Time-dependent approach to three-body rearrangement collisions: Application to the capture of heavy negatively charged particles by hydrogen atoms

We present a theoretical method for Coulomb three-body rearrangement collisions solving a Chew-Goldberger-type integral equation directly. The scattering boundary condition is automatically satisfied by adiabatically switching on the interaction between the projectile and hydrogen atom. Hence the outgoing wave function is obtained without the tedious procedure of adjusting the total wave function in the asymptotic region. All the dynamical information can be derived from the outgoing wave function obtained on pseudospectral grids numerically. Taking ${\mu }^{-}+\mathrm{H}\left(1s\right)$ and $\overline{p}+\mathrm{H}\left(1s\right)$ collisions as examples, we demonstrate the usefulness and powerfulness of the method and present the state-specified capture cross sections of heavy negatively charged particles by hydrogen atoms. The convergence and accuracy of the numerical procedure are examined with sufficient care.

Figure 1

(Color online) Muon-capture cross sections calculated by the three methods (see the text) as functions of the propagation time $\tau$ for $L=10$ and $E_c=2.0\mathrm{eV}$.

Figure 2

(Color online) $n$-dependent muon-capture cross sections and channel contributions of different $l_e$ for $L=10$ and $E_c=2.0\mathrm{eV}$.

Figure 3

(Color online) Antiproton-capture cross sections calculated by the $T$ method and the C1 method as functions of the propagation time $\tau$ for $L=25$ and $E_c=2.72\mathrm{eV}$.

Figure 4

(Color online) $n$-dependent antiproton-capture cross sections and the channel contributions of different $l_e$ for $L=25$ and $E_c=2.72\mathrm{eV}$.

Figure 5

(Color online) Two-dimensional plot of the total wave function [${\mid {\Psi }^{+}\left(0\right)\mid }^2$, see Eq. (7)] for $L=10$, $E_c=2.0\mathrm{eV}$, and $l_e=0$.

Figure 6

(Color online) Total muon-capture cross sections (open circles) and antiproton-capture cross sections (filled circles). The total muon-capture cross sections calculated by Cohen [15] (open squares) and Sakimoto [2] (filled squares) are also plotted.

Figure 7

(Color online) Total angular momentum $L$-dependent muon-capture cross sections normalized to the total capture cross sections at the incident energies of 2.0, 4.0, 6.0, 8.0, and $10.0\mathrm{eV}$.

Figure 8

(Color online) Angular momentum $l$-dependent muon-capture cross sections normalized to the total capture cross sections at the incident energies of 2.0, 4.0, 6.0, 8.0, and $10.0\mathrm{eV}$.

Figure 9

(Color online) Principle quantum number $n$-dependent muon-capture cross sections normalized to the total capture cross section at the incident energies of 2.0, 4.0, 6.0, 8.0, and $10.0\mathrm{eV}$.

Figure 10

(Color online) $n$- and $l$-dependent muon-capture cross sections at $10\mathrm{eV}$ incident energy.