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Concerning the su(2)-Lipkin model, the calculation of the excitation energyto the 1st excited-state gives rise to the following fact: The two resultsbased on the exact treatment and the conventional random phase approximation(RPA) are in unexpected disagreement. In order to remove this discrepancy, theconventional RPA is renewed. With the aim of this renewal, the terms, whichcannot be dealt with in the conventional one, are estimated. The basicframework of this new form is not reorganized from that of the conventionalone. In addition, the su(2)-Lipkin model itself is also modified so as to beapplicable to the case with non-closed shell system. To this modification, onemore su(2)-algebra, which has been already proposed by the present authors, isapplied. Through the use of this algebra, the su(2)-Lipkin model is applicableto the case with any total fermion number permitted in the model.

A possible trial beyond the conventional random phase approximation for the su(2)-Lipkin model including the case of non-closed shell system