Spectroscopy of 212Rn

Nuclear Physics A#6 (1988) 397-413 North-Holland, Amsterdam

SPECTROSCOPY A.E. STUCHBERY,

G.D.

OF *‘*Rn

DRACOULIS

and

A.P. BYRNE

Deparrmenf of Nuclear Physics, Research School of Physical Sciences, Australian National University, GPO Box 4, Canberra, ACT 2601 Australia A.R.

POLETTI

Department of Physics, University of Auckland, Private Bag, Auckland, New Zealand Received

27 April

1988

AbstracP Excited states of “*Rn have been studied using y-ray and electron spectroscopy following the reactions zosPb(9Be, 5n) and ‘04 Hg(‘%, 5n). With the exception of the energy of the yrast 8++ 6+ transition, the previously proposed level scheme has been verified. New transitions have been placed in the level scheme and new lifetime and g-factor results obtained. The level. scheme and electromagnetic properties of selected isomeric states are compared with the results of shell model and semi-empirical shell-model calculations, including coupling to octupole vibrations.

E

NUCLEAR REACTIONS 20aPb(9Be, 5n), E =45&O MeV; 2oaHg(‘3C, 5n), E = 72-75 MeV, measured yy(t), xy(r), Ey, Iy(fJ), I(ce), ly(B, H, f), ly(E, r).*‘*Rn deduced levels planar Ge, Si(Li), J, n, TX,,, g> B(h), ICC. Enriched targets, pulsed beam, Ge hyperpure, Compton suppressed detectors. 2’*Rn, calculated levels, B(A), g. Shell model. NUCLEAR STRUCTURE

1. Introduction The nucleus *“Rn, with four valence protons outside the ‘*‘Pb core, shows many features in its level scheme 132) which can be interpreted using the nuclear shell model ‘-‘). In a series of recent publications 7-1o) we studied the electromagnetic properties

of core-excited

At, Fr and Rn, including

isomers

and certain

related

states in several

2’2Rn. In this paper we report new experimental

isotopes

of

information

and a theoretical study of *‘*Rn. Comparisons are made between experiment and shell-model calculations of excitation energies, transition rates and gyromagnetic ratios. As the structure of the core-excited states of 2’2Rn has been discussed already 7), we focus here upon the spectroscopy and structure of the non core-excited levels (those below the yrast 20+ state). 2. Experimental The experimental results reported in this paper were obtained in the course of a study of ‘13Rn, the details of which have been described earlier ‘*). Briefly, high-spin states of ‘i2Rn were populated following the 208Pb(9Be, 5n) and 204Hg(‘3C, Sn) reactions

using 9Be and 13C beams

from the Australian

0375-9474/88/$03.50 @ Elsevier Science Publishers (North-Holland Physics Publishing Division)

B.V.

National

University

14UD

398

A.E. Stuchbery

pelletron populated

et al. / ‘12Rn

accelerator. Although the experiments were optimized to study ‘13Rn, in the 4n channel in each case, information on the structure of *l*Rn was

also obtained

from excitation

angular

distribution

beam-y

timing

g-factor

measurements.

function

measurements,

measurements

measurements,

observation

3.1. LEVEL

of conversion

and time-differential

3. Experimental

yy-coincidence

perturbed

and

electrons,

y-ray pulsed

angular-distribution

results

SCHEME

The level scheme of *12Rn deduced the -y-rays assigned

to 212Rn together

from our work is shown in fig. 1. Table 1 lists with their relative intensities

the 9Be induced reaction at a beam energy of 57 coefficients are also listed in table 1. As the inclusion fitted angular distributions was generally unjustifiable, were obtained with oq set to zero. (Angular-distribution

observed

following

MeV. Angular-distribution of a P,(cos 0) term in the the results given (table 1) coefficients, obtained from

