Direct production of muon pairs by high-energy muons

For ultrarelativistic muons, the cross section for the process μ+Z→μ+Z+μ++μ− is calculated with allowance for the nuclear and atomic form factors. It is shown that the nuclear form factor affects significantly the cross-section value. The transverse-momentum distribution of muons is calculated. An approximate formula determining the total cross section to within 2 to 3% is derived. The fluxes of groups of cosmic-ray muons generated by the above process are estimated at various depths. It is shown that calculations performed earlier overestimate significantly the fluxes of such groups.