The effects of a new triple-$alpha$ reaction rate (OKK rate) on the helium flash of a helium accreting neutron star in a binary system have been investigated. Since the ignition points determine the properties of a thermonuclear flash of type I X-ray bursts, we examine the cases of different accretion rates, $dM/dt (dot{M})$, of helium from $3times10^{-10} M_{odot} rm yr^{-1}$ to $3times10^{-8} M_{odot} rm yr^{-1}$, which could cover the observed accretion rates. We find that for the cases of low accretion rates, nuclear burnings are ignited at the helium layers of rather low densities. As a consequence, helium deflagration would be triggered for all cases of lower accretion rate than $dot{M}simeq 3times10^{-8} M_{odot} rm yr^{-1}$. We find that OKK rate could be barely consistent with the available observations of the X-ray bursts on the helium accreting neutron star. However this coincidence is found to depend on the properties of crustal heating and the neutron star model.We suggest that OKK rate would be reduced by a factor of $10^{2-3}$ for $10^8$ K in the range of the observational errors.
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