Spin assignments for 16O + 12C resonances at low energies

Volume

72B, number

3

PHYSICS

SPIN ASSIGNMENTS

LETTERS

2 January

FOR l6 0 + 12C RESONANCES

1978

AT LOW ENERGIES

W TREU, W GALSTER and H FROHLICH Phyakalmhes

Instrtut der Umversltat Erlangen-Nurnberg,

8520 Erlangen, W Germany

and H VOIT and P DUCK * Cyclotron Institute,

Texas A & A4 Unwerslty, College Statlon, TX 77843, USA Received

Spm and parity

values have been determmed

7 October

for subCoulomb

The reactions l2 C + 12C and 160 + 12C are the only reactions for which resonances have been found at ener@es m the vlcmlty of the Coulomb barrier To understand these resonances it 1s essential to know more than the resonance energies In particular J” values are important for comparison with predlctlons of several model calculations [l-5] Extensive work has been done very recently m several laboratories [6-81 to pm down the unknown Jr values of the 12C + 12C resonances In the case of the 160 + 12C reaction no P assignments have been made so far even though there exist calculations which predict these values Therefore a Jn determination for several 160 + 12C sub-Coulomb resonances has been carried out, the results are reported m this letter The reaction used for this mvestlgatlon was 12C(160, .)24Mg Excitation functions of transitions to states of the residual nucleus 24Mg were measured at several angles simultaneously Thus angle-integrated excitation functions could be obtained which in turn were used m order to determine resonances m the 160 + 12C system Those excitation functions m particular were chosen which contam contrlbutlons from many smgle transitions Finally angular dlstrlbutlons of the transitions to the ground state and the O+ 6 43 MeV state m 24Mg measured at or close to the resonance energies were used for the J” assignments The measurements were performed at the Erlangen EN tandem accelerator The experimental technique * Permanent

address Erlangen-Nurnberg,

Physlkahsches Instltut der Umversitat 8520 Erlangen, W Germany

1977

resonances

of the 160 + 12C system

was the same as used for the 7 assignments to the 12C + 12C resonances described in ref [8] In contrast to the latter case, however, an attempt was made to measure angular dlstrlbutlons m the full angular range between ecrn = 0” and 180” m order to get (1) angle-integrated cross sections and (11) reliable J” assignments This could be done, however, on1 for the transitions to the first four excited states m x4 Mg In these cases measurements were performed at 30 angles between = 6” and 17.5” (15 of which were measured simulI9 &?ously) For the higher-lying states m 24Mg no data could be taken at large backward angles due to the rather low energy of the emerging a-particles In order to get angle-integrated cross sections for these states It thus had to be assumed that the angular dlstrlbutlons exhlblt symmetry about Bc m = 90” This assumption 1s not strictly fulfdled as can be seen m fig 2 It was checked, however, for the transitions to the first four states (where complete angular dlstrlbutlons were taken) that this symmetry assumption does not change the resonance pattern of the correspondmg excitation functions slgmflcantly compared with excltatlon functions obtained from an integration between Bc m = 0” and 180” Angular dlstrlbutlons were measured m the energy range E, m = 6 O-9 5 MeV m steps of m, m = 86 keV The 12C targets used were between 15 and 40 pg/cm2 thick The thickness was measured before and after the exposure of the target to the beam The excitation functions given below contam corrections to the energy and the absolute cross sections due to the 315

Volume

72B, number

40-

z $302 ,I m 30-

3

PHYSICS

LETTERS

2 January

measured at or close to the resonance energies given m table 1 These angular dlstrlbutlons have been used m order to determine .P values In each particular case, the dlstrlbutlon for that state was chosen whose excltatlon function shows a pronounced resonance behavlour Fig 2 also contains Legendre polynomials pi and Legendre polynomial fits using the expression Lmax

20I

1978

40)

a

c L=O

2 A&COSB)

)

15wth AL bemg complex coefficients

IO0

The values for

L max were gradually increased until no Improvement of the fit could be achieved Both Lmax and the values of the AL coefficients determme the J value of the reso.

