  For matter wave scattering from passive quantum obstacles, we propose a phase
diagram in terms of phase and modulus of scattering coefficients to explore all
possible directional scattering patterns. In the phase diagram, we can not only
have the physical bounds on scattering coefficients for all channels, but also
indicate the competitions among absorption, extinction, and scattering cross
sessions. With help of this phase diagram, we discuss different scenarios to
steer scattering probability distribution, through the interference between
$s$- and $p$-channels. In particular, we reveal the required conditions to
implement a quantum scatterer, i.e., a quantum dot in semiconductor matrix,
with a minimum (or zero) value in the scattering probability toward any
direction. Our results provide a guideline in designing quantum scatterers with
controlling and sensing matter waves.
