Role of virtual break-up of projectile in astrophysical fusion reactions

We study the effect of virtual Coulomb breakup, commonly known as the dipole polarizability, of the deuteron projectile on the astrophysical fusion reaction ${}^3\mathrm{He}\left(d,p\right){}^4\mathrm{He}$. We use the adiabatic approximation to estimate the potential shift due to the $E1$ transition to the continuum states in the deuteron and compute the barrier penetrability in the WKB approximation. We find that the enhancement of the penetrability due to the deuteron breakup is too small to resolve the longstanding puzzle observed in laboratory measurements that the electron screening effect is surprisingly larger than theoretical prediction based on an atomic physics model. The effect of ${}^3\mathrm{He}$ breakup in the ${}^3\mathrm{He}\left(d,p\right){}^4\mathrm{He}$ reaction, as well as the ${}^7\mathrm{Li}$ breakup in the ${}^7\mathrm{Li}\left(p,\alpha \right){}^4\mathrm{He}$ reaction is also discussed.

Figure 1

The effect of virtual Coulomb breakup of colliding nuclei on the $d+{}^3\mathrm{He}$ reaction. $f$ is the enhancement factor of penetrability due to the breakup, measured from unity. The dashed and the dotted lines show the effect of breakup of the $d$ and the ${}^3\mathrm{He}$ nuclei, respectively. The solid line is the combined effect of mutual breakup of both the projectile and the target nuclei.

Figure 2

Same as Fig. 1, but for the effect of ${}^7\mathrm{Li}$ breakup on the $p+{}^7\mathrm{Li}$ reaction.