Stringent upper limit on the direct <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>3</mml:mn><mml:mi>α</mml:mi></mml:mrow></mml:math> decay of the Hoyle state in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">C</mml:mi><mml:mprescripts/><mml:none/><mml:mn>12</mml:mn></mml:mmultiscripts></mml:math>
R. Smith, M. Gai, M.W. Ahmed, M. Freer, H. O. U. Fynbo, D. Schweitzer, S. R. Stern
Abstract
We investigate an implication of the most recent observation of a second ${J}^{\ensuremath{\pi}}={2}^{+}$ state in $^{12}\mathrm{C}$, which was measured using the $^{12}\mathrm{C}(\ensuremath{\gamma},\ensuremath{\alpha})^{8}\mathrm{Be}_{(\mathrm{g}.\mathrm{s}.)}$ reaction. In addition to the dissociation of $^{12}\mathrm{C}$ to an $\ensuremath{\alpha}$-particle and $^{8}\mathrm{Be}$ in its ground state, a small fraction of events (2%) were identified as direct decays and decays to excited states in $^{8}\mathrm{Be}$. This allowed a limit on the direct $3\ensuremath{\alpha}$ partial decay width to be determined as ${\mathrm{\ensuremath{\Gamma}}}_{3\ensuremath{\alpha}}\phantom{\rule{0.16em}{0ex}}<\phantom{\rule{0.16em}{0ex}}32(4)$ keV. Since this ${2}^{+}$ state is predicted by all theoretical models to be a collective excitation of the Hoyle state, the $3\ensuremath{\alpha}$ partial width of the Hoyle state is calculable from the ratio of $3\ensuremath{\alpha}$ decay penetrabilities of the Hoyle and ${2}^{+}$ states. This was calculated by using the semiclassical Wenzel-Kramers-Brillouin approach and we deduce a stringent upper limit for the direct decay branching ratio of the Hoyle state of $\frac{{\mathrm{\ensuremath{\Gamma}}}_{3\ensuremath{\alpha}}}{\mathrm{\ensuremath{\Gamma}}}<5.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$, over an order of magnitude lower than previously reported. This result places the direct measurement of this rare decay mode beyond current experimental capabilities.