Electron-positron pair creation in low-energy collisions of heavy bare nuclei

A method for calculations of electron-positron pair-creation probabilities in low-energy heavy-ion collisions is developed. The approach is based on the propagation of all one-electron states via the numerical solving of the time-dependent Dirac equation in the monopole approximation. The electron wave functions are represented as finite sums of basis functions constructed from B-splines using the dual-kinetic-balance technique. The calculations of the created particle numbers and the positron energy spectra are performed for the collisions of bare nuclei at the energies near the Coulomb barrier with the Rutherford trajectory and for different values of the nuclear charge and the impact parameter. To examine the role of the spontaneous pair creation, the collisions with a modified velocity and with a time delay are also considered. The obtained results are compared with the previous calculations and the possibility of observation of the spontaneous pair creation is discussed.

Figure 1

Positron energy spectrum for the $\mathrm{U}-\mathrm{U}$ collision at energy $E_{\mathrm{cm}}=740$ MeV for the different values of the impact parameter $b$.

Figure 2

Positron energy spectrum for the $\mathrm{Fr}-\mathrm{Fr},\mathrm{U}-\mathrm{U}$, and $\mathrm{Db}-\mathrm{Db}$ head-on collisions at energies 674.5, 740, and 928.4 MeV, respectively.

Figure 3

Number of created pairs $P$ in the head-on collision of identical nuclei as a function of the nuclear charge numbers $Z_A=Z_B=Z$ for the projectile energy $E_0=6.2$ MeV/u in the nuclear rest frame.

Figure 4

Number of created pairs $P$ in the head-on collision with the artificial trajectory $R_{\alpha }\left(t\right)$, defined by Eq. (31), as a function of the dimensionless parameter $\alpha$. The solid line indicates the results for the $\mathrm{Fr}-\mathrm{Fr}$ collision at $E_{\mathrm{cm}}=674.5$ MeV; the dashed line corresponds to the $\mathrm{U}-\mathrm{U}$ collision at $E_{\mathrm{cm}}=740$ MeV.

Figure 5

Positron energy spectrum for the $\mathrm{Fr}-\mathrm{Fr}$ head-on collision at $E_{\mathrm{cm}}=674.5$ MeV with different time delays $T$.

Figure 6

Positron energy spectrum for the $\mathrm{U}-\mathrm{U}$ head-on collision at $E_{\mathrm{cm}}=740$ MeV with different time delays $T$.