Angular correlation measurements in the O18(p, p′ γ)O18 reaction

I

.E.I: I

Nuclear Physics 66 (1965) 161--175; (~) North-Holland Publishing Co., Amsterdam

2.B

Not to be reproduced by photoprlnt or m i c r o f i l m without written permission from the

]

publisher

ANGULAR CORRELATION MEASUREMENTS I N T H E orS(p, p' ~)O Is R E A C T I O N R. W. OLLERHEAD t, j. S. LOPES tt, A. R. POLETTI, M. F. THOMAS and E. K. WARBURTON ttt Nuclear Physics Laboratory, Oxford Received 27 October 1964

Abstract: The levels at 3.92, 4.45, 5.09 and 5.25 MeV in Ois have been investigated using p-~, angular correlation measurements in the OXS(p,p'7)O xs reaction. The spin of the level at 4.45 MeV has been established as one. This level was found to decay 64±5 ~o to the 3.63 MeV 0+ level and 36-4- 5 Yoto the 1.98 MeV 2+ level, with an upper limit of 4 Yoplaced on the ground state transition. The 3.92 MeV 2+ level decayed 15 ~-~2 ~o to the ground state (0+), and 85±2 ~o to the 1.98 MeV 2+ level. The E2/M1 intensity ratio in the 3.92 -* 1.98 transition was measured as < 8 ~o, with a probable value of 3 Yo. The 5.09 and 5.25 MeV levels were found to decay > 90 ~ and 60+8 ~o, respectively, to the 1.98 MeV level, with ground state transitions of < 10 ~o and 40~8 ~o. A comparison of levels in Oxs with T = 1 levels in F 18 has been made. E [ NUCLEAR REACTIONS O18(p, P'7), E = 7-9 MeV; measuredo'(E, Ep,), p'7-coin, p'7(0). Deduced jr, 62(E2/M1). Enriched target I

1. introduction Several theoretical investigations 1-4) o f the mass 18 nuclei have been made, p r o m p t e d b y their relatively simple structure o f two n u c l e o n s outside the closed shell o f 016. The energy levels o f 0 1 s a n d F 1s are fairly well established 5 - 6 ) , a n d n e w inf o r m a t i o n o n the properties o f several o f these levels has been o b t a i n e d i n recent exp e r i m e n t a l w o r k 7-11). T h e present experiment has used the OlS(p, p ' ) O 18" react i o n to o b t a i n i n f o r m a t i o n o n the levels at 3.92, 4.45, 5.09 a n d 5.25 MeV in 01 s. The energy spectra o f 01 s a n d F 1s have been c o m p a r e d i n a n effort to identify the T = 1 levels i n F i s , or, where these are k n o w n , to predict properties of the corres p o n d i n g levels i n 01 s. The experimental procedure a n d m e t h o d s o f analysis used i n the present w o r k have been described i n detail elsewhere 11). The p a r t i c l e - g a m m a a n g u l a r correlation m e t h o d of L i t h e r l a n d a n d F e r g u s o n 12) has been used. Inelastically scattered p r o t o n s were detected i n a n a n n u l a r c o u n t e r placed at 180 ° to the b e a m axis, so that g a m m a t NATO Postdoctorate Science Fellow, 1963-4. Present address: Atomic Energy of Canada Ltd., Chalk River, Ontario, Canada. tt On leave from Laboratorio de Fisica e Engenharia Nucleares, Sacavem, Portugal. ttt National Science Foundation Senior Postdoctoral Fellow, 1963-4. Permanent address: Brookhaven National Laboratory, Upton, New York, USA. 161

162

S . W . OLLERHEADe t al.

rays detected in coincidence with the protons must have originated from magnetic substates of the excited level having magnetic quantum numbers limited to 0~ = 0, _ 1. This effective "alignment" results in p-~ angular correlations characteristic of the spin of the level and the multipole mixing ratio of the radiation, allowing these properties to be determined. Branching ratios were determined from the spectra obtained by summing all the spectra taken at different angles during the correlation measurements and subtracting the contributions due to random coincidences. The latter were determined by simultaneously accumulating "real" and " r a n d o m " spectra in a multichannel analyser gated by real and random coincidence pulses respectively. The experiments were performed using protons from the Harwell Tandem Van de Graaff generator in the energy range 7-9 MeV. The targets were prepared by evaporation of tungsten oxide enriched to approximately 50 ~ O ts onto a thin carbon backing. 2. E x p e r i m e n t a l Results

