Hyperdeformed band in the 36Ar nucleus?

Complete text of publication follows. The exotic shapes of atomic nuclei has attracted much attention recently both from the experimental and from the theoretical sides. E.g. the superdeformed (SD) shape in N = Z nuclei were observed experimentally during the last decade. In particular the SD band of the 36Ar nucleus was detected in 2000 [1]. Following the experimental observation a considerable theoretical effort has been concentrated on this band. In [2] e.g. the possible binary clusterizations of this state was studied systematically. Similar studies have been done also for the ground, and the hyperdeformed band. The latter one had been predicted from alphacluster model calculations [3]. The possible binary cluster-configurations are important not only for the better understanding of the structure of the shape isomers, but also from the viewpoint of predicting the favoured reaction channels to populate these states. This is the straightforward consequence of the close relation between the clusterization and reaction channels. (In fact, a cluster-configuration is defined by the reaction channel in which it can be observed.) One of the interesting conclusions of the work [2] was, that the hyperdeformed (HD) state of the 36Ar nucleus could be populated in the 24Mg+12C and 20Ne+16O reactions. A recent analysis of the 24Mg+12C elastic scattering [4] revealed the fact that the cross section can be described only by supposing resonances on top of the potential scattering. This very careful analysis incorporated phase-shift study, as well as Regge-pole and energy-dependent resonance calculations. The existence of five resonances have been proved, which have angular momenta 2, 4, 6, 7, 8. These states together with the resonances from the 20Ne+16O reactions seem to establish a rotational band, as shown in the upper part of Fig. 1. Its moment of inertia is in a very good agreement with that of the HD shape predicted from alpha-cluster model [3]. The similarity of the (predicted and observed) moments of inertia, and the fact that the resonances were seen in exactly those reactions, which define the preferred cluster-configurations of the HD shape suggest that the recently observed band in Fig. 1. is a good candidate for the hyperdeformed shape isomer of the 36Ar nucleus. For comparison also the ground and superdeformed bands are indicated in Fig. 1. Since a candidate for the HD state showed up, the exciting question arises if such a shape can be seen in shell-model calculation as well. In [5] we have carried out Nilssonmodel+ quasi-dynamical SU(3) calculation in order to find the answer. In this kind of study the shape isomers are obtained from the SU(3) symmetries, not from the minima of the potential energy surface. They are determined as the horizontal plateus of the stair-like functions, shown in Fig. 2. (In lighter nuclei, where detailed comparison could be made, the two method gave results in very good agreement with each other.) As it is seen in Fig. 2. in addition to the ground and superdeformed states the shell model predicts two candidates (a slightly triaxial, and a cylindrical one) for the hyperdeformed shape. The cylindrical state has exactly the same symmetry as that from the alpha-cluster model, and consequently the same moment of inertia, as well. To sum up: from cluster studies [2,3] we have predicted [2] the 24Mg+12C and 20Ne+16O channels to populate the HD state in the 36Ar nucleus. Recently a highly-deformed rotational band has been observed [4] experimentally in these reactions. The moment of inertia is in complete agreement with the prediction. Furthermore, the same state has been found in Nilsson-model calculation [5]. Therefore, we conclude that it is a good candidate for the hyperdeformed band in the 36Ar nucleus, as shown in Fig. 1. Thus it might very well be that the 36Ar nucleus is the first N = Z nucleus in which the ground, superdeformed and hyperdeformed bands have been observed.