Study of 15O by means of 3He+12C reactions

Nuclear Physics A129 (1969) 6 4 - 8 0 ; (~) North-Holland Publishiny Co., Amsterdam N o t to be reproduced by photoprint or microfilm without written permission from the publisher

STUDY OF lSo BY MEANS OF SHe + t2C REACTIONS H. R. W E L L E R A N D H. A. V A N R I N S V E L T

Department of Physics and Astronomy, Unicersity of Florida, Gainescille, Florida Received 7 February 1969 A b s t r a c t : A n g u l a r distributions a n d excitation curves have been m e a s u r e d for the t~C(SHe, 3Hc)rzC,

~C(3He, cto)~lC and lzC(SHe, cq)ttC reactions between E(SHe) .... 5.0 and 8.0 MeV in 100 keV steps. Strong resonance structures have been observed. A n optical-model-plus-resonance ( O M P R ) analysis o f the elastic scattering data indicates that a potential similar to that used at higher energies can describe m u c h o f o u r data if two resonances are introduced near 7 MeV a n d two between 4.5 a n d 6.0 MeV. A phase shift analysis o f these data was also p e r f o r m e d with results in accord with the O M P R analysis. A Legendrc polynomial expansion was m a d e o f the ~o data. E I

I

NUCLEAR

R E A C T I O N S lzC(aHe, SHe), (SHe, ~t), E : 5-8 MeV; m e a s u r e d cr (E; E=, 0). N a t u r a l target.

1. Introduction The study of 3He scattering from 12C has been the subject of several authors. Kuan et aL 1) studied several 12C+ 3He reactions at E ( a H e ) = 1.8 to 5.4 MeV. Their results indicate appreciable compound nucleus formation. On this basis some spin formation was extracted in the 3 MeV region. In other studies by Schapira et al. 2), Blake et al. 3), and Cirilov el al. 4), detailed angular distributions for the elastic, alpha and proton channels were measured from 2.0 to 6.0 MeV. in the work of Schapira 2) an attempt was made to analyse the elastic data in terms of an opticalmodel-plus-resonance amplitude. The results of this analysis were quite unsatisfactory, and the authors concluded that this approach was not very promising. Although resonance structures were seen in all channels with sufficient correlation to establish their physical reality, no definite conclusions with regard to angular momentum were obtained. More recently Park 5) analysed the elastic data of Schapira along with some of the data to be reported here and some higher energy (15 MeV) data of Kellogg and Zurmiihle 6) using the optical model. Although the fits which he obtained were quite good, we shall attempt to show that there are strong resonance structures in these data below 8 MeV which can be accounted for in a more consistent manner by means o f an optical-model-plus-resonance amplitude. Still other workers have reported results on the 3He+ 12C processes. Schwartz et al. 7) measured elastic and alpha cross sections from 8.5 to 10.0 MeV. In addition 64

65

~'c('H~, ".~). ("..,. ~) eE,,,cnoNs

G r a y and Fletcher s) measured the cross sections in the range of 12 to 18 MeV. These workers have attempted to view the process as direct in this energy region with only limited success. The data of this work concentrate on the previously neglected region of 5.0 to 8.0 MeV. We have measured the angular distributions in 100 keV steps through this region. It is shown that much of the elastic data can be accounted for by means of an optical-model-plus-resonance ( O M P R ) amplitude. A phase shift analysis has also been performed on much of these data with results in accord with the O M P R calculations. The measured 0t-particle angular distributions have been expanded in terms of Legendre polynomials. Recent results of a 1 4 N + p reaction study 9) which examines sO in the same region as this experiment can be compared with these results. 2. Experimental procedures

The data of this experiment were taken using the doubly charged 3He beam from the University of Florida 4 MV Van de Graaff accelerator. Three 50 #m thick solid state ~tc

+SHe

E,.. : 7.5 M e V

8,

.ooiA.oo D-

~ l t , dl,'~l

.o=oo

d-O

0

0

~LA0: 140 o

~ ooo ® z

800

l~

ZOO

O0

~i

:'5

le$~

SO CH&NNEL

Fig. 1. Spectra for the ~ C + a H e

T8

I00

NUMBER

reactions at 0~ab = 40 ° and 140 ° at 7.5 M e V .

