The radiative decay of the 7.66 MeV level of C12

I I.E.I: 3.A

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Nuclear Physics 53 (1964) 673---684; (~) North-Holland Publishing Co., Amsterdam

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Not to be reproduced by photop~nt or microfim without written permission from the publishe~

T H E RADIATIVE DECAY OF T H E 7.66 MeV L E V E L O F C 12 I. HALL and N. W. T A N N E R

Nuclear Physics Laboratory, Oxford, England Received 12 December 1963 Abstract: The 7.66 MeV excited state of C ll has been studied using the reaction BIO(He*, p)C xs.

Coincidences were recorded between protons detected by a scintillation counter and the corresponding recoil carbon ions detected by a semi-conductor counter after magnetic analysis. The branching ratio of the decay of the 7.66 MeV state to the ground state, F~ = / ~ e , + F 7 to the decay to BeS+u was deduced a s / ' J F = ( 3 . 5 + 1 . 2 ) x 10-4. This result is in agreement with other recent measurements.

1. Introduction 1.1 ASTROPHYSICS

The astrophysical significance of the 7.66 MeV level of C x2 is fully discussed elsewhere l - a ) . Briefly it is recalled that to furnish the luminosity typical of a red giant star Hoyle x) demanded that the three alpha process

~-I-ct ~ Be 8, Be 8 + ~ ~- C 12., should exhibit a resonance near the effective stellar energy (a few hundred keV at temperatures of order 10s °K). The 7.66 MeV state, which lies at 375 keV above the rest energy o f three alpha particles, provides just this resonance. For purposes of element synthesis as well as energy generation, a leakage to ground is required in the second of the above reversible processes to preserve some of the C 12 formed. Thus the rate of synthesis of C 12, which is then the vital link between helium and the heavier elements, is directly proportional to the width F s = Fe± + F 7 (Fe± is the pair width for the direct ground state transition and F 7 is the width for the cascade 0 + --, 2 + --, 0 + decay). This fact, coupled with prior knowledge of F,, is the motivation for an experimental determination of the branching ratio Fs/F. 1.2. PREVIOUS E X P E R I M E N T A L W O R K

In complementary experiments Alburger 4) and Ajzenberg-Selove and Stelson 5) determined the branching ratio F , , _ (6.6+2.2) × 10 -6. F 673

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I. HALL AND N. W . TANNER

From the electron scattering data of Fregeau 6) the pair width is deduced: F,~ = (5.5+_+_3)x 10 -s eV, showing F~ = F to be close to the Wigner limit of 7.5 eV. However, Ferrell 7) had made a single-particle estimate of F~ ,~ 1.4x 10 -3 eV so that the 3u reaction rate should be determined by the strength of the cascade gamma decay via the first excited state at 4.43 MeV. The direct ground-state transition was believed to be forbidden. Alburger 8) has observed p-y-y triple coincidences from the reaction B 1° (He 3, p)C 12 and reported F___~= (3.3+0.9) x 10 -4. F Seeger and Kavanagh 9) have observed C t2 recoil ions from the second excited state in the reaction N~a(d, u)C 12 and have deduced Fs - (2.82+0.29) x 10 -4. F From the detection of C t2 recoils using the reaction B1°(He3, p)C 12 we report a further corroborative figure: Fs - (3.5_.+ 1.2)× 10 -4. F

2. Experiment The essence of the technique is to excite C 12 to the 7.66 MeV state and to search for C 12 ions which have not decayed into ~ particles. In this way Fg/F is obtained providing the counting efficiency of the apparatus is determined by observing C 12 ions corresponding to the excitation of the 4.43 MeV state which cannot decay into particles. In the final analysis one must correct for any systematic difference in the efficiencies of collection of the ions recoiling in the two states. In the reaction B l ° + H e 3 ~ Ct2(i)+pi kinematic differences (table 1) have been exploited to select the feeding of the 7.66 MeV level (i = 2). The method has thus rested on the suppression of various backgrounds (see below) beneath a detectable number of p2-C12(2) coincidences. The recoil ions were detected by a semi-conductor counter at the focus of a magnetic spectrometer and the coincident protons by a 5 mm thick NaI crystal.

