Lifetimes of levels in 21Ne

Nuclear Physics A90 (1967) 122--134; ( ~ North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

LIFETIMES

OF LEVELS

I N 21Ne

R. D. BENT t

Department of Physics, Indiana University, Bloomington, Indiana, USA ~* and Atomic Energy Research Establishment, Harwell, England J. E. EVANS ***,G. C. MORRISON ++,N. H. GALE ++~and I. J. VAN HEERDEN ~

Atomic Energy Research Establishment, Harwell, England Received 4 July 1966 Abstract: Attenuated Doppler shifts have been measured for the decay of the levels in 2~Ne at 1.74, 2.80 and 2.87 MeV using 24 MeV 1nO ions from the HarwelI tandem Van de Graaff accelerator and the reaction 9Be(leO, c~V)21Ne. From these results, the mean lifetimes of the 1.74 and 2.87 MeV levels were found to be, in units of 10 13 sec, 1.5_+~0 and 1.1+~7~, respectively. The observed Doppler shift for the decay of the unresolved doublet at 2.80 MeV is consistent with the recent lifetime limits and branching ratios given by Smulders and Alexander for levels at 2.790 and 2.797 MeV. The data are combined with branching ratio and multipole mixing ratio data to obtain the partial mean lifetimes of eight transitions in 21Ne. The results are discussed in terms of the systematics of transitions in the 2s-ld shell and in terms of several nuclear models. The lifetimes and branching ratios of the 1.74 and 2.87 MeV levels are consistent with the predictions of the Nilsson model with K-band mixing for spin and parity assignments of ~+ and ~+, respectively, to these two levels. The results for the 2.797 MeV level are consistent with the predictions of the Nilsson model, the Chi-Davidson asymmetric core model and the Dreizler excited core model if a ½+ spin and parity assignment is made to this level. However, the results for the 2.790 MeV level are inconsistent with its interpretation as the ~+ level predicted in this energy region by the Nilsson and Dreizler models, since these models overestimate the M 1 transition probabilities for decay by several orders of magnitude and fail to give the correct branching ratio. E [

/

NUCLEAR REACTIONS 9Be(a60, ~V), E = 24 MeV; measured cr(E~, Ee), 17, ~y-coin, Doppler-shift attenuation, 21Ne deduced levels, J, :r, T~, B(M 1), B(E2).

1. Introduction T h e N i l s s o n m o d e l 1,2) h a s

been successful in describing m a n y o f the

main

f e a t u r e s o f n u c l e i i n t h e 2 s - l d shell. S u r v e y s o f t h e a p p l i c a t i o n o f t h i s m o d e l t o n u c l e i i n t h e 2 s - l d shell h a v e b e e n m a d e b y G o v e 3) a n d b y B h a t t 4). , Part of this work was performed while this author was a John Simon Guggenheim Fellow (1962-63) at Harwell, on leave from Indiana University. t* Work supported in part by the United States National Science Foundation. *** Dr. J. E. Evans died suddenly on December 17, 1965 while the manuscript for this paper was in the final stages of preparation. ** Present address: Argonne National Laboratory, Argonne, Illinois, USA. *** Present address: Department of Geology and Geophysics, the University of Oxford, England. ~;* On leave 1962-63 from Southern Universities Nuclear Institute, Faure, South Africa. 122

LIFETIMES IN 21Ne

123

Freeman s) has calculated the level scheme for 21Ne predicted by the Nilsson model, employing an analysis similar to that used by Paul and Montague 6) for 23Na" A qualitative fit to the level positions, spins and parities was obtained. The present authors 7) measured the lifetimes of the low-lying levels of 21Ne in order to test further the applicability of the Nilsson model to this nucleus. Qualitative agreement between experiment and theory was obtained except for the case of the 2.80 MeV level, which was found to have a lifetime 230 times greater than that predicted by the 1+ Nilsson model for a z spin and parity assignment to this level. Also, it was found necessary to make a ~9 + assignment to the 2.87 MeV level in order to obtain agreement between the lifetime data and the predictions of the Nilsson model. Recently Chi and Davidson 8) have applied an asymmetric core rotator model to nuclei throughout the 2s-ld shell, and Dreizler 9) has discussed the low-lying levels of 21Ne in terms of a model implying the weak coupling of an s-d particle to a rotational 2°Ne core. Recent experimental investigations of de-excitation g a m m a radiations from the low-lying levels of 2iNe have been reported by Pelte et al. 1 o, 11), Howard et al. 12), Catz and Amiel 13) and Smulders and Alexander 14). In the present paper, a complete description is given of the lifetime measurements reported earlier 7), and the results are interpreted in light of the recent theoretical and experimental work.

