  A new theoretical framework named as deformed base antisymmetrized molecular
dynamics that uses the localized triaxially deformed Gaussian as the single
particle wave packet is presented. The model space enables us to describe
sufficiently well the deformed mean-field structure as well as the cluster
structure and their mixed structure within the same framework. The improvement
over the original version of the antisymmetrized molecular dynamics which uses
the spherical Gaussian is verified by the application to $^{20}{\rm Ne}$
nucleus. The almost pure $\alpha + ^{16}{\rm O_{g.s}}$ cluster structure of the
$K^\pi$=$0^-$ band, the distortion of the cluster structure in the
$K^\pi$=$0^+_1$ band and the dominance of the deformed mean-field structure of
the $K^\pi$=$2^-$ band are confirmed and their observed properties are
reproduced. Especially, the intra-band E2 transition probabilities in
$K^\pi$=$0^+_1$ and $2^-$ bands are reproduced without any effective charge.
Since it has been long known that the pure $\alpha + ^{16}{\rm O}_{g.s.}$
cluster model underestimates the intra-band $E2$ transitions in the
$K^\pi$=$0^+_1$ band by about 30%, we consider that this success is due to the
sufficient description of the deformed mean-field structure in addition to the
cluster structure by the present framework. From the successful description of
$^{20}{\rm Ne}$, we expect that the present framework presents us with a
powerful approach for the study of the coexistence and interplay of the
mean-field structure and the cluster structure.
