Staggering behavior of the low-lying excited states of even-even nuclei in aSp(4,R)classification scheme

Abstract

We implement a high order discrete derivative analysis of the low lying collective energies of even-even nuclei with respect to the total number of valence nucleon pairs N in the framework of F -spin multiplets appearing in an algebraic sp(4, R) classification scheme. We find that for the nuclei of any given F -multiplet the respective experimental energies exhibit a ∆N = 2 staggering behavior and for the nuclei of two united neighboring F -multiplets well pronounced ∆N = 1 staggering patterns are observed. Those effects have been reproduced successfully through a generalized sp(4, R) model energy expression and explained in terms of the step-like changes in collective modes within the F -multiplets and the alternation of the F -spin projection in the united neighboring multiplets. On this basis we suggest that the observed ∆N = 2 and ∆N = 1 staggering effects carry detailed information about the respective systematic manifestation of both high order α particle-like quartetting of nucleons and proton (neutron) pairing interaction in nuclei.PACS number(s):21.10.Re, 21.60.Fw

Systematics in the structure of low-lying, nonyrast bandhead configurations of strongly deformed nuclei

“…Here we review systematics in the structure of key levels (bandheads of the ␥ and ␤ bands relative to that of the ground state) in the lowenergy spectra of a series of heavy deformed nuclei that differ from one another by ␣-particle-like structures. Such an approach has been tested empirically and shown to be convenient for a unified description of the low-lying yrast energies of the even-even nuclei [5,6]. The K =0 2 + ͑␤͒ and K =2 ␥ + ͑␥͒ bandheads show some rather sharp oscillations, in contrast with the smooth and periodic behavior of the yrast bandhead configuration, especially in regions with clearly observed rotational bands.…”

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

“…In nuclear structure physics, staggering behavior of the second type is observed when one changes in a systematic way the usual nuclear characteristics such as proton (Z), neutron (N ), mass (A) or isospin projection (|Z − N |/2) numbers. Examples of these nuclear phenomena include odd-even mass staggering (OEMS) [1,15,16,17,18,19,20,21], odd-even staggering in isotope/isotone shifts [22,23], and zigzag patterns of the first excited 2 + 1 state energies in even-even nuclei [24]. The staggering behavior of a nuclear observable is most easily seen when discrete derivatives of second or higher order in its variable(s) are considered.…”