2. Apparatus and experimental techniques Fig. 1 shows the experimental arrangement that was used in the present work. G a m m a rays were detected in a 7.62 cm × 7.62 cm N a I crystal which was placed at

I

/

//

/

/

x

\\

\

\

t x/ \

x

/ -\

/ \\

......

\\\), / /

/J

~

016

~I a DETECTOR

8g/

TARGET Fig. 1. Experimental a r r a n g e m e n t .

45 ° or 135 ° with respect to the beam direction with its front face 9 cm from the target. Alpha particles were detected in a silicon surface-barrier detector 0.5 c m 2 in area

124

R. i~. BEyT e t

al.

placed 3 cm from the target at 0n = 0 °. Targets were prepared by evaporating beryllium to a thickness of about 60/~g- cm -2 onto aluminium and copper foils o f sufficient thickness (approximately 4 mg" cm -z) to stop the ZlNe recoil ions. Standard fast-slow coincidence circuitry and a Nuclear Data 512-channel pulseheight analyser were arranged so that g a m m a rays could be studied in time coincidence with alpha particles of a selected energy.

3. Experimental results Fig. 2 shows a charged particle spectrum obtained from the bombardment of a 9Be target with 24 MeV ~60 ions. Windows were set on the 1.74 and 2.8 MeV peaks to obtain the coincidence spectra shown in figs. 4 and 5. The 0.35 MeV state was not studied in the present work. Fig. 3 shows a gamma-ray singles spectrum. The strong peak at 1.64 MeV probably arises from the first excited state of 2 ONe populated in the reaction 9Be( 160, c~n)2 °Ne. Fig. 4 shows a gamma-ray spectrum coincident with alpha particles corresponding to the 1.74 MeV state, and fig. 5 shows a typical gamma-ray spectrum coincident with alpha particles corresponding to the 2.80 and 2.87 MeV (unresolved) levels of 2~Ne. Fig. 5 is the result of a 4 h run taken with an average beam current of approximately 0.1 /~A. These spectra were taken many times with the gamma-ray detector alternately in the forward and backward positions. Energy calibrations were m a d e before and after each coincidence run using a number of radioactive sources. For both the calibration and the coincidence spectra, energies were determined from the centroids of the observed peaks. The r.m.s, error associated with this procedure was found experimentally by repeating the spectrum from a 2ZNa source 20 times. This r.m.s, error depended on the number of counts, but a typical error for the Dopplershift measurements was _+0.4 ~o in energy. This is to be compared with the calculated full shifts between forward and backward observations (for a thin target with no. backing) of about 3 ~ . In addition to the statistical error, there were errors in the results due to drifts in the over-all gain of the electronic system, since no special kind of stabilization was used for the early runs v). However, the results of calibrating before and after each run showed that the drifts were usually small compared to the statistical fluctuations. The same Doppler-shift measurements were made on several occasions, and the deviations found were no worse than those expected statistically. Since these earlier runs 7), the measurements have been repeated employing electronic stabilization of the gain of the gamma-ray detector. The system was stabilized with respect to the photopeak of the 1.37 MeV gamma-ray transition f r o m a radioactive source of 24Na. It was further arranged that the g a m m a rays used for stabilizing were coincident with/~- particles from the source recorded in a surface barrier silicon detector. Thus the stabilization was independent of variations in counting rate associated with variations in beam intensity. These later results were analysed by

I

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I

l

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I

0oo t xO

o

(3 ::1-, 4 0 0 ,,o LU

2-

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Z

5.9

---X

u

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200

-4 3.7

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0

28 "

