half life of the 830 keV level in Bi 211 and the 351 keV level in T12°7 were attempted, but both turned out to be too short for this method and we can only put an upper limit on the half lives of these two levels. 7.1. T H E

404 keV LEVEL

I N P b ~11

Pb 2~ 1 sources as well as Ra 223 sources were used for these measurements. For the 426 keV 3,-404 keV 3' cascade two Naton 136 scintillators, each. 2.5 cm by 2.8 cm diam. were used. The two slow channels were set to accept the upper third of the Compton distribution from the 400 keV y-rays. We could not distinguish between a 426 keV y-ray and a 404 keV ~;-ray and the same slope appeared on both sides of the time analysis of these coincidences, as shown in fig. 9.

t i

i

i /~ / ~

i

i

i

Bi211 :

I k

Ulo~l Z

<>

i ; I I DECAY OF 404 keY LEVEL 1

,-,,.EASUREMENT t' 2 = 3 02~ 0 sec ' = 3100x|olOsec

10 3

6

491

SCHEME OF Pb 211

DECAY

J

~

\

:;

, I~:#

10 I~/, '

1 I i

4

~

~kt

I

-2

.

I

0 TIME 10-9sec

1

, !-

*T- i

/

] 1-I

I ~ I lil ;l i 2 4 6 8 UNITS (ARBITRARY ZERO)

l

Fig. 9. T h e time analysis o f the decay o f the 404 k e V level in Bi2XL 7-7 coincidences. T h e r a n d o m coincidences h a v e b e e n subtracted. i

i

Bi 211 :

DECAY OF 404 keV LEVEL 12--y MEASUREMENT

103

sec

z o uW 10 2 z l.iJ a

Z 0u 10 ~ RANDOMS

2 O TIME 10-gsec

'

~

2 4 6 UNITS (ARBITRARY ZERO)

Fig. 10. T h e t i m e analysis o f the decay o f the 404 keY level in Bi m . fl-y coincidences. T h e r a n d o m coincidences h a v e been subtracted.

492

s . E . VANDENBOSCH el aL

The time spectra of the coincidences between fl's with a maximum energy of 951 keV and the 404 keV v-ray were also analysed. The same scintillator described previously was used for the ?-ray, and for the fl's, a 0 . 1 5 c m by 1.3 cm diam. Naton 136 scintillator was used. This scintillator was covered with 10 mg/cm 2 A1 foil to stop the a-particles from Bi 2xz and R a 223 and its daughters. The y-ray counter triggered again on the upper third of the Compton distribution from the 404 keV transition and the fl-detector triggered on the upper part of the fl-continuum which feeds the 404 keV level. The time analysis of these coincidences is shown in fig. 10. The calibration of the pulse amplitude spectra in terms of time is done by lengthening the cable delay from one of the counters by a measured amount and observing the shift of the distribution along the amplitude scale. A standard error of 3 ~o has been adopted to take account of errors in this procedure. Six independent measurements were made and the value adopted for the half life of the 404 keV level in Bi 2~1 is 4 = (3.15_+0.20) x l0 - * ° s e c . 7.2. T H E 830 keV L E V E L IN Bi 2xx

The 830 keV level in Bi 211 is populated directly by fl-de c a y ( E ~ , = 525 keV) and it decays partly with an 830 keV ?-ray to the ground state. The scintillators and stopi

t

J

- Bi TM: D E C A Y O F T H E 8 3 0 k e V L E V E L

A~

~i02

/I

D O

/

t,,~ =

!0

082xl0 sec t(~NSIRUMENTaL )

7

N (J 7

~I0

1

1

', -

I 0

.tl 1

TIME 10-19sec UNITS (ARBITRARY Z E R O ) Fig. 11. The time analysis o f the decay o f the 830 keV level in Bi ' n . N o half life longer than 0.82 × l 0 -1° see was observed, and the experimental limit has been taken as 0.9 × 10-l° sec.

ping foil were the same as those used in the measurement of the half life of the 404 keV level by fl-? coincidences. The time analysis of these coincidences is shown in fig. 1 I. The curve shows only the instrumental resolution of the apparatus. The slopes on both the right-hand edge and the left-hand edge are the same and correspond to 4 = 0.82 x 10 - ' ° s e c , indicating a half life of less than 0 . 9 x 10 -~° see.