detectors were used to obtain most of the data. The detectors collimated to an 0.15 cm aperture were placed in the 60 cm scattering chamber described in detail by Prior lo), at a distance of 10 cm from the target. The beam was collimated to an

66

H. R. WELLER AND H. A. VAN RINSVELT

0.15 cm x0.30 cm spot on the target which was set at 45 ° with respect to the beam. Spectra were accumulated in a 512-channel pulse-height analyser opelated as four 128-channel analysers. A typical pulse height spectrum is shown in fig. I. A proportional counter solid state detector system was used as a mass identifier to verify the identification of the peaks and to check the direct energy pulse data. It was found that the elastic and ground state or-particle data were reproduced and that mass identification was unnecessary for these groups. The carbon targets used were approximately 20/~g/cm 2 and were made by cracking methyl iodide o n a t h i n Ni foil and dissolving the foil in aqua regia. The absolute cross section was measured by using a 2 MeV 3He beam and assuming Rutherford scattering at small angles to obtain the target thickness. The results agreed well within the estimated 15 ~ error with those of other workers where overlap occurs. The machine energy was determined by means of a Li(p, n)Be threshold measurement. It is estimated that the absolute energy is determined to within 15 keV.

3. Data analysis 3.1. O P T I C A L

MODEL

ANALYSIS

The attempt to apply the optical model to these data began by trying to fit the data at 6.0, 7.0, and 8.0 MeV using a set of parameters similar to those obtained by Kellogg 6 ) a t 12.0, 15.0, and 18.0 MeV for the laC(aHe, a H e ) l a c d a t a . T h e s e p a r a m eters were extrapolated to 8.0 MeV and applied to the t aC elastic data at 8.0 MeV 11). The form of the optical potential assumed is:

V = V(r)+iW(r)+ Vc(r)+ V,.o.(r)i'a where

V(r) =

-

V(1 + e ~)- i,

r - ro A ~ X

--

Vs.o.(r) = V~.o.fs.o.(x),

f,.o.(X)=

W(r) = W(I +er) - t ,

y _

~ '

r-roA

(1 +e~) - ',

+

t/'

Vc(r) = Z, ZA e2/r,

r >= rcA ~,

Vc(r) = [Z~ ZA e2/2rc A+](3 -

r2/r~¢A*),

r < r¢A ~.

A good fit was obtained in this case 11). The best fit criterion in these calculations was determined by seeking a minimum in the quantity X2 defined by Z2 = ~ l°'e~P(i)- a,h(i)l 2 , ]dtr,~p(i)[ 2 '

IIC(IHe,IHe),(IHe,~.)REACTIONS where acxp and respectively and tions were done The] ~2C elastic

67

trth are the experimental and theoretical values of the cross section dtrcxv is the statistical uncertainty associated with ac,p. These calculaat the Oak Ridge National Laboratory using the code H U N T E R t2). data at 8.0 MeV were now fitted quite successfully with only minor

:

~c (~H,,~,~ 4¢~¢i~ ~

7.0 MIV

lO¢

i

¢ ¢ I I 50" ?0"

i

I 90"

I ,,0"

!

I 50*

I

130" ~0"

I 70"

Oc.m.

910" HIO* l~O* ll~"

Oc.rn.

I00 t'C(IHe,~.le)'~ 80 MeV Ii

!

j I I 50" ?o*

90"

I

i

I

riO" I$0" 150'

Oc.rn. Fig. 2. Optical model fits to the ItC(aHe, aHe)tzC angular distributions at 6.0, 7.0 and 8.0 MeV. Parameters are given in table I.

variations in the parameters. However, attempts to fit the t2C data at 6.0 and 7.0 MeV indicated that variation of V, W and r~ was not sufficient to fit the 7.0 MeV data. The resulting fits are shown in fig. 2; the parameters are presented in table 1 (ref. t t)). An extensive search on the optical parameters was made on these data by Park s). In this work both surface and volume absorption were investigated. It was found

