Volume 69B, number 4 PHYSICS LETTERS 29 August 1977

YRAST LEVELS IN 27 Al SUGGESTED BY RESONANCE

STRUCTURE IN THE l2 C( l5 N, a) REACTION *

J. GOMEZ DEL CAMPO, J.L.C. FORD Jr. and R.L. ROBINSON Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830, USA

and

M.E. ORTIZ, A. DACAL and E. ANDRADE Instituto de Fisica, Universidad National Autonoma de Mexico, Mexico 20, D.F., Mexico

Received 11 June 1977

A large number of correlated resonances with -400 keV (cm.) widths were observed in addition to statistical fluctuations in the 12C(15 N,cu) reaction. The resonant portion of the cross sections suggest the population of high- spin levels close to the yrast line of the compound nucleus.

Resonances have been observed in the excitation functions for a number of heavy ion reactions, although most notably in the exit channels of 12C + 12C and

12C t l60 [e.g. 1,2]. Explanations of the presence of nonstatistical structure in such reactions have been offered in terms of quasi-molecular states [ 1,2] and intermediate structure possibly requiring a-particle nuclei in the entrance channel [2,3]. In this paper we report the observation of many strong resonances in the 12C(15N,o)23Na reaction as well. However, in this case we suggest that the nonstatistical resonances may be due to the strong population of non-over- lapping states near the yrast line in the compound nu-

cleus 27Al. These resonances and their interpretation in terms of Hauser-Feshbach and resonance analyses are discussed.

A total of 30 excitation functions were measured in 200 keV intervals with 80 keV resolution for bom- barding energies between 21.4 and 39.0 MeV, at a lab- oratory angle of 7”. Excitation functions for an additi- onal 11 states from 9.5 to 12.2 MeV in 23Na were measured over a more limited range of bombarding energies. These measurements covering a wide interval of incident as well as excitation energies then yield a very large sample (containing over 300 cross-section

* Research sponsored by the U.S. Energy Research and Devel- opment Administration under contract with Union Carbid Corporation.

values) for comparison with the statistical model. Typical measured excitation functions are indicated

by the solid lines in fig. 1. Despite the rapid fluctua- tions observed in the data, and expected from the sta- tistical model to be strongest at a forward angle such as 7’ (lab), a second underlying structure is neverthe- less apparent. For example, the excitation function for the 3.67 MeV state shows two resonances about 500 keV wide between 10 and 12 MeV (c.m.). A measurement of the coherence width by the conven- tional peak counting method [e.g. 41 yields a width, F 2f

, of 1.58 keV at an excitation energy of 32 MeV in Al, a value in reasonable agreement with systematics

for this mass region [S]. However, the autocorrelation functions for many of the levels display a structure which can be fitted by two overlapping Lorentzians with widths of about Ff and 3I’,, respectively.

In order to emphasize the underlying resonant structure, a running average of the data was performed using an averaging interval, A, equal to three times the coherence width. The averaged cross sections are given by dashed curves in fig. 1. In this figure, corre- lated resonances can be observed at various incident energies for the different particle groups. Correlations occur, for example, at 10.7 MeV (c.m.) between the 0,0.44 and 3.67 MeV states, and at 15.1 MeV between the 3.67, 6.58, 7.98, and 9.04 MeV states. The bot- tom curve of the figure shows that the resonances dis-

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Volume 69B, number 4 PHYSICS LETTERS 29 August 1977

averaged to obtain values for the average resonant en- ergy, E, and the standard deviation, AE, which was typically 0.1 MeV. Fig. 3a displays the number of such o-particle groups as histograms whose positions and widths correspond to i? + AE. The observed struc- ture then shown large widths, *3I’r, and large devia- tions from the average cross sections as well as the cor- related maxima and these three features of the data appear unlikely to be due to statistical fluctuations alone.

The solid and dashed lines drawn through the aver- aged excitation functions displayed in fig. 2 are the results of Hauser-Feshbach (HF) calculations with and without the effects of angular momentum cutoff. The values for the angular momentum cutoff, J,, were obtained by fitting Hauser-Feshbach calculations to regions of the excitation functions of known spin states where the correlated structure was absent. Such regions occur, for example, above 12 MeV (c.m.) for the 0 and 4.43 MeV states, above 13 MeV for the 2.7 MeV doublet and 4.77 MeV level, and between 13 and 15 MeV for the 0.44 MeV state. The J, values deter- mined by the procedure are given by E, = (8.7)-l J,_(J, + 1) t 16.25 MeV for excitation energies, E,, in

(2 (4 46

Fig. 3a. A histogram indicating the number of correlated states observed as a function of the incident energy (c.m,). See text for further explanation. Fig. 3b. The sum of the yields, or resonance strengths, for the correlated resonances of fig. 3a. Solid and dashed lines are calculated theoretical resonance cross sections with the spins and parities indicated.

