Deformed Base Antisymmetrized Molecular Dynamics and its Application to ^{20}Ne

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

Nuclear Alpha-Particle Condensates

The $\alpha$-particle condensate in nuclei is a novel state described by a product state of $\alpha$'s, all with their c.o.m. in the lowest 0S orbit. We demonstrate that a typical $\alpha$-particle condensate is the Hoyle state ($E_{x}=7.65$ MeV, $0^+_2$ state in $^{12}$C), which plays a crucial role for the synthesis of $^{12}$C in the universe. The influence of antisymmentrization in the Hoyle state on the bosonic character of the $\alpha$ particle is discussed in detail. It is shown to be weak. The bosonic aspects in the Hoyle state, therefore, are predominant. It is conjectured that $\alpha$-particle condensate states also exist in heavier $n\alpha$ nuclei, like $^{16}$O, $^{20}$Ne, etc. For instance the $0^+_6$ state of $^{16}$O at $E_{x}=15.1$ MeV is identified from a theoretical analysis as being a strong candidate of a $4\alpha$ condensate. The calculated small width (34 keV) of $0^+_6$, consistent with data, lends credit to the existence of heavier Hoyle-analogue states. In non-self-conjugated nuclei such as $^{11}$B and $^{13}$C, we discuss candidates for the product states of clusters, composed of $\alpha$'s, triton's, and neutrons etc. The relationship of $\alpha$-particle condensation in finite nuclei to quartetting in symmetric nuclear matter is investigated with the help of an in-medium modified four-nucleon equation. A nonlinear order parameter equation for quartet condensation is derived and solved for $\alpha$ particle condensation in infinite nuclear matter. The strong qualitative difference with the pairing case is pointed out.Comment: 71 pages, 41 figures, review article, to be published in "Cluster in Nuclei (Lecture Notes in Physics) - Vol.2 -", ed. by C. Beck, (Springer-Verlag, Berlin, 2011