Angular correlations in the reactions C12(He3, αγ)C11 and C12(He3, pγ)N14

Nuclear Physics 71 (1965) 113--128; ~ ) North-Holland Publishing Co., Amsterdam Not to be reproduced by photoprint or microfilm without written permission from the publisher

ANGULAR CORRELATIONS I N T H E R E A C T I O N S C12(He s,

~ I ) C 11 A N D

Ct2(He s, pT)N t4

J. O. NEWTON, R. S. BLAKE, D. J. JACOBS and J. P. SCHAPIRAt University of Manchester, England Received 3 March 1965 Abstract: Particle-gamma angular correlations in which the particles were detected at 180° to the beam direction have been studied. It is shown that the 2.00 MeV level in C11 is likely to have spin ½, though spins of { or ~ with restricted values of the quadrupole-dipole amplitude ratios are also allowed. The spin of the 5.10 MeV state in N ~4is shown to be 2 and the transition to the ground state to contain El, M2 and E3 components. The amplitudes of the quadrupole and octupole components relative to that of the dipole are --0.18-4-0.03 and 0.12-4-0.04 respectively. The phase convention of Devons and Goldfarb is used. The correlation through the 4.91 MeV state of N x4is found to be consistent with isotropy and the intensity of decays to the 0+ state at 2.31 MeV and to the 3.95 MeV state are shown to be (0.44-0.7)% and (1.3q-l.0)Yo of that to the ground state. These results are consistent with the expected spin of zero for the 4.91 MeV state, spin one is unlikely but spin two is still possible.

El

NUCLEAR REACTIONS 12C(3He,~7), (3He, py), E = 6 MeV; measured ?, ~?(0), p?(0). 11C, I~N deduced level J, ~(E2/M1).

1. Introduction It was first p o i n t e d out by N e w t o n 1) a n d later by L i t h e r l a n d a n d F e r g u s o n 2) that there is a special s y m m e t r y in a three stage a n g u l a r correlation process where two of the " r a d i a t i o n s " are observed along the same direction. This special symmetry causes i m p o r t a n t simplifications in the i n t e r p r e t a t i o n of three stage a n g u l a r correlations in n u c l e a r reactions. Thus in certain cases the dependence of the interpretation o n a m o d e l is entirely r e m o v e d a n d in other cases it is reduced. It is easy to see for example that in a reaction in which a spin zero projectile is incident on a spin zero nucleus a n d a spin zero particle is emitted along the direction o f the projectile then the residual nucleus can only be left in its magnetic substate of a n g u l a r m o m e n t u m zero. This arises simply because of a n g u l a r m o m e n t u m conservation along the projectile direction a n d will therefore be true whatever is the m e c h a n i s m of the reaction. The p a r t i c l e - g a m m a a n g u l a r correlation, for given spins of the residual nucleus a n d multipolarities of the de-excitation g a m m a rays, depends only o n the relative p o p u l a t i o n s of the magnetic substates of the residual nucleus before its decay by g a m m a emission. Hence in this case there will be n o reaction d e p e n d e n t parameters * Present address: Institut du Radium, Orsay, S and O, France. 113

114

~. o. NEWTON e t al.

in the correlation function. In the more general case the number of reaction dependent parameters will be given by the number of magnetic substates which can be populated (excluding sign) minus one. Goldfarb 3) has recently pointed out that a study of these reaction dependent parameters can be of interest in the study of reaction mechanisms. From the nuclear structure point of view, however, it is advantageous to study cases where there are no reaction dependent parameters or perhaps only one. This paper is concerned with experiments of this type which lead to information on levels in the nuclei C 11 and N 14. The C12(He 3, ct~)C11 angular correlation was studied in order to gain information on the spin of the first excited state of C 11. Naively one might expect the first excited state of C 11 to have spin 1 - corresponding approximately to the ( j j ) coupling configuration [(p~)4]p, [(p~)2 P~]n. The evidence so far on this has been rather inconclusive. The reactions Bl°(d, n)C 11 in the region of energy from 7 to 9 MeV show 4, 5) neutron angular distributions characteristic of simple lp = 1 stripping for the groups leading to the ground and first excited states. This result suggests a spin value lying in the range from 3 - to -92- for the first excited state. At low bombarding energies, less than 1 MeV, lp = 3 was suggested 6, 7) but distortion effects are very serious here and must be taken into account. However the transition to the [(p~)4]p, [(p~)2 P½]n configuration from the configuration [(p~)a]p[(p~)3] n of B 1° cannot go by the simple transfer of a proton with lp = 1, so that if this assumption about the states were correct a simple stripping process would not be expected to occur. Therefore it seems that the evidence from the B 1°(dn)C 11 angular distributions is not conclusive. Freeman 8) has measured the (n, 7) angular correlation in this reaction at three angles and found it to be consistent with isotropy and hence with spin ½ for the first excited state. However the large experimental errors of ___20 together with lack of knowledge of the reaction mechanism are in fact likely to make the result consistent with almost any possibilities. Probably the most suggestive evidence on the spin of the first excited state comes from a comparison of C 11 with its mirror nucleus B 11. There are similar difficulties in the interpretation of the Bl°(d, p)B 11 angular distributions as there are in the case of the Bl°(d, n)C 11 angular distributions. In fact it is only rather recently 9) that the spin and parity of the first excited state of B 11 has been conclusively shown to be ½-. It has been shown by Donovan et al. 10) and by Freeman 8) that the gamma ray branching ratios of the second and third excited states to the first excited state and ground state are almost identical in B 11 and C 11. This suggests strongly, but does not prove, that the first three excited states and ground states of B 11 and C 11 correspond. Some further evidence is given by the calculations of Fairbairn 11) on the Coulomb energy differences between the levels of the mirror pair, assuming intermediate coupling wave functions and using first order perturbation theory. The calculated level shifts are in fair agreement with experiment, though not as good as those for the other mirror pairs which are considered. Other evidence on the spin of the first excited state of C 11 is more model dependent

