Shell Correction (- C/Z2 ) of DNA and Liquid Water

The energy loss by a swift proton beam in condensed materials is very important for hadron therapy.  Shell corrections are accounted for in a self-consistent manner through analytic dispersion relations for the momentum dependence of the dielectric function. It is shown that widely used dispersion schemes based on the Plasmon phase approximation (PPA) can result in sizeable errors due to the neglect of damping and local field effects that lead to a momentum broadening and shifting of the energy-loss function. The shell correction prevents the stopping number L from being negative at low velocity and corrects the assumption that the ion velocity is much larger than the target electron velocity. This emplies that for high-z 2 materials,shell corrections may be non-negligble even at rather high projectile speed. In the present work  the shell correction of swift proton by using  PPA of the dielectric formalism  of DNA and Liquid water targets has been calculated. Good agreement achieved with previous work.