Binding Energies of4He and3H in Reaction Matrix Theory

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Abstract
The binding energies of 4He and 3H are calculated with some realistic potentials in the reaction matrix theory. The reaction matrix equation is derived from the internal Hamiltonian. The energy denominator is given after careful consideration of the difference between the total energies of the starting state and the intermediate state. The Pauli operator is treated without approximation in the two-particle scattering process in nuclei. The calculated binding energies of 4He and 3H with Hamada-Johnson potential are 19.5 MeV and 6.3 MeV, respectively. The scattering wave function is also obtained. The root mean square radii with the correlated wave functions are 1.64 fm and 1.67 fm for 4He and 3H, respectively. It is found that the contribution from tensor force in 3E state is very large, as compared with that in nuclear matter, and it is very important in order to obtain the sufficient binding energies of light nuclei to take into account this contribution through the two-particle scattering process in nuclei. The D state mixing ratios are about 14% and 8.5% for 4He and 3H, respectively. The various correlation energies are estimated and it is found in the case of 4He with H-J that the hole-hole diagram contributes about 3 MeV and potential insertion in the particle states just above the Fermi surface brings about 2 MeV. It is concluded that validity of the independent pair model is confirmed very well in the lightest nuclei similarly to the case of nuclear matter.

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