2.1. THE 4.45 MeV LEVEL IN 0 TM A typical proton energy spectrum obtained during the experiment is shown in fig. 1. The proton groups are labelled according to the target nucleus and its excitation energy, in the case of 018 levels or the usual labelling o f the proton groups in other cases. The groups corresponding to excitation of the 3.92 and 4.45 MeV levels in O 18 were clearly resolved, and angular correlation of gamma rays in coincidence with these two protons groups were measured simultaneously. The measurements were carried out at a proton energy of Ep = 9.02 MeV, where these two levels were preferentially excited. The summed energy spectrum of the gamma rays from the 4.45 MeV level is shown in fig. 2. The decay scheme and branching ratios measured in this experiment are also indicated on the figure. The 4.45 MeV level was found to decay 64___5 ~ to the 3.63 MeV 0 + level, giving rise to cascade gamma rays having energies of 0.82, 1.65 and 1.98 MeV, and 36___ 5 ~o to the 1.98 MeV 2 + level, yielding 2.47 and 1.98 MeV gamma rays. No 4.45 MeV gamma rays were observed, and an upper limit of 4 ~ was placed on the ground state transition. These results are in excellent agreement with Gobbi et al. 7) who obtained 634- 5 ~o, 374- 5 ~ and < 3 ~ for the branches to the 3.63, 1.98 and 0 MeV levels, respectively. Both these results are in slight disagreement with the measurements of Eswaran and Broude s), who obtained 74_6, +3 26_+6 and < 2 ~o for the same decay modes. Gobbi et aL 7) and Eswaran and Broude s) have established by careful energy measurements that the 0.82 MeV gamma rays definitely arises from decay to the 3.63 MeV 0 + level and that there is no evidence for decay to the 3.55 MeV 4 ÷ level. Angular correlations were obtained for both the 0.82 and 2.47 MeV gamma rays. These are shown in fig. 3, where the experimental points have error bars indicating the statistical uncertainty in their position. The analysis of the data proceeded as follows. The experimental distributions were first fitted by the least-squares method

ANGULARCORRELATIONMEASUREMENTS

163

Proton Spectrum O;e(p,p') 0IB Ep=8.6OMeV Z~2p,• 0m5.09.5.25

+o I 0B3t92 8

0m3.63

0~B1,98

U

* 0,s4.46~

~n6

f~

11

40

80

x I110 -

01B3'55

~,~o+o,,0o

120 160 Channel Number

200

240

Fig. 1, Proton energy spectrum obtained in the reaction OlS(p, p')O Is* at an incident proton energy of 8.60 MeV.

100C

80C

600

~n =~4Oo

3

'0.~2I

o.T1

,

t

i

1.65

~I

3.63 •

÷

li98

0÷"

-: b v

2* ~t

%

t

i,

~ 1.98-

t~ °+

200 0

I 40

I

I

i

I

80 120 Channel. Number

160

l

200

Fig. 2. Energy spectrum of gamma-rays in coincidence with protons corresponding to excitation of the 4,45 MeV level of Ots.

164

R.W.

e t al.

OLLERHEAD

with a simple Legendre polynomial expansion of the form

W(O) = ~ akek(cOS 0),

k = 0, 2, 4,

(1)

k

where 0 is the angle between the directions of the proton and the coincident gamma ray. The distributions are plotted versus cos20 in order to illustrate that there is no A N G U L A R CORRELATIONS

OB 4.45-MeV Lever 200

100 4 . 4 5 "-'~'L 98

"o >4./-,5-~-J- 3 . 6 3

~

J=3

~ -~

0°

3l I

8 45*

60 °

90 °

,:o

0175

o!5o

o125

;

COS2 S

Fig. 3. Angular distributions of gamma-rays in coincidence with protons detected at 180 ° corresponding to excitation of the 4.45 MeV level of O xs.

evidence for terms in Pk (COS0) having k > 2. The results of a computer fitting programme including terms up to k = 4 bear this out, as shown in the table below: Gamma-ray energy (MeV)

ai/ ao

0.82 2.47

--0.394-0.05 --0.084-0.08

aJ ao 0.044-0.06 --0.08 -4-0.11

The theoretical fits of the form W(O) = ao+a2P2(cos 0), computed with terms only up to k = 2, are shown in fig. 3 by the solid lines, having az/ao = -0.38___0.05

ANGULAR CORRELATION MEASUREMENTS

165

for the 0.82 MeV transition and a2/a o = - 0 . 0 9 +_0.08 for the 2.47 MeV gamma ray. The "goodness of fit" is indicated by the parameter X2 defined by la) X2 = _1 E [ r ( o , ) - W ( O , ) ] ~ n

i

E2(0i)

(2) '

where Y(Oi), IV(0~) and E(O~) are the experimental yield, theoretical distribution and statistical uncertainty in Y(Oi) evaluated at angle 0i, and n is the number of degrees of freedom. In this case, since there are two independently variable parameters in the theoretical distribution, n = (number of angles at which data have been taken) - 2 . The expectation value of X2 defined as in eq. (2) is unity. In the cases illustrated in fig. 3, X2 = 1.01, in the fit to the 0.82 MeV gamma ray data, and X2 -- 0.75 for the 2.47 MeV transition. The measured angular correlation of the 0.82 MeV gamma ray was then fitted with the theoretical distribution a ~)

