Analysis of gamma-ray energies for 56 excited superdeformed rotational bands of nuclei of lanthanons La to Dy and of Hg, Tl, and Pb on the basis of the two-revolving-cluster model, with evaluation of moments of inertia and radii of revolution and assignment of nucleonic compositions to the clusters and the central sphere.

Abstract

Analysis of the vray energies of 28 excited superdeformed bands of lanthanon nuclei by application of the two-revolving-cluster model yields the result that the central sphere for all 28 has the semimagc-magic composition p4n-", with the range p8n'2 to p'4n'8 for the clusters and the radius of revolution increasing from 7.31 to 7.76 fin. Similar analysis of 28 excited bands of Hg, Tl, and Pb nuclei leads to p56n82 (semimagic-magic) for the central sphere of 24 bands, p64n82 (semimagic-magic) for 2, and p"n9' (doubly semimagic) for 2, with cluster range p8n'2 to p'4n"6 and values of the radius of revolution from 8.70 to 8.92 fm for 26 bands and 9.2 fm for 2.The first discussion of excited rotational bands of nuclei corresponding to superdeformed structures that I know about is that of Morinaga (1), who discussed bands in 160 and 24Mgwith unusually large values of the moment of inertia, suggested that they corresponded to the linear sequences a-aa-a and a-a-a-a-a-a, respectively, of a particles, and surmised that 12C and 20Ne should have similar excited bands. It is now known that his structures do not apply to the bands that he discussed: the 160 band corresponds to revolution of a helion about 12C, and the 24Mg band corresponds to revolution of two helions about 160. It is also now known that spheron-spheron distances are about 3.6 + 0.4 fm. An excited 0+ to 6+ band for 160 of 16.75 to 19.35 MeV corresponds to the linear structure (2, 3) with a-a = 4.0 fm, and a recently observed (4) excited band of 24Mg beginning at 32.5 MeV gives a moment of inertia of 950 Da fm2 and a-a = 3.7 fm for a linear arrangement of six helions. In 1965 I suggested that the fission of U, Pu, and heavier nuclei involves an intermediate superprolate structure (5), and a similar suggestion was made in 1966 by Strutinsky (6) on the basis of the double-humped potential function calculated by his microscopic-macroscopic method. An excited superdeformed band of 66Dy was reported in 1968 by Twin et al. (7), and during later years Twin et al. and many other investigators reported many more for lanthanon nuclei and isotopes of Hg, Tl, and Pb. A review article giving the -ray energies for 56 excited superdeformed bands has been compiled by Han and Wu (8). Ground-State-Band Superdeformed NucleiA few years ago, while I was calculating moments of inertia (I) for the levels J = 2+, 4+, 6+,. . . of the ground-state bands of the even-even lanthanon nuclei and assigning values ofthe nucleon number ofthe single revolving cluster to these levels, I noticed that at large values ofJ, usually beginning at 12+ to 20+, the values of the moment of inertia became too large to be explained by a single cluster revolving about a central sphere at a radius compatible with the known nuclear dimensions. The values could be accounted for, however, by the assumption that there has occurred a transition to a superdeformed structure consisting of a central sphere with two clusters, on opposite sides, revolving about it. The properties of 35 such ground-state two-...

Empirical evidence for magic numbers of superdeformed shapes

“…[7,8]. In the past, much attention has been paid to the SD bands in the A = 150 mass region, where 152 Dy (Z = 66, N = 86) has been used as a doubly magic core to obtain some of these unique features such as the incremental alignment and the identical band nature of the SD bands [9][10][11][12]. An empirical analysis of the SD bands [13], based on the dynamical features of a semiclassical analysis of the cranking and the particle rotor models [14,15], also pointed out many general features such as the rigid-body nature of the moment of inertia and a negative alignment.…”