On the electron transfer in low-energy collisions of the fully-ionized muonic boron with helium atoms

In connection with recent experiments on the observation of the metastable 2s state of muonic boron (μB)⁴⁺ formed in helium with a small admixture of diborane (B₂H₆) we estimated the cross-section of the electron transfer from helium to the muonic ion. The collisions energy T was considered to lie between the thermal energy and 1 a. u. The muonic ion (μB)⁴⁺ was treated as a heavy beryllium isotope Be4+. It was found that the main reaction responsible for the electron transfer at the energies specified above was: Be⁴⁺ + He → Be³⁺(1s) + He²⁺ + e^-. . Its mechanism is the Auger effect in the two-electron quasi-molecule (Be-He)⁴⁺. In our estimation of its cross-section we used adiabatic quasi-molecular terms obtained by diagonalizing the electronic Hamiltonian on a basis of several diabatic states constructed from two-centre orbitals. The electronic wavefunctions built with this way were employed to calculate Auger effect rates. The outgoing electron was treated to be free. The relative motion of the nuclei was considered classically. It was found that in the region 0.001 ≤ T ≤ 0.01 (in atomic units) the cross-section was a decreasing function of T and it was small (～ 10^-2 Ų). Then it starts to increase and mounts to typical atomic values (1 Ų) at T = 1 ÷ 2. The comparison of the reaction rate constant estimated on the basis of the obtained cross-section with experimental results establishes the upper limit of the energy of muonic boron during the 2s state lifetime (≈ 40 ns). It proves to be about 25 eV. This limit is in agreement with the typical value of 1 eV resulting from the energy transfer in the muon capture by the diborane molecule and the recoil energy acquired in the cascade. However, it does not exclude the possibility of an additional acceleration of muonic boron during its formation in the molecule.