IV(O) = ~_~Pk (J)tk(JJ')QkPk (COS 0),

(3)

k

where the Q~ are attenuation coefficients 12) for the gamma ray detector, the pk(J) are statistical tensors which describe the alignment of the initial state having spin J and therefore depend on the relative populations of its magnetic substates, and the Fk (JJ') are coefficients which depend specifically on the gamma-ray transition between the levels having spins J and J'. Details of the application of this formula and tables of coefficients are given in ref. 11). The Fk(JJ') contain a dependence on the multipole mixing ratio of the radiation, defined by the ratio of reduced matrix elements xl) S - (J'IIL+ lllJ) (J'[[ L I l J ) '

(4)

where L is the lowest allowed value of the multipolarity of the transition. In the case o f the 0.82 MeV gamma ray, the transition is to a level having J ' = 0, so that L = J, and X -- 0. The least-squares computer fit was made by varying the population parameters P(0) and P(1), which appear in the statistical tensors pk(J) and correspond to magnetic quantum numbers 0 and 1 +, until the minimum value of Z2 (eq. (2)) was obtained. This was done for initial spins J = 1, 2 and 3, with resulting values of X2 = 1.01, 86 and 142 respectively. The fit for J = 1 was identical to the Legendre polynomial fit, and is therefore given by the solid line in fig. 3. In this case, P(0) = 59.49/0 and P(1) = P ( - 1 ) = 2 0 . 3 ~ . The fits for J = 2 and 3 are indicated by broken lines in the same figure. These results definitely establish the spin of the 4.45 MeV level in 016 as I. This is in agreement with the value deduced by Gobbi et al. 7) from measured values of the lifetime 10) and branching ratio 7), and a comparison with single particle Weisskopf estimates o f transition strengths 14). The distributions of both the 0.82 and 2.47 MeV gamma rays were then fitted simultaneously with theoretical distributions of the form given by eq. (3), using

166

R . W . OLLERHEAD et aL

J = 1, as a function of the mixing parameter Xwhich appears in the 2.47 MeV transition. In this case, L = 1, and L + 1 = 2, corresponding to dipole and quadrupole radiation. Since X can lie anywhere in the range - ~ to + oo, the values of X2 obtained in fitting for each value of X are plotted versus arctg X as a convenient method of presenting the results. The results, calculated at 5 ° intervals from - 9 0 ° to + 90 ° in arctan AT, are presented in fig. 4. The "34 ~o limit" indicates that there is a statistical i

i

i

i

i

i

i

i

i

018 4,45-MeV Lever

4 4 . 4 5 ~

1

3 . 6 3 ~ 0

1.98--~

+

2+

0.2 0

I

0,1 -80

¥

I

-60

'f

I

-40

0+

I

I

-20 0 Arctg X

I

20

I

40

60

d

0

Fig. 4. Z 2 versus arctgX obtained in fitting theoretical curves simultaneously to the angular distributions measured for the 0.82 MeV and 2.47 MeV gamma-rays observed in the decay o f the O TM 4.45 MeV level, assuming d = 1.

probability of 0.34 that a correct solution will have a X2 equal to or greater than the indicated value 13) and this is, therefore, one standard deviation from all minima. There are two minima in the Z2 curve, corresponding to X = t g ( - 5 °) = - 0 . 0 9 _ 0.36, P(0) = 0.593, P(1) = 0.204, and X = t g ( + 8 0 °) = 5.7_+°~ 3.9, P(0) = 0.596, P(1) = 0.202. Both of these values give fits to the experimental distributions which are virtually identical to those of the Legendre polynomial analysis, so that there is no way of choosing between them. I f the 4.45 MeV level had odd parity, then X is the amplitude ratio of M2/E1, and the value near X = 0 is almost certainly the correct one; if the parity is even, then X is an E2/M1 ratio, and either value is possible. There is some evidence that the parity of this level is odd, but at present it is not conclusive. In recent measurements of the stripping reaction O17(d, p)O is, Yagi et aL have reported is) a strong 1, = 1 transition to the 4.45 MeV level, which implies odd parity with J = 1, 2, 3 or 4. However, these results are in complete disagreement with recent measurements on the same reaction by Hewka, Middleton and Wiza 9), who observed that the 4.45 MeV level was very weakly excited by the (
ANGULAR CORRELATION MEASUREMENTS