68

H.R. WELLER AND H. A. VAN RINSVELT

TABLE 1 Optical m o d e l p a r a m e t e r s for the 2zC(SHe, SHe)I~C fits at 6.0, 7.0 a n d 8.0 MeV, and the ~*C(Sl-ie, SHe)X*C fit at 8.0 MeV along with the higher energy p a r a m e t e r s f r o m ref. ' ) Optical p a r a m e t e r s lsC(SI-{e, aHe)18C V (MeV)

W (MeV)

156.0 158.0 161.0 161.4

6.80 6.75 5.37 4.73

ro (fm)

a (fm)

r'0 (fm)

a' (fro)

rc (fm)

Vs.o (MeV)

8He lab energy

0.93

0.81

2.25 2.25 2.25 2.56

0.65

1.4

6.0 6.0 6.0

18.0 15.0 12.0 8.0

0.65

1.4

I~C(IHe, SHe)]sC 165.0 165.2 139.5

4.43 4.43 5.50

0.93

0.81

2.05 1.90 2.25

8.0 7.0 6.0

Energies are given in MeV; geometrical parameters are in fro.

that good fits could be obtained to the 7.0 MeV data only by introducing a highly energy-dependent spin orbit term. The spin orbit parameter V,.o. varied from 0.0 to 10.0 to 2.5 MeV in fitting the 6.0, 7.0 and 8.0 MeV data respectively using volume absorption. At the same time the imaginary well depth varied from 20.0 to 11.0 to 14.2 MeV. 3.2. O P T I C A L - M O D E L - P L U S - R E S O N A N C E

ANALYSIS (OMPR)

The strong energy dependence of these optical model parameters suggests the existence of resonance structures in this region, a surmise which is supported by the excitation function of elastic scattering from 4.4 to 8.2 MeV at 140°, shown in fig. 3. In addition to the strong resonance structure centered around 7.0 MeV we observe

01 140" 0tma

./.'-.

./2 •

12

i 8 •,~.

.

.

:

4

,

,,

...

•

"'...~ ,

I

5"0

,

,

,

,I

,,

60

."

. ." ./

,

,

I

,,

70 LA8 (uev)

,

o

I , , ,

80

,

I

..

9"0

Fig. 3. M e a s u r e d excitation curve at 01~b = 140 ° for the t~C(aHe, aHe):eC process. T h e solid lines are theoretical fits to the data obtained using the O M P R f o r m u l a t i o n . T h e p a r a m e t e r s are given in table 2. T h e statistical error on the data points is less t h a n 1.5 ~o.

12C(aHe, aHe), (aHe, :0 REACTIONS

69

two additional resonances at about 5.0 and 5.7 MeV, these latter two have been previously reported by Schapira et al. 2). In order to include the resonance structure at 7.0 MeV into our calculation of the cross-section data in this region we obtained a computer code from Tamura 13) which added a Breit-Wigner resonance to the optical model amplitude for the case o f spin ½ on spin 0. In this code the amplitude is written 13) as:

S(O) = A(O)+ B(O)(o. n),

A(O) =

Ao.,(0)+

1 Zexp(Zia,) "

1 B(O) = Bo,,(O)+ 2k ~ exp (2ia,)

(E-E

.R~+ila )+½ir

[(/+1)6 i

'

,+½+lfj t_½]P°(cos0), '

Rz+ilz [6i.,+ ½- 6,.t- ~]P~ (cos 0). (E-E~)+½iF~

The complex amplitude in the Breit-Wigner term added on allows for an arbitrary phase. Here we point out that the amplitude used by Schapira 2) did not allow for this "resonance mixing phase" 14). This may account for some of their difficulty in obtaining good fits. The quantity at is the Coulomb phase shift; Aopt (0) and Boo,(O) are the usual optical amplitudes, Bopt(0) being zero in the absence of a spin-orbit interaction. The analysis began by taking the 8.0 MeV optical model parameters for 12C and searching on the resonance parameters in an attempt to fit the 7.0 MeV angular distribution. In this calculation we ignored the spin of the projectile and sought only to determine the I value of the resonance involved. Previous experience as well as the results of Schapira et al. 2) indicated that the results of these calculations would not be sensitive to./'. It was found that the best fit was obtained by setting I = I. As before, the best fit was determined by seeking a minimum of the quantity X2. We then calculated values of the resonance parameters which maintained the shape of the angular distribution on resonance, but varied the energy dependence so as to fit the 140 ° yield curve. It was found that the shape of the excitation curve was very sensitive to the value of l. After obtaining the best fit, we re-searched the optical parameters attempting to fit the offresonance data with the resonance included. It was found that introducing a second p-wave resonance improved the results although some of the structure was still unaccounted for. The final fits obtained for the 6.0, 7.0 and 8.0 MeV data are shown in fig. 4. The fit to the 140 ° yield curve using the same set of parameters is shown in fig. 3. The O M P R parameters used here are presented in table 2. Perhaps the difficulty in fitting the 6.0 MeV region reflects our neglect of any energy dependence of the parameters as well as other nearby resonances. Although the formulation used here allows for a violation of unitarity, this was checked, and it was found that no such violation occurred for the parameters used. A more detailed consideration of tbis point is given by Vesser and Haeberli 1s).