I

f

~

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20

0.35

40

60

80 CHANNEL

.74

, ~"~

I00 NUMBER

120

140

160

Fig. 2. C h a r g e d particle s p e c t r u m f r o m the b o m b a r d m e n t o f beryllium with 24 M e V 160 ions taken at zero degrees with respect to the beam direction. [

I

I

I

6000 I0.66 z

0.89

103

4000

1.64

g O

2000

III

0.2,

0 I

¥ t~

X I I~ I .0

2 0

3.0

4.0

E~. ,~/-M~V)

Fig. 3. G a m m a - r a y singles s p e c t r u m f r o m the b o m b a r d m e n t of beryllium with 24 M e V 160 ions.

l 150

I - 0.15

-o 0.35

o O9 ('4

I0O

o

U.l 1.40 uQ

J't

5o

z

5 u

0

)/2 • ol. 7 4

t 1.0

Fig. 4. G a m m a - r a y

2.0

s p e c t r u m f r o m t h e r e a c t i o n 9Be(160, c~y)21Ne c o i n c i d e n t w i t h a l p h a p a r t i c h c o r r e s p o n d i n g to the 1.75 M e V s t a t e o f ZaNe. T

i40

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r~

,.D :::L12C 0

o ~oo~-

z

60

o~

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~ z

20~ ]

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0

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• .

.....

• "-

~

1.5

•

/

",....ga,

A

/

k..... 2 0

2.5

3.0

Ey(MeV)

Fig. 5. G a m m a - r a y s p e c t r u m f r o m the r e a c t i o n 9Be(l~O, ~),)21Ne c o i n c i d e n t w i t h a l p h a p a r t i c l e c o r r e s p o n d i n g to t h e 2.80 a n d 2.87 M e V s t a t e s o f 21Ne; 0~ = 0 °, 0~ ~ 45 °, t = 4 h.

LIFETIMES IN 21Ne

127

m a k i n g a G a u s s i a n fit to the total a b s o r p t i o n p e a k in the g a m m a - r a y spectra by m e a n s o f a least-squares c o m p u t e r p r o g r a m . The D o p p l e r shifts were d e t e r m i n e d f r o m the p o s i t i o n s o f the p e a k centroids. The results agreed with those o b t a i n e d earlier within the c o m b i n e d e x p e r i m e n t a l errors. T h e final m e a n lifetimes given in table 1 are an average o f the two i n d e p e n d e n t runs. The nuclear lifetime z was calculated a s s u m i n g t h a t the a t t e n u a t i o n o f the D o p p l e r shift due to slowing d o w n in the target b a c k i n g is given by a factor ~/(e+r), where is the " s l o w i n g d o w n " time. This assumes t h a t the velocity in the b a c k i n g is an e x p o n e n t i a l function o f time (v = v 0 e-'/=). The c~-values were f o u n d by e x t r a p o l a t i n g f r o m the values f o u n d for oxygen ions by P o r a t a n d R a m a v a t a r a m as) to those for 2~Ne ions, a n d a s s u m i n g with L i t h e r l a n d et al. 16) that (i) dE/dx = (Z2)cp(v) a n d TABLE 1 Doppler shifts and experimental mean lifetimes Transition

71(1.75 -+ 0.35) p4(2.80 -~- 0) ~5(2.87 -~ 1.75)

E~ (MeV)

Maximum Observed Experimental mean o/ shift /o ~ shift lifetime of the 45 ° to 135 ° 45 ° to 135° initial state (10 la sec)

1.40 2.80 1.12

2.8 2.9 2.9

1.92-0.5 1.9-~0.5 2.1±0.5

(ii) the d e p e n d e n c e of the m e a n square charge state _ Z2

1.5+I:~ 1 1+~ 5 •

--0.7

( Z z) on velocity is given by

f(flZo})-

The values o f ~ o b t a i n e d in this w a y were f o u n d to d e p e n d to some extent on velocity, so t h a t the e x p o n e n t i a l time d e p e n d e n c e was n o t exact. A s r e a s o n a b l e averages (in view o f other uncertainties) the following values were a d o p t e d : ~A~ = 6X 10-13 sec,

