  We name strongly localized quantum crystalline state (SLQCS) a determinantal
wave-function of the single-particle wave-functions obtained by crystalline
translations of a wave-function different from zero only within a primitive
cell of the considered quantum crystalline phase. SLQCSs accurately reproduce
the low density behaviour of the quantum crystals that, as Wigner's crystalline
phase of the jellium model, can become very dilute. Our analysis explicitly
deals with this system. We show that the SLQCS energy per particle at large
dilution ($r_s$) behaves as $-M_{dl,\sigma}/r_s+C_{\sigma}/{r_s}^{3/2}$, where
$M_{dl,\sigma}$ turns out to be the Madelung constant of the considered cubic
symmetry $\sigma$ and $C_{\sigma}$ is a positive constant only numerically
determined. Moreover, as the density gets smaller and smaller, each electron
becomes more and more confined to the centre of its cell.