167

and suggest that since the target used by Yagi et aL contained only 1 ~ 017 it is possible that their identification was incorrect. This point will have to be clarified before a definite assignment of odd parity can be accepted. Hewka et aL have noted 9) that since the 4.45 MeV level was also weakly excited by the O16(t, p)O is reaction 16) whereas it was very strongly excited by the F 19(t, 00018 reaction 6), it is probably a negative parity state arising from the removal of a proton from the 016 core. The recent assignment of 9, 2 o) j~ = 3 + to the 5.37 MeV level in 0 is has completed the identification of the positive parity states arising from the coupling of two neutrons in the ld~-2s~ configurations. These are (d~)20 +, 2 +, 4+; (s½)2 0+; and (d~s~) 2 ÷, 3 +, identified with the levels at 0, 1.98, 3.55, 3.63, 3.92 and 5.37 MeV, respectively. Harvey 4) has made estimates of the odd parity levels arising from excitation of the 016 core. The lowest of these is predicted to lie between 4 and 5 MeV, with J = 1. The level at 4.45 MeV is the only level in this energy region, has a spin of 1, and is therefore a likely candidate for this odd parity level. Moreover, the levels in F 1s at 5.59 and 5.66 MeV are the most likely possibilities for the isobaric analogue of the 4.45 MeV level in 01 s, and both these levels have odd parity, which implies that the 4.45 MeV level must have odd parity also. This point is discussed more fully in a following section of this paper. In summary, the spin of the 4.45 MeV level in O 1s has been definitely established as J = 1, and while all the experimental evidence is consistent with its parity being odd, this has not been unambiguously proven. 2.2. THE 3.92 MeV LEVEL IN 018 The first five levels in O 1s bear a strong resemblance to the vibrational sequence found in medium weight nuclei: a 0 + ground state, a "one phonon" 2 + level, and a "two phonon" (0, 2, 4) + triplet of about twice the excitation energy of the first excited state. If this is indeed a vibrational sequence, we should expect the 2 -~ 2 transition to be predominantly E2, since the vibrational model excludes M1 radiation: also, it should be much stronger than the 2 ~ 0 ground state transition which would require a two quantum jump 14). It is therefore of great interest to determine the decay properties o f the 3.92 MeV 2 + level in 018. The summed energy spectrum of the gamma rays from the 3.92 MeV level in 01 a is shown in fig. 3. The principal decay mode was to the 1.98 MeV 2 + level, which resulted in gamma rays of 1.94 and 1.98 MeV which were not resolved. A ground state branch yielding 3.92 MeV gamma rays was also observed. The branching ratio of the 3.92 MeV level was determined to be 85 +_2 ~ to the 1.98 MeV level, and 15 ___ 2 ~ to the ground state. This is in excellent agreement with the recent results of Gobbi et al. 7), who obtained 85 ___5 ~ and 15 + 5 ~ for these transitions; but again both are in slight disagreement with Eswaran and Broude s) who report 9.35_4~ +2 s ~ and 6 •~-2.5 ~+4.5 ~ for this branching ratio. The angular correlations measured for the two transitions are shown in fig. 6. The solid line shown on the 3.92 MeV gamma ray distribution is the theoretical fit ob-

I

'

[

I

0183.92-MeV Level

800

I

l

+

3.92

1

2+ m

1.98

1.94 1.98

==6oo

z~

2 ~J

o

o+ o

~ 40O

3.92

U

120 160 Channel Number

BO Fig.

200

~240"

5.E n e r g y s p e c t r u m o f g a m m a - r a y s in coincidence with p r o t o n s c o r r e s p o n d i n g to excitation o f t h e O is 3.92 M e V level.

ANGULAR CORRELATIONS 1800 1700 1600 1500

~

eV Level

3.92-'-1.98 TRANSITION

t

~

1400 1300 "o ._~ >-

1200 300

~ . ~ ""- I

200

3.92--.-.>0 TRANSITION

J

=

2

~

100

8 0o

20°

3o °

~:o

'

o.'~5

45 °

o15o

cos2 8

80 o

9o °

o12~

6

Fig. 6. A n g u l a r distributions o f g a m m a - r a y s in coincidence with p r o t o n s detected at 180 ° cor= r e s p o n d i n g to excitation o f the 3.92 M e V level in O zS.

ANGULAR

CORRELATION

169

MEASUREMENTS

tained from eq. (3) including terms up to P4(cos 0), with J = 2 and J ' = 0. The relative populations used in this ease were P(0) = 0.204 and P(1) = 0.398, with a X2 value of 0.86. The dashed lines indicate the best fits possible for J = 1 and J = 3, with Z2 = 4.00 and 5.04, respectively. These results confirm the assigned spin value of J = 2 for the 3.92 MeV level. The distributions of both transitions were fitted simultaneously as a function of the E2/M1 mixing ratio in the 3.92(2 +) ~ 1.98(2 +) transition. The resulting Z2 018 3.92-MeV

Level

// 10

!