~cu = 3 x 10-13 sec-

The m e a n lifetimes which were experimentally d e t e r m i n e d using a c o p p e r b a c k i n g are given in table 1. Results o b t a i n e d using an a l u m i n i u m b a c k i n g showed larger D o p p l e r shifts which were consistent with the lifetimes given in table 1. The exp e r i m e n t a l errors are those associated with the statistical uncertainties in locating the p o s i t i o n s o f the p e a k centroids. N o value is given t o r the lifetime o f the 2.80 M e V level in view o f e x p e r i m e n t a l i n f o r m a t i o n which has been recently o b t a i n e d 14). G a m m a - r a y b r a n c h i n g ratios were calculated using the k n o w n 17) energy d e p e n d e n c e o f the efficiency o f a 7.62 cm x 7.62 cm N a I crystal for detecting g a m m a rays. It was assumed t h a t the a n g u l a r d i s t r i b u t i o n o f the g a m m a rays was the same for b o t h branches. A l t h o u g h this is incorrect, the effect o f any difference in the a n g u l a r distributions was m i n i m i z e d by the large solid angle (0.3 sr) o f the g a m m a detector.

128

R. D, BENTet al.

The branching ratios obtained in this way are given in fig. 6. The agreement with other measurements is good for the decay of the 1.75 and 2.87 MeV levels. The branching ratio for the 1.75 MeV ~ g.s. transition (72) was measured to be 7 ~ + 1 % by Howard et al. 12), 6 ~o by Pelte et al. 10) and 4.6 ~o_+2.0 ~o by Pronko et al. 18). The latter authors determined that the 2.87 MeV level decays 63 ~o +__4~o to the 1.75 MeV level. Discrepancies exist, however, concerning the decay of the 2.80 MeV level. Howard et al. 12) and Pelte et al. 11) found, using the Z°Ne(d, p)ZlNe reaction, that this level decays about 90 ~ to the ground state, whereas it was found in the present experiment, and also in the experiment of Pelte et al. 1o) using the 19F(3He, p)Z°Ne reaction, that the branching ratio for decay of the 2.80 MeV level to the ground and 0.35 MeV states was more nearly 50 • 50. These discrepancies have been resolved by the work of Smulders and Alexander ~4) who measured the g a m m a ray spectra from the lSO(:~, nT)ZlNe reaction using a 25 cm 3 Ge(Li) detector and found levels at 2.790±0.005 and 2.797+0.005 MeV with lifetimes of > 1.0 psec and <0.05 psec, respectively. They found that the 2.790 MeV level decays to the ground and first excited states in the ratio of 15 " 85 and that the 2.797 MeV level decays to the ground state with a probability greater than 93 ~ . The different branching ratios can be reconciled by assuming that the (d, p) reaction populates primarily the upper level, whereas the (~60, ~) and (3He, p) reactions populate both members of the doublet with approximately equal intensities. In this case the peak labelled Y4 in fig. 5 is due to ground state transitions from both the 2.790 and 2.797 MeV levels. With this assumption, the observed Doppler shift given in table 1 for this unresolved doublet (?'4 : 2.80 - , 0) is consistent with the lifetime limits and branching ratios given by Smulders and Alexander for the two levels. The large separation of 73 and 76 at 45 ~ shown in fig. 5 can also be understood on the basis of the results of Smulders and Alexander; Y3 shows no Doppler shift since it arises mainly from the decay of the long lived level at 2.790 MeV, whereas 76 does show a Doppler shift and is increased in energy at the forward angle. At 135 ° 76 is decreased in energy due to the Doppler shift, and the separation of 73 and ?6 was indeed observed to be less at the backward angle. However, it was not possible to deduce the properties of the doublet at 2.80 MeV from these results alone because of the poor resolution and counting statistics of the present experiment. Table 2 gives the experimentally determined transition probabilities for nine transitions in 21Ne as deduced from the experimental lifetimes and the experimental branching ratios. The E2 partial transition probability for ~1 was obtained using ~5 = + 0 . 1 5 ± 0 . 0 2 for the multipole mixing amplitude, which is an average of the value 3 -- 0.l 1 ±0.04 measured by Pelte et al. 10) and a more recent value of 6 = 0.18 +_0.03 measured by Pronko et al. 18). The E2 partial transition probability for )'s was obtained using the multipole mixing amplitude c5 = 0.12±0.06 measured by Pronko et al. ~8). The experimental values for 7o (0.35 MeV ~ g.s.) are taken from the literature 19-2 ~). The lifetime limits for the 2.790 and 2.797 MeV levels are those