DECAY SCHEME OF

Pb~11

493

7.3. T H E 351 keV L E V E L I N Tl t°~

The 351 keV level in Tl 2°7 is populated in 17~o of the ~-decays of Bi 211. Coincidences between these ~-particles and the 351 keV ~-rays were recorded. Pb 2: t sources with 2.2 min Bi 211 in equilibrium were used. A 0.01 can by 1.3 cm diam. plastic scintillator was used as the alpha detector and the ~-detector was a 1.5 cm by 2.1 cm. diam. Naton 136 scintillator. The ~-counter triggered on the upper part of the Compton distribution from the 351 keV ~-ray. The time analysis of these coincidences is shown in fig. 12. This curve shows only the instrumental resolution of the apparatus with a slope on its right-hand edge corresponding to t t = 0.50 x 10-1 o see indicating a half life of less than 0.6x 10 -1° sec. i -- TI207: DECAY OF T H E 351keV LEVEL

103 o3 o o (INSTRUMENTA

10 2 z UJ o Z

5 10 ~

0 T I M E 10"9sec UNITS ( A R B I T R A R Y Z E R O )

Fig. 12. The time analysis o f the decay o f the 351 keV level in TP eT. N o halflife longer than 0.50 x 10-1° see was observed, and the experimental limit has been taken as 0.6 x 10 -x0 see.

8. Discussion 8.1. S P I N A N D P A R I T Y A S S I G N M E N T S

u..211 nucleide. All o f the levels o f Bi 211 populated by Pb 211 fl-decay 8.1.1. The sa~.~12s must have the same parity since they are connected by either pure M1 or mixtures of r,.209 • 9 E2 and M1 transitions. The measured value for the ground-state spin of s3t~1126 is (ref. lo)). The lowest energy single-particle level for the 83rd proton is h t- (ref. 11)). Supported by these considerations, the ground state o f Bi 211 is assigned a spin and parity of 9 - .

494

s.E.

VANDENBOSCH et al.

The next single-particle proton state of the same parity is fi_. The M1 transition between the fi- and tq- states is /-forbidden. The observed slowness (cf. sect. 4) of the 404 keV Mt'transition does not contradict an f~- assignment to the 404 keV first excited state of Bi 211 The angular correlation between the 426 keV and 404 keV ?-ray transitions is consistent with the measured conversion coefficient of the 404 keV transition only if the spin and parity of the 830 keV level are assumed to be x9 - . The 1104 keV level is populated directly by fl-decay with l o g f t -- 5.9. It decays to the ground state and by predominantly M1 transitions to the 404 keV state. This limits the spin and parity choices to 3 - or ~9 - . 8.1.2. Interpretation of the Bi 211 levels. It is reasonable to describe the ground state and 404 keV state as single-particle states. The 830 keV and 1104 keV levels can arise from coupling of the odd proton to excited states of the two neutrons outside of the closed shell. Bi 211 can be thought of as Pb 2t° plus a proton. Levels in pb 210 at 780 keV (2 + ) and 1084 keV which may be excited neutron states are populatedby the fl-decay of T121° (ref. 12)). The 830 keV and 1104 keV states in Bi 211 perhaps can be described as a proton coupled to these neutron states. Although either the f~- or h t- proton could be involved in this coupling, the h t- proton is preferred because the log ft value of 5.9 for the fl-decay to these states is the same as to the ground state whereas the l o g f l value for decay to the f~- state is 7.3. Before any conclusions on this point can be drawn, it would be useful to have more detailed information about the levels in Pb 21° 8.1.3. The Pb 2~ nucleide. The lowest energy single-particle state for the 129th neutron is gt÷ (ref. 11)). The l o g f t values of 5.9 and 7.3 for fl-decay to the h~- and f~- levels of Bi 211 are consistent with this assignment. 8.1.4. Transition probabilities. From the measured value of 3.15 x I0-10 sec for the half life of the 404 keV level and the 55~o M1-45~o E2 mixing ratio experimental M1 and E2 half lives can be obtained. After correcting for internal conversion, the photon half lives a r e 6 . 5 5 x 10 - i v sec for M1 and 8.00x 10 -1° sec for E2. The MI transition is/-forbidden and therefore it is not surprising that the half life is 2 x 103 longer than the Weisskopf estimate ~3). As a rough yardstick of the E2 transition rate we make the usual comparison with the value given by the Weisskopf single-proton transition probability formula with the statistical factor taken as unity. The experimental E2 half life is a factor of 1.15 longer than the simple Weisskopf half life. One refinement to the formula used above is to include the statistical factor 14) arising from the angular integration. The Weisskopf estimate with the statistical factor applied is given in table 6. For one proton outside of a closed shell it is appropriate to make a more careful analysis based on the model of a single proton in a potential well undergoing the transition f~- ~ 1~-. The radial matrix elements involved in the E2 transition probability calculation are estimated using more realistic wave functions than in the Weisskopf model. The

