Single $\alpha$-particle orbits and Bose-Einstein condensation in ${}^{12}$C

Abstract

The $\alpha$-bosonic properties such as single-$\alpha$ orbits and occupation numbers in $J^{\pi }$=$0^{+}$, $2^{+}$, $1^{-}$ and $3^{-}$ states of ${}^{12}$C around the $3\alpha$ threshold are investigated with the semi-microscopic $3\alpha$ cluster model. As in other studies, we found that the $0_2^{+}$ ($2_2^{+}$) state has dilute-$3\alpha$-condensate-like structure in which the $\alpha$ particle is occupied in the single $S$ ($D$) orbit with about 70% (80%) probability. The radial behaviors of the single-$\alpha$ orbits as well as the occupation numbers are discussed in detail in comparison with those for the $0_1^{+}$ and $2_1^{+}$ states together with the $1_1^{-}$ and $3_1^{-}$ states.

32 pages, 13 figures