70

H . R . WELLER AND H. A. VAN RINSVELT

I00(~ '~

c'10o,~,a,)'~ 7.0 I ~ V

IOC t~t

/ I,

IC

I I'IJiJ /

50*

70"

90"

liO*

,/t* I 130" 150"

~o °

'

I)0" ' O~m.

OC.m.

I00

8.0

MoV

\

Ii

!

/, ÷~Jt

I

80°

I

70"

I

90'

I

IiO*

n

t

a

lIFO* III0°

O~m. Fig. 4. Measured angular distributions for the ~tC(SI-(e, SHe)ltC process at 6.0, 7.0 and 8.0 MeV. The solid lines are theoretical fits to the data obtained using the O M P R formulation. The parameters are the same as those used in fitting the 140 ° data of fig. 3 and are given in table 2.

The results obtained here encouraged an attempt to re-analyse the two lower resonances first treated this way by Schapira et al. 2). We began this calculation by searching on the optical parameters to fit the 6.0 MeV angular distribution with the two resonances above 6.0 MeV included. It was felt that this could be justified as a result of the neglect of any energy dependence in the calculation from 6.0 to 8.0 MeV. We then tried adding two resonances with various l values (0, 1, 2, and 3) and searched

71

12C(SHe, :He), (SHe, ~) REACTIONS TABLE 2 Optical-model-plus-resonance parameters used in fitting the data from 6.0 to 8.0 MeV Optical-model-plus-resonance parameters for 6.0 to 8.0 MeV "C(:He, SHe)12C V (MeV)

W (MeV)

ro (fm)

a (fro)

r'o (fro)

a" (fro)

re (fm)

Vs.o. (MeV)

' H e lab energy

165.0

4.40

0.93

0.81

2.05

0.65

1.4

0.0

6.0, 7.0, 8.0

Resonance parameters R = --0.087 R = --0.018 1 = 0.037 I = 0.008 Ere8 = 5.44 Er~ = 5.92 F = 0.6 T' = 0.2 1=1 I=1 Energies are in MeV; geometrical parameters are in fm.

"C(~ e,~e)"C

5.5r4

0 ~'eV

~eV

b

trite* i

i

i

i

i

t

~o.

~4~,

7~*

90"

iio a

i~1.

J i~o •

i 170 a

3~ ° I .

rl0. ~0" u~"

150'1 150"1 I~0"

t÷tf~f ~3" 70"

90 °

I10°

I~O*

'$0 °

0crn.

Fig. 5. Measured angular distributions for the 12C(aHe, :He)tzC process at 5.026, 5.574 and 6.0 MeV. The data at 5.026 and 5.574 MeV are taken from ref. 2). The solid lines are the theoretical fits obtained using the OMPR formulation with the parameters of table 3. o n t h e r e s o n a n c e p a r a m e t e r s to s i m u l t a n e o u s l y find a m i n i m u m v a l u e o f X2 w i t h r e g a r d to the a n g u l a r d i s t r i b u t i o n d a t a a n d the p r o p e r s h a p e as a f u n c t i o n o f e n e r g y as o b s e r v e d in the 140 ° e x c i t a t i o n curve. A g a i n wc o b t a i n e d g o o d fits w i t h the results s h o w n in figs. 5 a n d 6. T h e p a r a m e t e r s for these O M P R fits are g i v e n in t a b l e 3. T h e success we h a v e a c h i e v e d here w o u l d a p p e a r to l e n d credibility to the h i g h e r - e n e r g y p a r a m e t e r s . A l t h o u g h S c h a p i r a was u n a b l e to o b t a i n a n y results for the 5.7 M e V r e s o n a n c e , he did c o n c l u d e t h a t the 5.0 M e V state was p r o b a b l y 1 = 2 o r 1 = 4. It is felt t h a t the p o o r q u a l i t y o f his fit m a k e s his result q u e s t i o n a b l e . A l t h o u g h the q u a l i t y o f o u r fits u s i n g I = 1 a n d I = 0 for t h e t w o r e s o n a n c e s in this r e g i o n is signi-

