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The Δ J = 1 staggering (odd-even staggering) in octupole bands of light actinides. is found to exhibit a "beat" behaviour as a function of the angular momentum J, forcing us to revise the traditional belief that this staggering decreases gradually to, zero and then remains at this zero value. Various algebraic models (spf-Interacting Boson Model, spdf-IBM, Vector Boson Model, Nuclear Vibron Model) predict in their su(3) limits constant staggering for this case, being thus unable to describe the "beat" behaviour. An explanation of the "beat" behaviour is given in terms of two Dunham expansions (expansions in terms of powers of / ( / + 1) ) with slightly different sets of coefficients for the ground state band and the negative parity band, the difference in the values of the coefficients being attributed to Coriolis couplings to other negative parity bands. 1 I n t r o d u c t i o n Rotational nuclear spectra have been long attributed to quadrupole deforma­ tions [1], corresponding to nuclear shapes produced by the revolution of an ellipsis around its maximum or minimum axis and rotating around an axis perpendicular to their axis of symmetry. In addition, it has been suggested that octupole deformation occurs in certain regions, most notably in the light actinides [2] and in the A « 150 mass region [3], corresponding to pear-like nu­ clear shapes [4,5]. In even nuclei exhibiting octupole deformation the ground state band, which contains energy levels with Ρ = 0, 2, 4, 6, . . . , is ac­ companied by a negative parity band containing energy levels with J i r = 1~, 3~, 5", 7", — After the first few values of angular momentum / the two bands become interwoven, forming a single octupole band with levels charac­ terized by Γ 0, 1", 2 + , 3~, 4, 5", . . . [2,3]. (It should be noted, however, that in the light actinides alternative interpretations of these bands in terms of alpha clustering have been proposed [6,7].) It has been observed [8] that in octupole bands the levels with odd / and negative parity (J* = 1~, 3~, 5~, . . . ) are displaced relatively to the levels with even J and positive parity (P = 0, 2, 4, . . . ), i.e. the odd levels do not lie at the energies predicted by an E(I) = AI(I + 1) fit to the energy levels, but all of them lie systematically above or all of them lie systematically below the predicted energies. This is an example of odd-even staggering or AI = 1 staggering, the latter term due to the fact that each energy level with angular momentum i" is displaced relatively to its neighbours with angular momenta J ± 1. The Δ J = 1 staggering effect is different from the AI = 2 staggering ef­ fect recently observed [9,10] in superdeformed nuclear bands [11,12], since the AI = 2 staggering effect refers to the systematic displacement of the levels with / = 2, 6, 10, 14, . . . relatively to the levels with / = 0, 4, 8, 12, . . . , i.e. in this case the level with angular momentum / is displaced relatively to its" neighbours with angular momenta I ±2. It should be noted that the odd-even staggering in octupole bands is much larger than the relevant experimental errors, while the AI = 2 staggering effect in superdeformed nuclear bands [9,10], is of the order of the experimental errors, with only one case (the (a) band of 1 4 Gd [9]) known to show an effect outside the limits of the experimental errors. The dependence of the amplitude of the staggering effect on the angular mo­ mentum i" presents much interest. The situation up to now has as follows: 1) Algebraic models of nuclear structure appropriate for the description of octupole bands, like the spf-Interacting Boson Model (spf-IBM) with u(ll) symmetry [13], the spdf-IBM with u(16) symmetry [13,14], and the Vector Boson Model (VBM) with u(6) symmetry [15], predict in their su(3) limits AI = 1 staggering of constant amplitude, i.e. all the odd levels are raised (or lowered) by the same amount of energy with respect to the even levels [16]. In other words, AI = 1 staggering takes alternatively positive and negative values of equal absolute value as J increases. 2) Algebraic models of nuclear structure suitable for the description of al­ pha clustering effects, like the Nuclear Vibron Model (NVM) with u(6)®u(4) symmetry [6], also predict in the su(3) limit AI = 1 staggering of constant

"Beat" Patterns of Odd-Even Staggering in Octupole Bands of Light Actinides