  Type Ia supernovae (SNe Ia) are successful cosmological distance indicators
and important element factories in the chemical evolution of galaxies. They are
generally thought to originate from thermonuclear explosions of carbon-oxygen
white dwarfs in close binaries. However, the observed diversity among SNe Ia
implies that they have different progenitor models. In this article, we
performed the long-term evolution of NS+He star binaries with different initial
He star masses ($M_{\rm He}^{\rm i}$) and orbital periods ($P_{\rm orb}^{\rm
i}$) for the first time, in which the He star companions can explode as SNe Ia
eventually. Our simulations indicate that after the He stars develop highly
degenerate oxygen-neon (ONe) cores with masses near the Chandrasekhar limit,
explosive oxygen burning can be triggered due to the convective Urca process.
According to these calculations, we obtained an initial parameter space for the
production of SNe Ia in the $\rm log\,$$P^{\rm i}_{\rm orb}-M^{\rm i}_{\rm He}$
plane. Meanwhile, we found that isolated mildly recycled pulsars can be formed
after He stars explode as SNe Ia in NS+He star binaries, in which the isolated
pulsars have minimum spin periods ($P_{\rm spin}^{\rm min}$) of $\sim
30-110\rm\,ms$ and final orbital velocities of $\sim \rm 60-360\,km\,s^{-1}$,
corresponding to initial orbital periods of $0.07-10\rm\,d$. Our work suggests
that the NS+He star channel may contribute to the formation of isolated mildly
recycled pulsars with velocity $\rm \lesssim 360\,km\,s^{-1}$ in observations,
and such isolated pulsars should locate in the region of pulsars with massive
WD companions in the $P_{\rm spin}-\dot P_{\rm spin}$ diagram.