the TDPAD g-factor measurements, are given in table 4, below.) Measured conversion coefficients are presented in table 2. The level scheme shown in fig. 1 is in substantial agreement with that of prior workers ‘,2), but, as well as adding a number of new transitions and level properties, differs significantly in that the energy of the yrast 8’ to 6+ transition is assigned as 54.2 keV, rather than 31 keV as suggested previously. Most of the gamma rays assigned to *‘*Rn feed the 170-ns 6+ isomer; therefore they occur in time before the 138 and 1274 keV transitions and appear in the “early” gates set on these lines, as shown in the upper panel of fig. 2. The inset in fig. 2 shows the 54.2 keV transition clearly. A 3 1 keV E2 transition would be highly converted ( CY~= 2500) and have an expected intensity of about 2% of that observed for the 54.2 keV line (a,= 150). As such it would not be clear in our spectra. Nevertheless, the transitions which appear “early” and “late” in coincidence with the 54.2 keV line (lower panel of fig. 2) establish its placement unambiguously between the yrast 170-ns 6’ isomer and the 1180-ns 8+ isomer. This, together with the measured total conversion coefficient which identifies

it as an E2 transition,

is the basis for our assignment

of the 54.2 keV

line as the yrast 8++ 6’ transition in 2’2Rn. Prompt coincidence gates on several transitions above the 8+ isomer are shown in fig. 3. As the 422 keV Ml transition does not appear in these spectra, but is clear in the “early” spectra shown in fig. 2, it is identified as the transition between the first and second 8+ levels at 1693.9 keV and 2115.9 keV. 3.2. MEASURED

LIFETIMES

AND

g-FACTORS

Sample decay curves obtained in the pulsed beam measurement 4. Mean lives derived from these and the yy-, yX- and TDPAD

are shown in fig. g-factor measure-

7’35.‘+A 25-

__?__ 96x3

-

61673tA 61673

-57723

22;;

150t-S

l9-

-54271

20*

81%

-

51145

!a-

-

4582.6

t7-

-3357-5 -

32977

I -

288l.3 27606 26549

l2t IIlO+

!-J -

1693.9 16397

8+ 6+

118onS IVORJ

y----

I5015

4+

13m

t2?33

2+

78

J

~

-0.D

Fig. 1. Level scheme

for *‘%n.

The width of the arrows in the 9Be induced

represents reaction.

the relative

i4+ ims r2t

3X, 8ns

0t

y-ray intensity

observed

A.E. Stuchbery

400

TABLE

Gamma

ET WV) “1 54.2 59.8 68.4 15.1 105.7 120.5 138.2 206.6 226.4 227.7 345.2 395.0 416.3 422.0 447.5 476.2 515.9 531.9 537.1 628.9 633.5 640.5 657.8 (670.4) 709.2 193.7 804.8 844.6 961.0 974.4 979.6 1002.1 1047.8 1273.8 1360.4

et af./ 2’ZRn 1

rays assigned

Ei (keV) 1693.9 3357.5 4135.1 4066.7 2760.6 2881.3 1639.7 (2967.2) 2881.3 1501.5 5712.3 6167.3 3297.7 2115.9 4582.6 3357.5 4582.6 5114.5 3297.7 3510.2 3991.0 3998.0 5772.3 (2171.9) 4066.1 4151.2 2306.3 5427.1 2654.9 (3735.0) 5114.5 2696.0 5114.5 1273.8 5427.1

to *12Rn

Intensity 5.3 (8) ‘)
(2) v (2) “1 (2) (1) (6)

4 (1) h, 254 (6) 725 (8) <3(l) Y 25 (4) 54 71 16 200

(6) (51 (4) “I (7)

42 (8) 39 (7) 33 (2) 6(l)‘) 163 (8) 12 (2) h, 35 (10) 4 (1) 16 (2) ‘1 140) b) 11(l) Y <7 (3) Y 422 (14) 8 (2) 5 (1) Y 16 (2) 38 (6) 1000 21(Z)

=2 0.28 (8,

-0.23

(1)

0.113 (5) 0.23 (1) 0.107 (5) -0.07 (3) 0.20 (5) 0.18 (2) 0.17 (2) 0.28 (3) -0.18 (3) -0.21(13) -0.11

(2)

-0.21

(4)

0.30 (5)

0.25 (1)

0.090 (5) 0.45 (6)

“) Uncertainties in y-ray energies are of the order of 0.2 keV. ‘) Intensity from coincidence measurement. Line either weak contaminated in singles.