129

L I F E T I M E S I N 21Ne

TABLE 2 Experimental and calculated transition probabilities Transition

Jj Jf (assumed)

Transition probability in units o f 1012 sec -~ Experimental

70(0.35

71(1.75

~2(1.75

--+ g.s.)

-+0.35)

--~g.s.)

73(2.790 -+ 0.35)

~

{

~

~

~

.~

(6)

~

Weisskopf a)

Nilsson with K-band mixing ~ -- 4

Dreizler e) excited core

Chi-Davidson b) asymmetric rotor

Case (a)

M1

> 0.005

1.4

0.01

6 × 10-4

0.04

0.05

E2

~ 0.001

0.00002

0.0003

7 × 10-6

0.0008

0.0008

MI

~-36+13

9.2

5.5

E2

n 1"~+o.4

0.02

0.45

0.009

0.7

0.7

E2

~'--0.2D~'+°'8

0.07

0.4

0.005

0.5

0.5

....

-0.08

M1

85

460

12

92

12

59

89

< 0.85 d) E2 74(2.790 ~ g.s.)

(~)

,~

Case (b)

0.37

MI

700 0.18 73 d)

E2

T3(2.797 --+ 0.35)

(½)

~

E2

74(2.797 -~ g.s.)

(I-)

~

M1

< 0.0774 d)

0.73

0.37 700

8 254 6.4

0.4 620

0.06 3760

6.3 256

0.12

2.4

0.002 23

0.04 13

51 6.0 266 1.5

2.2 742

> 20 d) E2

75(2.87

~ 1.75)

~-

{

MI E2

T6(2.87

-+ 0.35)

~-

~

MI

0.73

6q+ll 4 v.~

O nO -+- 00.4 .07

....

E2

2.8 +4.8 - 1.7

6.3 +11

75(2.87

--+ 1.75)

~-

~-

M1

76(2.87

~ 0.35)

~

~

E2

E2

43 0.008 500 0.43

43

0.04

0.06

3.3

3.0

6.7

0.006

0.01

0.01

0.4

84 7

10

onq + °'4 -0.07

0.008

0.11

9- ' v~+4.8 - - 1. 7

0.43

9.7

....

a) F w ( M 1 ) = (2.1 × 10-2)E 3 eV; Fw(E2 ) = (4.9 × 108)A~ E 5~ eV; E b) Calculated by Davidson 32). ~) Calculated by Dreizler

34).

a) Measured by Smulders and Alexander 14).

0.003

in MeV (See ref.

22)).

130

R.D.

BENT et aL

o f Smulders and Alexander ~4). The g a m m a rays were observed in the present experiments only at the two mean angles of 45 ° and 135 °, so the branching ratios could be in error because o f the gamma-ray angular distributions. On this account the transition probabilities would also be in error, but probably only by a small a m o u n t compared to the error involved in the lifetime measurements.