72

H . R . VC'ELLFR A N D H . A . V A N R I N S V E L T • •

ficantly better, the difference between the fits for other/-values Is.not so great as to leave these results unambiguous in this case. Perhaps more data would resolve these ambiguities.

I=C(3He?He)~=C $ t . ~ = 140"

I01 .,,

rx

:

FI., (MeV] Fig. 6. D a t a and fit for the 140 = excitation curve from 4.5 to 6.5 MeV using the p a r a m e t e r s o f table 3. The statistical error on the d a t a p o i n t s is less t ha n 1.5 %. TABLE 3 O p t i c a l - m o d e l - p l u s - r e s o n a n c e p a r a m e t e r s used in fitting the da t a from 4.5 to 6.0 MeV O p t i c a l - m o d e l - p l u s - r e s o n a n c e p a r a m e t e r s for 4.5 to 6.0 MeV 12C(SHe, 8He)a2C V (MeV)

W (MeV)

136.5

10.6

ro (fm)

a (fro)

r'o (fm)

0.93

0.81

2.17

a' (fm) 0.65

Resonance parameters R 1 Ere. F

= --0.027 = 0.115 = 3.82 = 0.350

1=

I

R = 1= Ere" = /~ = l=0

0.026 0.018 4.36 0.170

R = --0.087 1= 0.037 Ere s = 5.44 /1 = 0.600 1= 1

R = --0.018 ! = 0.008 Ere a = 5.92 I" = 0.20 I= I

Energies are in MeV; geometrical p a r a m e t e r s are in fm. 3.3. P H A S E S H I F T A N A L Y S I S

A phase shift analysis of the elastic data of this experiment was performed in an attempt to corroborate our 1 = 1 assignment to the 7 MeV structure as found in our OMPR analysis. In this case the cross section can be expressed in terms of the partial scattering amplitudes f / f i = i ( 1 - UI), where U/is the diagonal element of the collision matrix. It may be written

Vl =

A/exp (2iA/),

where A is the damping parameter and A is the phase shift (both are real)•

“@He,

$He),

(3He,

0~) REACTIONS

13

Sets of phase shifts and damping parameters with various partial waves resonating (i.e., A = 90”) were searched in an attempt to fit the 7.0 MeV angular distribution data using the computer code SCRAM IV. The best fit was determined by minimizing the quantity x2 defined in subsect. 3.1. The results indicated a preference for a p-wave resonance. In order to obtain a more realistic result we next took the phase shifts

8cm. Fig. I. The laC(*He, 8He)1ZC angular distributions measured from 6.0 to 7.8 MeV in 100 keV steps. These data were taken in 5” steps with a statistical uncertainty of less than 7 %.

from the optical model fit at 8.0 MeV as starting values. Since no (1 . s) interaction has been included, the phase shifts were only a function of 1. So with equal values for the I+ 4 and I- 3 phase shifts we searched each of our measured angular distributions shown in fig. 7 from 6.0 to 7.8 MeV including partial waves up to I = 3. The resulting phase shifts and damping parameters are shown in fig. 8. The near-zero values obtained for the I = 2 (and I = 3) phase shifts implies that enough partial waves were

14

H. R. WELLER

AND

H. A. VAN

RINSVELT

taken into account. In fig. 9 we have plotted the partial scattering amplitude ff. For the case of more than one open channel the behaviour of the phase shift and damping parameter found for I = 1 and j = 4 is characteristic of a resonance, i.e.,

IMAGINARY AXIS

I 0

L-L_-_-_.-,_A

5.0

ZO

60

3He

ENERGY

8.0

90

h4eV)

Fig. 8. The phase shifts and damping parameters obtained by fitting the data of fig. 7.