or

ments, together with the deduced transition rates, are presented in table 3. Lifetimes for the yrast 4+, ll- and 20+ 1evels were obtained for the first time. Apart from the lifetime of the 6+ state our results overlap within the assigned uncertainties with values quoted (without error estimates) by others ‘,*). Figs. 5, 6 and 7 show the time-di~erential perturbed angular distributions (TDPAD) measured for several transitions, and the gyromagnetic ratios inferred

A.E. Stucbbery el al. / ZIZRn

401

2

TABLE

Conversion coefficients in “‘Rn E (keV)

Type

54 60 68 106 138 226/228

T T T T T L M K L K L K L K L M K L K L M K L K L M K L M

416 422 476 516

532 658

710 961

1274

are summarized excellent

Experiment 180 (30) 50 (40) 15 (6) 1.4 (5) 2.18 (5) 0.19 (4) 0.067 (8) 0.24 (3) 0.031 (9) 0.21 (2) 0.035 (5) < 0.032 (2) 0.009 ( 1) co.172 (2) 0.059 (8) 0.036 (5) 0.153 (10) 0.042 (5) 0.050 (3) 0.018 (2) 0.006 (2) 0.028 (5) 0.021 (3) 0.007 (1) 0.0016 (2) 0.0009 (1) 0.0043 (5) 0.0008 (1) 0.00024 (6)

in table 4. Our results

agreement

Assigned

with previous

Ml Ml E2 Ml

Ml Ml

E3 E2

E2

150 9s M1:8.3 E2:S2 E1:0.43 M2:90 2.15 0.116 0.042 0.213 0.038 0.21 0.038 0.026 0.019 0.12 0.02 0.003 0.11 0.019 0.063 0.011 0.003 0.028 0.013 0.0069 0.001s 0.0004 0.0042 0.0008 0.0002

for the yrast 8’, 17- and 22+ levels are in

measurements

4. Calculations

Ml(+E2?) El(+M2?) E2 E2

Theory

‘,2).

and discussion

As the structure of the core-excited states of *“Rn and neighbouring nuclei has been the subject of several recent publications ‘-lo), the following discussion will be confined to the non-core-excited states; i.e. leveh below the yrast 20f state.

4.1. EMPIRICAL

SHELL-MODEL

CALCULATIONS

4.1.1. Without particle-uibration coupling. Empirical she&model calculations assuming pure con~gurations, similar to those reported 3*4B6-12) for isotopes of PO, At, Rn and Fr, were performed for *12Rn. Our results confirm and extend those of

402

A. E. Stuchbery

et al. / 2’2Rn

sum of 138 & 1274 ‘earlies’ -(40

to 2000)ns

3 Xl02 54 gate ‘eorhes’- ‘totes’

2 I

* (40

to 2000)ns

0 -1 -2 -3

l

0

IO00

500

213Rn

1500

energy ikeV)

Fig. 2. Selected coincidence r-ray spectra observed in the Compton suppressed spectrometer (CSS) and in the LEPS detector (inset). The upper panel and the inset shows those transitions which occur above the yrast 8+ isomer. The lower panel shows the difference between “early” and “late” gates on the 54.2 keV transition. Transitions which follow the isomer below the 54.2 keV transition appear as negative peaks. A 54.3 keV tine occurs in ‘r3Rn [ref.“‘)] but does not confuse the placement of the line in “*Rn.

Liinnroth [ref. “)I. The calculated and measured excitation energies are compared in fig. 8. (For clarity in fig. 8 only the yrast levels and those yrare configurations which are candidates for the observed levels are shown.) With the exception of the 18- level (con~guration h2if), the calculated excitation energies agree well with those measured. As noted previously (e.g. refs. 7*9*‘o)),the energy of the 18- level is underestimated because of Pauli blocking of octupole contributions in the maximally coupled (if),o- configuration. This case will be discussed further below (sect. 4.1.2).

A.E. Sruchbery ef al. f “‘Rn

516 gate

476

2 26

176

gate

634

6

416

4

516

961 gote

‘451 2

395

0L 0 energy

Fig. 3. Prompt coincidence

CkeV )

spectra in the CSS with gates as indicated.

