Isobaric-Spin-3/2 States and Intermediate Symmetry States in Three-Body Nuclei

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Abstract
The ground state wave functions of H3 and He3 are constructed separately by explicitly taking account of small charge asymmetry of nuclear forces and the Coulomb force between two protons in the He3 nucleus. Charge independence is assumed for the range parameters of the nuclear force but not for the depth parameters. It is found that: 1) The isospin T = 3/2 admixture in He3 owing to the Coulomb force alone is about 4 ×10-6 in probability. Small violation of charge independence hypothesis in actual nuclear forces (namely, the difference in n-p and p-p) induces the isospin admixture of about 5 ×10-6 in H3 and 2 ×10-5 in He3 if the charge symmetry is assumed. These values are not much dependent on the hard core radius and on exchange character of nuclear forces. 2) The calculated Coulomb energy of He3 (assuming extended protons) suggests that the n-n potential will be stronger than the p-p nuclear potential in the singlet state though no more than 1% for which the isospin admixture in H3 is about 10-6. 3) The polar vector matrix element for the β-decay of H3 is smaller than unity by only of the order 10-4. 4) The S′-state probability increases as the hard core radius increases so that a large difference between the charge form factor of H3 and that of He3 observed in electron scattering experiments is consistent with the hard core radius of 0.4 fm or larger. The conclusions are qualitatively correct even if any “realistic” nuclear force is used.

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