On the Nuclear Spins and Magnetic Moments of the Principal Isotopes of Potassium

The spin of the ${\mathrm{K}}^{39}$ nucleus and the hfs separation of the ${}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ normal state were measured by the deflection of a beam of neutral atoms in a weak inhomogeneous magnetic field, produced by a system of parallel wires carrying current. To attain the required resolution narrow beams and long beam paths (141 cm) were used. The nuclear spin of ${\mathrm{K}}^{39}$ was found to be 3/2. The hfs separation, $\Delta \nu$, of the normal state was measured by the method of "zero moments," which utilizes the fact that the magnetic moment of the atoms in some of the magnetic levels vanishes at certain values of the magnetic field. A plot of the variation of intensity at the center of the pattern with respect to field yields distinct maxima at these fields. If the magnetic field is known the hfs separation can be deduced with accuracy. The value of $\Delta \nu$ was found to be 0.0152±0.0006 ${\mathrm{cm}}^{-1\mathrm{}}$. Using the modified Goudsmit formula, one obtains the value of 0.39 for the nuclear magnetic moment (in units of $\frac{{\mu }_0}{1838}$). The resolution was sufficient to resolve a "peak" due to ${\mathrm{K}}^{41}$ by the method of "zero moments." The nuclear spin was found to be greater than 1/2, and the ratio of the magnetic moments $\frac{{\mu }_{41}}{{\mu }_{39}}$ was found to be between the limits of 0.42 and 0.88 depending on the spin of ${\mathrm{K}}^{41}$.