A. E. Stucbbery

ef ai. / “‘Rn I04

+!I

I03 I02

c? 102

Id

IO’

100

100

104

104

103

I03

102

102

IO’

101

I00

300

200

IO0 time

Fig.

4.

0

100

200

100

0

(nsl

Time spectra with respect to the beam pulse for the individual y-rays indicated.

Gyromagnetic ratios and transition strengths catculated for the nominal configurations are compare with experiment in table 5. For the E2 transitions an effective charge of 1.5e was used and the radial integrals were evaluated using harmonicoscillator wavefunctions. E3 transition strengths were estimated using the same “empirical” E3 matrix elements as employed in previous studies 7*f0).Most of the measured g-factors are reproduced well, as is the trend of the E2 strengths. A

A. E. Stuchbery

et al. / 2’2Rn

405

TABLE 3 Measured

transition

strengths

in “*Rn

y-w 4

6167+A 5427 4067 3358 2881 2761 1694 1640 1502

5

Ji

A 1360 845 76 709 60 576 121 226 106 54 138 228

22+ 20+

7

(ns)

150 (10) 7.5 (7)

17-

41.7 (20)

14+

10.7 (12)

12+

3.0 (2)

118+ 6+ 4+

8.0 (3) 1180 (90) 170 (20) 12.7 (5)

branching ratio 100 67 (15) “) 33 (15) 19 (6) ‘) 81 (6) 0.38 (3) 99.62 (3) 0.8 (4) 99.2 (4) 100 100 100 100

B(EL) e2(fm)2L

Type

+

E2 E3 E3 E2 E3 E2 E2 El E2 El E2 E2 E2

0.009 0.029 32 0.016 95 0.040 3.9 0.337 0.43 150 2.15 0.337

“) Transition strength is insensitive to the value of A within reasonable limits. b, The intensity of the 845 keV line is difficult to determine experimentally. ‘) Branching ratio deduced from intensities of 634 and 709 keV lines in coincidence transitions above the 17- level.

IO’

L-----L 30

20

IO

0 time

Fig. 5. Time spectra

and fits obtained

l_,,.. w

-68 “) [18.0 (4.4)] x lo3 [244 (113)] x lo3 213 (19) [55 (lo)] x lo3 269 (36) 2.2 (2) [lo (5)] x 1o-9 339 (23) [4.7 (2)] x 1o-5 9.8 (8) 30 (4) 79 (3)

spectra

20

gated on

IO

(ns)

for the 395 keV and 634 keV y-rays

in the TDPAD

measurement.

406

A. E. Stuchbery

et al. / “‘Rn

t lme

Fig. 6. Time spectra and fits obtained

,

I

8

30

( “S )

,

20

for the 476 keV and 961 keV transitions

IO

in the TDPAD

measurement.

104. 2’2 Rn

1274

keV

IO2’ 1.3

1.2

II

1.0

0.9

0.8

0.7 time

Fig. 7. Time spectra

and fits obtained

0.6

0.5

0.4

0.3

02

0.1

(ps)

for the 1274 keV transition

in the TDPAD

measurement.

00

A.E. Stuchbery et al. / ‘12Rn

407

TABLE 4 Measured

gyromagnetic

ratios in “‘Rn g-factor

Level

J”

Transition

a2

6167+ A 4067

22+ 17-

395 634 476

-0.17 (1) -0.15 (2) 0.18 (1)

3358

14+

476 961

0.18 (1) 0.20 (1)

1694

8+

1640 1502

6+ 4+

228 1274 1274 1274

0.20 0.18 0.18 0.18

(1) (1) (1) (1)

present

refs. I,‘)

0.72 (1)

0.72 (1)

1.05 (1)

1.05 (2)

1.07 (3) 0.895 (7)

0.894 (2)