REAL AXIS

Fig. 9. The partial scattering amplitude fi3 in the complex plane through the 7.0 MeV anomaly. Note that the center of the unitary circle is an exterior point with respect to the path of the tip of the vector fit.

the phase shift A never passes through 90” as the exterior point with respect to the path of the tip of tude) 16). This will be true subject to the condition tion which seems quite reasonable for this reaction.

center of the unitary circle is an the vectorf(the scattering ampli(r&I) < + (ref. 16)), a condiAlthough the phase shift analysis

r2C(aHe,

‘He),

(*He,

a)

REACTIONS

75

favors a spin assignment of 3, it cannot be claimed that the set of phase shifts obtained is unique. However, the I = 1 resonating result is consistent with the result of our previous analysis. 3.4. THE *QsHe,

a)W

REACTION

The angular distribution data obtained for the ‘2C(3He, ao)“C reaction are shown in fig. 10. The lines through the data were obtained by fitting the data with a series expansion in terms of Legendre polynomials (~~=,, A,P,(cos 0)) up to and in50 20

5.0 Me”

5.1 Mev

52 MeV

5.3 Mev

I-

5A MeV

5.5 MeV - 50

-

8

cm.

Fig. 10. The measured angular distributions for the lZC(JHe, a,,)‘% reaction. The solid lines were obtained by fitting the data with a series expansion of Legendre polynomials up to and including Ps (cos 8). The error bars represent the statistical error associated with the data points.

eluding P, in a least squares manner. The coefficients of the Legendre polynomials divided by A, are shown in fig. 11. The results from 5.0 to 6.0 MeV agree well with the results obtained by Blake et al. “). In fig. 12 we see that A, (which represents the integrated cross section) shows a peak at 5.6 MeV and also at 7.2 MeV. A slight indication of another resonance is seen at 6.6 MeV. If we integrate only over angles greater than 90”, as shown in fig. 12, we see that the 6.6 MeV resonance is seen quite

20

1.0

1.0

0.0

0.0

-1.0

-1 .o

E,,.(MeV) Fig. 11. The Legendre coefficients divided by A, resulting from the fits of fig. 10. The solid lines are smooth curves through the data points. The error bars represent the statistical error in the ratios shown.

20-

I I I 7.0 6.0 E,,,IMeV)

5.0

II

0 8.0

t

4.0

50

11

ttt

f

60

70 E 3hIL*m

Fig. 12. The integrated cross section obtained by integrating only over angles greater than 90” for the data of fig. 10. The full integrated cross section (obtained from the coefficient A,) is also shown. The error bars indicate the statistical uncertainty. The effects of the incomplete angular range available are not accounted for.

80 t Maw

Fig. 13. Theexcitation curve for the ‘*C(*He, a.,)lC reaction at Olab = 140”. The statistical error on the data points is less than I .5 “/u. The arrows indicate the positions of the resonances as determined by the position of the maxima.

I OBSERVED

RESULTS

LEVELS

OF OMPR

I

(Imr

fog.13)

ANALYSIS

I9

I*

-

--a)

--p.l

--a)

-

=a)

1.1

II -

16 -

-aa) c) a) d

-1.0 -

iez::,

I5 -

), _ Cl/i,

13

12

-

b) b) c)

1

Fig. 14. Levels of “0 observed in the W(*He, a)“C reaction are shown on the left. On the right are the levels determined from the OMPR analysis of the elastic scattering data. a) The levels determined from this experiment (see fig. 13). b) Taken from ref. I). c) Taken from ref. ‘).

01 ’ 5.0

’

6.0

’

’

7.0

’

’

8.0

EsHs (MeV) Fig. 15. The l*C(sHe, a,)“C excitation curve at 71°. The solid line is a smooth curve drawn through the data points.

H. R. WELLER

78

clearly.

