Angular-correlation studies of the reaction 24Mg(α, pγ)27 Al

1.E.1 1

Nuclear Physics A126 (1969) 49--59; (~) North-Holland Publishing Co., Amsterdam

Not to be reproduced by photoprint or microfilmwithout written permissionfrom the publisher

ANGULAR-CORRELATION

STUDIES

OF THE REACTION ~Mg(~t, p~')~Al K. W. CARTER, R. V. ELLIOTT *, D. C. KEAN and R. H. SPEAR Research School of Physical Sciences, Australian National University, Canberra

Received 22 November 1968

Abstract: The 3.68, 3.96, 4.05 and 4.58 MeV levels of 27A1have been studied via angular correlation measurements of the reaction 24Mg(ct, p),)ZTAI.The results are used in conjunction with previous information on lifetimes and branching ratios to impose limitations on possible spins, parities and multipole mixing ratios. New information on the gamma-ray decay scheme of the 4.58 MeV level is presented. E

NUCLEAR REACTIONS 24Mg(~,py), E : 9.1, 13.0 MeV; measured tr(Ep, E~, 0pr); 27AI levels deduced y-branching, J, :t, t$. Enriched target.

/

J

1. Introduction As the result o f a large a m o u n t o f experimental work, the properties o f the energy levels o f 27A1 at excitation energies E X < 3.0 MeV are now fairly well k n o w n ; the theoretical significance o f this i n f o r m a t i o n has been discussed by n u m e r o u s a u t h o r s [see, for example, refs. 1-5)]. N o nuclear model has yet p r o v i d e d a c o m p l e t e l y a d e q u a t e description o f these levels. Recently there has been an increasing effort to establish the properties o f the levels a b o v e 3.0 MeV in the realisation that such i n f o r m a t i o n is necessary for the d e t e r m i n a t i o n o f a satisfactory model for 27A1. F o r example, C h a l k River g r o u p s have studied the 4.51 MeV level 4.6) and suggested that it is the 1--2±+m e m b e r o f the g r o u n d - s t a t e r o t a t i o n a l band, the other m e m b e r s o f the band being the levels at E x = 0.00, 2.21 a n d 3.00 MeV with J= = 2~+, 5 + a n d +, respectively. However, ratios o f g a m m a - r a y transition rates within the p r o p o s e d b a n d d o not agree with predictions o f the simple r o t a t i o n a l model. F o r this reason, R 6 p k e and Lain have suggested 7) that possibly the 4.51 MeV level is the ~2*-+ m e m b e r o f a K = -~ r o t a t i o n a l b a n d based on the 3.00 MeV 2o + level, and that it would therefore be o f interest to find the second excited 3 + state, which would p r e s u m a b l y belong to the K = s g r o u n d - s t a t e band. T h e present p a p e r describes a n g u l a r - c o r r e l a t i o n studies o f the 3.68, 3.96, 4.05 a n d 4.58 MeV levels o f 27A1 using the reaction 24Mg(~, p],,)27Al and the p r o c e d u r e c o m m o n l y referred to as M e t h o d II o f Litherland and F e r g u s o n a); the collinear g e o m e t r y ÷ Now at McMaster University, llamilton, Ontario, Canada. 49

50

K . W . CARTER et al.

ensures that only m = + T magnetic substates of the final nucleus are populated, thus simplifying the correlation functions. No attempt was made to study the 4.51 MeV level. Attempts to populate the 4.41 MeV level to a degree sufficient for correlation studies were unsuccessful.

