Mathematics – Probability
Scientific paper
Aug 1947
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1947phrv...72..312s&link_type=abstract
Physical Review, vol. 72, Issue 4, pp. 312-320
Mathematics
Probability
14
Scientific paper
In order to account for the measured magnetic moment of the triton it is necessary to assume that the wave function in the ground state is a linear combination of 2S, 2P, 4P, and 4D functions. An attempt is made to determine the amplitudes of these functions from the magnetic moment on the assumption that the intrinsic nucleon moments are additive and relativistic effects are negligible. With certain reasonable assumptions concerning the nature of the wave functions, it is found that the relative probabilities for finding the system in the 2P, 4P, 4D states satisfy the relation shown by the curves in Fig. 1. Wherever the results would otherwise be arbitrary, the wave functions have been chosen in such a way as to minimize the amount of P state, with the exception that only the lowest one-particle configurations have been considered. If the amplitude of the 2S state is taken to be as large as possible, the wave function contains no 4D state, 8 percent 4P state, and 17 percent 2P state. A wave function of this form would seem to indicate that there is a spin-orbit coupling other than the tensor interaction acting among nuclear particles. In the other extreme case that the wave function contains a maximum of the 4D function, the 2S state probability is zero, the 4D probability is 22 percent, the 4P is 30 percent, and the 2P is 48 percent. If the wave function of He3 has the same form as that of H3, the He3 moment would be expected to lie on one of the curves shown in Fig. 2.
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