\

~(2

O!

, • . 10'/o limit

3 . 9 2 ~ 2 * 1.98 ~ - - -

02

0.1

0

I '-80

I -60

~

2* ~

1 -40

O+ I t -20 0 Arct 9 X

I 20

I 40

I 60

I 80

arctg X obtained in fitting simultaneously the angular distributions measured for the 3.92 MeV and 1.94-1.98 MeV gamma-rays observed in the decay of the 3.92 MeV level in

Fig. 7. Z= versus

018 .

values are plotted as a function of arctg X by the solid curve in fig. 7. The minimum value of X2 was obtained for a value of X = tg 10° = 0.18_+0.1, with P(0) = 0.211 and P(1) = 0.394. The solid lines in fig. 6 indicate the theoretical fits to the experimental data obtained using these values for the multipole mixing ratio and population parameters. Since the proton counter was not infinitesimally small and located at 180 °, but an annulus of finite size centered at 170 °, it was possible to have magnetic substates with > 1 populated to a small extent tl, 12). The effect of this was estimated by repeating the calculations assuming a mixing of P(2) = 0.1 P(1). The results of this calculation, shown by the dashed curve in fig. 7, indicate that a value of X nearer to zero may be correct. These combined results indicate that the E2/M1 intensity ratio is almost certainly less than 8 %, and probably less than tg 2 10° = 3.1%. This is in good agreement with the results of Litherland et al. 18), who assigned an upper limit

170

R.W. OLLERHEAD e t al.

of 4 ~ from their 7-7 angular correlation measurements of the reaction H 3 ( O 16, p?) 0 18"

From the measured lifetime value lo) of 1.8x 10 -13 see, the partial widths in Weisskopf units 14) calculated from the present measurements of branching and mixing ratios are 0.3 for the (2 ~ 0) ground state transition and 1.5 for the E2 component (3 ~ ) of the (2 --* 2) transition. Since the average value for E2 transitions in light nuclei is about 5 Weisskopf units 14), there is no evidence here for collective enhancement in the decay of the 3.92 MeV level. The partial width for the M1 comI

'

I

'

I

'

Proton Spectrum 018(p,p')018 Ep = 7.62- MeV

o

~

•

s.o9 I

,45 /

I

g

m

}

jS,o ,

100

I

140

J

~1

T"

I

180 220 Channel Number

i

260

Fig. 8. Portion of proton energy spectrum observed in the reaction OlS(p, p')O xs* at an incident proton energy of 7.62 MeV, expanded to show the region corresponding to excitation energies around 5 MeV in O xs.

ponent of the (2 ~ 2) transition is 2.0 x 10 - 2 Weisskopf units, which is within the range of 10 - 2 to 1 usually found in light nuclei 14). While the (2 ~ 2) E2 branch does show a factor of 5 enhancement over the (2 ~ 0) transition, this is not as great as one might expect from a simple vibrational model, which predicts zero matrix elements for all transitions except those between neighbouring levels. A recent survey 19) of the properties of even nuclei has revealed that virtually all the 2 + -~ 2 + transitions from the second 2 + state in nuclei from the vibrational region of the periodic table have an E2/M1 mixing ratio greater than 3, i.e. the transition is 90 ~ E2. The value of 3 ~ measured for the 3.92 MeV level in 01 s indicates that the low-energy spectrum of this nucleus is almost certainly not vibrational in nature. 2.3. T H E 5.09 A N D 5.25 MeV LEVELS IN O TM

An expanded portion of the proton energy spectrum from the reaction O 1s (p, p,) O is* taken at an incident proton energy of 7.62 MeV is shown in fig. 8. The proton groups corresponding to excitation of the 5.09 and 5.25 MeV levels in O 1s were superimposed on a high background, arising from slit scattering of inelastic peaks and to a

ANGULAR CORRELATION MEASUREMENTS

171

large extent from excitation of the 4.43 MeV level in C 12 from the target backing. This resulted in a very low coincidence rate, so that an angular correlation was not obtained. It was possible, however, to obtain decay schemes for these two levels. The summed energy spectra of the gamma-rays from the 5.09 and 5.25 MeV levels in 01 a are shown in fig. 9. The decay schemes are also indicated on the figure. The 5.25 MeV level was found to decay 60___8 % to the 1.98 2 + level and 40___8 % to the 0 + ground state. Spin and parity of 2 + have been assigned t6) to this level f r o m the 20(

J

I

J

I

(b)

10C

"k,

H

I I 5.25-~-~

' J

I

3.27

g

I

-

55

~-J

•

•

• ee e •

(a) ,.n

1 98

5 . 0 9 ~

~

,o, ee

• ,

TI

~-I

;. , * - F + , "

