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Gdańsk University of Technology

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Static electric and magnetic multipole susceptibilities for Dirac one-electron atoms in the ground state

We present tabulated data for several families of static electric and magnetic multipole susceptibilities for hydrogenic atoms with nuclear charge numbers from the range $1\leq Z\leq137$. Atomic nuclei are assumed to be point-like and spinless. The susceptibilities considered include the multipole electric polarizabilities $\alpha_{\mathrm{E}L\to\mathrm{E}L}$ and magnetizabilities (magnetic susceptibilities) $\chi_{\mathrm{M}L\to\mathrm{M}L}$ with $1\leq L\leq4$ (i.e., the dipole, quadrupole, octupole and hexadecapole ones), the electric-to-magnetic cross-susceptibilities $\alpha_{\mathrm{E}L\to\mathrm{M}(L−1)}$ with $2\leq L\leq5$ and $\alpha_{\mathrm{E}L\to\mathrm{M}(L+1)}$ with $1\leq L\leq4$, the magnetic-to-electric cross-susceptibilities $\chi_{\mathrm{M}L\to\mathrm{E}(L−1)}$ with $2\leq L\leq5$ and $\chi_{\mathrm{M}L\to\mathrm{E}(L+1)}$ with $1\leq L\leq4$ (it holds that $\chi_{\mathrm{M}L\to\mathrm{E}(L∓1)}=\alpha_{\mathrm{E}(L∓1)\to\mathrm{M}L}), and the electric-to-toroidal-magnetic cross-susceptibilities $\alpha_{\mathrm{E}L\to\mathrm{T}L}$ with $1\leq L\leq4$. Numerical values are computed from general exact analytical formulas, derived by us elsewhere within the framework of the Dirac relativistic quantum mechanics, and involving generalized hypergeometric functions ${}_{3}F_{2}$ of the unit argument.

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