4. Discussion 4.1. SYSTEMATICS A comparison of the measured transition probabilities and the Weisskopf single particle estimates 22) is made in table 2. This comparison reveals several trends which are characteristic of collective effects. The E2 transitions ~1,72, 75 and Y6 are all enhanced by about an order o f magnitude. The M1 transitions 71 and Ys are both retarded by about an order of magnitude and 73 and 74 by several orders of magnitude. In this comparison spin assignments o f ~+ t+ and 9 + have been assumed for the 2.790, 2.797 and 2.87 MeV states, respectively (see discussion that follows). Similar systematics are observed for other nuclei in the 2s-ld shell. Gove 23) finds enhancements of 10-20 for E2 transitions within a band around A = 20, and enhancements of about 7 for E2 transitions between bands. In this connection it can be noted that the enhancement factor for the 7o(E2) transition in 2XNe appears unreasonably large. These trends are qualitatively consistent with the rules first obtained by Alaga et al. 24) for transitions within and between rotational bands of axially deformed nuclei, insofar as the E2 transitions are enhanced and the M1 transitions between bands are weaker than the M1 transitions within a band. For the case of 21Ne, the strong interaction between rotational and particle motion, which is an effect of the Coriolis force, causes strong K-band mixing, so that the distinction between transitions within a band and transitions between bands is largely lost; nevertheless, the transitions 71 and 7s do occur between states which are predominately K = 3, whereas 73 and 7, are due to transitions from states which are predominately K = ~ or } to states which are predominatety K -- ~. The effects of band mixing are considered in detail in the discussion that follows. 4.2. NILSSON MODEL WITH K-BAND MIXING The low-lying levels o f 21Ne were interpreted by Freeman 5) in terms o f the mixing of rotational bands as described by K e r m a n 25). The analysis followed closely that o f Paul and M o n t a g u e 6) for 23Na. Fig. 6 shows the three interacting rotational bands, with K = ½, 3 and 25, which were mixed to fit the observed level scheme o f 21Ne. The ground and first two excited states are fit reasonably well, and the model predicts a ~ + , ~-+ and 9 + triplet at about 3 MeV. At the time our lifetime measurements were begun, two levels had been experimentally observed near 3 MeV, a level at 2.80 MeV with ~,+ spill and parity 26, 27), which was taken as the K = ½ band head in Freeman's analysis and a level at 2.87 MeV of u n k n o w n spin and parity.

13 l

LIFETIMES I N 2]Ne

In the present analysis, the excitation energies for the band heads given by Free, man 5) were accepted, and the transition probabilities between the mixed states were calculated using the formulae of Kerman 25)t, which neglect single-particle E2 effects. The quantity fi2/2J was taken as 0.25 MeV to be in reasonable agreement with that derived from the energy of the first excited state in Z°Ne. We chose 77 = 4 for the value of the distortion parameter, which is consistent with the assignment of ~+ for the spin and parity of one member of the doublet at 2.80 MeV and with other recent work 26). Since the measured zs) ground state electric quadrupole moment is 7/2

9/2/.'p' 9/2

7/2

5/2

5,. /

4.45

t

_~.89 . 3 .1 2. .

X 712-"\

N .5/z

5/2 /

/

59 // 22

5.67 -~2.87

-¢ .¢ Y~:rs

_a

/

170"'-"

I

e~14'ol

-

; pG'o !

S77Z.

3/z K=I/2

K=3/2

K=5/2

LEVELS

MIXED

>

T T 12,-,

we

\,74z./

- 4

&74--..

{ i

4,

3/2'-Jo

OBSERVED

OF Ne za

Fig. 6. Energy levels of 21Ne s h o w i n g interacting rotational b a n d s with K = x, 2 ~ a n d ~ on the left a n d the experimentally observed levels a n d g a m m a - r a y transitions on the right.

0 . 0 9 3 + 0 . 0 1 0 b, our choice of q = 4 corresponds to a value of tc = 0.1 for the spinorbit coupling parameter, Since it is expected that the intrinsic collective electric q u a d r u p o l e m o m e n t s will n o t vary drastically from one state to a n o t h e r , we have chosen Q o ( K = ~) = Q o ( K = ~) = Q o ( K = ~) = 5 x 10 -25 cm z, which is the value for the g r o u n d state. We have t a k e n g~ = Z / A = 0.48 for the core g-factor. The mixing parameter A n = ( K l ( f i 2 / 2 J ) J _ [ K + 1) was calculated to be - 0 . 2 8 8 MeV for K = -} (mixing of the K = ½ a n d K = -} b a n d s ) a n d + 0 . 5 5 for K = 3 (mixing of the K = -~ a n d K = ~ bands), The wave functions o b t a i n e d for the low-lying states t W e are indebted to Drs. D. K u r a t h a n d J. Wills for p o i n t i n g o u t to us that eqs. (7b) p. 10 of ref. z~) s h o u l d read bin ~ e alL , blL ~ -- e alH, where e is the sign o f the off-diagonal m a t r i x element

HK, K + I = - - [ I ( I + I ) - - K ( K + I ) 1 ½ ( K

i2~,1

[K+I).