675

DECAY OF 7.66 MeV LEVEL OF C 12

2.1. B A C K G R O U N D S

The dominant decay mode of the 7.66 MeV state of C ~2 into three 0cparticles was completely suppressed by the momentum selection of the magnetic spectrometer. It was calculated that a simple counter without a momentum filter would have suffered from a considerable background arising from the simultaneous detection of two of the three u particles. TABLE 1

Kinematics A n g l e (lab.) o f recoil ion 0 e = 20 ° B10(He a, p ) C 12 4.43 MeV state C ~9 p r o t o n an gle p r o t o n energ y (MeV) recoil i o n energy (MeV)

140.6 ° 15.7 4.58

7.66 M e V state C ~ 138.4 ° 12.9 4.10

BlX(He a, p ) C is g r o u n d state C 1~

139.6 ° 14.2 4.02

The B 11 impurity in the separated B 1° target gave rise to C la ions, from B H (He 3 , p)C ta, close in energy to the C12(2) ions (see table 1). However, only a part of the low energy tail of the mass 13 group was admitted by the magnet and this about 8 ~o below the ClZ(2) energy. C12(1) events were indistinguishable in the Si counter pulse-height spectrum from genuine C~2(2) events. To evaluate this background it was necessary to seek and maximize the pt-C12(1) coincidence rate R{px-Ct2(1)). Then selecting the P2 group from the proton counter the pl-C'2(1) rate was reduced to DpR{pt-C12(!j) where DD was defined as the proton discrimination factor. Similarly a magnet discrimination factor D~ was measured by selecting the pt proton group and recording the pl-C12(1) coincidence rate with the magnet set for the momentum of C12(2). A sensible measurement of Fg/F required

FDpDc ~ Fs F where F was the ratio of the feeding of the first excited state by the reaction B 1° (He 3 ,p)C 12 to the feeding of the second excited state. A preliminary experiment showed that F was not strongly sensitive to angle or bombarding energy although its value was slightly lower at the higher available energies (5 MeV) and at backward proton angles. 2.2. A P P A R A T U S

The apparatus was assembled round the 180 ° double-focussing magnet (similar to the magnet described in ref. 1o)) associated with the 6 MeV Van de Graaff at A.W.

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I. HALL AND N. W. TANNER

R.E. Aldermaston. A He a + beam of 5 MeV energy was used and the magnet was fixed at a laboratory angle of 20 °. At this forward angle the C 12 ions had an easily detected energy and a factor of 3.5 was gained in the c.m. solid angle over the laboratory system solid angle of the magnet aperture (5 x 10 -3 sr). view

Plon

Magnet coupling

.,

.

1'1.5 c m . - - ~ 30_cm

.

Slide-in beam collimator

0.08 mm "~llmPx"

window to external proton counter Fig. 1.

Target chamber geometry.

II

.i

UI

e (He .p) C

3"/.

P.

1

Fig. 2. Spectrum of protons from BI°(Hes, p)Ca~ at 140° at 5 MeV bombarding energy.

Fig. 1 shows a simple plan of the target chamber geometry. The targets consisted of a 30 #g/crn 2 layer of boron (better than 90 ~o B 1°) on a 10 /~g/cm z carbon backing.

DECAY OF 7.66 MeV LEVEL OF

C tt

677

The magnet had no facility for measuring the field but it was possible to work from the potentiometer on the stabilized magnet current. Cycling the magnet at each change o f current was found to give a field reproducible to well within our requirements. It was necessary to use the charge state 3 + for C12(2) detection since the most populated 4 + state was swamped by random scattered He 3+ + particles in the pulseheight spectrum. Unfortunately at the higher field required for the 3 + ions the fieldmagnet current relationship was non, finear. However, since a 4.5 MeV C~2(3 +) ion has the same magnetic rigidity as a 6 MeV He 4 + + ion, it was possible to determine the departure from linearity ( ~ i8 %) with the two strongest ~ lines from Am 241 and C m 244.

Amplifiers Fig. 3. Block circuit.

The silicon counter at the focus of the magnet was a 2 cm diameter O R T E C type 380 A100. The momentum acceptance 10) was in consequence 1.3 %. F r o m the proton spectrum (fig. 2) it is seen that good resolution was needed in the usual half-width sense to separate the P2 and Po ((213) groups clearly. In addition a high peak to tail ratio was required to suppress the pl-Ct2(1) yield (low Dp). The tail was largely determined by edge-scattering by the collimator and a double collimator was devised. The width of the collimator was defined by a cam-driven shutter with a second identical shutter interposed between it and the 3.8 cm diameter NaI crystal. The height was defined by one of a set of sfide-in windows in front of the first shutter; a second window could be inserted between the two shutters. All edges were machined from 1 m m tantalum. The photomultiplier was an E.M.I. 9536 B which, being an unfocussed type, was insensitive to stray field from the neighbouring magnetic spectrometer. A block diagram is shown in fig. 3. Coincidences were taken between proton and carbon-ion pulses with a time resulution of 0.2 #sec. Pulse height spectra were displayed on a 100 channel C.D.C. kicksorter. 2.3. CARBON ION DETECTION, COINCIDENCE EFFICIENCY, AND DISCRIMINATION FACTORS

