Angular correlation studies of excited states in 23Mg

Nuclear Physics A I 0 7 (1968) 253--265; (~) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

A N G U L A R C O R R E L A T I O N STUDIES OF EXCITED STATES I N 23Mg R. S. BLAKE t, E. B. PAUL tt and C. H. SINEX T. W. Bonner Nuclear Laboratories, Rice University, Houston, Texas, USA ttt

Received 18 September 1967

Abstract: Alpha-gamma angular correlation measurements in the reaction 24Mg(3He,uT)23Mglead to the assignments J = ~, ~, ~ ~, ~ ~, (~, ~, ½) and ~ [[ to the 2SMglevels at 0.45, 2.04, 2.35, 2.78, 3.78 and 4.35 MeV, respectively. The branching ratios of these levels and the mixing ratios of some of the 7,-rays are reported. E

NUCLEAR REACTION 24Mg(3He,cry), E = 9.00 MeV; measured tr(E~,E~,,0~7) 2aMg levels deduced J, 6, branchings. Natural target.

1. Introduction The collective model has been applied ~-4) with considerable success to the lowlying levels of 2 aNa" The level scheme of the mirror nucleus 23Mg was found to be (refs. ~o, 11)) very similar to that of 23Na" Until recently further information on 23Mg was scarce: from a study of the reaction 24Mg(3He, ~)23Mg, Parry et al. ~3) concluded that the spins and parities of the ground and first excited states are J~ = 3 + and ~+, respectively. Recently, however, several studies 14-~7) on this nucleus have been published. Using the 24Mg(p, d)23Mg reaction, Kozub 17) determined In = 0 for the 2.35 and 4.35 MeV levels, and In = 2 for the 0.45 and 5.3 MeV states. From the measurement of particle angular distributions and angular correlations in the reaction 24Mg(3He, ~tT)2aMg, Dubois and Earwaker 16), concluded that the spins and parities of the 0.45, 2.04, 2.35, 2.78, 2.90, 3.78 and 4.35 MeV levels are ~+, 7(~), ½+, (½, 3 ) - , (3, ~)+, 3 - and ½+, respectively. Recently de Silva et al. 14) reported spins of ~(½), ~(~), < 3, 3(~) for the 0.45, 2.04, 2.35 and 2.90 levels. In this paper we report the results of ~t-y angular correlations measurements in the reaction 24Mg(3He, ~?)23Mg. The experiment was performed with 9 MeV 3He+ + ions and 2aMg states as high as 4.35 MeV were identified. We examine the states which are strongly excited, viz. those at 0.45, 2.04, 2.35, 2.71, 2.78, 3.78 and 4.35 MeV. No g a m m a rays were detected which could be attributed to the 2.90, 3.86 and 3.97 MeV states. Our results are compared with other data in sect. 4. t Present Address: Institut du Radium; Orsay, France. tt Present Address: National Physical Laboratory, Teddington, England. tit Work supported in part by the U. S. Atomic Energy Commission. 253

R . S . BLAKE et al.

254

2. Experimental details In the c o r r e l a t i o n g e o m e t r y o f L i t h e r l a n d and F e r g u s o n 18), particles are observed at 180 ° or 0 ° to the beam. In this case, m . . . . the highest substate o f the g a m m a emitting state which can c o n t r i b u t e to the correlation, is the sum o f the spins o f the ingoing and o u t g o i n g particles a n d the target nucleus. I n t h e case o f the r e a c t i o n 24Mg(3He, ~)23Mg we find mmax = ½. Since the electronic a r r a n g e m e n t has been described elsewhere ~9), it will suffice to give a few details. C o i n c i d e n t electrical signals c o r r e s p o n d i n g to s-particles a n d y-rays a n d the o u t p u t of a t i m e - t o - a m p l i t u d e converter were fed into the Rice U n i versity 1401 3 - p a r a m e t e r 1000× 1000x 1000 channel analyser, a n d all coincident TABLE 1 Summary of the coefficients .43 and .44 of the Legendre polynomial expansion of the gamma-ray angular correlations Level (MeV)

