Spontaneous vacuum decay in low-energy collisions of heavy nuclei beyond the monopole approximation

The problem of spontaneous vacuum decay in low-energy collisions of heavy nuclei is considered beyond the scope of the monopole approximation. The time-dependent Dirac equation is solved in a rotating coordinate system with $z$-axis directed along the internuclear line and the origin placed at the center of mass. The probabilities of electron-positron pair creation and the positron energy spectra are calculated in the approximation neglecting the rotational coupling. The two-center potential is expanded over spherical harmonics and the convergence with respect to the number of terms in this expansion is studied. The results show that taking into account the two-center potential instead of its spherically symmetric part preserves all the signatures of the transition to the supercritical regime that have been found in the framework of the monopole approximation and even enhances some of them.

Figure 1

Total pair-creation probability as a function of $\eta$ with $R_{\min }=17.5\mathrm{fm}$. Solid blue lines depict results obtained with $|\kappa {|}_{\max }=3$, dashed orange curves correspond to the monopole-approximation results.

Figure 2

Derivative of the pair-creation probability $dP/d\eta$ at $\eta =1$ as a function of $Z=Z_1=Z_2$.

Figure 3

Energy spectra of the positrons emitted in head-on ${\mathrm{U}}^{92+}‐{\mathrm{U}}^{92+}$ collisions with energy $E=6.218\mathrm{MeV}/\mathrm{u}$. Maltsev et al. refers to [46].

Figure 4

Positron spectra for the symmetric collisions with $Z=Z_1=Z_2=84–96$ at $R_{\min }=17.5\mathrm{fm}$ and $\eta =E/E_0=1$, 1.1, 1.2.