A Boson exchange approach for Helium Burning Stars

Theodoros Depastas; Aldo Bonasera

A Boson exchange approach for Helium Burning Stars

Theodoros Depastas, Aldo Bonasera

Abstract

Helium burning plays a key role in the hierarchy of stellar nucleosynthesis and evolution, as the archetype of a bosonic 3-body system. Here, we examine the kinetic and nuclear aspects of the 3$α$ reaction, under the auspices of the Thomas-Efimov theorem. Due to the 92.08 keV ground state of $^8$Be, multiple $α$-cluster resonances appear especially at the lowest temperature (Thomas State), while with increasing temperature the system is dominated by the Hoyle/Efimov state. We extend our previous methodology for the sequential channel to describe the direct mechanism, that results in an equilateral geometry similar to the Thomas state. This is accomplished by developing a general approach to the N-body scattering, via successive particle-exchanging 2-body collisions, which eliminates long range Coulomb complications, in a similar manner to the Thomas-Efimov mechanism. We furthermore, discuss the e$^+$e$^-$ decay of the compound state with a perturbation based methodology. Due to the symmetry of the system and the resulting reaction rates, we favor the E0 decay scheme over the E2. The E0 reaction rates obey all the available astrophysical and nuclear constraints and are compared to theoretical data from the literature, whose limitations are discussed. Our extended methodology provides a physically sound description of the debated low temperature region.

A Boson exchange approach for Helium Burning Stars

Abstract

Helium burning plays a key role in the hierarchy of stellar nucleosynthesis and evolution, as the archetype of a bosonic 3-body system. Here, we examine the kinetic and nuclear aspects of the 3

reaction, under the auspices of the Thomas-Efimov theorem. Due to the 92.08 keV ground state of

Be, multiple

-cluster resonances appear especially at the lowest temperature (Thomas State), while with increasing temperature the system is dominated by the Hoyle/Efimov state. We extend our previous methodology for the sequential channel to describe the direct mechanism, that results in an equilateral geometry similar to the Thomas state. This is accomplished by developing a general approach to the N-body scattering, via successive particle-exchanging 2-body collisions, which eliminates long range Coulomb complications, in a similar manner to the Thomas-Efimov mechanism. We furthermore, discuss the e

decay of the compound state with a perturbation based methodology. Due to the symmetry of the system and the resulting reaction rates, we favor the E0 decay scheme over the E2. The E0 reaction rates obey all the available astrophysical and nuclear constraints and are compared to theoretical data from the literature, whose limitations are discussed. Our extended methodology provides a physically sound description of the debated low temperature region.

Paper Structure (22 equations, 5 figures)

This paper contains 22 equations, 5 figures.

Figures (5)

Figure 1: (Color online) Diagrammatic representations of the Thomas (left panel) and Efimov (right panel) mechanisms. The vertices ($V_{i=1,2,3})$ and intermediate particle trajectories are denoted for the former.
Figure 2: (Color online) The integrad quantity $\sigma_{\alpha\alpha}(E)f_{MB}(E)$ normalized by its value at $95$ keV as a function of the $\alpha-\alpha$ energy for different temperatures, according to the key. The data are obtained via the H$\alpha$C model, as described in Ref Depastas2024EPJ.
Figure 3: (Color online) The 3-body to (2+1)-body reduced reaction rate ratio as a function of stellar temperature. The numerator is calculated with either the $\gamma\gamma$ or $e^+e^-$ decays, according to the key.
Figure 4: (Color online) Total reduced reaction rate $\langle \alpha\alpha\alpha\rangle=\langle \left(2+1\right)\alpha\rangle+\langle3\alpha\rangle$ as a function of stellar temperature (top) and the same quantity normalized by the NACRE data Angulo1999 (bottom). The results of $\gamma\gamma$ and $e^+e^-$ exit channels are presented along with theoretical data from Ref.s Angulo1999Ogata2010Nguyen2013Ishikawa2013Akahori2015Suno2016, according to the key. We furthermore signify the astrophysical upper limit by Suda Suda2011. The additional $E_{min}=0$ results in the bottom panel are shown for comparison to the CDCC techniques, as explained in the text.
Figure 5: (Color online) Temperature dependence of the total reduced reaction rate as a function of stellar temperature. The results of $\gamma\gamma$ and $e^+e^-$ exit channels, as well as, theoretical data from Ref.s Ogata2010Nguyen2013Ishikawa2013Akahori2015Suno2016 and the lower Suda constraint Suda2011 are shown with similar notation to Fig. \ref{['Fig3']}.