Firstly, pi-CX2(1) coincidences were observed for C12(1) ionic charge states of

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I. HALL AND N. W. TANNER

q = 3 +, 4 +, and 5 + with a population distribution of approximately 2 : 5 : 1. The gated C12(1) pulse height spectrum showed a counter resolution of 6 % (fig. 4). The optimum pl-C~2(1) coincidence rate was about 6 per 100 Pl protons which was understood from (i) a loss of ¼ due to charge state population (q = 3 +), (ii) a loss of ½ due to limited momentum acceptance of the magnet (fig. 9), Off) a geometric loss of ½ arising principally from the finite target area illumination from a beam spot of about 5 mm diameter.

50

/

°o,°o-

,,ooop,

g'/.

t

/jL

]

t _.1

43

44

45

4e

Petentlometer settlnll (*tmallnet ourrent)

Fig. 4. Response of Si counter to 4.5 MeV carbon ions: gated CX~(l) pulse height spectrum.

Fig. 5. Profile of CXa(1) ions: px-ClZ(1) coincidences versus magnet potentiometer setting.

Fig. 5 shows the profile of coincident p1-Ct2(1) counts against magnet stabilizer potentiometer reading. As shown in subsect. 3.3 the energy loss of the carbon ions in the target was deduced from this profile to be 0.24 MeV i.e. a mean loss of 6 = 0.12 MeV. In calculating the optimum magnet setting for C12(2) ions from that found for C12(1) ions 6 did not have to be known accurately since the expression T2-6 T1 - 6

V

(where 7"1 and T 2 are the respective carbon ion energies) is insensitive to 6; equal energy losses have been assumed for the two ions. Allowing for hysteresis in the manner described in subsect. 2.2 the calculated profile centre for C12(2) ions was 42.1 on the magnet potentiometer scale. In the final search for p2-ClZ(2) coincidences three magnet settings were used viz. 42.0, 42.2, and 42.4

DECAY OF 7.66 MeV LEVEL OF Cxl

679

and the magnet discrimination factor De, which was not expected to vary significantly across these, was determined at the setting 42.4. In all yield and discrimination factor measurements counts were summed over the same band of the spectrum which was about 1.7 times the full width at half maximum (embracing 92 % of the total C12(1) count in fig. 4). The discrimination factors were evaluated as Dc = ~ with a statistical error of 16 % and

Dp = ~ ~ o with a statistical error of 9 %.

The feeding factor F being 11 ___0.5 the quantity F D c D p ~ 6.2x 10 -5,

so that if F s / F > 10 -4 then p2-C12(2) events should be well detectable above the residual px-C12(1) count. The latter was calculated to be 0.069+0.014 counts per 104 pC of beam. 2.4. F I N A L S P E C T R U M

In an exploratory run particle groups were found, one on either side of the prospective C12(2) position in the pulse-height spectrum. The upper (random coincidence) group was found to have m/q 2 ~ 0.9(8) and were therefore ~ particles; protons of the requisite energy would not have been stopped in the counter depletion layer. By variation of magnet current it was observed that this group was selected from a continuum of ~ particles which could arise from the Bt°(He 3,~)B 9 ~ p + 2~ reaction. TABLE 2 R u n s at 3 magnet settings Magnet setting 42.4 42.2 42.0

Total b e a m charge (10 s / z C ) 185 200 187.5

Counts per l0 s /zC 4.3 -4-1.5 6.5-4-1.6 5.3:k 1.7

The lower (true coincidence) group had m/q 2 ~ 1.6(8) suggesting mass 15 and charge state 3 +. These were then kinematically identified as N15(3 +) ions from C 13(He 3, p)N 15. This group has been useful as a marker in the pulse-height spectrum; since it lays only 20 % below the mass 12 pulse height it was used as the zero of the pulse-height display thus compensating for the small spectral shifts which arose from the use o f three magnet settings. Table 2 gives the yield of mass 12 counts at the three magnet settings and notwithstanding poor statistics confirms 42.1 as the optimum magnet setting for C12(2) ions.

680

L HALL AND N. W.

TANNER.