Transition

A~

A4

0.45

1 -+ 0

--0.4810.06

--0.124-0.11

2.04

2~ l 1 -+ 0

--0.41i0.09 --0.564-0.11

--0.1510.14 --0.034-0.10

2.35

3~ 0 3 -+ 1 1 "+ 0

0.044-0.09 --0.024-0.07 0.004-0.07

--0.054-0.10 0.01 ±0.09 0.034-0.10

2.78

5~ 0

0.044-0.05

--0.054-0.06

3.78

7 -+ 1 7 --~ 5

--0.194-0.04 0.194-0.17

--0.10-k0.09 0.224-0.25

4.35

10 --~ 0

--0.044-0.17

--0.034-0.18

The coefficients have been corrected for attenuation effects.

events were stored sequentially on magnetic tape. Subsequently, digital w i n d o w s c o u l d be i m p o s e d on the t i m e - t o - a m p l i t u d e parameter. All events whose time p a r a meter fell within one o f these w i n d o w s were tagged as " t r u e a n d r a n d o m " or " r a n d o m " . The a d v a n t a g e o f this system is t h a t coincidence losses due to drifts o f the time p e a k are a v o i d e d a n d t h a t for each experiment the o p t i m u m resolving time can be obtained w i t h o u t fear o f losing coincident events. The resulting two-paramete~ d a t a were p r i n t e d out in 100 × 100 channel format. The a n n u l a r particle c o u n t e r e m p l o y e d h a d a resistivity o f 1000 f2 • c m a n d a surface area o f a b o u t 300 m m 2. I t was m o u n t e d 5.0 c m f r o m the target, a n d its m e a n angle o f o b s e r v a t i o n was 173 ° in the l a b system. In o r d e r to minimize b a c k scattering, the b e a m was s t o p p e d after passing t h r o u g h the target at the end o f a lead-lined pipe 3 m long. The particle d e t e c t o r bias was set at 10 V so as to discriminate against

2aMgEXCITEDSTATES

255

protons from the reaction 24Mg(aHe, p)26Al. To accentuate the difference as much as possible, short integrating and differentiating time constants were used in the linear part of the particle channel. This allowed the fast component pulses to pass relatively unaltered, whilst the amplitude of the slow component pulses from particles stopped in the dead layer behind the depletion layer was greatly reduced. The gamma-ray counter was a 12.5 × I0 cm NaI(T1) crystal mounted on an l 1stage photomultiplier. The detector was shielded with 5 cm of lead and could be rotated to subtend an angle of 30 ° with respect to the b e a m direction. The target was situated 30 cm from the front fact of the gamma-ray detector. Corrections for the attenuation of the correlation were taken from tables by Rutledge 20). With the exception of the 0.45 MeV g a m m a ray where we used Q2 = 0.972 and Q = 0.907, the normally used values were 0.974 and 0.913, respectively. The data were analysed on the Univac 1107 computer at Orsay, France. Efficiencies of the gamma-ray detector were obtained from graphs by Jarczyk et al. 21) and from Nuclear Data Tables 22). The data were analysed in terms of a Legendre polynomial series of the type W(O) oc 1 + A 2 P 2 (cos O)+A4P * (cos 0). The resulting coefficients for all the measured correlations are summarized in table 1. These coefficients have been corrected for the attenuation effects mentioned above. In order to calculate the goodness of fit with theoretical predictions, the AC5 code of Warburton 23) was used to calculate the •2 of the fit for each choice of spin. Several parameters were fed into the programme, but one parameter, the mixing ratio, was allowed to vary in fixed steps from one extreme value to another. Since the expectation value of ~2 is 1, we have taken the allowable error in ~ to be those values for which 2 ~ 1. All fits which at no time dropped below the 0.1% confidence level ~2 ~ ~min.. were rejected. The theoretical expression to which the angular correlations are fitted has the form W(O) = ~. P(~)Fk(ab)QkP k (cos 0), where the P(~) represents the population of substates of state a. The g a m m a ray is emitted from state a to state b. The Qk are the attenuation coefficients. The coefficients Fk(ab ) are defined in ref. 2 3). The phase convention used at all times is that of Litherland and Ferguson is) but where a mixed transition is encountered involving multipolarities L and L4. 1, the sign of ~ is that of transition M(L)4. E(L4. 1). This convention is adhered to even if there is reason to suspect that the transition is actually E(L) 4. M ( L 4.1). In the analysis, the effect of contributions from higher substates was also calculated. It was assumed that the maximum contribution from the mmax4-1 substate did not exceed 3 %. In no case did this affect our results materially and thus these calculations are not shown in the Z2 versus arctg 6 diagrams. The errors in the 6 quoted are those obtained without including higher substates.