Perhaps

this result indicates

AND

H. A. VAN RINSVELT

that there is a significant

amount

of direct reac-

tion present which is interfering in the forward angles. If we now look at the 140” r0 yield curve shown in fig. 13, we observe a set of apparent levels as determined by the position of the maxima in the cross section. The two structures at 5.0 and 5.6 MeV are well correlated with corresponding structures in the elastic channel as seen in fig. 3. In the region of 7 MeV we see, as in the elastic channel, a strong resonance effect. However, the shape is somewhat different from

3d

)

,,,,,,,,,I,

56

76

90”

Ilo’

I36

150” 17d

8c.m.

at 6.0, 7.0, and 8.0 MeV. The Fig. 16. The angular distributions for the 12C(SHe, a,)*‘C reaction solid lines arc smooth curves drawn through the data points. The statistical error associated with these data points is less than the size of the dots.

the elastic channel. It is tempting to assume that the 7 MeV structure in both channels has a common basis. In the elastic channel we found that the structure appeared to be primarily I = 1 with a clear indication of three states. Indeed there are also three states showing near 7 MeV in the r,, channel. If we identify the peaks in the 140” yield curve as shown in fig. 13, we obtain a set of levels in “0 which are shown in fig. 14. It is estimated that these energies are correct to within 50 keV. Fig. 15 shows reaction. The structures at the 71” yield curve obtained for the ‘ZC(3He, a,)“C 7 MeV are clearly seen in this channel. Unfortunately most of the X, data at other

‘*C(‘Hr,

angles were lost in proton

energy-loss

‘He),

(3Hc, I)

REACTIONS

pulses. However,

79

angular

distributions

obtained

using the proportional counter - solid state detector assembly at 6.0, 7.0, and 8.0 MeV are shown in fig. 16. The angular momentum information gathered at these levels from this work is also shown in fig. 14. The I = 2 or 4 assignment to the 16.07 MeV level is due to Schapira et al. ‘). Our calculations indicate that I = I is a credible assignment. The two I = 1 level assignments near 17.5 MeV as found from the OMPR analysis are also shown. Two additional levels in ‘“0 which are prominent in the ‘2C(3He, cz)“C cross section have been reported by Kuan et al. ‘) at 14.27 and 14.46 MeV. The 3’ assignment for the 14.27 MeV level is due to Kuan er al. The level at 14.47 MeV appears to decay primarily by protons ‘). If we go back to fig. II, we see that the coefficient A,jA, shows a strong resonance shape at a 3He energy of 6.8 MeV, the energy which corresponds to the resolved doublet of fig. 13. From the properties of the Z coefficients this indicates that I = 4 is involved in this doublet.

4. Conclusions The results of this study have shown that the ‘2C(3He, 3He)‘2C process is susceptible to analysis by means of an optical-model-plus-resonance amplitude below 8 MeV. We have seen that resonance structures are quite important in the region below a bombarding energy of 8 MeV. Furthermore, it appears as though the parameters obtained by Kellogg “) at higher energies, which are similar to the parameters used here, provide a realistic background when extrapolated down below 8 MeV. In the study of the 14N+p reactions, Shrivastava et al. ‘) observed a broad aparticle state at about 14.3 MeV in ’ 50. This level would correspond to a ‘He energy of about 3.0 MeV in the present problem. Indeed a level is seen at E(3He) = 3.0 MeV in the ‘2C(3He, ~)rrC reaction ‘). However, the spin assignment of Shrivastava et al. ‘) is in disagreement with that of Kuan et a/. ‘) This observation emphasizes the fact that the spin information on the levels at this excitation energy is somewhat uncertain. The energy distribution of the level scheme observed in “0 in this experiment shows a strong resemblance to the low-lying level scheme of r ‘C. This observation suggests that a model of I50 in terms of an excited ’ 'C core plus an alpha particle may be useful. Further experimental and theoretical investigations of this model are in progress. We wish to thank Dr. Tamura for providing us with his code JUPITOR II which was used in the OMPR calculations. The help of Dr. R. M. Prior, Mr. R. M. Keyser and Mr. J. J. Ramirez in accumulating these data is greatly appreciated. Discussions with Dr. N. R. Roberson were very helpful. The calculations were done at the University of Florida Computing Center.

80

Ii. R. WELLER

AND

H. A. VAN

RINSVELT

References 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16)

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