0.909 (8) 1.01 (6)

marked discrepancy occurs for the decay of the 4: state for which the calculated E2 strength underestimates that observed by more than a factor of two. The effect of configuration mixing on the decay of this and the other states nominally of calculation configuration rrh& is explored through a more extensive shell-model described in sect. 4.2. The 12+ + ll- and 1 l-+ lO+ El transitions are very weak, (4*2) x lop9 and (2* 1) x 10h5 single-particle units, respectively, in reasonable agreement with the assigned configurations for which El transitions are forbidden. The strength of the E3 transition between the yrast 20+ and 17- levels is underestimated by a factor of two by the “nominal configuration” calculation and, in part, motivates the octupole-coupling calculations. 4.1.2. With particle-vibration coupling. Empirical shell-model calculations which explicitly account for the coupling between the single-particle orbitals and the 3vibration of the core have been described in several recent publications 7,8,‘o). Calculations along the lines of those reported ‘*lo) for the core-excited states of “‘Rn and for related levels in 213Rn were performed for the 14+, 17-, 18- and 20+ levels of *12Rn. Although in the resultant mixed states the occupation probabilities of the nominal configurations (table 5) are ~70%, there are also, as expected, significant admixtures of certain octupole-coupled components. For example, the 20+ level, predominantly 1h2i2; 20+), has admixtures of 1h2if0 3-; 20’), 1h3i 0 3-; 20+), lh2f20(3-)2; 20+) etc. similarly, the 17; and 17; levels, mainly jh3i; 17) and jh2if; 17-), respectively, have admixtures of lh3f03-; 17-), lh2f203-; 17-), and lh2i2@3-; 17-). The complete basis states and amplitudes are available 13). The calculated excitation energies, g-factors and B(E3) strengths are compared with experiment in table 6. Excitation energies are also displayed in fig. 8. In contrast with the “nominal configuration” calculation (sect. 4.1 and table 5), the E3 strength of the 20:-+ 17, transition is well reproduced. While the octupole coupling calculation slightly overestimates the energies of the 17- and 18- levels,

0

I

2

3

4

5

Fig. 8. Comparison coupling (described

(MeV)

Ex

6

14+

IT

20’ 18-

-

-

(exp)

212 Rn

__

14+ 12+

1;:

16-

0’

2+

2+

18:

8’

+ _ lb-

* 12’

/

,

17-

18-

20+

19-

22+ 20+ I--

h4

stotes

0’

core- excited

-+

h3f

__j

=t

1 /

- 8+

$

IO+

h3i

~

iz+

12+ 13+ 14+

lo9II-

h2f2

h2,f

h212

-

,

13’ 12’ 14+

17l8-

20’

19+

of the experimental levels with results of semi-empirical shell-model calculations. Calculations which do not include particle-octupole in sect. 4.1.1) appear on the right of the experimental levels; those which include the octupole coupling for selected states (described in sect. 4.1.2) appear to the left. The core-excited states were discussed in ref. ‘).

octupole coupled

-

w

A.E. Stuchbery et al. / “‘Rn TABLE

Calculated

g-factors

and transition

strengths

409

5

for nominal table 6)

configurations

compared

with experiment

NEL) Transition

20++ 17; + 17, 17;+ 15; + 14: 14: + 12: + 12; 12:-+ 11, + 10: 11;+10: 8:+6; 6:+4: 4;+2:

Nominal final configuration

Nominal initial configuration

h3i h3f h4 h3i h4

Initial state g-factor

ezfmZL -

Type talc.

h’i h’if h3i h3f h3f h4 h’i h4 h4 h4 h4 h“

h’i*

(cf.

exp.

7x10’ 84x lo3 160 60x 10’ 160 0.4 0 275 0 8.9 22 32

E3 E3 E2 E3 E2 E2 El E2 El E2 E2 E2

talc.

18 (4) x lo3 240(110)x103 210 (20) 55 (10) x 10s 270 (40) 2.2 (3) 10 (5) x 10-9 340 (20) 4.7 (2) x 10-s 9.8 (8) 30 (4) 79 (3)

exp.

1.113 1.040

1.05 (1)

1.066

1.07 (3)

0.913 0.913 0.913

0.894 (2) 0.909 (8) 1.01 (6)

TABLE 6 Experimental

and measured

g-factors

and E3 strengths levels in “‘Rn

g-factor

for some particle-vibration

Decay

mixed

B(E3) x 103e2fm6

J” talc.

exp.

22:

0.707 “)

0.72 (1)

20:

1.089

17; 14:

1.049 1.073

1.05 (1) 1.07 (3)

from

to

talc.

exp.