256

R . s . BLAKE et al. I

1

I

I

I

"6 4-

800

÷

0

~

I

600

400

200

0

I 4O

3O

I 50

J

£

O

[

1

o"6

~1

~

weoker

gLoups

I

70

6O

80

90

IOO

Chonnel n o

Fig. 1. A particle spectrum obtained by bombarding a natural =4Mg target with 9 MeV 3He++ ions. The depletion layer of the particle detector was thick enough to stop the alpha particles completely. Protons with an energy greater than 1 MeV lost only part of their energy in this zone. The lowenergy continuum is probably due to protons.

IO o

¢d O

A

8

i ~0

,,, 6

r,q

oa 4-

,3

O O

4

o r,-,

0

i I

i 2

i 3

.J.,

i I

4

i 2

3. i-' :3

E~(MeV)

Fig. 2. Typical ~-ray spectra of (a) the 3.78 MeV state and (b) the unresolved pair of levels at 2.71 and 2.78 MeV.

ZaMg EXCITED STATES

257

In our experiment, a 150/zg/cm 2 thick natural Mg target on a carbon backing was bombarded with 0.1/~A of 3He + + ions at 9.0 MeV. No groups attributable to other naturally occurring Mg isotopes were observed. The beam current was held low so that a true-to-random ratio of better than 8 : 1 was maintained at all times. A coincident counting rate of 6000 per h was deemed adequate. Where branching ratios were calculated, the angular-distribution effects of both the background and the g a m m a ray under consideration were taken into account. It was assumed that incorrect estimation of the background gave rise to 20 % error in the results and that the error of the efficiency curve did not exceed 15 %. Competing reactions such as 160(3He, ~)150 were observed but these did not interfere with our measurements. Fig. 1 shows a spectrum of coincident alpha particles; the low-energy background is due to protons. The peaks marked ~7 and ~1o sit on top of the background, therefore it is possible that some of the coincident g a m m a rays are due to reaction 24Mg (3He, p)26A1. Figs. 2a and 2b are the g a m m a spectra for the unresolved doublet at 2.71 and 2.78 MeV and for the 3.78 MeV state.

3. Experimental results Table 2 lists the mixing ratios, branching ratios and spins deduced from our experiment. These results are also shown in the decay scheme in fig. 7. 3.1. BR'ANCHING RATIOS The observed branching ratios are shown in column 4 of table 2. In table 4 they are compared with the results of da Silva et aL 14). Only the decays of the 2.71, 2.78 and 3.78 MeV states need further explanation. The particle groups corresponding to the 2.71 and 2.78 MeV levels were not resolved. The coincident y-ray spectrum contained strong 0.45 + 0.05, 0.67 +_0.05 and 2.78 +-0.05 MeV g a m m a rays. Comparing the spectrum in fig. 2b with fig. 2 of ref. 14), it is noted that the 2.78 MeV peak is much more intense in our spectrum. The 2.30 MeV y-ray seen by da Silva et aL 14) is understandably obscured in our case. The relative strength of the decays to the 2.04 and 0.45 MeV levels, 30_+5 % and 70+_5 % agrees with the values of da Silvaetal. of 3 2 + 3 %, and 68+_3 % (table 4). The greater intensity of the 2.78 MeV group in our case does not affect this ratio appreciably, so that we may conclude that if the 2.78 MeV state decays either to the 2.04 or 0.45 MeV levels, it does so __< 5 %. Both cascades originate from the 2.71 MeV state. It is not possible to say whether the 2.71 MeV state decays to the ground state as well because of the intense 2.78 MeV peak. In view of this uncertainty the relative intensities of the two cascades from the 2.71 MeV state are given in brackets. The intensity of a ground state transition from the 2.71 MeV state would not exceed the intensity of the 2.75 MeV ~-ray in ref. 14), and therefore cannot be a serious contamination of our 2.78 MeV peak.

