Muon transfer from muonic hydrogen to atomic oxygen and nitrogen

The results of diabatic hyperspherical close-coupling calculations are presented for the charge exchange of a negative muon from muonic hydrogen to oxygen and nitrogen for collision energies from ${10}^{-3}$ to ${10}^3\mathrm{eV}$. It is shown that converged results can be obtained using a much smaller number of channels than in the traditional adiabatic approach. For the energy range below 10 eV our results for nitrogen are in good agreements with the available experimental data and the recent calculations within hyperspherical elliptic coordinates. However, discrepancies were found in the case of oxygen, where a $p$-wave shape resonance is shown to contribute significantly to the cross sections. We show that for oxygen the $p$-wave resonance extends to a large volume and is sensitive to the many-body effect. Calculations including outer screening of the oxygen atom have been performed to illustrate the importance of this effect.

Figure 1

(Color online) Thomas-Fermi effective charge for oxygen and nitrogen as function of the distance from the nucleus. The fittings to Eq. (12) are also shown as ▵ (oxygen) and + (nitrogen).

Figure 2

(Color online) $J=0$ diabatic potential curves for $p\mu \left(1s\right)\text{−}{\mathrm{O}}^{8+}$ up to the ${\left(\mathrm{O}\mu \right)}^{7+}(n=8)$ threshold.

Figure 3

(Color online) Partial and total muon-capture probability, as function of collision energy, in $p\mu \left(1\mathrm{s}\right)\text{−}{\mathrm{O}}^{8+}$ for $J=0$.

Figure 4

(Color online) Partial-wave muon-transfer rate in $p\mu \left(1s\right)\text{−}{\mathrm{O}}^{8+}$ as function of collision energy below 10 eV.

Figure 5

(Color online) Comparison between 56-channel and five-channel calculations for $p\mu \left(1s\right)\text{−}{\mathrm{O}}^{8+}$ at low energies.

Figure 6

(Color online) Comparison of transfer rates for the cases with and without Thomas-Fermi screening in oxygen.

Figure 7

(Color online) Similar to Fig. 4, but for nitrogen. Total transfer rate is also shown [lighter (brown) curves].

Figure 8

(Color online) Similar to Fig. 6, but for nitrogen.

Figure 9

(Color online) High-energy convergence test for $p\mu \left(1s\right)\text{−}{\mathrm{O}}^{8+}$.

Figure 10

(Color online) Total muon-transfer rate for $p\mu \left(1s\right)$ colliding with oxygen and nitrogen at collision energies below 1 keV.