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From Current Literature
Spin and Magnetic Moment of Light Helium (He³)
To determine the magnetic moment of He³, the gyromagnetic ratio of this isotope was accurately measured¹ by a modified magnetic-resonance method². Ten cm³ of isotopically pure He³ was obtained as the product of the radioactive decay of tritium (H³). The sample was placed inside a small coil, which was one of the elements of a radio-frequency bridge. The coil together with the sample was placed between the poles of an electromagnet in such a way that the axis of the coil was perpendicular to the direction of the field. Under these conditions a nucleus with spin \(I\) can orient itself relative to the field in \(2I+1\) ways. Transitions between neighboring states were induced by a weak alternating field produced by passing a radio-frequency signal through the coil. Such transitions most probably occur at resonance between the frequency of the weak field and the Larmor precession frequency. The resonance condition
\[ 2\pi\nu = |\gamma|H \tag{1} \]
makes it possible to determine \(\gamma\)—the ratio of the magnetic moment to the mechanical moment:
\[ \gamma=\frac{\mu}{I\hbar}. \]
From the resonance condition it is clear that, in order to determine \(\gamma\), one must know \(\nu\) and \(H\). Since \(\nu\) can be determined considerably more accurately than \(H\), it is expedient to compare \(\nu\) for the nucleus under study with that for a definite standard nucleus at one and the same field strength \(H\). If the nucleus of light hydrogen is chosen as the standard nucleus, then at the same \(H\), from condition (1), one obtains
\[ \frac{\gamma}{\gamma(\mathrm{H}^1)} = \frac{\nu}{\nu(\mathrm{H}^1)}, \]
whence, knowing \(\gamma(\mathrm{H}^1)\), the desired \(\gamma\) can be calculated. The precise measurements led the authors¹ to the following value of the ratio:
\[ \frac{\gamma(\mathrm{He}^3)}{\gamma(\mathrm{H}^1)} = 0.7617866 \pm 0.0000012. \]
Hence, taking into account the correction for diamagnetism, one obtains
\[ \frac{|\gamma(\mathrm{He}^3)|}{|\gamma p|} = 0.76815. \]
The magnitude of the magnetic moment of the He³ nucleus in nuclear magnetons is obtained from this ratio if one uses the exact value
with the value³ \(\mu_p = 2.79353\) and assume that the spin of the \(\mathrm{He}^3\) nucleus is \(1/2\). This gives
\[ \mu(\mathrm{He}^3) = (-)\,2.79353. \]
The minus sign is placed in parentheses, since it has not yet been justified.
Although the value of the spin of the \(\mathrm{He}^3\) nucleus equal to \(1/2\) is the most probable, it nevertheless needs direct experimental confirmation. For the purpose of such confirmation, the alternation of intensities⁵ in the molecular spectrum of \(\mathrm{He}_2^3\) was studied.⁴ A sample containing 88% \(\mathrm{He}^3\) was excited to glow in a Geissler tube by a weak condensed discharge. The spectrum was studied in the first order of a 21-foot grating. For detailed measurements the band at 6400 Å was selected. The rotational lines of this band show a distinct alternation of intensities. Photometric measurements in the \(P\)-branch of this band gave an intensity ratio of 2.8:1. The results obtained in other bands gave a ratio of 3:1. The theoretical values for the cases of spins \(1/2\), 1, and \(3/2\), as is known, are 3:1, 2:1, and 1.67, respectively. Thus it may definitely be asserted that the spin of the \(\mathrm{He}^3\) nucleus is \(1/2\), as is also the spin of the \(\mathrm{H}^3\) nucleus.
In the case of the molecule of ordinary helium, \(\mathrm{He}_2^4\), in the 6400 Å band there are absent (in the \(P\) and \(R\) branches) lines corresponding to odd values of the rotational quantum number \(K\), since the spin of the \(\mathrm{He}^4\) nucleus is zero and \(\mathrm{He}^4\) obeys Bose statistics. On the contrary, in the same band of \(\mathrm{He}_2^3\) the lines corresponding to odd \(K\) are the most intense, whence it follows that \(\mathrm{He}_2^3\) obeys Fermi statistics, as was to be expected for a nucleus consisting of an odd number of nucleons.
E. Sh.
Cited Literature
- H. L. Anderson, Phys. Rev. 76, 1460 (1949).
- See, for example, Ya. G. Dorfman, Magnetic Properties of the Atomic Nucleus. Gostekhizdat, 1948, pp. 143–206; J. Kellogg and S. Millman, UFN 34, 72 (1948).
- H. Taub and P. Kush, Phys Rev. 75, 1481 (1949).
- A. E. Douglas and G. Herzberg, Phys. Rev. 76, 1529 (1949).
- See S. E. Frish, Spectroscopic Determination of Nuclear Moments. Gostekhizdat, 1948, p. 105.