258

R.S. BLAKEet al.

Fig. 2a shows four strong g a m m a rays from the decay of the 3.78 MeV level: 3.80__0.05, 3.35___0.05, 1.00___0.05 and 0.45-t-0.05 MeV. The strong 3.35 and 0.45 MeV y-rays form the 3.78 --* 0.45 ~ 0 cascade; the weak 3.80 MeV y-ray is the g r o u n d state transition. The 1.00 MeV y-ray is t h o u g h t to arise from the t r a n s i t i o n 3.78 2.78 MeV. The c o m p l i m e n t a r y 2.78 MeV y-ray is obscured by the first escape peak of the intense 3.35 MeV y-ray. TABLE2 Summary of the spins, mixing ratios and branching ratios observed Level (MeV) 0.45 2.04 2.35

Spin

Transition E~ -+ E t

~ ~ (½, ~, ~)

2.71

0.45 -+ 0 2.04 -+ 0 2.04-+0.45

Branch

Transition

(°~o)

Jl -+ .It

100 19-4-5 814-5

2.35-+0

334-5

2.35 4- 0.45

67+5

2.71 --~ 0.45 2.71 -+ 2.04

(704-5) (304-5) 100

2.78

(½, t, ~)

2.78 -+ 0

3.78

({, {, {~)

3.78 -+ 0 3.78 ~ 0.45

74-2 854-5

3.78 -+ 2.78 4.35 -+ 0

(84-3) 100

~ -+ ~t ~-+~ ½-+~t { -+ { { -+ { ½--->Ii { -+ { {~-+ ~

(½, ~, {)

0.04±0.04 not determined 0.08±0.07 all~5 0.204-0.15 or 14.3 --0.204-0.10 all 0.09 4-0.06 0.404-0.14 not determined not determined

½~ { -+ { -+ {

4.35

Mixing ratio

~ -+ ~ {~ { { -+ { { -+ {t {-+~

all d~ 0.23 4-0.05 or >_ 14.3 or --8.1 --0.21 4-0.04 not determined --0.074-0.07 0.584-0.13 --0.104-0.04 not determined all 0.26 0.1~ or >= 11.4 --0.174-0.10

The origin of the 1.40 MeV a n d other m i n o r peaks could n o t be determined with any degree of certainty; since they possibly might be due to the reaction 24Mg (3He, p j 2 6 A 1 . 3.2. ANGULAR CORRELATION RESULTS T h e 0.45 MeV s t a t e . The a n g u l a r distribution was fitted to assumed initial spins of up to 9. The spin of the g r o u n d state is 13) {+. Fig. 3 shows that only the Z2 curves for J = { and ~2 drop below the 0.1 ~ confidence level. The J = { possibility

is ruled out below.

I

I

I

I

I

I

I

I

1

I00

I0.0

\1\1\

t/.V

,.oo,.

::o:.,o.o, 1.0

X

,

v

23Mg

Ol

I

I

- 00"

-60"

I

-40"

I

I

-20"

0

I

20 °

I

40 °

I

60*

I

80*

Arc)g Fig. 3. The X= versus arctg & curves for the decay o f the 0.45 M e V leve] to the ground state.