132

R.D.

B E N T et al.

of 2~Ne were the following:

g,~ ( U ) = - 0 . 1 4 t K = ½)+0.991K = ~), 5+

4'o.~(~ ) =

-0.161K

½)+0.781K

})+0.6ILK = s

0i.~(-I +) = 0.771K = ~ ) + 0 . 6 4 [ K = {), 02.~o(½ +) = IK = ½>, 5 5+ 4'~.~o(~ ) = 0.60IK - ½)-O.80IK = ~-), ,+ 5

0.601K = ~a)-0.80IK = z),

.+ g'2.8~(~ ) = 0.751K = ~)+0.661K = ~). It was important to include the K = } admixture in the ground and 0.35 MeV states in calculating 73 (E2) and ]'4 (E2) for the ~1 + (K = 3) assignment to the 2.797 MeV state. This small admixture gives a collective contribution to these E2 transitions which is much larger than the single-particle contribution. The K = ½ admixtures could be ignored for the other transitions. The transition probabilities which were calculated using the above parameters and wave functions are given in table 2. In order to compare the experimental lifetime results with the predictions of the Nilsson model with K-band mixing, we have identified the 2.790 and 2.797 MeV levels with the I + and 3 + levels predicted in this energy region by the model. The transitions ]'5 and ~6 were examined under two different assumptions for the spin of the state at 2.87 MeV. If the Nilsson model calculation iN at all realistic here, it is clear from both the absolute transition probabilities and the ]'5/76 branching ratio that o is favoured for the spin of this state. Table 2 shows that the experimental results and the predictions of the Nilsson model with K-band mixing are consistent to within a factor of 2 for the transitions 0 + assignment is made to the ]'~(M1), 3,1(E2), 7z(E2), 3,5(M1), ]'5(E2) and 3,6(E2) if a -~ 2.87 MeV level. The lifetime limits for 3,3(E2; 2.797 --, 0.35) and 3,4(M1 ; 2.797 --+ g.s.) are consistent with the model predictions if a 3 + assignment is made to the 2.797 MeV level. The model gives an improvement over the Weisskopf estimate for 3'3 (M1; 2.790 --+ 0.35) and 3,4(M1; 2.790 --+ g.s.) for a ~-+ assignment to the 2.790 MeV level but still overestimates these transition probabilities by several orders of magnitude and fails to give the correct 3,3/3,4 branching ratio. In the present analysis the J = ~1 + and 5 + levels at 2.80 MeV are assumed to be particle states arising from the excitation of the last unpaired neutron from Nilsson orbit 7 to orbits 9 and 5, respectively. Pelte and Povh 29), however, by applying the 2 J + 1 rule to the averaged cross sections of the ZaNa(d, e)ZtNe reaction, deduce spin assignments of J = ½ for both states at 2.80 MeV and interpret the second J = ½ level as a hole state arising from the excitation of a nucleon from the filled Nilsson orbit 6 to orbit 7, in analogy to Clegg and Foley's 30) interpretation of the 2.64 MeV level of 23Na" The fact that the 9Be (160, e)ZtNe reaction seems to populate equally the two levels at 2.80 MeV supports their argument, if the 2 J + 1 rule is ap-

