Symmetries and Staggering Effects in Nuclear Rotational Spectra

Abstract

We study the fine structure of nuclear rotational spectra on the basis of both dynamical and discrete symmetry approaches. In this framework we show that the odd-even (∆I = 1) staggering effects observed in various rotational bands carry detailed information about the collective band-mixing interactions and the collective shape properties of heavy nuclei.

Staggering behavior of0+state energies in theSp(4)pairing model

“…In order to account correctly for the T = 1 mode of the pn pairing one should consider in ( 13) the E 0 energy of the odd-odd (N +1 , N −1 ) nucleus (that is, the energy of the isobaric analog state rather than its ground state energy, BE). For the remaining even-even nuclei in (10), replacing the symbol E 0 with BE is justified. In the computation of ∆, all odd-A binding energies in ( 12) and ( 13) cancel so their theoretical calculation is not required.…”

“…The ∆ relation of the gaps is a measure of the difference in the isovector pairing energy between even-even and odd-odd nuclei. For odd-odd N = Z nuclei information about ∆ is extracted via the Stg (2) 1 (i) energy filter (10). Both experimental and model estimations yield ∆ ∼ = 0 for all the odd-odd i = 0 nuclei in the 1f 7/2 shell (for example, see solid (purple) line with open squares in Figure 8 for A = 46, i = 0).…”

“…Most studies of staggering focus on two aspects of the phenomena. There are discrete angular momentum dependent oscillations of physical observables; namely, of M 1 transitions in nuclei [2] or of the energy levels themselves (e.g., in octupole [3,4,5], superdeformed [6,7,8], ground and γ [1,9,10] bands in atomic nuclei, as well as in molecular rotational bands [11]). And then there are sawtooth patterns of different physical quantities (most commonly binding energies) that track with changes in the number of particles in a system (both in nuclei [12] and in metallic clusters [13,14]).…”

“…The algebraic pairing model [33,34] we exploit is based on a fermion realization of the symplectic sp(4) algebra which is isomorphic to so (5) [35,36,37]. It includes an isovector (isospin T = 1) pairing interaction as well as a diagonal (in an isospin basis) pn isoscalar (T = 0) part.…”