clZ(He a) REACTIONS

1 15

and hence should be treated less seriously, insofar as the main object of establishing the spin of a state is to see whether particular models agree with experiment or not. Thus the intermediate coupling model calculation of Kurath 12) suggests, on the basis of the systematics of calculations in all of the lp shell nuclei, that the ground states of both C 11 and B 11 will be ~2- and the first excited states ½-, with an intermediate coupling parameter a/K of about 5.5. The work of Clegg et al, 14) on the Ca2(p, pn)C ~I reaction gives some support to this conclusion. Their value of 0.08 +0.03 for the relative cross section for the formation of C 11 in its first excited state to that of its ground state, indicates, assuming a simple knock out model for the reaction, a value of 6.4__ 1.0 for a/K, which is consistent with Kurath's calculation. The mirror CX2(p, 2p)B ~ reaction has been shown by Gooding and Pugh ~1) to leave B xa mainly in its ground state thus implying that the ground states of B 11 and C ~1 have the same structure and hence are both ~ - . Since Kurath's calculations appear only to allow the spins of the ground and first excited states to be ½- and 3 or ) - and ½- for any reasonable value of a/K, this result implies that the spin of the first excited state of C 11 must be ½-.

S.lO

,,.9, r t t - ( ~ - /

CI2+ 3.9s~~[ll]~]l ~:~ '~ (0)

He3

,+

2.31 ~_

0

NJ4+ p

O+

"~i~-o

20

l

C/t4+n. (I.ISg)

%-

I+

(°4.772) Fig. 1. Scheme for the reactions C12+He~. The figures in brackets are the energies in MeV relative to that of C1LI-He3. It therefore appears that there is good indirect evidence, but very poor direct evidence, that the first excited state of C 11 is a ½- state. In order to provide further direct experimental evidence on the spin we have measured the CI2(He 3, ~7)C ~1 angular correlation through the first excited state. In order to gain information on the 5.10 MeV and 4.91 MeV excited states of N 14, the level scheme of which is shown in fig. I, the C~/(He 3, p ) N ~4 reaction was studied. At the time of commencement of this investigation the 5.10 MeV level was thought to have isobaric spin zero and angular m o m e n t u m two 15,16). The parity was not established though it was usually thought to be odd. The mean lifetime of the level

116

J.o.

NEWTON et al.