LIFETIMES 1N 21Ne

133

plicable to this reaction. A 71 + spin and parity assignment to one of the levels at 2.80 MeV is well established from the Z°Ne(d, p)ZlNe angular distribution measurements of Burrows et al. 27) and the 2 ONe(d ' p7)2 lNe studies of Howard et al. 26). In table 2 the 2.797 MeV level is identified as the z1 + particle state because the lifetime and branching ratio limits for this state are consistent with the Nilsson model predictions for this assignment. Bunker 31) has calculated the transition probabilities for the decay of a ½+ hole state (orbit 67 to be 73 (E2; ½+ ~ 5 + ) = 2.6 x 1012 sec- 1 and 74 (M1; ~1 + --, 23+) = 220 x 10 ~2 sec - I . These results are consistent with the decay properties of the 2.797 MeV state but are in no better agreement with the lifetime and branching ratio data for the 2.790 MeV level than the predictions given in table 2 for the s + assignment to the 2.790 MeV level. 4.3. CHI-DAVIDSON AND DREIZLER MODELS Table 2 lists several transition probabilities which were calculated on the ChiDavidson asymmetric core model 8, 32). The results are consistent with experiment for 7~(M17, 74(M1; 2.797 ~ g.s.) and 73(E2; 2.797 --* 0.357. However the model underestimates the transition probabilities for To(M1), ~;o(E2), ~;x(E2) and 72(E2), and overestimates 73(M1; 2.790 --* 0.35) and 74(MI; 2.790 --* g.s.). It should be pointed out that the second 23+ level and the first 9 + level are predicted by the ChiDavidson model 8) to be at about 4.l and 4.2 MeV, respectively. Better agreement with the lifetime measurements might be obtained if these levels where first brought down in energy, for example, by the inclusion of ~- and 7-vibrational effects s). However, the success of the Nilsson model indicates that there may be no need to assume axial asymmetry for 21Ne. This conclusion is supported by the recent calculations of Bar-Touv and Kelson 33), which predict regions of axial symmetry for doubly-even nuclei in the 2s-ld shell around A = 20, 28, and 36 and regions of axial asymmetry around A = 24 and 32. The final column of table 2 gives transition probabilities which were calculated by Dreizler 9, 3 4 ) using a core parameter g~ = 0.4. These results are consistent with experiment for 71(M1), 7~(E2), 72(E27, 73(E2; 2.797 ~ 0.357, 74(M1; 2.797 ~ g.s.) and 7s (for a 23+ assignment to the 2.87 MeV level). However, this model also badly overestimates the M1 transition probabilities for the decay of the 2.790 MeV state. 4.4. COMPARISON OF THE MODELS The Nilsson, Chi-Davidson and Dreizler models all fit reasonably well the energies, spins and parities of the first three excited states of ZlNe. The Nilsson and Dreizler models predict practically identical level structure up to about 3 MeV and similar transition probabilities except for 7o(M1), 73(E2; ~1 + ___>5+) and ~4(E2; ~1 + ~ 3+). However, the lifetime predictions of the Chi-Davidson model are quite different for many of the transitions, as can be seen from table 2. Although the present lifetime measurements are accurate only to within a factor of two or three, the results favour the Nilsson and Dreizler models over the Chi-Davidson model in its present form.

134

R.D. BENT et al.

A g r e e m e n t b e t w e e n e x p e r i m e n t a n d t h e N i l s s o n a n d D r e i z l e r m o d e l s is s a t i s f a c t o r y f o r t h e 0.35, 1.75, 2.797 a n d 2.87 M e V levels, b u t b o t h o f t h e m o d e l s o v e r e s t i m a t e b y at least two orders of magnitude the MI transition probabilities for the decay of the 2.790 M e V level. We wish to thank Dr. G. Dearnaley for making the silicon surface barrier detectors w h i c h w e r e u s e d i n t h e s e e x p e r i m e n t s , D r s . D . K u r a t h a n d J. W i l l s f o r c r i t i c a l a d v i c e c o n c e r n i n g t h e N i l s s o n m o d e l l i f e t i m e c a l c u l a t i o n s a n d D r s . J. P. D a v i d s o n a n d R. M . Dreizler for performing the lifetime calculations based on their models. R . D . B . is i n d e b t e d t o t h e J o h n S i m o n G u g g e n h e i m

Foundation

for a Fellowship

G r a n t w h i c h e n a b l e d h i m t o p u r s u e t h e i n i t i a l p a r t o f t h i s w o r k , t o D r . E. B r e t s c h e r f o r e n c o u r a g i n g h i m t o w o r k a t H a r w e l l a n d t o D r . J. M . F r e e m a n f o r t h e h o s p i t a l i t y of the Harwell tandem Van de Graaff group.

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