Perturbation-theory calculation of hyperfine structure in muonic helium

The lowest-order correction in the hyperfine splitting of muonic ⁴He due to excitation of the effective (μ-He)⁺ nucleus is precisely evaluated numerically. The result is Δν₁ᵉ=-45.670(8) MHz, in agreement with previous approximate analytic calculations. The mass-polarization correction to the hyperfine splitting is found to be Δν₁ᵐ=0.0785(2) MHz. The total perturbation-theory value for the hyperfine splitting is Δν=4464.3(1.8) MHz, which is consistent with experiments at the Swiss Institute for Nuclear Research and at the Clinton P. Anderson Meson Physics Facility at Los Alamos.