27Al between 27.3 and 34.5 MeV; for this energy

range one has J, > 2 l/2. In general, the Hauser- Feshbach calculations gave reasonable fits to nonres- onant regions of the excitation functions or pass

through the minima in the resonant structure, and thus adequately account for the portion of the ob- served cross sections due to statistical fluctuations. However, the average cross sections are not predicted by the Hauser-Feshbach calculations (for example, the experimental ratio of the average cross sections for the 2.98 MeV and 0 MeV states is about two, see fig. 2, while those calculated, with or without cutoff are less than one).

Angular momentum considerations may account for the origin of the resonant structure. When the com- pound nucleus 27 Al is formed at an excitation energy of 32.8 MeV the grazing angular momentum in the en- trance channel is 2512, whereas the value of Jc is 2312. An extrapolation from the known, low-lying, yrast states according to the relation Ej a J(J + 1) yields a value of 27/2 for the yrast state near this excitation

energy if a constant moment of inertia is assumed. Ac- tually, this value represents a lower limit since the mo- ment of inertia has been shown to increase for the neighboring nuclei 26Al [6] and 28Si [4]. Therefore, in the present experiment we are in the vicinity of, or approaching the members of the yrast line at high ex- citation energies in 27Al.

The resonance ?t?en’ghts may yield the compound nuclear spins involved, as demonstrated by analyses of (a,~) reactions [7,8]. Fig. 3b shows the resonant areas as a funcion of the c.m. energy. The solid and dashed curves in fig. 3b correspond to calculations (for posi- tive and negative parity states) in which the particle widths in the entrance and exit channels have been re- placed by the appropriate optical model transmission coefficients [7].

It is necessary to normalize the set of calculated curves to the data at one point. Only a narrow range of spin values can contribute to the observed resonant structure. Spins less than Jc will be included in the Hauser-Feshbach calculations and the contribution of levels with these angular momentum values will be in the general background underlying the resonances. If the total angular momentum is greater than 27/2 then the transmission coefficients are vanishingly small. Consequently, only spin values between 2 l/2 and 27/2 can produce resonances since these levels are

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Volume 69B, number 4 PHYSICS LETTERS 29 August 1977

close to the yrast line and, therefore, have widths com- parable to, or less than, the level spacing. Only normal-

izing the curve for 23/2+ to the second resonance at 10.7 MeV provides the satisfactory fit to all the data seen in fig. 3b. Note that the curve for each J value terminates at the excitation energy calculated from the equation for E, as a function of J, since for higher energies overlapping resonances are to be expected.

Therefore, the observed 12C(15N, ol) resonances ap- pear associated with a limited range of high spin values near the yrast line of 27 Al. If the resonances at inci- dent energies of 10.4 and 16.0 MeV (c.m.) are inter- preted as due to 23/2+ and 27/2+ levels, then the ex- citation energies of these states, 27.6 and 33.2 MeV, respectively, are close to those predicted by an extra- polation of the ground-state band. Thus the curves in fig. 3b suggest a value for the spin of the level in 27Al

corresponding to each observed resonance. Angular distribution measurements may help determine the

spins involved and so test the validity of conclusions based on the resonance strengths of heavy-ion reac- tions and their energy dependence.

References

[ 1 ] D.A. Bromley, PIOC. Second Intern. Conf. on Clustering Phenomena in nuclei, College Park, Maryland, 1975, p. 465.

[2] H. Feshbach, J. de Phys., Colloq. 37 (1976) C5-177. [3] H. Voit et al., Phys. Rev. Cl0 (1974) 1331. [4] J. Gomez de1 Campo et al., Nucl. Phys. A262 (1976) 125. [5] D. Shapira, R.G. Stokstad and D.A. Bromley, Phys. Rev.

Cl0 (1974) 1063. [6] R.G. Stokstad et al., Phys. Rev. Lett. 36 (1976) 1529. [7] E. Sheldon et al., Proc. Intern. Conf. on Statistical prop-

erties of nuclei, ed. J.B. Garg (Plenum, New York, 1971) p. 121.

(81 W.A. Schier et al., Nucl. Phys. A254 (1975) 80.

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