has been reported 17) to be > 0.3 psec, which is consistent with decay by El, M2, M1 or E2 radiation. Warburton, Rose and Hatch 17) have made measurements on the anisotropies, and in a few cases the angular distributions, of the decay gamma rays at two resonances in the C13(p, ] ) ) N 14 reaction. From these measurements they concluded that the spin of the 5.10 MeV state was two. Now however, their arguments for this result appear considerably less strong because they depend on an incorrect value 18) for the lifetime of the 5.83 MeV state in N 14. Previously Broude, Green, Singh and Willmott 19) had indicated that the state should have spin one using arguments based on the strength of the transition from the 0 - level at 8.70 MeV in N TM. However, as Warburton, Rose and Hatch 17) pointed out, the transition to the 5.10 MeV state seen by Broude et al. may have come from another state. Thus the previous assignments of spin for the 5.10 MeV state could not be regarded as decisive. Warburton et al. iv) also concluded that the quadrupole to dipole amplitude ratio 6 in the 5.10 MeV transition lay within the ranges - 0 . 1 > 6 > - 0 . 2 or 3.6 < 6 < 6, the phase of 6 being that of Devons and Goldfarb 2o). These conclusions however depend on the assumption of no octupole component and are also subject to uncertainty because of the incorrect lifetime assumed for the 5.83 MeV state. A more recent experiment 2t) on the angular distributions of the gamma rays in the C 12(He 3, py)N 14 reactions led to the result 6 = - 0 . 1 2 _ 0.03 on the same assumption of no octupole component. Very recently Warburton et al. 2z) using an intermediate image magnetic pair spectrometer have shown that the 5.10 ~ 0 transition is predominantly electric dipole and hence that the parity of the 5.10 MeV state is odd. Limits to the possible amplitudes of magnetic quadrupole and electric octupole components were also given as 16(M2)I < 0.45 and I6(E3)I < 0.5. Harvey et al. 23) have also recently obtained evidence that the 5.10 MeV state has odd parity from observation of the Blair phase rule in the inelastic scattering of 47 MeV He 4 by N 1~. The objects of this study of the decay of the 5.10 MeV state were to get better evidence for the spin value and to obtain more detailed information on the gamma ray decay to the ground state. If it could be shown that there was an appreciable octupole component then this would be strong evidence that the decay must involve a change of parity, as M3 radiation would hardly be expected to compete with M1 and E2. The Weisskopf single particle lifetime for M3 radiation is about 3 x 105 times larger than that for E2, and E2 transitions are rarely less than single particle strength. The observation of an octupole component would also be of interest in its own right. The gamma rays from the 5.10 MeV level are known iv, 21) to branch to the ground state (72 ~ ) and to the 0 +, T = 1 level at 2.31 MeV (28 ~ ) . The transition to the 0 + state must be a pure multipole so that a measurement of the angular correlation of this gamma ray will give a value for the relative population of the M = 0 and M = 1 substates of the 5.10 MeV level. This population ratio can then be used to interpret the angular correlation of the ground state gamma ray. Considerably less information is available on the 4.91 MeV level. It was originally suggested 17) that the level should be 0 - belonging to the configuration (p~, s~).

C12(l-Ie 3) REACTIONS

117

The experimental evidence for this assignment was not vely strong, being based mainly on a C 1a(d, n)N 14 stripping experiment 24) and the absence of any observed gamma ray transitions to states other than the ground state. If any transitions were observed to the T = 1, 0 ÷ level at 2.31 MeV it would of course eliminate the 0 - assignment to the 4.91 MeV level. Previously the observed upper limit to any transition to the 2.31 MeV level was of the order of 20 }/o of the ground state transition. More recently Harvey et al. 23) have obtained evidence that the parity is odd, from the phase rule in inelastic alpha scattering, and that the state arises from the promotion of a single nucleon. Trost, Rose and Riess 25) have investigated the direct capture of protons to states in N 14 and their evidence, reported after this work was completed, suggests that the 4.91 MeV level may belong to the configuration (s~ p~). It was decided to investigate the (p, 7) angular correlation to the 4.91 MeV state, which should be isotropic if the 0 - assignment is correct, and also to try to get a better value for the branching ratio between the 2.31 MeV and ground states.

2. Experimental Method A singly charged beam of He 3 ions from the Manchester University 6 MeV electrostatic generator was magnetically analysed and focussed on the target by means of magnetic quadrupole lenses. The diameter of the beam at the target was approximately 2 mm. The alpha particles and protons were observed with an annular silicon surface barrier type counter, constructed in this laboratory. The counter, through which the beam passed, was mounted at 180 ° and subtended a half angle of 7 °. Gamma radiation was detected by a 7.5 cm x 7.5 cm diam. NaI(TI) counter, usually at i0 cm radial distance from the target. The front face of the counter was shielded by lead approximately 1.25 cm in thickness in order to reduce the counting rate for low energy radiation. The beam, after passing through the target, entered a flight tube of 3 m length and eventually hit a tantalum plate, coated with aquadag in order to minimize backscattering. The target consisted of a self supporting carbon foil of thickness about 30 /~g. cm -2, prepared by evaporation. The coincidence circuit was of the crossover type. It had a resolving time 2z of 60 nsec which was measured both by the random counting method and by taking delay curves. A true to chance ratio of about eight or better was achieved in most of the work. The random counts during a run were obtained from the number of counts obtained in another coincidence circuit of resolving time 2z = 2/~sec, after taking into account the ratio of resolving times; allowance was made for the relatively small number of true counts. A single-channel analyser was used to gate on the required particle group and the coincident gamma ray and particle spectra were recorded on 512-channel analysers. The shape of the random spectrum was assumed to be that of the singles spectrum. A number of runs were taken for each angle; the angles were taken in approximately random order in order to minimize any possible drifts. The anisotropy of the correlation apparatus was checked by measuring the angular