I00

~512

I0.0

iC

, - T -~o~ ,.--~-o,5

~io = fixed,see fexl

\\ ~

~3/2 ~3 1 ~ // /7,2-s,2-3,2 ~J

20 z

80%--

O.I 60*

80"

Arctg Fig. 4. T h e Z ~ v e r s u s a r c t g ~ c u r v e s o b t a i n e d for a s i m u l t a n e o u s fit o f the 2.04 ~ 0.45 --~ 0 c a s c a d e g a m m a rays. O n l y t h e t w o cases y i e l d i n g t h e l o w e s t v a l u e s o f Z 2 are s h o w n here.

R . S . BLAKE et al.

260

The 2.04 MeV state. This state was not strongly excited. We simultaneously fitted the angular distribution of the 1.59 and 0.45 MeV 7-rays from the 8 1 % cascade 2.04 ~ 0.45 ~ 0 MeV. The value of 51o was fixed at one of the three values obtained from fig. 3 and 621 was allowed to vary. Only the spin sequence ~ ~ { ~ ~ leads to a Z2 which drops below the 0.1% confidence level. This is shown in fig. 4 where the next lowest X2 value for { ~ ~ --+ ] is also depicted. 1

X2

I

I

!

i

i

!

i

712+ 512 ioo

3/2~5/2

IO.C

--01%1%J U --

fO%

--(X~>

5/2 +

3'78 ~

Z3Mg

0 45 ,/2 - 5/2

tO

Ol

1

3/2--5/2

I -80 °

I -60 °

I -40 °

I -20 °

I 0

I 20 °

I 40 °

I 60 °

I 80 °

Arctg

Fig. 5. The Z~versus arctg 6 curves for the decay of the 3.78 MeV level to the 0.45 MeV level. The 2.35, 2.78 and 4.35 MeV groups. All the observed angular correlations of these groups were isotropic. The 67 % branch decay of the 2.35 MeV state to the 0.45 MeV level could be fitted for assumed initial spins of J = ½, 3, 5, 5. The 33 % ground state transition on the other hand only allowed J = ½, ~ and ~ thus eliminating 5The correlations for the ground state decays of 2.78 and 4.35 MeV decays allow possible spins of J = ½, ~ and {. The corresponding values of the mixing ratios are given in table 2. The 3.78 MeV group. As seen in fig. 5, the angular correlation for the strongest g a m m a ray (the 85 + 5 7oodecay to the 0.45 MeV state) can be fitted for assumed initial spins J = ~, ~ or 5. In view of the uncertainty of the spin of the 2.78 MeV state, no attempt was made to analyse the angular distribution of the 1.0 MeV g a m m a ray.

23Mg EXCITED STATES

26 1

4. Discussion

I n table 3 the spin assignments deduced from this experiment are c o m p a r e d with those of da Silva et al. 14) a n d D u b o i s a n d Earwaker 16). I n the last c o l u m n we have included the In values from the (p, d) work of K o z u b 17). TABLE 3 A comparison of the results of these experiments with other recently published work Level (MeV)

Present work J

da Silva et al. 14) J

Dubois and Earwaker 16) .In

0.45 2.04 2.35 2.71 2.78 2.90 3.78 4.35

[ ½ _--<~

~(~) ~(~) ~

~-+ ½, (~) ½+

~(~)

(½, D(L D ÷

~ (~, ~, ~) =<

Kozub 17) In 2 o

½+

TABLE4 Comparison of the branching ratios published by da Silva et al. 14) with those of the present experiment Level (MeV)

Transition El --~ Et (MeV)

0.45 2.04

0.45 -+ 0 2.04 --~ 0 2.04 -+ 0.45 2.35 4- 0 2.35 ~ 0.45

100

2.71 4- 0.45 2.71 ~ 2.04 2.78 ~ 0

(704-5) (304-5) 100

2.35 2.71 2.78 2.90

2.90 ~ 0 2.90 -~ 0.45

Present work (~)

194-5 81 :t-5 334-5 674-5

da Silva et al. 14) (%) 100 164-3 844-3 324-3 684-3 (682_3) (32~:3) 684-2 324-2

The values for the decay of the 2.71 MeV level are given in brackets since an additional ground state transition could not be excluded.

