Shaking process due to nuclear recoil during heavy ion-atom collisions

A theoretical study on the shaking process accompanying swift heavy ion-atom collisions is presented. Using the nonrelativistic hydrogenic wavefunctions, analytical expressions for the survival and shakeup/shakedown probability have been derived for the $K-\text{,}L-$ and $M-$shell electrons of hydrogen-like atomic systems. The resulting expressions are used to calculate the shaking and shakeup/shakedown probability in the typical case of the recoiling nucleus of the multielectron $\left({}^{63}{\mathrm{Cu}}^{+}\right)$ and hydrogen-like $\left({}^{63}{\mathrm{Cu}}^{28+}\right)$ atomic systems, respectively. Interestingly, it is found that the requirement of the high colliding energy for the suddenness of the perturbation, can well fulfill the limiting condition of the necessary nuclear recoil for finite electron shaking during the ion-atom collisions. Further, the dependence of the shaking probability on atomic number has been depicted, and it has emerged that for a particular value of the recoil energy per nucleon, the shaking processes are more significant in the lower atomic number region.