  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 a
symplectic sp(4,R) classification scheme. We find that for the nuclei of any
given F- multiplet the respective experimental energies exhibit a Delta N=2
staggering behavior and for the nuclei of two united neighboring F- multiplets
well pronounced Delta 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 Delta
N=2 and Delta N=1 staggering effects carry detailed information about the
respective systematic manifestation of both high order alpha - particle like
quartetting of nucleons and proton (neutron) pairing interaction in nuclei.PACS
number(s):21.10.Re, 21.60.Fw
