A Simple Picture of the Binding Energies ofH3andHe5

It is shown that an approximate application of Wheeler's method of resonating groups to the nuclei, ${\mathrm{H}}^3$ and ${\mathrm{He}}^5$, makes it possible to evaluate the magnitude of different contributions to the total energy. The energy expressions are separated into terms representing the internal energy of a favorable sub-group, the kinetic energy of a particle outside the sub-group, and its "ordinary" and "velocity dependent" interaction with the sub-group. For ${\mathrm{H}}^3$ the sub-group is the deuteron and for ${\mathrm{He}}^5$ the $\alpha$-particle. The results indicate considerable polarization of the deuteron and little polarization of the $\alpha$-particle. The total energies found were $E\left({\mathrm{H}}^3\right)=-6.58\mathrm{}$ mMU and $E\left({\mathrm{He}}^5\right)=-19.51\mathrm{}$ mMU (for the most reasonable value of one parameter since no true minimum was found for ${\mathrm{He}}^5$). These results are compared with those of other methods. The current two-body exchange forces were used (see Table I). The approximate method is quick and easy to handle. Application of the complete resonating group method to ${\mathrm{H}}^3$, however, proved to be very laborious and difficult to make accurate. By this procedure $E\left({\mathrm{H}}^3\right)$ came out -6.68 mMU. The smallness of the improvement over the approximate method is attributed to the fact that the complete method does not take polarization into account. The calculated ground state energy for ${\mathrm{He}}^3$ was -5.88 mMU by the approximate method and -5.94 mMU by the complete method. No bound excited state was found.