DECAY SCHEME OF Pb21x

495

transition probabilities evaluated from harmonic oscillator wave functions using Nilsson's choice 15) of hoJo = 41 A - j MeV turned out to be slightly smaller than the Weisskopf estimate including the statistical factor. Recently, Wahlborn ~6) has shown that the radial matrix elements for E2 transition probabilities evaluated from realistic wave functions in a rounded square well potential often differ considerably from those evaluated with harmonic oscillator wave functions. For f~---, tqtransitions the E2 transition probability is 2.9 times less than the harmonic oscillator estimate. The experimental E2 transition probability is appreciably greater than these refined theoretical estimates (cf. table 6). TABLE 6 C o m p a r i s o n o f the 404 keV f~ --->h t E2 transition probability with theoretical one-particle estimates (The statistical factor has been included in the theoretical estimates). Exp. t t X 10 -1° see T(E2) x 108 see -1 B(E2) x eZl0 -4s cm 4

8.00 8.7 6.6× 10 -s

Weisskopf 13)

H a r m o n i c oscillator 15)

64 1.1 0.81 × 10 -s

78 0.88 0.66× 10 -s

W a h l b o r n ,e) 220 0.32 0.24× 10 -a

One of the factors which may account for tiffs increased E2 transition probability is the interaction between the single proton and the rest of the nucleus, as a result of which the core is slightly deformed and contributes an extra quadrupole moment which adds to the quadxupole moment of the particle. The same proton transition (fl- --' h i - ) is observed in the closed shell plus one proton nucleus Bi 2°9, and it may be faster than the Wahlborn estimate 17). Tiffs enhancement can be taken into account quantitatively by associating with the single proton an effective charge (eeer). The effective charge is related to the reduced transition probability by ~ eeff = V"B(E2)~p "

(l)

In Bi 2°9 one finds experimentally e©ff ~< 2.6 (ref. 17) when the Wahlborn estimate is used for the B(E2)s p value. As a first approximation one can associate an effective charge with the single proton in Bi 21~ by formula (1) and one then obtains e~rf = 5.3 when the Wahlborn estimate is used. The enhancement in Bi 21~ is larger than the enhancement in Bi 2°9, which indicates that the influence o f the neutron pair outside the doubly closed shell cannot be neglected. Additional independent evidence that the neutrons are not unimportant in the wave functions of the f~- state is the position of the analogous level in Bi 2°9. The 910 keV f~- state o f Bi 2°9 should be a pure proton state since there is only one proton outside of a doubly closed shell. The influence of the two additional neutrons in Bi 211 brings the f~- level down to 404 keY. We are indebted to Professor Niels Bohr for the excellent working conditions in his Institute, and to Dr. J. O. Rasmussen for help/hi discussions.

496

s.E. VANDENBOSCHet al.

References 1) 2) 3) 4) S) 6) 7) 8) 9) 10) 11) 12) 13) 14)

D. Strominger, J. M. Hollander and (3. T. Seaborg, Revs. Mod. Phys. 30 (1958) 585 Von Thorgerd P6tzelberger and B. Karlik, Sitzungsber. Osterr. Akad. Wiss. No. 15 (1959) 284 J. Danon, J. Am. Chem. Soc. 78 (1956) 5953 S. Bjornholm, O. B. Nielsen and R. K. Sheline, Nature 178 (1956) 1110 E. J. Freiling and S. W. Mayer, J. Am. Chem. Soc. 75 (1953) 5647 R. C. Pilger, Jr., University of California Radiation Laboratory Report UCRL-3877 (1957) M. E. Rose, Internal conversion coefficients (North-Holland Publ. Co., Amsterdam, 1958) M. E. Rose, Phys. Rev. 91 (1953) 610 P. R. Christensen, Nuclear Physics 37 (1962) 482 J. E. Mack, Revs. Mod. Phys. 22 (1950) 64 B. R. Mottelson and S. G. Nilsson, Mat. Fys. Skr. Dan. Vid. Selsk. 1, No. 8 (1959) T. Mayer-Kuckuk, Z. Naturforsch. 11a (1956) 627 V. F. Weisskopf, Phys. Rev. 83 (1951) 1073 S. A. Moszkowski, in Beta and gamma ray spectroscopy, ed. by K. Siegbahn (Intersciencc, New York, 1955) 15) S. (3. Nilsson, Mat. Fys. Medd. Dan. Vid. S¢Isk. 29, No. 16 (1955) 16) S. Wahlbom, Nordita notes (1960) 17) O. Nathan, Nuclear Physics 30 (1962) 332