2. Experimental procedure A beam of '*He + ÷ ions from the A N U tandem accelerator was used to bombard a target consisting of approximately 100 vg/cm 2 of 24Mg (99.96 95 enrichment) deposited on a thin carbon foil mounted at the centre of a thin-walled chamber. For the 3.68, 3.96 and 4.05 MeV levels, a bombarding energy E~ of 13.045 MeV was used. An annular surface-barrier counter detected protons emitted at angles between 165 * and 171 ° to the beam axis giving an acceptance solid angle of 130 msr. Aluminium foils of total thickness 32 pm were placed in front of the counter to ensure that the proton groups of interest were separated in energy from scattered alpha particles. "lhe beam was stopped in tantalum at a distance of approximately 2.0 m from the target. G a m m a rays were detected at angles of 20 °, 42.5 °, 67.5 ~ and 90 ° by a 12.7 cm x 10.2 cm NaI(TI) crystal located 20 cm from the target spot. Tests made with a radioactive source at the target spot showed that anisotropies in the experimental arrangement were negligible. A bombarding energy of 9.100 MeV was used to study the 4.58 MeV level. Protons v~ere detected using a 5 cm × 6 mm position-sensitive solid-state detector at the focal plane of a 61 cm double-focussing magnetic spectrometer 9) set at 0 ~ to the beam direction. The acceptance aperture of the spectrometer is rectangular (6.5 ° vertical half-angle and 2 ° horizontal half-angle) and therefore not strictly axially symmetric; however, since the larger asymmetry of the aperture is in the vertical plane and the correlations were measured in the horizontal plane, errors intrcduced by this effect are assumed to be negligible to). G a m m a rays were detected at angles of 90 ~, 1102, 135 :, 150: and 157.5 * using two 12.7 cm × 10.2 cm NaI(TI) crystals. Gain changes produced by the magnetic field of the spectrometer were observed when the crystals were in the forward quadrants; therefore all measurements were taken at backward angles. For all levels ccincidence events were detected by a slow-fast coincidence system using crossover timing with a resolution of 140 ns: when the position-sensitive detector was used, timing was based on the energy signal. The ratio of random to real coincidences ( ~ 5','~) was obtained from a time-to-pulse-height converter. The data for the 3.68, 3.96 and 4.05 MeV levels were collected simultaneously using a dual-parameter system consisting of two lntertechnique CA13 ADC coupled to an IBM 1800 computer, which stored the proton spectrum in 32 channels and the gamma ray spectrum in 128 channels. The gamma ray spectra for the 4.58 MeV level were stored in a 256-channel pulse-height analyser. All gamma-ray spectra were analysed using the line-shape fitting procedure described by Elliott et al. ~).

~4M¢(=,pT)2~Ai 3.

51

Results

The resolution of the magnetic spectrometer was sufficient to adequately resolve the proton group corresponding to the 4.58 MeV level, but the annular counter system was unable to completely resolve groups corresponding to the 3.68, 3.96 and 4.05 MeV levels (fig. 1). Spectra of g a m m a rays in coincidence with protons populating the four levels under investigation are shown in fig. 2. The full curves represent fits to the data obtained from the line-shape analysis. The spectra for the 3.68, 3.96 and 4.05 MeV levels were obtained using the windows shown in the spectrum of fig. 1; because of the inferior resolution of the annular counter system, weak gamma rays from levels other than the one of immediate interest are present in each spectrum, e.g. the 3.00 MeV radiation present in some spectra is attributed to de-excitation of the 3.00 MeV level.

'3.68

600C

!

4000

3"96

Z 0 ('J

4'05

2000 e o •

4

i

"', 8

,

1'2 16 2'0 CHANNEL

i • , r

i

24

o °°

218

32

Fig. ]. Annular-counter spectrum of protons corresponding to the 3.68, 3.96 and 4.05 M c V levels of 27AI.

Since the decay schemes of these three levels were known from previous work, angular correlations were measured for appropriate gamma rays from each level. The number of coincidence counts at each setting of the gamma-ray detector was normalised to the total proton counts in a windew encompassing all three levels. In order to check the implicit assumption that the relative population of each level remained constant throughout the measurement, the bombarding energy was varied by + I0 keV and no change of relative population was observed, presumably because the target thickness was sufficient to smear out any fine structure present in the excitation function.

