Search for 8+ strength in 16O via the 12C(α, α2)12C∗(7.66 MeV) reaction

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Physics

A363 (198 1) 280-286

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SEARCH FOR 8+ STRENGTH IN 160 VIA THE ‘*C(a, a,)‘*C*(7.66 MeV) REACTION A. D. FRAWLEY,

A. ROY ‘, J. F. MATEJA

‘+ and

l

N. R. FLETCHER

Department of Physics, Florida State Unwerslty, Tallahassee. Florida 32306, USA Received (Revised

15 September 22 January

1980 1981)

Abstract: Closely spaced angular distributions have been measured for the r’C(a, a,)“C*(7.66 MeV) reaction between E, = 17.39 and 20.5 MeV in a search for 8+ strength in 160. No evtdence of 8+ strength IS found. but evidence is found for a narrow 7- resonance at 21.52 MeV excrtatton. I

E

I

NUCLEAR

REACTIONS

‘%a, G(),E = I7 39920 5 MeV, measured resonance J, A. Natural target

cr(E. 0). ‘(‘0 deduced

1. Introduction Since the observation ‘) in the 12C(q 8Be)8Be reaction of three resonances having the correct spins and energy spacings to be members of a highly deformed rotational band in i60, considerable effort has gone into exploring that possibility. Abgrall et al. 2, were able to generate levels with the correct spacing from a Hartree-Fock calculation of an 8p-8h deformed intrinsic state, and Suzuki et al. 3, were able to do the same thing with a linear a-chain model. The extrapolated excitation energy of the 8+ member of the proposed rotational band is about 21.6 MeV, and there have been detailed investigations of the i2C(or, *Be) reaction 4-6) in an effort to identify an 8+ level near this energy. All have been unsuccessful. She11 mode1 calculations restricted to four particles in the s-d shell ‘-lo) have predicted an 8+ member of a 4p-4h band based on the 6.05 MeV (O+) state in 160 at about 20 MeV excitation. Qualitatively, the members of the 4p-4h band would be expected to decay primarily to the ground state of 12C, with relatively little strength going into the *Be+ ‘Be and ’ 2C*(7.66 MeV) + ~1~channels. Detailed studies of ’ *C + LX elastic scattering ’ ‘) and a-transfer reactions on ’ 2C [refs: ’ 2 - ’ ‘)I have not located such a level. Recently a broad, very weak state was reported 16) at E, N 22.5 MeV from a study of the 12C(i2C, 8Be)160*(ao)12C reaction, and was tentatively assigned a spin of 8+. If the level reported at 22.5 MeV should be con*

This work supported in part by the National Scrence Foundation. + Present address: Tata Instttute of Fundamental Research, Bombay, India. ++ Present address: Tennessee Technological Universtty, Cookeville, Tennessee. 280