~• I

40 F i g . 9. E n e r g y s p e c t r a o f g a m m a - r a y s

3.11

.]1 •

J

,

•

018

~k I ~i-

,

80 Channel Number

in coincidence

I

,

120

with protons

160 corresponding

to excitation of

levels in Ois at (a) 5.09 MeV and (b) 5.25 MeV. OrS(t, p)O ts double stripping reaction. I f this assignment is correct, the transition to the 1.98 MeV 2 + level would be a mixture of E2 and M I , while the ground state transition would be pure E2; the observed branching ratio is compatible with this assignment. N o ground state transition was observed in the decay of the 5.09 MeV level in O' 8, and an upper limit of 10 % was estimated for this branch; the decay was more than 90 % to the 1.98 MeV 2 + level. It is possible that this is the second level in a negative parity rotational band predicted by Harvey 4), in which case it would have a spin and parity of 2 - . This would account for the predominant decay to the 2 + level, which would be an E1 transition, whereas the ground state decay would be pure M2. The single particle Weisskopf estimates 14) for the partial widths of these are 14 eV and 3.5 x 10 -4 eV, respectively.

3. Summary Information has been obtained on four levels in 01 s. The 4.45 MeV level was found to decay 64-t-5 % to the 3.63 MeV 0 + level and 36___5 % to the 1.98 MeV 2 + level,

172

R.W. OLLERHEAD et aL

with an upper limit of 4 ~ placed on the ground state transition. The spin of this level has been definitely established as unity, and there is some evidence that its parity is odd. The 3.92 MeV level decays 85 ___2 70 to the 1.98 MeV level, with a 15 ___ 70 branch to the ground state. The angular correlation measurements confirmed its assigned spin o f 2 and established the E2/M1 intensity ratio in the 2 ---, 2 transition as < 8 70, with a probable value of 3 70. The 5.09 and 5.25 MeV levels were found to decay > 90 and 60-1-8 70, respectively, to the 1.98 MeV level, with ground state branches o f < 10 70 and 4 0 + 8 70. These results are summarized in table 1. TABLE 1

Energy levels in 0 TM ~r,~ Energy (MeV)

This experiment

3.92

2t+)

4.45 5.09 5.25

1 (Possibly 2-)

*) Ref. 6).

Previous assignment

To ground state

To 1.98 MeV 2+ level

2+ a)

154-2 ~o

(_) b)

4~ 10 ~o 404-8 70

854-2 E2 intensity 8 70 364-5 70 90 70 604-8 70

2+ e) b) Ref. xs).

Branching ratios To 3.63 MeV 0+ level

644-5 70

e) Ref. xe).

4. Comparison of the Energy Spectra of O Is and F 18 It is of some interest to compare the energy spectrum of O 18 with the spectrum o f the known or possible T = 1 states of F 18. By this means some predictions can be made as to the possible spin-parity assignments for the O 1s levels above 4 M e ¥ excitation. The energy level spectrum of O 18 up to 6.4 MeV excitation and a partial spectrum of F 1s are shown in fig. 10. The O 18 spectrum has been displaced upwards by 1.05 MeV so that the O 18 ground state coincides in energy with its F 1s isobaricspin analogue 5) at 1.05 MeV in F is. Following previous work 5,21) the O is 1.98 MeV level is associated with the F 18 3.06 MeV level which has yet to be rigorously proven to have (J~; T) = (2+; 1). The F is 4.65 and 4.74 MeV levels have been shown s) to be most probably T = 1 and so they are tentatively associated with the O is 3.55 and 3.63 MeV levels. The association of the O is 3.92 MeV and F is 4.97 MeV levels is based on their energies and is probably correct unless there are one or more undiscovered states of F 1s in the region of 5 MeV excitation. The situation regarding the F is 5.59 and 5.66 MeV levels is rather puzzling. Both have been studied by the N14(~, ~)N 14 and N14(~, 7)F is reactions 22--25). The elastic scattering results indicate l, = 1 and thus J~ = 0 - , 1-, 2 - for both levels. The (~, 7) results rule out J" = 0 - for both levels since the gamma-ray transitions are anisotropic. Both levels appear 23, 25) to decay by strong dipole transitions to the

ANGULAR CORRELATION MEASUREMENTS

173

T = 0 1.08 MeV level, (not shown in fig. 10), and to the T = 1 3.06 MeV level. Because of the inhibition o f A T = 0 E1 and M1 transitions in self-conjugate nuclei these decay modes would appear to be inconsistent. A possible explanation, which we tentatively adopt, is that the two levels are both J~ = 1- and share the T = 1 wave

6.34 ,19

5.52 ..5.25533 ~-~7 5.09

I

6.39

[ I - .....

