  In the recent experiments designed to synthesize the element 115 in the
$^{243}$Am+$^{48}$Ca reaction at Dubna in Russia, three similar decay chains
consisting of five consecutive $\alpha$-decays, and another different decay
chain of four consecutive $\alpha$-decays are detected, and the decay
properties of these synthesized nuclei are claimed to be consistent with
consecutive $\alpha$-decays originating from the parent isotopes of the new
element 115, $^{288}115$ and $^{287}115$, respectively\cite{ogan.03}. Here in
the present work, the recently developed deformed RMF+BCS method with a
density-independent delta-function interaction in the pairing channel is
applied to the analysis of these newly synthesized superheavy nuclei
$^{288}115$, $^{287}115$, and their $\alpha$-decay daughter nuclei. The
calculated $\alpha$-decay energies and half-lives agree well with the
experimental values and with those of the macroscopic-microscopic FRDM+FY and
YPE+WS models. In the mean field Lagrangian, the TMA parameter set is used.
Particular emphasis is paid on the influence to both the ground-state
properties and energy surfaces introduced by different treatments of pairing.
Two different effective interactions in the particle-particle channel, i.e.,
the constant pairing and the density-independent delta-function interaction,
together with the blocking effect are discussed in detail.
