Appearance of the Hoyle state and its breathing mode in C-12 despite strong short-range repulsion of the nucleon-nucleon potential

In the C-12 nucleus, the Hoyle state (0(2)(+) ) is considered to be an alpha-condensed state, and the 0(3)(+) state is considered to be its breathing mode. We investigated whether the alpha condensation in C-12 is realized using a microscopic 3 alpha cluster model with short-range correlation induced by nucleon-nucleon interactions, where we used the Argonne v(4)' potential having a short-range repulsion constructed from the realistic Argonne v(18) potential. Short-range correlation was treated using the unitary correlation operator method, and the Bloch-Brink wave function was adopted as a variational wave function where the alpha cluster motions were treated by generator coordinates. We obtained four 0(+) states, including short-range correlation, and analyzed them in terms of the Tohsaki-Horiuchi- Schuck-Ropke (THSR) wave function. In addition to the ordinary THSR wave function, we defined a second -order TSHR wave function to describe the 2 h over bar omega excitation of the alpha-condensed state. The 0(2)(+) state (the Hoyle state) is an alpha-condensed state mainly comprising the Be-8(0(+)) +alpha (0S-wave) configuration, and the 0(3)(+) state mainly comprises the Be-8(0(+)) + alpha (2S-wave) configuration, which is regarded as the breathing mode of the alpha condensation excited from the Hoyle state.