Fig. 6 shows the sum of the silicon counter pulse-height spectra taken from these runs and represents some 30 hours' running. The C12(2) count was expected about 26 channels above the N 15 peak; the random coincidence u peak is off scale. The residual C 13 count should be about I0 channels below any CX2(2) count. By summing over n channels at a time and replotting, the curves of fig. 7 are produced for n = 5 and 3 respectively. The mass 12 and 13 groups are then recognized.

t

I I

n=5

't',

.8"/*

].

ii ii 3 i| N (3") from C (He.p)N 16

"

i',,,

I\I

t

?+

!j)]

,,/ 0

8

16

2&

20

C~

2&

211

C' t

32

n~3

t ~ + rr ~t't.~4+ ~.ra.~+i ~~+t ~ + 32

40

K / S charmer reletive to N 1It peak

Fig. 6. Aggregate pulse-height spectrum in search

of pi-C12(2) coincidences.

Fig. 7. Pulse-height distribution of fig. 6 summed over n channels at a time and replotted.

3. Analysts 3.1. BACKGROUNDS F r o m subsect. 2.3 the expected residual p1-C12(1) count in the aggregate spectrum of fig. 6 was 3.9. The error in this due to the uncertainties in the discrimination factors is +0.8. However, since the actual p1-C12(1) residual count is not known to better than the statistical error on the number 3.9 this count is taken to be 4-1-2. One long randoms run of l0 s/~C gave but one count and that in channel 31 relative to the N 15 peak. Momentum selection and available energy ruled out elastic He 3 or knock-on B x° or C 12 events and this count was taken to be from the tail of the random u peak. In figs. 6 and 7 the Ct2(2) count appears to sit on such a small tail. F r o m the meagre information afforded by the randoms run and inspection of the aggregate spectrum this contribution is estimated at 4 4-2 counts. 3.2. NUMBER OF pi-CXl(2) EVENTS

In comparing the px-C12(1) and p2-C12(2) yields it is necessary to sum the mass 12 count over 14 channels in the spectrum of fig. 6. However, the low energy side merges

DECAY OF 7.66 MeV LEVEL OF C l i

681

with the C 13 yield. Since the two groups are of comparable size it is convenient to slice halfway and take the counts in channels 25-35: these number 29. The error in this number is twofold. Firstly ~/29 would be the r.m.s, deviation on 29 counts in an isolated peak. Secondly there is an additional error due to the proximity of the C 13 group rendering 29 uncertain as the number of counts which would have been obtained in the same run in the absence of the C 13 peak; this error is t a k e n to be the number of counts in one channel on either side of the halfway point. Table 2 would indicate that inclusion of the run with magnet setting 42.4 would incur an underestimate of F=/F; such error is of little consequence in view of the sheer need of counts. Subtracting backgrounds and combining errors the number of pz-C12(2)counts is 21_7. Thus F= _ R{pz-ClZ(2)} FC = ( 3 . 3 + 1 . 1 ) x I 0 - " C F R{pl-CtZ(1)} where C is the efficiency correction factor. 3.3. E F F I C I E N C Y C O R R E C T I O N S

3.3.1. y-Recoil. The momentum profiles of C12(1) and C12(2) ions approaching the magnet aperture were different on account of the differing recoils suffered by these ions in 7-decaying to ground. The energy distribution of moving C12(1) ions after 7-decay is rectangular as, o f course, is that due to target losses. The coupling of two rectangular distributions o f separate widths 61 and 62 results in an energy spectrum in the form of a symmetric trapezium of base width (61 +62) and of plateau width 161-62l. Since the spectral width is small compared with the mean energy this will also be the form of the momentum distribution. This, o f course, was found experimentally as represented in fig. 5. The finite magnet acceptance would be expected to distort the trapezium only slightly. The base corresponds to 0.48 MeV and subtracting the calculated 7-recoil broadening o f 0.24 MeV a target energy loss of 0.24 MeV is deduced. Extrapolating from the measured stopping powers of Porat and Ramavataram 11) gives a B 1° thickness of 34/~gm/cm z in agreement with the nominal thickness of 30/~gm/cm 2. The 7 recoil broadening of the C1z(2) ion profile is complicated by the cascade decay; it is, however, calculable from the directional correlation

W(O) = 1 - 3 cos 2 0 + 4 cos4 0 between the successive 7 rays assuming a spin sequence 0+-2+-0 +. The calculated energy spectrum is shown in fig. 8. It is a simple matter to prove that to combine two distribution functions one of which is rectangular and of width 6, then to find the ordinate at point x on the composite distribution one takes the area under the nonrectangular distribution function bounded by x - ½ 6 and x+½6. In this way the

682

I. HALL AND N. W. TANNER

y-recoil distribution of fig. 8 is combined with target thickness broadening to produce the full curve of fig. 9. On this same diagramme the known C 1z(1) energy profile is plotted so that the areas under the two curves are equal. Then the ratio of the areas bounded by these curves artd the magnet acceptance yields the relative efficiency and. a correction factor of 1.18. 3.3.2. Geometric losses. Excited Ct2(1) or C12(2) nuclei may be deflected away from the magnet aperture by the recoil of V emission.