118

J . o . NEWTON et al.

distribution of the gamma rays at the 340 keV resonance in the reaction F19(p, ~7)O16. This angular distribution has been carefully measured and is almost isotropic 15). Corrections for anisotropy amounted to a few per cent only. The experimental angular correlations were fitted to a power series in even Legendre polynomials by a least-squares programme on the Manchester University Atlas computer. In comparing the experimental results with those of theoretical calculations the corrections for finite geometry of West 26) were used. cts.

He 3 RING COUNTER

IO00~. cm I000

P3 50C

:""" :'~"~~"','J ~'&...A 20o channel n u m b e r - - -

Fig. 2. A typical s p e c t r u m o f the particles f r o m the reactions C ~ 2 + H e a t a k e n in an a n n u l a r counter. T h e groups are denoted by the n u m b e r s o f the excited states in the residual n u c l e u s to w h i c h they lead, g r o u n d states being d e n o t e d by zero.

-.,,~r

1 63

s.,o 4.9

(2) (,0)

2.31

3000

--

1 ..% •.':....

3.9S

I~

2.31

O*

,':.... 2000

%

Counts

per Chrome! 0

I°

NI4 lO00

~j

2.79

3.38

3.9S

4.9

& S.l

~......:/'.. . ~.:". ..:.:,... ...:.,,...,. "" " :":" :'v.!." ":''" ""...':':.:..._ . II

0

50

I

I

I00 150 Chormel N u m b e r

I " % ;':": >'""';'"""~"

200

Fig. 3. A typical u n g a t e d s p e c t r u m o f the g a m m a rays f r o m the reactions CZ2+He a at 4.96 MeV.

C12(He3) REACTIONS

119

3. Results

A typical spectrum of the particles obtained in the annular counter is shown in fig. 2. It is seen that an energy resolution of about 40 keV is obtained. A typical singles gamma ray spectrum is shown in fig. 3. The bombarding energies were chosen, except where otherwise stated, to give maximum yield for the group of interest relative to other groups 27). Cl2

He 3

~

2.00MeV

600

e~.

400 Counts per

z.oo (i/2,3/2) o

(3/2-)

: 180"

ENe~ : S.I McV

Channel

200

2.31 (random$)

~ , I o

.',........-.;; "........ " I. . . . . " " " ....

I

lO0

SO

I so

Channel Number

Fig. 4. Summed coincident spectrum of the gamma rays from the reaction C~3(He a, c0C u (2.0 MeV). Randoms are not subtracted.

(A)

I0

q8 w

!

I

I0

I [I[I[ I

I-

.oo

4.g ;---.~ (o-~

('/,5

o

4

3

~D '

0

'

90

'

'

'

150

30

7 1 +

'

9

~

'

150

4

Oy

Fig. 5. Angular correlations. (A)Between the alpha particles and gamma rays in the reaction CaZ(He a, ~ , ) C 11 (2.0 MeV), (B) between the protons and gamma rays in the reaction C12(He a, p~:)N 14 (4.91 MeV).

120

NEWTONet

J.O.

al.

3.1. THE CtS(He8, c¢7)Cix (2.0 MeV) REACTION The (~]:) angular correlation was measured at angles of 90 °, 120 ° and 150 ° at a bombarding energy of 5.1 MeV. In fig. 4 is shown the summed coincident g a m m a ray spectrum in which the 2.0 MeV g a m m a ray from the decay of the first excited state of C 11 is clearly dominant• Fig. 5A shows the angular correlation measurements at a beam energy of 5.1 MeV. The least-squares fitting programme gives 1 - (0.01 +__0.04)P2(cos 0) for the correlation function. This is clearly consistent with isotropy for the coincident radiation. 3.2. THE CX~(He8, py)N14 (5.10 MeV) REACTION The (p~) angular correlations from the decay of the 5.10 MeV state in N 14 to the 2.31 MeV state and to the ground state were measured at a bombarding energy of 4.1 MeV. A summed coincident g a m m a ray spectrum for all angles is shown in fig. 6; the 5.10 MeV and 2.79 MeV g a m m a rays can be clearly seen. He3+CI 2

OI,= leo ° ,i

ISO

5.1

2.31

(2)

Coultt s per

2.31

Channel

•

:..

tO0

•...:!o:

O÷

2.79

..:.

l

. ...