O u r value for the mixing ratio of the 0.45 MeV y-ray, 61o = 0 . 0 4 + 0 . 0 4 , agrees well with the value of 61o = 0.06___0.02 reported by da Silva et al. 14). F o r the t r a n s i t i o n 2.04 --. 0.45 MeV, we f o u n d 621 = 0.08 +0.07, m u c h lower t h a n the value of da Silva et al., 621 = 0.23__0.03, b u t in better agreement with their theoretical prediction of 0.15. W e r n b o m - S e l i n and Arnell 26) have observed anisotropic y-rays

262

R . S . BLAKE et al.

originating from a level at about 2.40 MeV in 23Na" Lancman et al. 4) believe that the 2.39 MeV level in 23Na is in fact a close-lying doublet with different modes of decay. There is no evidence in our work of such a doublet in 2 3 M g . In table 4 we compare the branching ratios deduced from this experiment with those of da Silva et ak 14); the two sets of results agree well. The strong resemblance of the level schemes of 23Mg and 2 aNa has been discussed before 1o, 11). Fig. 6 demonstrates this great similarity. The first excited states both 443

3.85

( I/2+,3/2 +-, 512 -+)

4.35

(112,312,5/2)

3.97

3,92

3.86

3,68

3/2 +

3.78

(3/2, 5/2, 7/2 )

2.98

290 2.78 2.71

9/2 (5/2)

2.64

(I/2, 3/2,5/2)

2.39

I/2 {+), (312 +)

2.08

7/2¢"1"),(3/2 'f )

0.44

5/2 + 3/2 +

23No

(J/2, 3/2,512 )

271

2.35

(1/2, 5 / 2 , 5 / 2 ) 7/2

2,04

l

o , 4 5

3/2 +

z3rvlg

F i g . 6. The level schemes of 2aNa and ~3Mg. The broken lines join the assumed analogue states. The information on ~ZNa was taken from refs. 2, n, 7), whilst the spins of ~aMg are those deduced from our work.

have spin {+ and apart from an expected difference in sign 6, 14), the mixing ratios 61o for the two cases are very similar, 61o = 0.04+0.04 in 23Mg compared with 61o = -0.045__0.015 and 61o = - 0 . 0 8 + 0 . 0 2 reported by Mizobuchi et al. 24) and Poletti and Start 6) in 23Na ' Although the spin of the 2.39 MeV level in 23Na has not been established uniquely, there is evidence 1, 5, 6) for J = ½. The present results for the analogous state in 2aMg, the 2.35 MeV state, are not unique either, but Kozub ~7) and Dubois and

