content_image/336959.jpg content_image/336957.jpg content_image/336956.jpg content_image/336955.jpg
annihilation rate is given by Γ$_{ann}$ = ( n$_{H}$ + 4 2 / $^{3}$n$_{He}$ ) σ ann p ¯ p v$_{¯}$ p with [41] 

<img src='content_image/336959.jpg'>

<img src='content_image/336957.jpg'>

where T = E − m$_{p}$ is the proton kinetic energy. We can use K$_{0}$ , δ , V$_{c}$ and L to classify the astrophysical models that are compatible with the B/C ratio into three types [8], where K$_{0}$ and δ appear in the diffusion coefficient K . And each type is characterized by the flux of anti-protons. To suppress the anti-proton flux, we choose the parameters which can produce the minimal anti-protons: δ = 0 . 85, K$_{0}$ = 0 . 0016 kpc $^{2}$Myr − $^{1}$, L =1 kpc, and V$_{c}$ = 13 . 5 km s − $^{1}$. 

Similarly, the anti-proton flux at the heliosphere boundary is formally solved to be 

where 

<img src='content_image/336956.jpg'>

<img src='content_image/336955.jpg'>

For details, please see Appendix B. 