"" • :.

oo

•

•

0

I÷

NI4 5.1

,o •

Oo

•o ,•• •,

o,

=oo * •

•

50

• °Oo°. •

•

•

•°

•

°'" *~°o •

0

=

I

~0

IO0

I

Cl~nnel

l 150

I

,,",

200

Number

Fig. 6. S u m m e d coincident spectrum o f the gam_ma rays f r o m the reaction CZ2(He 3, p ~ ) N 14 (5.10 MeV). R a n d o m s are not subtracted.

The angular correlations of the two g a m m a rays are shown in fig. 7. It is of interest that the 2.79 MeV correlation is highly anisotropic; the correlation function was found to be given by IV(0, 2.79) = 1 q- (0.96___ 0.35)P 2 (cos 0) - (0.97 +__0.4)P4(cos 0),

121

C12(He 3) REACTIONS

whilst the angular correlation of the 5.10 MeV g a m m a ray could be fitted by the function

W(O, 5.10)

= 1 + (0.03___ 0.04)P2(cos 0 ) - (0.28 +__0.07)P4(cos 0).

It should be pointed out that the errors indicated are not normal standard errors because the coefficients of the P2 (cos 0) and of the P4(cos 0) terms are not independent.

(A)

5.10 ~ 2.31

(8)

5.10~ 0

3o[ 20

I0

q ii1 I

~o ,~ 19

17

15

13

30

60

90 0~

120

150

Fig. 7. A n g u l a r correlations between the p r o t o n s a n d g a m m a rays f r o m the reaction ClZ(He z, p y ) N a4 (5.10 MeV) for (a) the 2.79 M e V g a m m a ray. T h e full line is the theoretical curve for 5 o~ p o p u l a t i o n o f the M = 1 substate. (b) the 5.10 M e V g a m m a ray. T h e full line is the least-squares fit to the points.

The error values indicate rather the ranges over which the coefficients can vary to give reasonable fits. It does not follow that if a value of one coefficient within its range is chosen then all values in the range of the other will be allowable. It turns out, as will be seen in the next section, that the correlation function for the 2.79 MeV g a m m a ray is that which would arise if mainly the M = 0 substate of the 5.10 MeV state was populated in the reaction. The bombarding energy was chosen simply on the grounds of high yield and there is no obvious reason at all why the M - - 1 substate population should be so low. For this reason it was decided to carry out measurements at another energy. In order to do this two NaI(T1) detectors

122

J.o.

NEWTON et al.

were set up at angles of 90 ° and 135 ° so that the anisotropy/(90°)//(135 °) could be measured by simultaneous recording of coincidences from both detectors. A check measurement at 4.1 MeV gave an anisotropy of 0.09+0.15 whilst that at 3.1 MeV gave an anisotropy of 0.7+0.27. It is clear that at 3.1 MeV bombarding energy the anisotropy is much less, implying a relatively higher population of the M = 1 substate than at 4.1 MeV. He 3

EHe3~4.96MeV

rqndoms A I. 6 : ~ l e V

400

+ Cl2

( ~ = 1 8 0°

:

1

2.31MeV

per

°.° ,,*° ~

0

I~

NI4

•

Channel

200

(o)

4.9 MeV

'l "

Counts

4.w

o*. • .°.*

~ ". ''.°

oQ

.-

. .

**:** **v,*

. . . . . ....

..; .*': •

.

•

.° .* .......*-..

.•

I

I

I

SO

IO0

I SO

Channel

I "*~J~

200

Number

Fig. 8. C o i n c i d e n t s p e c t r u m o f the g a m m a r a y s f r o m the d e c a y o f the 4.91 M e V s t a t e i n N ~4. R a n d o m s are n o t s u b t r a c t e d . 3.3. T H E

C l Z ( H e 3, p y ) N 14 (4.91 M e V ) R E A C T I O N

The angular correlation for the 4.91 MeV (py) correlation, taken at 4.96 MeV bombarding energy, is shown in fig. 5b. The correlation function 1 - (0.04+0.05) P2(COS 0) is consistent with isotropy. A long run was taken in order to measure the branching ratio to the 2.31 MeV state, and the coincident g a m m a ray spectrum obtained is shown in fig. 8. When the randoms are subtracted the peaks at 1.63 and 2.31 MeV disappear. It can then be deduced that the intensity, relative to that of the ground state, of any decay to the 2.31 MeV state is (0.4 + 0.7) ~ and to the 3.95 MeV state is (1.3+1) ~ . 4. Discussion

The theoretical angular correlation functions of the form 1 + ~ A,,P,(cos 0) are worked out on the assumption that the particles are detected along the same line as the incident projectiles. Thus for the case of C12(He3, ~T)C 11 we assume that

