Protonium formation in the $\overline{p}\text{−}\mathrm{H}$ collision at low energies by a diabatic approach

We present a diabatization technique in combination with the recently developed hyperspherical close coupling (HSCC) method. In contrast to the strict diabatization, our simple diabatization procedure transforms only sharp avoided crossings in the adiabatic hyperspherical potential curves into real crossings. With this approach, the weak collision channels can be removed from the close-coupling calculations. This method is used to study the antiproton-hydrogen collision at low energies. In the case of a scaled down (anti)proton mass, we show that a 10-channel calculation is enough to obtain converged cross sections at low energies. The results also indicate that protonium formation occurs mostly to the lowest states of the different excited protonium manifolds.

Figure 1

(Color online) Hyperspherical adiabatic potential curves $\left(J=0\right)$ for $\overline{p}\text{−}\mathrm{H}$ collisions. Only protonium manifolds $n=5,6,7$ and 8 are shown together with the entrance channel which dissociates to $\mathrm{H}\left(1s\right)$ and $\overline{p}$.

Figure 2

(Color online) Hyperspherical diabatic potential curves $\left(J=0\right)$ for $\overline{p}\text{−}\mathrm{H}$ collisions. Only protonium manifolds $n=5,6,7$ and 8 are shown together with the entrance channel which dissociates to $\mathrm{H}\left(1s\right)$ and $\overline{p}$.

Figure 3

(Color online) Diabatic channel functions of selective protonium states represented in the $(\theta ,\varphi )$ angular plane. The protonium states are the $\mid 7,1⟩$, $\mid 7,3⟩$, $\mid 7,5⟩$ and $\mid 7,7⟩$ states of the $n=7$ manifold. The hyperradius is fixed at $100\text{a.u.}$

Figure 4

(Color online) Evolution of the $\mathrm{H}\left(1s\right)$ and $\text{Pn}\left(\mid 7,1⟩\right)$ diabatic channel functions with respect to hyperradius.

Figure 5

(Color online) Radial couplings between some protonium channels as functions of hyperradius.

Figure 6

(Color online) Main hyperspherical diabatic potential curves for $\overline{p}\text{−}\mathrm{H}$ included in the 10-channel calculation. The 6 channels which dissociate to the two lowest protonium states of manifolds $n=6,7$ and 8 are shown together with the $\mathrm{H}\left(1s\right)$ entrance channel.

Figure 7

(Color online) Protonium formation cross sections time the velocity obtained by a 10-channel calculation, as functions of the antiproton kinetic energy. The total protonium formation and elastic cross sections are also shown.