Bound-free electron-positron pair production in combined Coulomb and constant crossed electromagnetic fields: a Schwinger-like process with intrinsic assistance

Abstract

The bound-free channel of electron-positron pair production by a highly charged bare ion in the presence of a strong constant crossed electromagnetic field is studied. To calculate the pair production rate, two different methods are applied and compared with each other: (i) a quasiclassical tunneling theory and (ii) a strong-field approximation, both equipped with appropriate Coulomb correction factors. The resulting rate, which depends nonperturbatively on both the Coulomb field of the ion and the constant crossed field, is calculated in a broad range of applied field strengths and nuclear charge numbers. Its functional form resembles the rate for a dynamically assisted Schwinger-like process, with the assistance being provided by the atomic binding energy of the created electron.

Figures (5)

• Figure 1: Schematic illustration of the pair production tunneling process. Initially the electron is in the negative energy continuum. $t=0, \ x=l \ \text{and} \ u=0$ denotes the tunnel entrance, as indicated, and $t=t_0, \ x=0 \ \text{and} \ u=u_0$ is associated with the final bound state.
• Figure 2: Coulomb correction factor as a function of the field strength $F$ in units of the atomic field strength $F_a=Z^3$ for different nuclear charges $Z=70, \ 90, \ 110$. The solid curves show the full correction factor from Eq. \ref{['eq:Q']} and the dashed curves depict the truncated factor in Eq. \ref{['eq:Q SFA']}.
• Figure 3: Total pair production rate as a function of the field strength $F$ in units of the atomic field strength $F_a=Z^3$ for different nuclear charges $Z=70, \ 90, \ 110$. The solid curves show the analytical expression in Eq. \ref{['eq: wpp']} and the dashed curves depict Eq. \ref{['rate_simplified']} multiplied by the truncated Coulomb correction factor \ref{['eq:Q SFA']}.
• Figure 4: Comparison of the Schwinger-like exponential function for $F=0.1 \ F_c$. The exponential of bound-free pair production \ref{['exponent_bfpp']} is depicted in red, the exponential containing the physically intuitive energy barrier \ref{['exponent_energy']} with $b=\frac{9}{4 \sqrt{2}}$ in green and \ref{['exponent_tunnel']} which includes the tunnel length in black.
• Figure 5: Normalized differential pair-production rates (a) $\frac{\text{d} R}{\text{d} ( \delta p_y )}$ and (b) $\frac{\text{d} R}{\text{d} ( \delta p_z )}$ for nuclear charges $Z=50, \ 70, \ 90, \ 110$ at $F=0.2 \ F_a$. The solid curves show the Gaussian distributions which result after Taylor expansion of the exponential in Eqs. \ref{['Rsr_integral']} and \ref{['rate']} around $\delta p_y = 0$ and $\delta p_z = 0$. The dotted lines show the differential pair production rate \ref{['Rsr_integral']} of the calculation in the WKB-theory, where one integral over the momentum has been carried out numerically. The dashed lines show the numerically resulting differential pair production rates in the SFA in \ref{['rate']} where the momentum dependent prefactor is included in the integration.