The Berry Phase and Diabolic Pair Transfer in Rotating Nuclei

A new manifestation of the Berry-Phase is presented in the theory of fast rotating superfluid nuclei: Diabolic Pair Transfer, i.e. oscillations of the pair transfer matrix elements as a function of the angular velocity, is shown to be the direct consequence the Berry-Phase, giving a non-trivial contribution a t the diabolical points of cranked Hartree-Fock-Bogoliubov (HFB) spectra. Considering a general Hamiltonian H(X,w, ...), which depends on more than one parameters X,o,... Berry discovered recently1), that a quantum system described as an eigenstate of this Hamiltonian, acquires a topological phase factor exp{i.d(C)>, when transported adiabatically around a path C in parameter space. This phase is of special importance in cases where the path includes a so called diabolical point, i.e. a point' in parameter space where two eigen energy surfaces E1(X,w) and E,(h,u) with the same symmetries of the Hamiltonian touch each other, as indicated schematically in Fig.1. These points are exceptional points in the sense, that they violate the no crossing rule of von Neumann and Wigner2)