Observations. The hyperfine structure patterns of some 30 or 40 lines in the spectrum of Mn I have been photographed by means of a prism spectrograph and silvered Fabry-Perot etalons. A tube, designed by Schüler, and operated at liquid air temperatures, has been used as a light source for most of the lines and a king vacuum furnace for the others. Patterns of from 2 to 6 components are found, some degrading in intensity and intervals toward low frequencies and others toward higher frequencies.

Interpretation. The strictly $\mathrm{LS}$ coupling in the well-known multiplet structure of Mn I, and $\mathrm{Ji}$ coupling in the hyperfine structure enable vector diagrams to be drawn for the space quantization of each valence electron with respect to the nucleus. Some of the hyperfine structure terms are computed directly from observed term differences while others are computed from the observed diagonal components. The normal state ${}_{}{}^6{}_{}{}^{}S_{2\frac{1}{2}}^{}{}_{}{}^{}\left(3\mathrm{}{d}^{5}4s^2\right)$ is found to be quite narrow, whereas the metastable ${}_{}{}^6{}_{}{}^{}D\left(3\mathrm{}{d}^{5}4s\right)$ terms show the widest separations. While the hyperfine structure intervals for any given term are proportional to $cos \mathrm{}\left(\mathrm{Ji}\right)\mathrm{}$ the total separations are approximately determined by $cos \mathrm{}\left(\mathrm{Si}\right)\mathrm{}$ the $l$ values of the electrons contributing but very little.

Theoretical computations. A study of the vector diagrams for the different multiplet terms shows quite definitely that while the hyperfine structure is determined primarily by the coupling between the $4s$ electron and the nucleus, the remaining valence electrons must also be taken into account. The hyperfine structure formula given by Goudsmit and Bacher for the interaction between an $s$ electron spin and the nuclear spin is extended so as to include not only the spins of all of the valence electrons but their $l$ values as well. From the derived general formula and the observed hyperfine structure term separations, coupling constants to be associated with each electron have been computed. While the energy of interaction between electron spin $s$ and nuclear spin $i$ is given by $\mathrm{ais} cos\mathrm{}\left(\mathrm{is}\right)\mathrm{}$ the energy of interaction between electron $l$ value and nuclear spin $i$ is given by $\mathrm{ail} cos\mathrm{}\left(\mathrm{il}\right)\mathrm{}$.

• Received 5 March 1930

DOI:https://doi.org/10.1103/PhysRev.35.1146