20+

17; 17; 14:

17.3 69.1 63.7

18 (4) 240(110) 55 (10)

17,

“) From ref. 7).

the predicted configuration”

energy

separation

calculation

is much

because

the

closer to experiment Pauli

blocking

than

the “nominal

of the octupole-coupled

components in the 18- level is taken into account explicitly. The octupole-coupling calculation gives g-factors for the 14+ and 17- levels in excellent agreement with the measured values. Calculations of E2 transition rates for the octupole-mixed wavefunctions were not pursued because, for the high-spin octupole-mixed states considered here, most of the E2 strength is carried by the components of the mixed wavefunctions corresponding to the “nominal” configurations and little improvement is expected over the results presented in sect. 4.1.1. This is not the case for the lower-spin

410

low-seniority transitions

levels; between

4.2. SHELL-MODEL

To examine

however

A.E. Siuchbery

et al. / “‘Rn

the possible

influence

low-excitation

CALCULATIONS

the influence

of octupole-coupling

levels in *12Rn is discussed

INCLUDING

CONFIGURATION

of configuration

mixing

on E2

in sect. 4.2.

MIXING

on the decay strengths

of E2

transitions shell-model

between the nominal h4, seniority-two configurations, we performed a calculation for *‘*Rn using the shell-model code OXBASH 14). An inert *“Pb core was assumed and the four valence protons allowed to occupy the lh,,,, were estimated using a surface-delta 2f,,, and li13,2 orbitals. Two-body interactions interaction (SDI) with a strength of 0.16 MeV, as used in earlier studies “) of 21032’1Rn.Transition strengths were calculated for an effective proton charge of 1.5e and with harmonic-oscillator wavefunctions. Similar calculations for the N = 126

isotopes have been performed by Zwarts and Glaudemans ‘). Although these authors used a slightly different interaction strength, our results and theirs (where reported) agree. In the following, we refer to the present calculation as the “SD1 mixedconfiguration shell model”, that of sect. 4.1.1 as the “pure-configuration empirical shell model” Calculated

and that of sect. 4.1.2 as the “octupole-coupled empirical shell model”. excitation energies and wavefunctions (strictly, configuration occu-

pancies) for selected states calculated in the SD1 mixed-configuration model are shown in table 7. Whereas the wavefunctions of the lO+ and 12+ levels (table 7) have an h4 component of >92%, justifying for these states the pure-configuration approach described in sect. 4.1.1, those of the yrast 4+, 6+ and 8+ levels have only about 76% of the nominal h4 configuration. It should be noted that (i) the main admixtures in these nominally h4 (v = 2) states are h:fi and h:it and, (ii) the degree TABLE Shell-model

wavefunctions

7

and energies

for selected

states in ‘12Rn

Configuration

E, (kev)

(%)

J” h’f

h2fz

h*?

57.7 76.9 75.8

0 0.8 0.6

20.7 12.5 13.3

16.6 9.5 9.9

1640 1694

77.0 76.1

1.0 2.2

12.2 11.9

9.4 9.3

2116 2307 2432 3022

2.1 93.4 92.1 0.1

78.9 5.1 7.4 97.4

0.2 0.7 0.2 1.6

0.5 0.7 0.4 0.6

talc.

exp.

h4

0: 4: 2+

0 1381 1262

0 1502 1274

6: 8,

1427 1448

s+ 10,: 12: 12:

2007 2655 2881 3298

others f’i* P 2.7 1.3

hf3 9.1

hf? 9.2

i4 1.0

A.E. Stuchbery

of mixing

et al. / “‘Rn

411

in the yrast 2+, 4+, 6+ and 8+ levels is uniform.

