Abstract
To study whether long-lived superheavy nuclei could really exist around $Z=120$ and $N=184$, the competition between $\ensuremath{\alpha}$ decay and spontaneous fission in the region $104\ensuremath{\le}Z\ensuremath{\le}124$ are systemically studied. The $\ensuremath{\alpha}$-decay half-lives are investigated by employing a generalized liquid drop model and the analytical universal decay law formula. The calculation of spontaneous fission half-lives are carried out based on generalized Swiatecki's formula. The competition between $\ensuremath{\alpha}$ decay and spontaneous fission is analyzed in detail and the decay modes are predicted for the unknown nuclei.
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