Single α-particle orbits and Bose-Einstein condensation in 12C

Bosonic properties of alpha particles such as single-alpha orbits and occupation numbers in J(pi) = 0(+), 2(+), 1(-) and 3(-) states of C-12 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.