Nognot Qc¢optonco

~-~ ^

ddE n

i(~i t !

Nomentum profiles

Fig. 8. Calculated 7-F-recoil broadening of a mono-energetic beam of C12(2) ions.

Fig. 9. R e l a t i ve m a g n e t acceptance. The full

curve is the profile of C1~(2) ions entering the magnet and the broken curve is that for C12(1) ions.

In height and width the angles subtended by the magnet aperture at the target were greater in the centre of-mass system than those of the proton counter. Furthermore this aperture was higher than it was wide and losses could only occur by lateral deflection. To calculate these explicitly would be difficult but the final correction is only small and has been estimated as follows. The angular width equivalent to the proton counter is combined with the finite target spot to give the no-recoil illumination over the angular width of the aperture. This illumination is then combined and integrated with the angular deflection probability distribution to determine the separate losses for the two ions. The latter is just the distribution of components of recoil momentum perpendicular to the ion path and is therefore a rectangular function again for the C12(1) ions and has the form of fig. 8 for C12(2) ions. The estimated correction is 4 %.

DECAY OF 7.66 MeV LEVEL OF C I I

683

3.3.3. Charge state population. The correction factor here is f ( 3 +) f ( 3 + ) + 6 f ( 3 +) where f (3 + ) is the fraction of C 12(1) ions occupying charge state 3 + and 6./'(3 + ) is the increase in this proportion at the lower energy of the C12(2) ions. We found f ( 3 +) ~ 0.25 and 6./'(3 +) is calculated from 6f(3 +) = ~

vq

6q*, f=0.25

where (df/aq)l: = o.2s is the slope of the population distribution at the point f = 0.25 and 6q* is the shift in average or effective charge of carbon ions due to an energy change equal to the difference in C12(1) and C12(2) ion energies. F r o m refs. 12-14) 6./'(3 +) is estimated at 0.04 giving a correction factor of 6.

4. Discussion The final result after applying the various correction factors is

r,/r

= (3.5_+1.2)x 10-4.

In effect the accuracy of the measurement was determined by the time available for recording data. An attempt to repeat the measurement was thwarted by the contamination of the He 3 beam with a 5 MeV carbon beam (,~ 10 -3 /~A) which caused ambiguous events after scattering and energy loss in the target. This carbon beam did not occur in the experiment described above as the ion source at that time was fitted with an analysing magnet. It is noted that, from different methods, there are now three independent measurements of I's/F all in agreement. In view of the earlier and. somewhat involved history of the 7 decay of the 7.66 MeV state of C 12 this is a very pleasing outcome. We thank Prof. K. W. Allen and Mr. R. Batchelor for the use of the A.W.R.E. 6 MV Van de Graaff, and the machine staff for their strenuous efforts on our behalf. We also acknowledge the generous assistance of Mr. W. R. G r a h a m in the final runs. One of us (I.H.) is grateful for support from the Department of Scientific and Industrial Research. References 1) 2) 3) 4)

F. Hoyle, Astrophys. J. Supp. 1 (1954) 121 E. M. Burbidge, G. R. Burbidge, W. A. Fowler and F. Hoyl¢, Revs. Mod. Phys. 29 (1957) 547 A. G. Cameron, Chalk River publication CRL-41 (1957) D. E. Alburger, Phys. Rev. 113 (1959) 608

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5) 6) 7) 8) 9) 10) 11) 12) 13) 14)

I. HALL AND N. W , TANNER

F. Ajzenberg-Selove and P. H. Steison, Phys. Rev. 120 (1960) 560 J. H. Fregeau, Phys. Rev. 104 (1956) 225 R. Ferrell, private communication to W. A. Fowler D. E. Alburger, Phys. Rev. 124 (1961) 193 P. A. Seeger and R. W. Kavanagh, to be published D. L. Judd, Rev. Sci. Inst. 21 (1950) 213 D. I. Porat and K. Ramavataram, Proc. Phys. Soc. 77 (1961) 97 E. L. Hubbard and E. J. Lauer, Phys. Rev. 98 (1955) 1814 R. G. Roll and F. E. Steigert, Phys. Rev. 120 (1960) 470 H. L. Reynolds, D. W. Scott and A. Zucker, Phys. Rev. 9[$ (1954) 671