nance Table 1 contams the J” values obtained from this analysis With two exceptions they are all clear-cut 5cases The exceptions occur at the resonance energies E = 7 1 and 8 9 MeV In both cases the angular dlstryb:tlons at forward angles are well reproduced by a 6 E,-m(MeV) 6 i 6 single L value In order to account, however, for the backward angular range one needs an addltlonal L Fig 1 Nuclear structure factors for the reaction ‘*C(160, 01)24Mg The different curves contam contrlbutlons from several smgle value (given m brackets m table 1) transitions to states m 24Mg In addition table 1 contains resonance energies and P values from refs [4,5] In both cases it was assumed energy loss m the target and the gradually increasing that the resonances are due to the existence of 160 target thickness + 12C nuclear molecules In ref [4] single-particle Fig 1 shows angle-mte rated excitation functions resonances m a phenomenologlcal optical model were obtained for the reaction f 2C(160, a)24Mg. The curves determined whereas m ref [S] the effective potential contain contrlbutlons from 4,7,18 and 24 single tranwas calculated mlcroscoplcally m a very elaborate way sitions, respectively They are displayed m the form of The optical model calculation gives roughly the exact nuclear structure factors S(E) using the relation number of resonance states and m addition reproduces the observed resonance energies very nicely. The mlcroscoplc calculation falls to give a sufficient number of a(E) = S(E)E-’ T (2‘5 + l&, resonance states in the energy range in question (states with very small widths have been omitted) In any case \nth Br,being the penetrablhtles All curves exhibit a the predicted P values are m rather poor agreement resonance structure with a substantial amount of corwth the data obtained experimentally relation among them The resonance energies extracted This raises the question whether the calculations can are gven m table 1 The resonance energies are accurate still be improved or whether the assumption that all to within * 60 keV The table also contains the enerresonances are single-particle states in an effective 160 @es of resonance structures found m the y-yield excl+ 12C potential 1s too stringent It has been su ested that some of the resonances have a 12C + Q + P! C tatlon function of ref [4] The agreement between these values and the presently measured values 1s quite structure [9] In particular it has been assumed m ref [lo] that a vibrating 12C + (Y+ 12C molecule gives reasonable Fig 2 shows angular dlstrlbutlons of the transitions rise to a negative parity band m 28Sl starting shghtly above the correspondmg threshold energy Members of to the ground state and the O+ 6 43 MeV state m 24Mg

IO-

316

Volume

72B, number

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PHYSICS

LETTERS

2 January

Table 1 Resonance energies and P values determined m the present work Column 2 contams measurement The columns 3,4, 6 and 7 are theoretlcal predlctlons for the resonance ._~ ~_ E exp WV)

Etheory ~_____

present work

ref

6 7 7 7 7 8

65 69 72 76 79 84

57 10 30 66 88 19

853 8 89 9 30

[4]

ref

[4]

ret

7 77 8 12

853 87 92

resonance energies deduced from a y-yield energies and the 7 values, respectively

fl values

(McV)

6 45 6 97 7 63 7 85 8 40

[5]

present work 2+ 2+(4+) 34+ 4+ 4+ + l-(3-)

ref ____

[4]

ref

[5]

_____ 12+ 30+ 4+

13-

1-

8 84

9 29

1978

5-

6+

5-

Fig 2 Angular dlstrlbutlons of the transitlons to the ground state (ore) and the O+ 6 43 MeV state (orb) in 24Mg measured close to the resonance energies given in table 1 The solid lines are Legendre polynomials Pi or fits using the expresslon o(0) ~IXLALPLI (see text)

at or

317

Volume

72B, number

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PHYSICS

this band have been observed as resonances at Ec m 8MeVhavmgPvaluesof9-, 1l-, and 13-, respectively The low-spin members of this band have been tentatively ass1 ned to states observed as resonances m the I60 + ’ j C fusion cross section [lo] and m the 12C(160, cz)24Mg reaction, respectively [ 1 l] In the light of the present measurement the .P = 3- and 5- members of this band are located at E, m = 7 3 and 8 9 MeV A plot of these states together with the high-spm members mentioned above versus J(J + 1) gives approximately a straight lme and predicts the resonance energy for the J= land 7- members as Ec m N 6 4 and 11 0 MeV, respectively In conclusion .P values have been determined for some of the low-energy 160 + 12C resonances The comparison with predlctlons made m a strict smgleparticle model 1s rather unsatisfactory This raises as m the 12C t 12C case - the question whether the resonances observed should be explained exclusively as single-particle states or whether all kinds of simple structures (for instance l2 C + a + 12C , as mentioned above) are necessary for a satisfactory explanation = 13 7, 17Oand21

318

LETTERS

2 January

1978

This work was supported by the Deutsche Forschungsgememschaft, Bonn, W. Germany

References

[II B Imamshl, Nucl Phys A125 (1963) 33 PI J Y Park, W Scheld and W Gremer, Phys Rev Cl0 (1974) 967 [31 Y Kondo, T Matuse and Y Abe, Reports from Research Center of Nuclear Physics, Osaka Umversity, Osaka, Japan (1976), unpublished 141 B N Nagorcka and _I0 Newton, Phys Lett 41B (1972) 34 [51 D Baye and P -H Heenen, Nucl Phys A283 (1977) 176, D Baye, Nucl Phys A272 (1976) 445 [61 K A Erb et al, Phys Rev Lett 37 (1976) 670 [71 Z Basrak et al , Phys Lett 65B (1976) 119 [81 W Galster et al , Phys Rev Cl5 (1977) 950, H Volt et al, Phys Lett 67B (1977) 399 191 R Stokstad et al, Phys Rev Lett 28 (1972) 1523, K Ikeda dnd Y Suzuki, Proc 2nd Conf on Cluster phenomena m nuclei, Maryland (1975), J N Scheurer et al , Proc 2nd Conf on Cluster phenomena m nuclei, Maryland (1975) 1101 H Prohhch et al , Phys Lett 64B (1976) 408 [Ill J R Patterson et al , Nucl Phys Al65 (1971) 545