# Low Energy Cross Section of Mesic Molecules Formation

*Muon Catalyzed Fusion 2* (1988) 261-272

## Abstract

Cross section of the formation of mesic molecular complex (MMC) in the reactions

(t μ)_{F} +(D_{2})_{νiKi}→ [(dt μ) ^{Jv}_{S} dee] _{νfKf} is calculated at low energies (E < 100 K). We
assume the Breit-Wigner energy dependence of the cross section. In calculating the
entrance widths the electron screening and various orbital moments of the incident
tμ-atom were taken into account. Owing to anharmonic corrections to a purely
harmonic approximation the reduced entrance width remains nonzero at E → 0. As the
result the conventional 1/*v* law for energy dependence of the MMC formation cross
section is restored. The entrance width for the transition

(*ν*_{i} = 0, *K*_{i} = 0) → (*ν*_{f}=2, *K*_{f}=1) proves to be the most important. The wave functions of D_{2} and MMC were
calculated in the Morse potential which proves to give the level positions with a high
precision and includes anharmonic corrections to full extent. Accounting for the
anharmonism modifies considerably both the energy dependence and the value of the
MMC formation cross section. Comparing calculated rates with the experimental data
one can estimate the positions of the resonance levels.

#### Keywords: muon catalyzed fusion, mesic molecular complex

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