800

(o)

E,, = :3.68 M e V Ea= 1 3 . 0 4 5 M e V 0 = 90 °

,o

z.o

s.o

(b)

Ex:3'96

,o

ond

4.05

Eo = 1 3 . 0 4 5 2oo

MeV

MeV

e = 42.5 °

I-z 0 (.~

=

I00

• ~.

3-u

"~A

•

T

i

•

I0

300

3.6

r

20

,o,

3O

(c)

L

Ex = 4 . 5 8

MeV

Ea=9'100

MeV

SUMMED 1-72 I 85

2oo

'!

40

OVER

ANGLES 4 58

221 2 37

I,

-#

,~.

,oo .

. ~~,/.

i ~,~

+ ,;i %

o

I 0

I0

,

J 20

J

L 30

, 40

,

' .":'~50

E:,. ( M e V )

Fig. 2. Coincidence g a m m a - r a y spectra for levels o f =~AI populated via the reaction '-"SMg(~t, py)~Al. T h e data have been corrected for r a n d o m coincidences. The spectra of (a) and (b) were obtained using the windows indicated in fig. I; the 4.58 MeV level spectrum o f (c) was obtained using a magnetic spectrometer as proton detector.

~Mg(:~, pz)~rAI

53

Correlation m e a s u r e m e n t s for five g a m m a rays are presented in figs. 3-7. The upper part of each figure shows the data a n d best fits for various possible spin assignments. The error bars are statistical only unless indicated otherwise in the discussion below• The lower part of each figure shows plots of Z2 versus the amplitude mixing ratio c5 for the spins considered; the sign c o n v e n t i o n used for fi is that of Rose a n d Brink 12). In all cases the effect on the fits o f a 5 o//op o p u l a t i o n o f m = __+~substates was investigated and found to be negligible. Table 1 summarises the results for fits which fall within the 0.1 o/ o/ c o n f i d e n c e limit. The errors listed for 6 correspond to the range of values which lies within the 0. I ~ limit; this conservative approach makes adequate allowance for uncertainties involved in the assignment of errors to the data points. TABLE I Results of Z2 analysis of angular correlation data Initial state (McV)

Final state (MeV)

J~ assumcd for final state

3.68

0.84

~~

3.68

1.01

_~-

Spins and mixing ratios which give fits within the 0.1 ~ confidence limit j j ½ ~ •

--0.29±0.08 or 4.1 -+0 .1.6 8

½ 0.26-'0.12 or > 8.9 or < --9.9 --0.19+0.18

3.96

0.00

~+

½ 0.06--0.07 0.42 -k0.07 --0.15 t-0.04

4.05 4.58

0.84 0.00

½~ ~+

½ ~..

or

J~.-O+ _1 0 1 83

o -q,~+0.17or 4. 7 +28.5 ....~ ' - - - 0.22 - 2.1

½ 0.10_l 0.08 or 3.1 -0.6 +1.0 ;~

0 • 38 +°"°° -0.06 --0.18=0.04

3.1. THE 3.68 MeV LEVEL It is well k n o w n 4,~t,13) that the 3.68 MeV level decays p r e d o m i n a n t l y to the 0.84 a n d 1.01 MeV levels, e.g. Elliott et al. find ~1) branches of 64 ~o and 36 'Yo to the C.84 a n d 1.01 MeV levels, respectively. It was found possible to measure correlations for the 2.84 MeV transition to the 0.84 MeV level a n d for the 2.67 MeV transition to the 1.01 MeV level. Statistical errors for these m e a s u r e m e n t s were sufficiently small that errors from other sources, e.g. line-shape fitting procedure, became significant

54

I~. W .

I

1

CARTER

e! tl[.

I

I

\

~.4

II

'

.

.

.