A. D. Frawley et al. 1 8+ strength

181

firmed as having J” = 8+, it is much more natural to associate it with the 4p-4h band starting at 6.05 MeV than with the highly deformed band discussed earlier, because the 8+ member of the highly deformed band would not be expected to be so broad, nor would it be expected to decay strongly to the ground state of “C. The moment of inertia required for the suggested highly deformed rotational band is very large, approximately equal to that of four &particles laid out in a chain and rotating rigidly. The idea of such a structure was first proposed by Morinaga I’) to describe the 7.66 MeV (O+) and 10.35 MeV (2+) states in “C. From a linear mchain model, Suzuki ef ai. 3, find that such states should decay very strongly into the 12C*(7.66 MeV) +cr-channel. This has prompted the present investigation, in which angular distributions of the 12C(a, CI~)reaction have been measured between E, = 17.39 and 20.5 MeV (E, = 20.2-22.5 MeV in 160) in steps of 50 and 100 keV. Analysis of the results shows no evidence of 8+ strength in 160 in this energy range. Evidence is found for a narrow 7- state in 160 at 21.52 MeV excitation. Previous studies of the “C(cr, CI~)reaction have been reported by Mitchell et al. Is) and Morgan and Weisser 19). The latter study was the more detailed of the two, consisting of an excitation function measurement in 100 keV steps from E, = 12 to 17.5 MeV (E, N 15-20.5 MeV in 160) with partial angular distributions measured at seven energies. 2. Experimental procedure A beam of @-particles from the FSU super FN tandem Van de Graaff accelerator was used to bombard self-supporting natura1 carbon foils of approximately 100 pg/cm2 thickness (corresponding to about 30 keV in the lab). Angular distributions of the 12C(ol, ~1~)l2 C * ( 7 .66 MeV) reaction were measured between E, = 17.39 and 20.5 MeV in steps of 50 and 100 keV. The energy step size was chosen on the basis of a preliminary excitation function measured in steps of 40 keV. Typically, about 35 angles were measured between Brat,= 7.5” and 165’ (f?,_,, = 1I”--173”). However, from 19.2 to 20.5 MeV the most forward laboratory angle was loo, and at the lowest few energies the most backward laboratory angle was 145”. Since the laboratory energy of the ~1~ group varies from about 10 MeV at forward angles to about 1 MeV at backward angles, it was necessary to use different particle identification techniques at forward and backward angles. Two or three conventional counter telescopes, consisting of 25 or 15 pm AE detectors and 300 pm E-detectors, were used for lab angles of 80” or less. A similar arrangement was used at back angles, but with the difference that the a-particles of interest were stopped in the AEdetectors. Events due to proton groups and higher energy cr-particles were eliminated by vetoing those signals from the thin detector which were in coincidence with signals from the thick stopping detectors. Relative no~alizations at each energy were obtained by referring to the l %(a, aa) or 12C(a, ~1~)yields from a fixed monitor detector. The relative energy dependence

282

A. D. Fruwley et al. / 8+ srrenyrh

of the angular distributions was obtained from comparison with an excitation function measured at em, = 30” and 70”. The CQyields were used for this purpose from E, = 17.39-19.14 MeV, but above this energy range the CI~yields are relatively small at 30” and 70” and so the energy dependence was obtained from a comparison of the CQyields. The uncertainty in the measured relative energy dependence should be everywhere less than 5 %. The over-all cross section normalization was obtained by measuring I60 elastic scattering from the same target at Elab = 15 MeV and I!&, = 20° and comparing with the calculated Rutherford scattering cross section. The absolute cross sections are believed accurate to k 15 %. The zero of the angle scale of the detector chamber was found by measuring the

900 -

600 -

d 2 5

500 -

E ii? 400

-

z’ = 300

-

8 200 -

-

100

t

OO r

900 .

600 . 700 . d I P Y E f 8

600 . 500 . rloo . 300 200 . 100 0!

Fig. 1. Alpha-particle

spectra obtained

at lab angles of 35O and 155O at Em = 18.24 MeV.

A. D. Frawley et al. /8+

283

slrength

left/right asymmetry of 160 elastically scattered from a Au target. The fact that the target spot forms the center of rotation of the detectors was established by measuring the elastic scattering of a 20 MeV 160 beam from a Au target at angles between Qlab= 10” and 90”, and comparing with the calculated Rutherford scattering cross section. 3. Results and discussion Fig. 1 shows typical spectra obtained at 35” and 155”. Some representative ’ %(a, CIJ angular distributions are presented in fig. 2. A linear Legendre polynomial expansion of the form k=16

da/dS2(8) =

1

(1)

A,P,(cos 0)

k=O

E,

= 18.24

MeV

E,

= 19.14

MeV

I -

O.‘o

Fig. 2. Representative

20

40

60

00

100 8 c.m.

