 Effective Bohr radius of a hydrogenic donor

In a scalar effective-mass dielectric model, the donor radius is $a_B^{\ast }={ϵ}_r(m_e/m^{\ast })a_0$. The effective mass reduces the kinetic-energy scale and dielectric screening weakens attraction. The corresponding binding energy scales as $(m^{\ast }/m_e){ϵ}_r^{-2}$ times the vacuum hydrogen binding energy.