.

o

o

E

. , ~

~

~

o

-

w

,o,,

~

-

~_ "<>

~

~

~ o

--

~ ._~ ~

I ::3 .'=~ I

o

o

--

--

0

0

--

O

O

o

O -

--

•~

o

07311 :IAIIV73~

o

4-

~ll ~

& o

~

g

/_~

"

l

7

I

i

,9

N

--

o

o

o

o

o

o

6

o

o

-

-~

o

._~ ~ g=

~-

I o

6

2"1M~(:=, m,)2rA1

55

and were included in assigning the overall errors depicted in figs. 3 and 4. The results (table 1) indicate that the spin of the 3.68 MeV level is ½ or ~. Smulders et al. have reported 4) that the mean lifetime of the level is less than 30 fs. Using this result and the branching ratios given above, it is found that for the 2.84 MeV transition, the larger of the two mixing ratios consistent with a ~ assignment, i.e. fi = 4.1* -+0 . 81.6 , can probably be rejected since the lower limit corresponds to an E2 enhancement of 17 Weisskopf units (W.u.). The largest E2 enhancement found in 27AI by Smulders et al. 4) was 12 W.u. Similarly, for the 2.67 MeV transition the larger magnitude values of 3 consistent with a ~ assignment are unlikely, since 161> 8.9 corresponds to an E2 enhancement of greater than 14 W.u.

I

I

I

I

I

!

I

I

0"18 J = 9/2

o

J-5/z-~

\

.;- \ \ 596 0-14

/

-

i

4

J T

0 I

1 I

20

5/2"

I

30

\

I

40

I

50

I

60

I

70

I

80

90

e (DEGREES) I000 a • 9/2a

.\

t

oo

,o:.. .......o......,..::.. .....

/---o-,,. ,.o

0"I

,o%

I -80

I -60

I -40

\

I -20

ARCTAN(~)

X_~.,,2

I 0

I 20

I 40

I 60

I 80

(DEGREES)

Fig. 5. A n g u l a r correlation results and Z'~ analysis for the g a m m a - r a y transition between the 3.96 and 0.00 MeV levels o f 2~A1.

56

K.W. CARTERet al.

3.2. THE 3.96 MeV LEVEL There is considerable disagreement among various workers as to the decay scheme of the 3.96 MeV level; the different results are summarised by Elliott et al. 11). However, the major decay mode is certainly to the ground state. The correlation measurements for this transition listed in table 1 indicate that J -- ~, ~, ~ or 5- The mean lifetime of the level has been measured as less than 20 fs by Smulders et al. 4). This result and the measured branching ratios for the level exclude some of the spins permitted by the correlation results. Elliott et al. report a l) a (5_+ 2)o//o transition to the 2.73 MeV ~+ level; a spin of ½ for the 3.96 MeV level implies an E2 strength of at least 89 W.u. (taking the lower limits of the branching ratio) and hence can be rejected. The transition to the 0.84 MeV ½+ level reported by Elliott et al. [(3_+2)~o] and by Smulders et al. (8 ~o) is much too strong for octupole radiation, and hence a J = ~ assignment for the level can be excluded. The same transition almost certainly eliminates the possibility that J'~ = ,~-, since the lower limit of 1 0/~ given by Elliott et al. would require an M2 strength of > 8 W.u. Thus, the present correlation results and the previous lifetime and branching ratio data indicate that the spin of the 3.96 MeV level is ~ or ~ with J~ = ~- a very unlikely possibility. 3.3. THE 4.05 MeV LEVEL There is general agreement as to the decay scheme of this level 4,1 l,a a). According to Elliott et al. la), there is an 89 ~o 3.21 MeV transition to the 0.84 MeV level and an 11 ~ 3.04 MeV transition to the 1.01 MeV level. "Ihe correlation for the 3.21 MeV transition was measured giving possible spins of ½ or ½ for the 4.05 level (table 1). 3.4. THE 4.58 MeV LEVEL The use of a magnetic spectrometer to detect the particle group associated with this level provides sufficiently high resolution to ensure that the coincident gammaray spectrum contains no contributions from neighbouring levels. Thus the present data may be used to determine branching ratios for the level. The results are given in table 2; they are obtained using data from all five angles, and hence angular distribution effects are allowed for. The upper limits for strengths of possible weak transitions were obtained in the manner described previously a~). The errors indicated are those inherent in the line-shape analysis. The gamma-ray singles spectrum used for subtraction of randoms was similar to that given by Elliott et al. 11) for a bombarding energy of 9.00 MeV. Also listed in table 2 are other measurements ofthis decay scheme. The present data are in good agreement with those obtained by Elliott et al. using the 27Al(p, p')27Al reaction. Both measurements indicate, in contradiction to the results of Smulders et al. 4), a definite transition to the 2.73 MeV level and a probable transition to the 1.01 MeV level.

