  We revisit kinetic relaxation and soliton/Boson star nucleation in fuzzy
scalar dark matter featuring short-ranged self-interactions $\mathcal{H}_{\rm
int} = -\lambda|\psi|^4/2m^2$, alongside gravitational self-interactions. We
map out the full curve of nucleation timescale for both repulsive ($\lambda <
0$) and attractive ($\lambda > 0$) short-ranged self-interaction strength, and
in doing so reveal two new points. Firstly, besides the two usual terms,
$\propto G^2$ and $\propto \lambda^2$, in the total relaxation rate
$\Gamma_{\rm relax}$, there is an additional cross term $\propto G\lambda$
arising due to interference between gravitational and short-ranged
self-interaction scattering amplitudes. This yields a critical repulsive
interaction strength $\lambda_{\rm cr} \simeq - 2\pi Gm^2/v_{0}^2$, at which
the relaxation rate is smallest and serves as the transition point between
typical net attractive self-interaction ($\lambda \gtrsim \lambda_{\rm cr}$),
and net repulsive self-interaction ($-\lambda \gtrsim -\lambda_{\rm cr}$).
Secondly, while in the net attractive regime, nucleation time scale is similar
to inverse relaxation time scale $\tau_{\rm nuc} \sim \Gamma^{-1}_{\rm relax}$,
in the net repulsive regime nucleation occurs at a delayed time $\tau_{\rm nuc}
\sim (\lambda/\lambda_{\rm cr})\Gamma^{-1}_{\rm relax}$. We confirm our
analytical understanding by performing 3D field simulations with varying
average mass density $\bar{\rho}$, box size $L$ and grid size $N$.
