Hyperfine Splitting in Deuterium

The hyperfine splitting in the ground state of deuterium was measured with very high accuracy a long time ago [70, 71[ 

The expression for the Fermi energy in (8.2), besides the trivial substitutions similar to the ones in the case of hydrogen, should also be multiplied by an additional factor 3/4 corresponding to the transition from a spin one half nucleus in the case of hydrogen and muonium to the spin one nucleus in the case of deuterium. The final expression for the deuterium Fermi energy has the form 

As in the case of hydrogen, after trivial modifications, we can use all nonrecoil corrections in Tables 9.1, 9.2, 9.2, 9.3, 9.4, and 9.5 for calculations in deuterium. The sum of all nonrecoil corrections is numerically equal to 

Unlike the proton, the deuteron is a weakly bound system so one cannot simply use the results for the hydrogen recoil and structure corrections for deuterium. What is needed in the case of deuterium is a completely new consideration. Only one minor nuclear structure correction [72, 73, 74, 75] was discussed in the literature for many years, but it was by far too small to explain the difference between the experimental result in (12.25) and the sum of nonrecoil corrections in (12.28) 

A breakthrough was achieved a few years ago when it was realized that an anal dic calculation of the deuterium recoil, structure and polarizability corrections is possible in the zero range approximation [76, 77]. An analytic result for the difference in (12.29), obtained as a result of a nice calculation in [77], is numerically equal 44 kHz, and within the accuracy of the zero range approximation perfectly explains the difference between the experimental result and the sum of the nonrecoil corrections. More accurate calculations of the nuclear effects in the deuterium hyperfine structure beyond the zero range approximation are feasible, and the theory of recoil and nuclear corrections was later improved in a number of papers [78, 79, 80, 81, 82]. Comparison of the results of these works with the experimental data on the deuterium hyperfine splitting may be used as a test of the deuteron models and state of the art of the nuclear calculations. 

---