24Me(~,

py)27AI

~"]

~

E E---:

II

!

~=

i

I

I

I

©

~-

o

o

o

d

d

d

o

o

-

0731A

I o

:I^IIV73~I

I

I -

-~.~

<~

I o

-

-:

0

--IX

--

~T~

E-

m

N

w

~

Io"~i

x

_~

®

o

o

o

; N . ~ o=

Io o

~

0

o

o

O. 0"1 ~11 A

':1a I .I. V"I ~ 8

o

.~ ,..--- Z X

It.,

K . W . CARTER et al.

58

The angular correlation of the ground state transition was measured. The results are consistent with spin assignments of ), ~}, ! and {. The observed transition to the 2.21 MeV ~+ level is much too strong for octupole radiation, and hence eliminates the possibility that J = ~. In addition, it eliminates a ~.- assignment and indicates a strongly enhanced E2 transition i f J " = ~.+; assuming a mean lifetime 4) of less than 30 fs aud a branching greater than 14 % (table 2), J= = ~}- would require an M2 strength of at least 300 W.u. and J " = {}+ would require an E2 strength of at least l0 W.u. TABLE 2

Gamma-ray decay scheme of the 4.58 MeV level of ~TAl Ref. 0

Branchings (%) to final states (/5x in MeV) 0.84 1.01 2.21 2.73 2.98 3.00

3.68

3.96

4.05

Present work

72 ! 2

< 1

4 +2

16-t-2 8--2

< 2

< 2

< 2

< 2

< 1

Elliott et al. ~) Smulders et al. 4)

79!2 79

< 2

3=3

I1 ±2 21

< 3

< 3

< 2

1 --i

< 2

6-! 2

Thus, the correlation results when combined with the branching ratio and lifetime data imply J'~ = ~+, -~+- or -~-+. 4. D i s c u s s i o n

WE have concluded from the present data that the spin of the 3.68 MeV level is ½ or -]. Lawergren 14) has observed a pronounced I = 0 stripping pattern for this level in the 26Mg(d, n)eTA1 reaction at a b o m b a r d i n g energy of 3.0 MEV, thus indicating that J~ - ½+. Assuming that resonances observed in the 26Mg(p, 7)27A1 reaction decay primarily to bound states whose spins differ by less than two units from the resonance spin, Sheppard and van der Leun have suggested 15) that J = [ or 3. Recently, H u a n g and Ophel 16) have produced strong evidence from angular correlation studies of the 26Mg(p, -/)27A1 reaction that the spin of the level is ½. Thus, all the available data are consistent with J~ = 2~÷. The present work demonstrates that the spin of the 3.96 MeV level is ~ or :~ with J~ = -[- a very unlikely possibility. Sheppard and van der Leun have suggested 15) a ~ assignment from their 26Mg(p, ?)27A1 data, and a suggestion that J = -[ or Ihas been made 17) on the basis of inelastically scattered proton angular distributions. Therefore the spin of the 3.96 MeV level is very probably ~, although a ~ assignment c a n n o t be excluded. For the 4.05 MEV level, we have concluded that J = ½ or .~-. This is in agreement with the 26Mg(p, ),)27A1 and inelastic proton scattering data, which both suggest 1s.~ 7) that J = -~ or ~, and with the 2aSi(d, 3He)ETAl results which strongly suggest 18) that J~ = -~.- or -23-.

