  We show the model wavefunctions for the neutral collective modes in
fractional quantum Hall (FQH) states have simple analytic forms obtained from
judicially reducing the powers of selected pairs in the ground state Jastrow
factor. This scheme of "pair excitations" works for the magneto-roton modes of
single-component Abelian and non-Abeliean FQH states, as well as the neutral
fermion mode for the Moore-Read (MR) state. The analytic wavefunctions allow us
to compute the "quadrupole gap" of the magneto-roton mode in the thermodynamic
limit, which was previously inaccessible to the numerics. The quadrupole gap is
related to the fusion of the charges in the two-dimensional plasma picture,
extending the plasma analogy to neutral excitations. A lattice diagrammatic
method of representing these many-body wavefunctions and FQH elementary
excitations is also presented.
