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Triple-alpha reaction plays an important role in nucleosynthesis heavier than 12C, because no stable nuclei exist in mass number A=5 and A=8 [1,2]. Followed by 12C(alpha,gamma)16O, it controls the C/O ratio at the end of helium burning phase in stars, and it affects up to the nucleosynthesis in supernova explosion. In contrast to 12C(alpha,gamma)16O, the 3-alpha reaction is currently well-understood through the experimental studies of the 0^+_2 state in 12C (E_r=0.379MeV) (e.g. [3,4]), and the reaction rates have been determined successfully with the sequential process via the narrow resonances: alpha+alpha= 8Be, alpha+8Be=12C.
As for the theoretical studies, formulae in hyper-spherical coordinates have been applied to tackle the 3-alpha continuum problem (e.g. [5]), and their adiabatic approaches have paved the way for a non-adiabatic full approach of [6]. The recent Faddeev method [7] and adiabatic channel function expansion method [8] may have also achieved the successful progress quantitatively. However, non-adiabatic quantum-mechanical description at off-resonant energies still seems to remain in unsolved problems. Apart from the sequential process, the 3-alpha reaction from continuum states is referred to as the direct 3-alpha process: alpha+alpha+alpha=12C. This process is generally expected to be very small, because 3-alpha almost simultaneously collide and fuse into a 12C nucleus.
In this presentation, the contribution of the direct 3-alpha process is estimated with a non-adiabatic method. In addition, Faddeev hyperspherical harmonics and R-matrix expansion method [9,10] is reviewed, and the difference between adiabatic and non-adiabatic calculations is discussed. In a result, the direct component is shown to be 10^-15 _ 10^-3 pico-barn order in the photo-disintegration cross sections of 12C (2^+_1 -> 0^+) for 0.15 < E < 0.35 MeV. This is far below the values (10^-11 _ 10^2 pico-barn) predicted by [7,8] including the long resonant tail of 0^+_2, i.e. sequential process. In spite of the large difference, the derived reaction rates at the helium burning temperatures are illustrated to be concordant with [4].
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R. Smith, et al., Phys. Rev. Lett. 119, 132502 (2017).
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[10] P. Descouvemont, Theoretical Models for Nuclear Astrophysics, (Nova Science Publishers, 2003).
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