The polarizability of hydrogen-like atoms is roughly proportional to the cube of their radius (~ 4pε0 a3 ); hence for normal hydrogen-like atoms (e.g. deuterium, tritium) is (almost) unchanged but for positronium one might expect to be roughly 8 times larger. For more detailed calculations, please see : J. Mitroy and M. W. J. Bromley "van der Waals coefficients for positronium-atom interactions.", Phys. Rev. A 68, 035201,  particularly Table II.

Best regards,

Mickey

Thank you Mickey. Please say something about Muonium atom. Positive Muon is almost 9 times smaller than proton.

 How much the polarizability of Mu differ from H?

Again would you please make help about the C_6 in Ps-Ps, Ps-Mu and Mu-Mu systems.

The reduced mass of muonium is 99.57 % of that of hydrogen; consequently the Bohr radius, the ionization energy and the polarizability are within 1% of those of hydrogen. Based on the results from table II of the above-mentioned article, one can approximate that C6 for H-H is ~6.5 au, for H- Ps is ~35 au and Ps-Ps is ~188 au, where H is any hydrogen-like atom except for Ps (but including muonium). The polarizability of Ps is only about 5 times larger than that of H (not 8) and the calculation errors are of the order of 1 percent.    

Thank you Mickey for your reply. I did not know the recent progress about the polarizability of Ps roughly 5 times larger than H. Would you please provide me references? Are you working on this area?

Again C_6 for Ps-Ps is 188 a.u. From where you got it? Would you please give me the reference? In a paper by Martin & Fraser (1980) it was ~208 a.u. obviously they considered the polarizability of Ps eight times higher than H.

Please take a look at the reference I already suggested, J. Mitroy and M. W. J. Bromley "van der Waals coefficients for positronium-atom interactions.", Phys. Rev. A 68, (2003) 035201; Table II shows that the polarizabiltiy of Ps is about 5.4 or so larger than that of the H atom.

Best regards,

Mickey

Hi Mickey,

I checked the article thoroughly as you told me. But find nowhere the above mentioned values of polarisability of Ps and Van der Waals C_6 coefficient. Would you please tell me the references?

Best wishes and regards,

Hasi

Dear Hasi,

According to London theory for the dispersion forces, the coefficient C6 is proportional to the product of the atom polarizabilities. Given that the ionization energies are about the same for H and Ps , if one compares C6 for Ps-H (line 1) and H-H (line 11 in Table II) , finds out that the polarizability of Ps should be about 36.021/6.816 ~ 34.785/6.499  ~ 5.35 times the polarizability of H. From here, one can assume that the polarizability for Ps is 5.35*4.50 (a0)^3 and that the  C6 for Ps-Ps is about 5.35 times larger than that for H-Ps, hence ~ 188 au.

Best regards,

Mickey

Thank you Mickey for your kind reply. I was waiting for it.

Anyway, I am not yet fully convinced and will look at it and inform you later.

Best wishes,

Hasi