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A new theoretical framework named as deformed base antisymmetrized moleculardynamics that uses the localized triaxially deformed Gaussian as the singleparticle wave packet is presented. The model space enables us to describesufficiently well the deformed mean-field structure as well as the clusterstructure and their mixed structure within the same framework. The improvementover the original version of the antisymmetrized molecular dynamics which usesthe 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 ofthe $K^\pi$=$2^-$ band are confirmed and their observed properties arereproduced. 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 thesufficient description of the deformed mean-field structure in addition to thecluster structure by the present framework. From the successful description of$^{20}{\rm Ne}$, we expect that the present framework presents us with apowerful approach for the study of the coexistence and interplay of themean-field structure and the cluster structure

physical review. c. nuclear physics/physical review. c, nuclear physics

Deformed-basis antisymmetrized molecular dynamics and its application to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mi mathvariant="normal">Ne</mml:mi><mml:mprescripts /><mml:none /><mml:mrow><mml:mn>20</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow></mml:math>

Deformed-basis antisymmetrized molecular dynamics and its application toNe20