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

Investigation of the Ground and Excited States of the 3H and 4He Nuclei by Using the Methods of Group Theory