## Abstract

Experimental and theoretical work has been carried out on the hyperfine structure of the 4f$^{67}$F ground multiplet of samarium. Hyperfine structure intervals have been measured in the levels J = 1, 2, 3 and 4 for both odd isotopes $^{147}$Sm and $^{149}$Sm by the method of atomic beams. These intervals have been fitted to magnetic dipole and electric quadrupole interaction constants. Further measurements at high magnetic field by the method of triple resonance have led to the evaluation of the nuclear magnetic dipole moments of the two isotopes. It is shown that a calculation of the breakdown of L-S coupling and of second order corrections, off-diagonal in J, is necessary for an interpretation of the spectrum. The application of these corrections is facilitated by the formulation of an effective Hamiltonian, and the whole problem is treated step by step as a practical example of the use of tensor operator techniques. The spectrum is described in terms of a few overdetermined parameters, and in particular three radial parameters are evaluated. They are defined by the operator describing the magnetic field produced by the electrons at the nucleus: $$T(e)^1 = 2\beta\sum_i {\langle r^{-3}_l\rangle 1_i-\langle r^{-3}_sC\rangle\surd 10(sC^2)^1_i+\langle r^{-3}_s\rangle S_i\}.$$ Their values are: \langle r$^{-3}_l$\rangle = 6.39$^0_6$ a$^{-3}_0$, \langle r$^{-3}_{sC}$\rangle = 6.5$^{13}_{12}$ a$^{-3}_0$, \langle r$^{-3}_s$\rangle = -0.20$^8_6$ a$^{-3}_0$. The most important result is a precise determination of the nuclear magnetic moment of $^{147}$Sm. It is $\mu^{147}_I$ = -0.807$^4_7$ n.m., uncorrected for diamagnetism. Also the ratio of the dipole interaction constants is A$^{147}_1$/A$^{149}_1$ = 1.2130$^5_2$ for all J, and there is no observable Bohr-Weisskopf anomaly It is shown that relativity is a plausible explanation for the non-vanishing of $\langle r^{-3}_s$\rangle in the contact term, but this explanation is not conclusive because the effect of relativity cannot be distinguished from that of configuration interaction in any part of the dipole interaction. The values of \langle r$^{-3}_l$\rangle and \langle r$^{-3}_{sC}$\rangle, which differ from each other, are compared with the value of an \langle r$^{-3}$\rangle integral calculated by other workers. From the quadrupole interaction a value of -\frac{1}{2}e$^2$Q$^{147}$ \langle r$^{-3}_Q$\rangle = 149$\cdot^{86}_{40}$ Mc/s is obtained and with less precision a value of Q$^{147}$ = -0.2$^0_2$ barn, uncorrected for shielding effects, is deduced. The ratio of the quadrupole moments is Q$^{147}$/Q$^{149}$ = -3.460$^1_3$, on the assumption that this ratio is the same as that of the quadrupole interaction constants.

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