120

140

160

I

angular distributions of the “C(a a2) reaction. The solid curves Legendre polynomial series fits ;o the data [eq. (l)].

are the linear

284

A. D. Frawley et al. / 8+ strength

0 2 0 -2

mb 5 4 3 2

0 2

-4

0

I

-2

I

17

t-’

I

I8

J9

20

-3

21

17

I8

19

20

21

E a (MeV) Fig. 3. Coefficients

of the linear Legendre polynomial series tits to the “C(c(, CQ) angular The estimated uncertainties in the coefficients are indicated.

distributions.

A. D. Frawle_v et al. / 8+ strength

285

was fitted to each angular distribution. The solid curves shown in Gg. 2 are typical of the fits obtained at all energies. The resulting values of the coefficients A, are presented in fig. 3. The coefficients for k = 16 are nowhere significantly different from zero, showing that there is no significant 8+ strength at any of the energies at which angular distributions were measured. If the 8’ member of the band proposed by Suzuki et al. is assumed to be at E, = 21.5 MeV and to have reduced widths equal to those of the 6+ member, then the resonant contribution to the various Legendre polynomial coefficients can be estimated. Using the same channel radii as Suzuki et al., we estimate contributions to A, and A,, of about 3 mb and 13 mb respectively. Clearly, even a much weaker 8+ resonance would have produced a significant effect in the experimental A,, coefficients. The large k = 8 and k = 10 coefficients indicate that at these energies the “C(a 3 a2) reaction is dominated by 4+ and 5- strength. The behavior of the k = 14 coefficient at E, = 19.14 MeV (21.52 MeV excitation) suggests the presence of a weak 7- resonance having r 5 50 keV. There are also indications of some broad weak 7- strength at the upper end of the energy range. The angular distributions were fitted with the non-linear expansion da/dQ = I 1 a,(2L+

~)+P,(cos~)~~,

(2)

L=O

where the ~1~are complex. It was found that L,,, = 7 was required to obtain good fits at 19.14 MeV and at the highest energies. Non-linear fits were made to each angular distribution, beginning from a wide range of starting parameters. Fits having about the same minimum X2 give a range of values at each energy for the complex coefficient ~1~.The resulting range of partial cross sections 47~ICY, 1’ is shown for all energies in fig. 4. Clearly a non-zero contribution from L = 7 is needed only at 19.14 MeV and at energies above 19.6 MeV.

3 mb

2

I

0 17

18

19 E.

Fig. 4. The vertical

20

21

(MN1

lines show the range of values obtained for the L = 7 partial eq. (2) is titted to the “C(a, cQ angular distributions.

cross

section

when

286

A. D. Frawley et al. / 8’ strength

The only 7- state previously reported in 160 is a state at E, = 20.9 MeV (E, = 18.3 MeV) having a width of approximately 600 keV. It has been observed in the 12C(‘Li, t) [ref. i2)], ‘2C(6Li, d) [ref. “)I and 12C(12C, *Be) [ref. 16)] reactions. We do not see any evidence of this state in the present work. While a strong resonance having approximately the correct width is observed at E, = 18.25 MeV, it is evident from the Legendre polynomial coefficients of figs. 3 and 4 that it does not have J” = 7-. The coefficients of fig. 3 suggest a spin of 5-. The coefficients of the linear Legendre polynomial expansion, fig. 3, indicate that there is relatively little 6+ strength present. The only large feature in the A,, coefficients is at E, = 19.14 MeV, and it can be attributed to interference between the 7- resonance at 19.14 MeV and the considerable underlying 5- strength. 4. Summary Angular distributions of the “C (CI,a2)i2C*(7.66 MeV) reaction have been measured in 50 and 100 keV steps between E, = 17.3 MeV and 20.5 MeV. Analysis of the angular distributions provides strong evidence for a narrow 7- resonance in 160 at an excitation energy of 21.52 MeV. No evidence of 8+ strength is found. References I) 2) 3) 4) 5) 6) 7) 8) 9) IO) I I) 12) 13) 14) 15) 16) 17) 18) 19)

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