  The method of group theory is applied to investigate the ground and the
excited states of the triton and helium nuclei by using the translation
invariant shell model with basis functions corresponding to even number of
quanta of excitations in the range 0 less than or equal to N less than or equal
to 20. Accordingly, the ground and first excited state wave functions and
energies, the S, P and D state probabilities, the root mean square radius and
the magnetic dipole moment of triton have been investigated. Also, the energies
and wave functions of the ground and the even parity excited states and the
root mean square radius of helium have been investigated. Two residual two body
interactions together with two three nucleon interactions have been used in the
calculations. Moreover, the convergence of calculations has been examined by
extrapolating the results with N less than or equals to 20 step by step to
reach N equals to 30 for the two nuclei.
