We make a variational calculation of the binding energy of helium, using a two-body central velocitydependent potential both in the l S and in the 8 S states. We have used the two-parameter Irving wave function, and its suitable modifications with three and four parameters, as trial functions. Our results show that the convergence is rather slow. Obviously the maximum binding energy is obtained for the four-parameter wave function. Our maximum value for the binding energy of helium is somewhat greater than the experimental value of 28.2 MeV, but is in reasonable agreement with similar calculations using hard-core potentials. E VER since Jastrow 1 postulated a hard-core potential to explain two-body scattering at high energies, his suggestion has been followed by a number of workers 2 in calculating the properties of few-nucleon systems and has led to better agreement with experiments. Also, the repulsive hard core favors the saturation of nuclear matter. 3 Subsequently, Levinger et al* and Green 5 have shown that velocity-dependent potentials give as good a fit to the relevant two-body data as the hard-core potentials. Moreover, because it is well behaved, a velocity-dependent potential, unlike a hard core, does not give infinite matrix elements. Therefore, it is possible to use the perturbation treatment of Euler 6 in solving the many-body problem with a velocity-dependent potential. 5,7 In an earlier paper Srivastava 8 has made a variational calculation of the binding energy of the trinucleons^ using a two-body, central velocity-dependent potential. In the present paper we make a similar calculation for the binding energy of the a-particle He 4 .We assume the effective two-body central interaction in the case of the a particle to be the same as that for the trinucleons, viz., the average of two-body interactions in x 5 and S S states. 9 Therefore, we use the effective two-body velocity-dependent potential of Srivastava in the case of the triton 8 :
The results of a variational calculation for the binding energy of the alpha particle with the tensor velocity-dependent potential of Werner and the Irving wave function, containing a mixture of the principal 'So and 'Do(') states are presented. A binding energy of 28.03 MeV for the alpha particle is found, which is in excellent agreement with experiments, but the r.m.s. radius obtained in this way is about 88 % of the experimental value.
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