Analysis of previous microscopic calculations for the second<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mn>0</mml:mn></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>state in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow/><mml:mrow><mml:mn>12</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mi mathvariant="normal">C</mml:mi></mml:math>in terms of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>3</mml:mn><mml:mo>−</mml:mo><mml:mi>α</mml:mi></mml:math>particle Bose-condensed state

The wave function of the second ${0}^{+}$ state of ${}^{12}\mathrm{C},$ which was obtained a long time ago by solving the microscopic $3\ensuremath{\alpha}$ problem, is shown to be almost completely equivalent to the wave function of the $3\ensuremath{\alpha}$ condensed state, which has been proposed recently by the present authors. This equivalence of the wave functions is shown to hold in two cases where different effective two-nucleon forces are adopted. This finding gives strong support for interpreting the second ${0}^{+}$ state of ${}^{12}\mathrm{C},$ which is the key state for the synthesis of ${}^{12}\mathrm{C}$ in stars (``Hoyle'' state), and which is one of the typical mysterious ${0}^{+}$ states in light nuclei, as a gaslike structure of three $\ensuremath{\alpha}$ particles, Bose condensed into an identical s-wave function.