  We investigated the effects of first-forbidden transitions in $\beta$ decays
on the production of the r-process $A \sim 195$ peak. The theoretical
calculated $\beta$-decay rates with $\beta$-delayed neutron emission were
examined using several astrophysical conditions. As the first-borbidden decay
is dominant in $N \sim 126$ neutron-rich nuclei, their inclusion shortens
$\beta$-decay lifetimes and shifts the abundance peak towards higher masses.
Additionally, the inclusion of the $\beta$-delayed neutron emission results in
a wider abundance peak, and smoothens the mass distribution by removing the
odd-even mass staggering. The effects are commonly seen in the results of all
adopted astrophysical models. Nevertheless there are quantitative differences,
indicating that remaining uncertainty in the determination of half-lives for
$N=126$ nuclei is still significant in order to determine the production of the
r-process peak.