7.50 7.31

(3-) (3-)

. ~ + + + "b+56 6./+7

o...+

.6.97

....

6.23 6.26 1 2( ;1 ' ~.tt.. 6.09-- 273;'4" -

/

5.79 4.45

1

/

4

- 5.59 ~

i;2--

~.w

5.29 + 2~

3.92 - 3155

3.63

o

,,+,._

I

2+!

1.98

- -"4.8/-. 4.97 (T=O) _

: : : : 4.7i-.T6 4.-.~('-~')(+--~--~ 4.40

(T=O)

3:35

2,3;0

-3.06 3.13 1 (2~1)

2.53

2+;0

1.05

0:1

019

F 18 Fig. 10. C o m p a r i s o n o f low-lying energy levels in O z8 a n d F xS. T h e F z8 energies are t a k e n f r o m ref. 0 , the O z8 energies are f r o m ref. 9), a n d spin-parity a s s i g n m e n t s are f r o m refs. 5, 9,z~). T h e F x8 T = 0 levels below 2.5 M e V excitation h a v e been o m i t t e d for clarity, as have all F ~8 levels between 3.5 a n d 4.4 M e V excitation, a n d all b u t two o f t h e levels above 6.64 M e V excitation. T h e O z8 energy levels are s h o w n c o n n e c t e d to their a n a l o g u e states in F xS, with definite identifications indicated b y solid lines a n d tentative identifications by b r o k e n lines.

function expected for the analogue of the O ~8 4.45 MeV level. That is, in the absence of the Coulomb field one of these two states would be T = 0 and the other T = 1 and, because of their proximity in energy, their wave functions have become highly mixed due to the Coulomb interaction between them. This explanation is consistent

174

R.w.

OLLERI"IEAD et aL

with their ~-particle reduced widths which are 22) 9 ~o and 17 ~ of the Wigner limit, respectively. The F is 1.08 MeV level was at one time thought to be the (J~; T) = (0+; 1) analogue of the 018 ground state 26) and the strength of the 5.66 ~ 1.08 transition was therefore said to favour T = 0 for the F 18 5.66 MeV level 17). N o w that the 1.08 MeV level is known to have T = 0 the strength of the 5.66 ~ 1.08 transition favours T = 1 for the F 18 5.66 MeV level to the same extent. The above explanation depends on experimental evidence which is somewhat contradictory and so the explanation may be in error; however it seems quite definite that one or the other of the odd parity states at 5.59 and 5.66 MeV in F 18 has a sizable T = 1 component which is to be associated with the analogue of the O 18 4.45 MeV level thus providing indirect evidence that the O 18 4.45 MeV level is J~ = 1-. A resonance in the N14(~, v)F is reaction at E~ = 2.350+0.003 MeV has been observed 24) with gamma transitions to the F z8 0.94 and 1.70 MeV levels. This resonance corresponds to a state at 6.23 MeV in F 18 with J = 2 and a large T = 1 component 17). A resonance has also been observed in N14(~, ct)N 14 at E~ = 2.353 _ 0.005 MeV, is formed with I~ = 3, and has an alpha width ~ 70 9/o of the Wigner limit 22). This latter work indicates a level at 6.23 MeV in F 18 which has J~ = 2 - , 3 - or 4 - and a large T = 0 component. I f the two resonances correspond to the same level then the experimental evidence demands a J~ = 2 - level at 6.23 MeV in F 18 which is highly mixed T = 0 and T = 1. In any case there is a state at this energy which has J = 2 and has a large T = 1 component and it is this state which we associate with the O 18 5.09 MeV level. The associations of the O 18 states at 5.25, 5.33 and 5.37 MeV with the F 18 states at 6.37, 6.47 and 6.56 MeV is based solely on their relative energies and is therefore highly tentative. We note that the the 6.56 MeV level 5) in F 18 has jR = 3+ ' 4+ or 5 + and this lends some support to the non-rigorous assigrmaent 9) of J~ = 3 + to the O 18 5.37 MeV level. The F 18 6.64 MeV level was observed as a resonance in both N14(~, ~)N 14 and N14(~, ~)F 18 reactions s,24). It decays to the F 18 3 + 0.94 and 1+ 1.70 MeV levels with transition strengths sufficiently strong to rule out M2 or higher for both and E2 for the transition to the 1.70 IV[eV level. Thus the 6.64 MeV level is j n = 1 + or 2 ± . Also the 6.64 ~ 1.70 transition is strong enough so that it most probably is A T = 1 so that the 6.64 MeV level is most probably T = 1. Thus we tentatively associate the F 18 6.64 MeV level with the 018 5.52 MeV level. If the spin-parity assignments for 018 and the identification o f isobaric-spin analogue states shown in fig. 10 are correct then the 018 4.45 MeV level is 1- and the 5.09 MeV level is most probably 2 - . This latter assignment is consistent with our lack o f observation o f a 5.09 ~ 0 transition in the present work. These two states are then candidates for the odd parity states formed by raising one nucleon from the p shell into the 2s, id shells. Harvey 4) has predicted that these states form a rotational band cut-offat J = 7 with the J = 1 state lowest and the excitation energies given approxi-

