The effects of target polarization in elastic scattering of electrons by endohedral A@C60

  Miron Ya. Amusia [1, 2]  ,  V. K. Dolmatov [3]  ,  L. V. Chernysheva [2]  
[1] The Racah Institute of Physics, the Hebrew University of Jerusalem, Jerusalem 91904, Israel
[2] A. F. Ioffe Physical-Technical Institute, St. Petersburg 194021, Russian Federation
[3] University of North Alabama, Florence, Alabama 35632, USA

We have developed a very efficient approximation to describe the low-energy electron elastic scattering off an endohedral A@CN. It accounts for polarization of A@CN by incoming electrons, without reference to complicated details of the electronic structure of CN itself. The approach permitted to demonstrate spectacular A@CN-polarization effects in low-energy e + A@CN elastic scattering, including that due to interaction between CN and A electrons.

It appeared that the contribution of a single A atom to the total electron elastic scattering phase-shift upon endohedral remains unscreened by the multi-atomic CN even if the projectile’s wavelength is bigger than the target A@CN. Inclusion of A and CN polarizability interference leads to violation of the previously predicted phase additivity rule. The partial cross-sections demonstrate prominent Ramsauer-type minima, whereas they almost disappear in the total cross-section. The analyses revealed notable trends in e + A@CN elastic scattering versus the polarizability of an encapsulated atom. We predicted also some negative ions (A@CN)-.

As concrete examples for calculations, we chose Ne, Xe and Ba as atoms A, and C60 as the endohedral CN. We start with single-electron Hartree-Fock (HF) method, but end up with account of electron correlations in the random phase approximation (RPAE) frame. We investigated first five scattering waves and demonstrated that almost each partial cross-section has deep Ramsauer-type minima in electron-atom scattering cross-sections. In e + A@C60 this effect is much more interesting than in atoms since the position of the minimum depend upon the electron scattering angle.

We perform numeric calculations of electron wave functions and scattering phases up to incoming energies of about 0.001Ry. By extrapolating scattering phase values to zero energy, we predicted new negative ions (A@C60)- with different total angular momenta.

Not only the individual impacts due to polarization of the atom A and C60 on e + A@C60 scattering are generally important, but the correction term to e + A@C60 scattering, brought about by interference of polarizabilities of the atom A and C60, contribute impressively. The significance of the impact of interference of polarizabilities of C60 and A upon e+A@C60 scattering essentially grows with increasing polarizability of the atom A. We demonstrated that the interference of polarizability leads to strong violation of the phase additivity rule that is a well observable effect. A good example proved to be Ba@C60 where this effect modifies considerably, both quantitatively and qualitatively, the partial cross sections for e + Ba@C60 scattering at lower energies, but largely annihilate the whole polarization impact on scattering of s, p, d, and f-partial waves at higher energies.

We hope that the present work will prompt other theorists to perform more rigorous calculations of e+A@C60 scattering. We urgently need experimental data on this process, and do hope that the result of this work will stimulate experimentalists to perform corresponding measurements.