On the Hyperfine Structure of Gallium

The hyperfine structures of the ground ${}_{}{}^2{}_{}{}^{}P_{\frac{1}{2}}^{}{}_{}{}^{}$ and the metastable ${}_{}{}^2{}_{}{}^{}P_{\frac{3}{2}}^{}{}_{}{}^{}$ states of ${\mathrm{Ga}}^{69}$ and ${\mathrm{Ga}}^{71}$ have been determined by the atomic beam magnetic resonance method. The h.f.s. levels for an atom whose nucleus has a magnetic dipole, electric quadrupole, and magnetic octupole moment are given by the formula $W=\frac{\mathrm{aC}}{2}+bC(C+1\mathrm{})+c(C^3+4\mathrm{}{C}^2+\frac{4C}{5})$, where $C=F(F+1\mathrm{})-I(I+1\mathrm{})-J(J+1\mathrm{})\mathrm{}$. For the metastable state of gallium, with $I=J=\frac{3}{2}$, there are four levels at zero external magnetic field, corresponding to $F=3, 2, 1, \mathrm{and} 0$. The determination of the separations of these levels permits the calculation of the constants $a$, $b$, and $c$ in the equation above. It was found that only the first two terms are needed to explain the hyperfine splitting of each Ga isotope, within the precision of these measurements. An upper limit for the value of $c$ is 3 × ${10}^{-9\mathrm{}}$ ${\mathrm{cm}}^{-1\mathrm{}}$. Other results are: