The field-theory model is proposed to study the electronic states near the
Fermi energy in spheroidal fullerenes. The low energy electronic wavefunctions
obey a two-dimensional Dirac equation on a spheroid with two kinds of gauge
fluxes taken into account. The first one is so-called K spin flux which
describes the exchange of two different Dirac spinors in the presence of a
conical singularity. The second flux (included in a form of the Dirac monopole
field) is a variant of the effective field approximation for elastic flow due
to twelve disclination defects through the surface of a spheroid. We consider
the case of a slightly elliptically deformed sphere which allows us to apply
the perturbation scheme. It is shown exactly how a small deformation of
spherical fullerenes provokes an appearance of fine structure in the electronic
energy spectrum as compared to the spherical case. In particular, two
quasi-zero modes in addition to the true zero mode are predicted to emerge in
spheroidal fullerenes. An additional 'hyperfine' splitting of the levels
(except the quasi-zero-mode states) is found.Comment: 9 page