We study the spatial distribution of the density of states (DOS) at zero bias N(r) in the mixed state of single and multigap superconductors. We provide an analytic expression for N(r) based on deGennes relation between DOS and the order parameter that reproduces well Scanning Tunneling Microscopy (STM) data in several superconducting materials. In the single gap superconductor $beta$-Bi$_2$Pd, we find that N(r) is governed by a length scale $xi_H=sqrt{phi_0/2pi H}$, which decreases in rising fields. The vortex core size $cal C$, defined via the slope of the order parameter at the vortex center, $cal C$ $propto (d Delta /dr |_{r to 0})^{-1}$, differs from $xi_H$ by a material dependent numerical factor. For two gap superconductors 2H-NbSe$_{1.8}$S$_{0.2}$ and 2H-NbS$_2$, we find that $cal C$ is field independent and has the same value for both bands. We conclude that, independently of the magnetic field induced variation of the order parameter values in both bands, the spatial variation of the order parameter close to the vortex core is the same for all bands.
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