Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics

In order to study the structure of excited states we perform a variational calculation after spin parity projection (VAP) within the framework of Antisymmetrized Molecular Dynamics (AMD). The framework is proven to be a new powerful approach for the study of the various structures of excited states because it is free from model assumptions such as inert cores, existence of clusters, and the axial symmetry. By using finite range interactions with a density dependent term we reproduce well all the energy levels below 15 MeV in $^{12}$C. This is the first theoretical model that reproduces many $E2$ transition rates and $\beta$ decays to $^{12}$C successfully.