C12(He3) REACTIONS

123

only the M = ½ substate in C 11. is excited. In fact, because the detector cannot be exactly at 180 ° there may be some population of other substates e.g. the M -- ~z substate in C 11.. Litherland and Ferguson 2) have indicated that the relative population of substates differing by one unit of angular momentum from those populated in our extreme assumption will have the order of magnitude of 42, where ~ is the half angle in radians subtended by the counter. In our case ~ is 0.12 rad so thai 42 = 1.4× 10 -2. Thus this effect is not very important in our case though we have included it in assessing the errors. The phases of the electromagnetic mixing ratios are taken to be those of Devons and Goldfarb 2o) rather than those of Litherland and Ferguson 2) in order to conform to the convention of Warburton et al. 16) used in previous experiments. The phases of Litherland and Ferguson differ from those of Devons and Goldfarb by a factor (--)L-L', where L and L' are the multipolarities of the transitions. 4.1. THE FIRST EXCITED STATE OF C11 The angular correlation is consistent with isotropy and hence with spin ½ for the excited state. Unfortunately it is still possible to obtain isotropy or near isotropy with other spin values for special values of the multipole mixing parameters. In order to find these other possible isotropic solutions it is necessary to know the ground state angular momentum of C 11. This has recently 15) been conclusively shown to be 3. If the spin of the excited state is ~ then decay can be by dipole and quadrupole radiation (we consider only the two lowest multipolarities here). In this case the angular correlation is given by W(O) -- 1 + (2 + 2~/~5)(1 + 5 z)- 1P2(cos 0),

where o -

(klQl~r)

Values of 5 of - (0.26 + 0.03), < - 17 go, or > 22 will satisfy the experimental result of - 0 . 0 1 +0.04 for the coefficient of P2(cos 0); the limits for large 16[ have been taken for values two standard deviations away from the mean. Assuming 5 spin for the excited state we get W(O) = 1 - ( 2 - ( 1 2 / x / 3 5 ) f - ~ - - ~ f 2 ) ( l + 6 2 ) - l P 2 ( c o s

0 ) + ~32 6 2 (1 +52)-1p4(cos 0).

A value of 6 of (0.19+0.02) will fit the experimental result in this case. The data cannot be fitted with spins higher than ~, since the decay would have to be by mixed quadrupole and octupole radiations or radiations of higher multipolarities. For single particle M1 and E2 transitions a value for [61 of about 0.02 would be expected. Thus with a slight retardation of the M1 transition and enhancement of the E2 transition the two smaller values of 6 above could be accommodated and

124

s . o . NEWTON et aL

hence they cannot reasonably be excluded. The larger values for 16[ do seem very unlikely. For single particle E1 and M2 transitions a value for 5 of about 10-3 would be expected. Since there is no isobaric spin selection rule for E1 transitions in C 11 it seems unlikely that [8[ could be even as high as the smaller value above. It seems therefore that the result of this experiment considerably increases the probability that the spin of the first excited state of C 11 is ½ in that only a small range of mixing parameters could give isotropy within the observed limits. The problem of proving conclusively that it is ½ is not easy. Possibly if the spins of higher states, which decay in part to the first excited state, could be established and the angular distributions and (YT) correlations of the decay gamma rays to the first excited state measured, then the ~ and 5 possibilities could be eliminated. The parity of the state could be established by measurements on the internal pairs coupled with a lifetime measurement. 4.2. THE 5.10 MeV STATE IN N 14

The angular correlation of the 2.79 MeV gamma rays to the 2.31 MeV 0 + state, at 4.1 MeV bombarding energy, is only consistent with spin 2 for the 5.1 MeV state. This implies that the relative population of the M = 1 substate to that of the M = 0 substate of the 5.1 MeV level is < 0.08. The anisotropy measurement at 4.1 MeV showed that the relative population of the M = 1 substate was 0.0 +°14, in agreement with the result from the full correlation. At 3.1 MeV a value of 0.8_+oo14 s was obtained. These results show that the reaction does not proceed by a simple direct reaction mechanism as is also evident from the excitation functions 27). The small population of the M = 1 substate at 4.1 MeV is convenient for this experiment because maximum anisotropy is obtained for 109 ~ population of the M = 0 substate. Since the main interest in studying this transition is to see whether there is an E3 component in the decay, this feature is of considerable importance. The theoretical angular correlation function for a mixed El, M2, E3 transition, when only the M = 0 substate is populated, is given by

