Phenomenological Study of Three-Body Force Based on the Energy Levels of the Alpha-Particle

The contributions of the three· body force to the energies of the alpha-particle are estimated both in the ground state and in the first three T = 0 negative parity (j" = 0', 2 -, l' ) excited states. These contributions just correspond to the deviations of the theoretical values of the energies of the alpha-particle, which are obtained with the realistic two-body force only, from the experimental ones not only in the ground state but also in the excited states. From this fact, it is shown that the three-body force is indispensable to reproducing the energies of nuclei with realistic nuclear interactions and that the three-body force may be determined in a phenomenological way. There have been no experimental phenomena which constitute a direct evidence of the nuclear three-body force. In the present paper, it is pointed out that there exists a fact taking the place of such phenomena, and it is shown that rough features of the three-body force such as its strength and type can be deduced. Recently A TMS method 1) has been proposed to solve few-particle systems under realistic two-body interactions. This method is of powerful one. In fact, the method gives the very close upper and lower bound energies of the ground states for three- and four-alpha-particle systems, where the alpha-particles in teract through phenomenological inter-particle potential with a strong repulsive part. 2 ) This means that ATMS method can make it possible to solve almost completely these alpha-particle systems. Using this method, wave functions and energy values have been evaluated for the triton and the alpha-particle with several realistic two-body forces. 1),3) We pay attention to the deviations of the theoretical energy values obtained with the realistic two-body force from the experimental ones in the first three T =0 negative parity (j"=0-, 2-, r) excited states of the alpha-particle as well as in the ground state. The theoretical value of the ground state energy of the alpha-particle, which is obtained by the use of ATMS method, deviates to a large extent from the experimental one in any case of the realistic two-body forces, and this deviation is considerably large compared with the differences among several theoretical values calculated with different types of the two-body force.