SSMg EXCITED

STATES

263

Earwaker 16) determined J~ = ½+. The observed intensity for its E2 decay to the first excited state in 23Mg i s 67 ~ (in 23Na for the analogous transition, 33 ~ ) implying a large inhibition in the M1 component of the ground state decay. Paul and Montague 1) found that the 2.39 MeV state in 23Na was strongly excited in the reaction 22Ne(d, n)23Na and showed an lp = 0 stripping pattern, suggesting that the level could be a single-particle state, the lowest member of a K = ½ band formed by promoting the unpaired particle to Nilsson orbit 9. The 2.64 MeV level was strongly excited 5) in 24Mg(p, 2p)23Na and is thought to be a hole state formed by a particle being promoted from orbit 6 to orbit 7. The calculations on 2aNa by Lancman et al. 4), using the Nilsson model with Coriolis coupling, predict a large M1 inhibition in the decay of the 2.39 MeV state. However, the 2.39 and 2.64 MeV levels were found to require nearly equal amplitudes of particle and hole state. Poletti and Start 6) demonstrated that these levels could have large particle and hole-state admixtures, but could still behave like one or the other. The M 1 amplitudes are assumed to interfere destructively in the case of the 2.39 MeV state in 23Na and constructively in the case of the 2.64 MeV state. Therefore, it is not surprising that the intensity of the ground state transition in 2aMg is 33 ~ compared with 67 ~o in 23Na. Where destructive interference is important, very small changes in the wave function in going from 23Na to 2aMg can have large effects on the transition strengths. A similar case of M 1 inhibition in 21Ne was observed and discussed by Pelte, Povh and Schtirlein 25). The 2.71 and 2.78 MeV states of 23Mg are believed to be the analogues of the 2.71 and 2.64 MeV states in 23Na. In both nuclei the 2.71 MeV states decay to the first and second excited state. In 2aNa no ground state decay has been observed from the 2.71 MeV state; for 23Mg the present results are inconclusive. The 2.78 MeV state in 23Mg and the 2.64 MeV state in 2aNa decay only to the ground state; in both cases the radiation is isotropic. The inverse order of the two states in 23Na and 23Mg may be related to the fact that the 2.64 MeV level in 2 aNa is a core excitation 5), whilst the 2.71 MeV state, with assumed spin 9 is a singleparticle state. The Coulomb energy for these states may be different. The 3.78 MeV state in 23Mg resembles the 3.68 MeV state in 23Na which has been shown 2.7) to have spin 2 +. The transition to the 2.78 MeV state (and in 23Na to the 2.64 MeV state) is remarkable, its intensity (8 ~ ) in competition with the energetically favoured decay to the first excited state may be due to the fact that both initial and final states belong to the same K = ½ band. The 4.35 MeV state in 23Mg is believed to be the analogue of the 4.43 MeV state in 23Na" Both decay only to the ground state and emit isotropic radiation, which can be reconciled with the spins o f J = ½, ½ or ~ [see ref. 2)]. The spin of the 23Mg state is ½+ because of the observed l n = 0 pick-up observed in the (p, d) work of Kozub 17). The applicability of a simple Nilsson model to the lower states in 23Mg has been discussed in da Silva et al. 14). They also compared their results with the multitude

264

R.S.

BLAKE

et al.

of calculations published 1- 9) on the low-lying states in 23Na" Because of the strong similarity of 23Mg and 23Na ' much of what applies to the latter also applies to 23Mg" As in 23Na, the properties of 23Mg levels below 4 MeV may be explained by invoking at least three interacting rotational bands with K = ~:, ½ and ½ [refs. 3, 4, 7,9)]. These bands are based on the ground state, the 2.35 and 2.78 MeV states. The ground state, 0.45, 2.04 and 2.71 MeV levels with spins ~+, ~+, ~+ and (~+) belong to the K = ½ band. The 2.35 and 2.90 MeV states with assumed spins of ½+ and ~+ form E 4.55

JTI (1/2,312,5/2)

3 78 ( :312. 512,712 ) 4-1

"4"1

2.7B (1/2,312,5/2) 271 ÷1

o

÷1

o

2 35 (112,312,5/2)

+~

+1

m

÷~

0 0

2.04

712

0.45

512

0

312+

0 0

Z3Mg

Fig. 7. A summary of the spins and branching ratios observed in this experiment.

part of the first K = ½ rotational band. Lastly the 2.78 and 3.78 MeV states with assumed spins 1+ and ½+ belong to the second K = ½ band. Our results are in accord with this picture. Apart from the cases of the 0.45 and 2.04 MeV states, our results are not explicit enough to exclude other explanations. The recently published article of Bouten et al. 27) on intermediate coupling in the 2s-ld shell showed that fair agreement was obtained between the theoretical and observed level schemes for the mass-23 nuclei. For best agreement the intermediate coupling parameter was on the low side (x ~ 2.4). The same effect was observed for other rotational nuclei. This is to be expected as one would expect the central force to play a greater r61e in those cases. Finally, we note the remarkable variation of the intensity of the various groups as a function of bombarding energy, even at high energies. In this experiment E(3He) =

~3MgEXCITEDSTATES

265

9.0 MeV the 2.90 MeV group e.g. is not seen whereas it has been plainly seen at E(aHe) = 5.55 and 4.90 MeV. References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27)

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