W(O) =

1 + (1 +52 + 6 2 ) - 1 { ( _ ½ . _ T4-v15 .~2 -7""-'6~2 2-L __#581 + ¢N/381 ~2 + ¢ 8 2 ) P 2 ( c o s O) 8 2 10 -18 + (~-81 + v1 f z2 +-~-x/55152 --7-62)P,(cos 0)},

where 61 and 8 2 a r e the relative amplitudes of the M2 and E3 components to that o f the E1 component. It is not possible to fit the observed angular correlation if only El and M2 multipoles are present, because of the observed negative sign of the A4 coefficient, so that E3 must also be present. The possible solutions for 51 and 82 were found as follows. The loci of the observed values of A 2 and A, in the experimental correlation function, corrected for geometrical attenuation, were plotted on the plane defined by the theoretical correlation functions with 31 and 52 as coordinates. The solutions are given by the points where

C12(I-le 3) REACTIONS

125

the loci o f the A2 a n d A 4 coefficients intersect. W h e n the points o f intersection h a d been l o c a t e d m o r e detailed surveys o f the regions in their vicinities were m a d e in o r d e r to o b t a i n m o r e accurate values a n d to d e t e r m i n e the errors. A p l o t in which arctg 81 a n d arctg 82 are used as c o o r d i n a t e s is shown in fig. 9.

"B \

-80

-60

-40

-20

20

40

60

, -20

. -40

,

,

,

._8,o . . . .

,C'>,

Fig. 9. Plot illustrating how the solutions for dl and ~ were obtained from the angular correlation of the 5.10 MeV gamma ray. Curve A corresponds to all points in the dld~ plane which give the experimental coefficient of P~(cos 0) (corrected for angular attenuation). Curve B is the corresponding curve for the coefficient of P4(cos 0). In this example only the M = 0 substate is assumed to be populated. The solutions occur at the intersections of curves A and B.

The f o u r possible solutions o b t a i n e d f r o m this analysis are: (i)

61 = -0.18__.0.03,

62 = 0 . 1 2 + 0 . 0 4 ,

(ii)

61 = 0.40_+0.05,

82 = 0.72_+0.05

(iii)

81 = 2.0_+0.35,

82 = - 4 . 3 _ + 0 . 7 ,

(iv)

lSal > 30,

lSzl > 30.

F o r the last solution, if we assume negligible E1 c o m p o n e n t , the o c t u p o l e - q u a d r u p o l e mixing ratio 82/81 is 0.50_+0.04. N o w very recently W a r b u r t o n et al. 22) have observed the internal pairs f r o m the decay o f the 5.10 M e V state a n d have shown that lSx[ < 0.45 a n d 1821 < 0.5. These limits rule o u t all the possibilities a p a r t f r o m the first one. W e can therefore c o n c l u d e f r o m this result a n d f r o m t h a t o f the present w o r k t h a t 61 = - 0.18 _+0.03 a n d 82 = 0.12_+ 0.04. T h u s we have here a very u n u s u a l case where E l , M 2 a n d E3 m u l t i p o l e s all give significant c o n t r i b u t i o n s to the transi-

126

s.o. NEWTONet al.

tion probabilities. This, as has been pointed out by Warburton and Pinkston 16), may arise because E1 transitions 28,29,30) and magnetic transitions 3~) in selfconjugate nuclei with A T = 0 are expected to have considerably reduced transition probabilities, whereas electric octupole transitions frequently show collective enhancement 32,33). Moreover, if the 5.10 state was a pure (p÷d~) configuration and the ground state a pure (p~)2 configuration, E1 radiation would be forbidden. Warburton, Rose and Hatch ~7) give a lower limit to the mean lifetime of the 5.10 MeV level of 0.3 psec. This implies a partial lifetime for the M2 transition to the 2.31 MeV state of 0.9 psec. For the transitions to the ground state the following values for the partial lifetimes are implied: for the E1 component > 0.45 psec, for the M2 component > 14 psec and for the E3 component > 30 psec. Warburton and Pinkston ~6) have calculated the M2 and E3 transition probability on the assumption that the 5.10 MeV level is a pure (p~d~) J = 2 state and that the ground and 2.31 MeV levels are pure (pi)2 states. They obtain values of 8 psec and 40 psec for the M2 transitions to the 2.31 MeV state and ground state and 80 psec for the E3 transition to the ground state, assuming a collective enhancement factor of ten. Unfortunately rather little can be concluded from these results apart from the fact that the E1 transition is > 5 x 104 times slower than the Weisskopf single particle value. It is interesting, but probably coincidental, that Warburton and Pinkston predict the observed value of 2 for the ratio of the intensity of the M2 to that of the E3 component of the ground state transition. The ratio of the M2 transition probabilities to the first excited state and to the ground state is however predicted to be 4.5, whereas it is found to be 12+4. However it is almost certainly incorrect to assume that the ground and first excited state can be described by a pure (p~)2 configuration. The calculations of True34), which neglect core excitation (which is likely to be important for these levels), indicate that the ground state and first excited state wave functions contain only 93 ~ and 90 ~ of the (p.~)2 configuration respectively. Very good agreement with the predictions of Warburton and Pinkston is not therefore to be expected in any case. If the lower limit to the lifetime measurement could be increased by a factor of 10, which should be possible with modern techniques, interesting comparisons could be made. It would be interesting to see, for instance, whether the octupole transition is in fact enhanced. It should be noted that this experiment gives very strong evidence to support the result of Warburton et al. that the parity of the 5.10 MeV state is odd. It seems almost inconceivable that M1, E2, M3 mixing of the amount found here could occur. This experiment also gives the most convincing evidence so far that spin of the 5.10 MeV state is 2. 4.3. THE 4.91 MeV STATE OF N14 The angular correlation result, which is consistent with isotropy, strengthens the original assumption that the spin of the 4.91 MeV state is zero, though it certainly does not prove it. Isotropy could occur if the spin were one, if by chance the magnetic substates were equally populated. Equal populations of the substates cannot occur