'-'4Mg(x, py)27Al

59

For the 4.58 MeV level, we have concluded that J " - -2 3+ , 2s± or ~-+. The only other information concerning the spin o f this level is a tentative assignment 7) of J " = 25+. The branching ratios obtained in thc present experiment for the 4.58 MeV level conlirm the results of a previous investigation in this laboratory 11) and are in disagreement with the results o f Smulders et al. 4). As pointed out in sect. 1 of this paper, RSpke and Lam have suggested 7) that it would be useful to find the second excited ~+ level, which may belong to the K = ~ rotational band. The present results indicate that none o f the 3.68, 3.96, 4.05 and 4.58 MeV levels has J = 92. The 4.51 MeV level most probably has 4,6,7) a spin o f ~ - . The measured decay scheme o f the 4.41 MeV level 11) taken in conjunction with the mean lifetime 4) o f less than 22 fs indicates that for this level J'~ = ½+, 3 ± or -3± with J'~ = 2 ÷ remaining a slight possibility; the ground state transition is much too strong for M2 radiation, thus eliminating J ' ~ = ½-; the 24 ~ branch to the 1.01 MeV ~.+ level is much too strong for octupole or M2 radiation, thus eliminating J = 92 and J~ = ~ - ; and a J'~ = ~-+ assignment would require an E2 enhancement o f greater than 21 W.u. for the transition to the 1.01 MeV level, which is most unlikely. The 4.81 MeV level has been assigned 15) a spin o f ~-. Thus it may be concluded that the second excited J'~ = o2 + state o f 27A1 is at an excitation energy greater than 4.81 MeV. The authors are grateful to Mr. J. S. Harrison for preparing the 24Mg target. References 1) 2) 3) 4) 5) 6) 7) 8) ' 9) 10) 11) 12) 13) 14) 15) 16) 17) 18)

T. R. Ophel and B. T. Lawergrcn, Nucl. Phys. 52 (1964) 417 V. K. Thankappan, Phys. Rev. 141 (1966) 957 D. Evers, J. Hertcl, T. W. Rctz-Schmidt and S. J. Skorka, Nucl, Phys. 91 (1967) 472 P. J. M. Smuldcrs, C. Broude and J. F. Sharpey-Schafer, Can. J. Phys. 46 (1968) 261 D. C. Kean, R. V. Elliott and R. H. Spear, Aust. J. Phys. 21 (1968) 405 O. Hiiusser, D. Pclte and J. F. Sharpey-Schafcr, Can. J. Phys. 46 (1968) 1145 II. R6pkc and S. T. Lain, Can. J. Phys. 46 (1968) 1649 A. E. Litherland and A. J. Ferguson, Can. J. Phys. 39 (1961) 788 R. V. Elliott, K. W. Carter and R. H. Spear, Nucl. Instr. 59 (1968) 29 A. E. Lithcrland, Radiative transitions in nuclear structure and electromagnetic interactions, ed. by N. MacDonald (Oliver and Boyd, Edinburgh, 1964) p. 108 R. V. Elliott, T. R. Ophel and R. H. Spear, Nucl. Phys. A l l 5 (1968) 673 H. J. Rose and D. M. Brink, Revs. Mod. Phys. 39 (1967) 306 P. M. Endt and C. van der Leun, Nucl. Phys. AI05 (1967) 1 B. Lawergren, Nucl. Phys. A90 (1967) 311 D. M. Sheppard and C. van dcr Lcun, Nucl. Phys. At00 (,1967) 333 F. C. P. Huang and T. R. Ophel, Australian National University Report ANU-P/423 (1968) S. S. Vasilcv, T. N. Mikhaleva and D. L. Chupunov, Izv. Akad. Nauk (ser. fiz.) 29 (1965) 181; 30 (1966) 214 B. M. WiIdenthal and E. Newman, Phys. Rev. 167 (1968) 1027