mixed-configuration the h9,z proton

It follows that in the SD1

shell model these levels all have g-factors - similar

to the prediction

(sect. 4.1.1) and in agreement rates, on the other hand,

with available

very close to that of

of the pure-configuration experimental

are much more sensitive

results

to configuration

shell model

(table 5). The E2 mixing

because

the transition strengths for the admixed h2 + h* components are a factor of 3 stronger than for the nominal h4 + h4 (v = 2) transitions. This is due to the cancellation which occurs at midshell for E2 strengths between states of the same seniority 16). It can be deduced immediately from the wavefunctions (table 7) that the SD1 mixedconfiguration shell model will precict B(E2)‘s for the decays from the yrast 8+, 6+ and 4+ levels, that are larger than those of the pure-configuration empirical shell model (sect. 4.1.1). Results of both of these calculations are compared with experiment in table 8. On the whole, the agreement between the measured and calculated E2 strengths is satisfactory, but not as good as obtained ‘) for similar states in the nucleus *i”Po which has only two valence protons. While experiment lies between the pure-configuration empirical calculation and the SD1 mixed-configuration model for the yrast 8+ + 6+ and 6++ 4+ transitions, both calculations underestimate, to a strengths. greater or lesser extent, the yrast 12+ + lO+ and 4++ 2+ transition The coupling between single-particle orbitals and the octupole vibration of the core is known to be crucial in determining the structure of high-spin isomers in 212Rn and neighbouring nuclei (see sect. 4.1.2). For the lower-spin states which usually have lower seniorities and inherently less-pure configurations (aside from any particle-vibration mixing), the influence of octupole coupling is more difficult to calculate. However, a likely effect of this coupling on the structure of the low-seniority states in “‘Rn would be the introduction of admixed components in the wavefunctions such as h:[h(i03-)I,, and also, obviously, to change the relative proportions of other admixtures. As noted above, E2 transitions between these admixed configurations can be much stronger than those between the predominant configurations, h:( u = 2). Consequently, the E2 decay strengths among the yrast levels in *‘*Rn below the 8+ state are sensitive to the presence of relatively small configuration admixtures. In contrast, transitions between the related low-lying TABLE E2 transition

strengths

between

WE21 Transition

12:-t 10: 8:+6: 6:+4: 4;+2:

8 nominal

h$,

states in *“Rn

( e2fm4)

expt.

empirical shell model

SD1 shell model

340 (20) 9.8 (8) 30 (4) 79 (3)

275 8.9 22 32

230 15 56 59

412

A..!?.

states of *“PO, nominally to the middle to configuration

Stuchbery

from the configuration

of the shell, so the calculated mixing

of the E2 transition

et al. / “‘Rn

h:, are not diminished

E2 rates for this nucleus

than those in 2’2Rn. This accounts

rates in 212Po than *I2Rn by shell-model

by proximity

are less sensitive

for better description

‘)

calculations.

5. Summary and conclusions Experimental information on the yrast and near yrast states of *l*Rn has been obtained for levels up to spin 25A. Overall, the excitation energies, transition strengths and magnetic moments can be well described by empirical shell-model calculations

assuming pure configurations. Exceptions are found for several coreexcited states ‘) and for the yrast 17-, 18- and 20’ levels for which improved descriptions are obtained when the mixing due to the coupling between the singleparticle orbitals and the octupole-vibration of the core is included explicitly in the empirical calculation. The strengths of E2 decays between the yrast 2+, 4+, 6+ and 8+ levels are also sensitive to configuration admixtures, in this case because E2 transitions between the nominal configurations (h&, u = 2) are hindered. Shell-model calculations using a surface-delta interaction provide a moderately successful description of the experimental B(E2)‘s among these states. We would like to thank Dr J. Gerl and R.A. Bark for contributions at various stages of the measurements, Dr C.L. Woods for assistance with the shell model code, and the academic and technical staff of the 14UD accelerator facility for their continuing

support.

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A.E.

Stuchbery

et al. / “‘Rn

413

13) A.E. Stuchbery, ANU internal report P/1009, 1988 14) B.A. Brown, A. Etchegoyen and W.D.M. Rae, OXBASH, the Oxford-Buenos Aires-MSU Shell Model Code, Internal report No. 524, November 1986, Cyclotron Laboratory, Michigan State University 15) A.R. Poletti, G.D. Dracoulis, C. Fahlander and I. Morrison, Nucl. Phys. A359 (1981) 180; A.R. Poletti, G.D. Dracoulis, C. Fahlander and I. Morrison, Nucl. Phys. A380 (1982) 335 16) A. de Shalit and I. Talmi, Nuclear shell theory (Academic Press, N.Y., 1963), eq. (28.40), p. 315