clZ(He a) REACTIONS

127

if the spin is two or greater because substates with angular momentum greater than one cannot be populated in this experiment. However it is possible to obtain a nearly isotropic correlation if the spin is one or two even if the substates are not equally populated. This occurs when the dominant mode of decay is by dipole radiation. The highest Legendre polynomial in the correlation function arising from this is P2(cos 0). It is normally possible to find a small quadrupole-dipole mixing ratio which will made the term in P2 (cos 0) vanish whilst giving rise to a negligibly small coefficient for the P~(cos 0) term. If the spin is greater than two, then the lowest order of decay is quadrupole or higher. Thus the correlation function will contain terms in Pz(cOs 0), P4(cos 0) and maybe others. In order to obtain a nearly isotropic correlation it is now necessary to make all of these coefficients vanish simultaneously for a certain mixing ratio. This is not generally possible, so that isotropy cannot be expected for spins greater than two. We shall firstly make arguments relating to the spin of the 4.91 MeV state based solely on the evidence of this work and on some other experimental results. If the spin is other than zero then transitions would be expected to the first excited state. The upper limit 35) to the mean lifetime of 0.5 psec allows El, M1, or E2 for the ground state transition multipolarities. If the state were 1 ___ then E1 or M1 transitions could occur to the ground state and to the T --- 1, 2.31 MeV state. That to the ground state would be inhibited by the isobaric spin selection rule but that to the 2.31 MeV state would not be. Assuming single particle dipole transition strengths and a retardation factor of 50 for the isobarically forbidden transition, the intensity of the transition to the 2.31 MeV state would be expected to be about eight times stronger than that to the ground state. The observed upper limit of (0.4+0.7) for the relative strength of the transition to the 2.31 MeV state makes a spin of 1 +for the 4.91 MeV state very unlikely. If the spin were 2 + then, making similar assumptions to those above, the relative intensity would be expected to be about 1 ~ , for 2 - and 3 + it would be even less. The branching ratio result therefore does not exclude spins 2 +- or 3 + for the 4.91 MeV state. Spin 3 for the state can be excluded by the isotropic correlation and by the fact that the 8.06 MeV T = 1, 1- state decays to the 4.91 MeV state by an M1 transition of strength 0.3 Weisskopf units 19). Spins 2 and 3 can also be excluded if we accept the results of the C13(d, n)N 14 experiments of Benenson 24). If his interpretation of his data is correct, the group to the 4.91 MeV state clearly shows an l = 0 stripping pattern implying 0 - or 1- for the spin. Nevertheless his results must be taken with caution because the statistics are poor and the groups to the 4.91 and 5.10 states are unresolved. A new measurement of this reaction using a pulsed accelerator could resolve this problem. The measured branching ratio of the decay to the 3.95 MeV state relative to that to the ground state of (1.3__+1 ) ~ is not surprising. Both transitions are forbidden by the isobaric spin selections rule but if both had the same matrix elements the branching ratio for E1 transitions would be 0.7 ~o.

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J.O. NEWTON et al.

I n c o n c l u s i o n it m u s t b e s a i d t h a t t h o u g h t h e r e is g o o d c i r c u m s t a n t i a l e v i d e n c e , b o t h e x p e r i m e n t a l a n d t h e o r e t i c a l , t h a t t h e 4.91 M e V s t a t e is t h e 0 - T = 0 s t a t e o f t h e (p~s~) configuration, this has not yet been proved.

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) 28) 29) 30) 31) 32) 33) 34) 35)

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