Observation of Diabolical Points in Rapidly Rotating Nuclei

Abstract

In a recent Letter Nikam and Ring 1 describe the existence of a series of "diabolical points" associated with minimum interaction between configurations of rapidly rotating superfluid nuclei differing by two quasiparticles. They discuss the connection of the diabolical points with the chemical potential X and the angular velocity of rotation co and propose Coulomb-excitation plus pair-transfer experiments circumscribing such points to study the Berry phase factor associated with such a singularity.Experimental contours of constant neutron number in the (X n ,co) plane are shown for erbium and ytterbium isotopes in Fig. 1. The experimental determination of X n and co is discussed in Ref. 2. To obtain data for each neutron number an analysis is made for both the evenspin, positive-parity yrast sequence in even-even isotopes, labeled (;r,a) =( + ,0), and the lowest negative-parity decay sequence in the odd-mass isotopes ( -, j ). Band crossings associated with the excitation of pairs of /13/2 quasineutrons should be identical in these decay sequences. Such a plot is the experimental analog of Fig. 1 of Ref. 1.A predicted 1 feature of the diabolical points, an increased density of single-particle levels associated with vanishing interaction between states differing by two quasiparticles, is observed experimentally (see Fig. 1). Specifically, a "bunching" of experimental levels is observed at hco^0.27MeV for both TV =90-92 and 96-97. Likewise, the observed bunching of experimental levels for TV =90-92 at hco^ 0.42 MeV could be associated with a second band crossing based on the excitation of either two additional /13/2 quasineutrons or another pair of quasineutrons (e.g., negative-parity mixed h9/2 and /7/2X The band crossing observed at hco^O.42 MeV has been associated with the excitation of a pair of A11/2 quasiprotons 3 with a strong interaction between the associated zero-and two-quasiprotons levels. No increased density of quasineutron states should be associated with such a quasiproton band crossing. Therefore, the physical basis for this increased density of states at high frequency is not yet known.In conclusion, the increased density of single-quasiparticle states, i.e., a diabolical point, predicted 1 at weakly interacting band crossings associated with the excitation of pairs of quasiparticles, is observed. Such data identify candidates for Coulomb-excitation plus twoparticle-transfer studies sensitive to the Berry phase factor associated with circumscribing such a diabolical point. 40361. Discussions with P. Ring are acknowledged. I 91 93 | 95 97J 99 | -9.0 -8.5 -8.0 -7.5 Xn(MeV) FIG. 1. Empirical contours of constant neutron number, TV, as a function of X n and co. For reference, the observed rotational frequencies of the lowest /13/2 quasineutron band crossings in the even-even yrast sequences are indicated by the horizontal dashed lines labeled hco c . The experimental data sources are summarized in Refs. 2 and 4.