ANGULAR CORRELATION MEASUREMENTS

175

mutely by E(J)

= A + B [1 + ( - ) : r f l ] j ( j +

1),

where the deformation parameter fl is predicted to be very small. The J" = 1- level is predicted to lie between 4 and 5 MeV. If we assume the 4.45 and 5.09 MeV levels are the 1 - and 2 - members of this band and set fl equal to zero then we find A = 4.13 MeV, B = 0.16 MeV, and the J = 3 level is predicted at 6.05 MeV. If our energy level diagram (fig. 10) is correct, the lowest 018 level which could be J'~ = 3 - is the one at 6.19 MeV. We note that there are two F 1s levels at 7.31 and 7.50 MeV which have most probable assignments 5) of J'~ = 3 - , and these could be the analogues of the 6.19 O 18 and/or 6.39 MeV levels. If the 6.19 MeV level is assumed to be the J= = 3 level of the band then we find A = 4.10 MeV, B = 0.17 MeV, fl = - 0 . 0 3 . Therefore the experimental evidence in O 18 and F 1s is quite consistent with the presence of the odd-parity rotational band predicted by Harvey 4). We would like to thank Dr. E. Bretscher for the use of the tandem Van de Graaff generator at A.E.R.E., Harwell and Mr. A. Muggleton of A.W.R.E., Aldermaston for the manufacture of the annular semi-conductor detectors and the O is targets. Special thanks are due to Dr. M. A. Grace who was instrumental in initiating the programme which resulted in these measurements being made. 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)

M. G. Redlich, Phys. Rev. 95 (1954) 448, 99 (1955) 1427, 110 (1958) 468 J. P. Elliott and B. H. Flowers, Proc. Roy. Soc. A229 (1955) 536 B. H. Flowers and D. Wilmore, Proc. Phys. Soc. 83 (1964) 683 M. Harvey, Phys. Lett. 3 (1963) 209 T. Lauritsen and F. Ajzenberg-Selove, Energy levels of light nuclei (1962), Nuclear Data Sheets, National Academy of Sciences, Washington, D.C.; F. Ajzenberg-Selove and T. Lauritsen, Nuclear Physics 11 (1959) 1 S. Hinds, H. Marchant and R. Middleton, Nuclear Physics 38 (1962) 81 A. Gobbi, A. Ruh, B. Gobbi and R. E. Pixley, Helv. Phys. Acta 37 (1964) 104 M. A. Eswaran and C. Broude, Can. J. Phys. 42 (1964) 1311 P. Hewka, R. Middleton and J. Wiza, Phys. Lett. 10 (1964) 93 A. E. Litherland, M. J. L. Yates, B. M. Hinds and D. Eccleshall, Nuclear Physics 44 (1963) 220 A. R. Poletti and E. K. Warburton, Phys. Rev. to be published A. E. Litherland and A. J. Ferguson, Can. J. Phys. 39 (1961) 788 G. J. Nijgh, A. H. Wapstra and R. van Lieshout, Nuclear spectroscopy tables (North-Holland Publ. Co., Amsterdam, 1959) D. H. Wilkinson, Nuclear spectroscopy, Part B (Academic Press, New York, 1960) K. Yagi et al., Nuclear Physics 41 (1963) 584 R. Middleton and D. J. Pullen, Nuclear Physics 51 (1964) 63 E. K. Warburton, Phys. Rev. 113 (1959) 595 A. E. Litherland, R. Batchelor, A. J. Ferguson and H. E. Gove, Can. J. Phys. 39 (1961) 276 E. Eichler, Revs. Mod. Phys. 36 (1964) 809 R. Moreh, T. Daniels and A. A. Jaffe, Proc. Phys. Soc. 83 (1964) 334 G. M. Matous and C. P. Browne, Phys. Rev. 136 (1964) B399 E. A. Silverstern, S. R. Salisbury, G. Hardie and L. D. Oppliger, Phys. Rev. 124 (1961) 868 P. C. Price, Proc. Phys. Soc. A68 (1955) 553 W. R. Phillips, Phys. Rev. 110 (1958) 1408 E. Almqvist, D. A. Bromley and J. A. Kuehner, Bull. Am. Phys. Soc. 3 (1958) 27 F. Ajzenberg-Selove and T. Lauritsen, Revs. Mod. Phys. 27 (1955) 77