The retardation long-range potentials between two 1
1S (or 2
3S) helium atoms are calculated. The complex dynamic multipole polarizabilities of 1
1S and 2
3S states of helium are obtained through a variation-perturbation approach with B-spline and Slater-type basis functions in a configuration-interaction scheme. They are used to calculate the retardation long-range potentials. The retardation coefficients are examined. Their relative magnitudes are different for different systems. The possibility of an excited state of helium dimer from the 1
1S--2
3S
He2 state is estimated. \textcopyright{} 1996 The American Physical Society.
For the interactions between a
He(23S) atom and a
He(23P) atom for like isotopes, we report perturbation theoretic calculations using accurate variational wave functions in Hylleraas coordinates of the coefficients determining the potential energies at large internuclear separations. We evaluate the coefficient
C3 of the first order resonant dipole-dipole energy and the van der Waals coefficients
C6,
C8, and
C10 for the second order energies arising from the mutual perturbations of instantaneous electric dipole, quadrupole, and octupole interactions. We also evaluate the leading contribution to the third-order energy. We establish definitive values including treatment of the finite nuclear mass for the $^{3}\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}S)\text{\ensuremath{-}}^{3}\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}P)$ and $^{4}\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}S)\text{\ensuremath{-}}^{4}\mathrm{He}(2\phantom{\rule{0.2em}{0ex}}^{3}P)$ interactions.
We theoretically investigate long-range interactions between an excited
L-state He atom and two identical
S-state He atoms for the cases of the three atoms all in spin-singlet states or all in spin-triplet states, denoted by He(${n}_{0}^{\ensuremath{\lambda}}S$)-He(${n}_{0}^{\ensuremath{\lambda}}S$)-He(${n}_{0}^{\ensuremath{'}\ensuremath{\lambda}}L$), with
n0 and ${n}_{0}^{\ensuremath{'}}$ principal quantum numbers, $\ensuremath{\lambda}=1$ or 3 the spin multiplicity, and
L the orbital angular momentum of a He atom. Using degenerate perturbation theory for the energies up to second-order, we evaluate the coefficients
C3 of the first-order dipolar interactions and the coefficients
C6 and
C8 of the second-order additive and nonadditive interactions. Both the dipolar and dispersion interaction coefficients, for these three-body degenerate systems, show dependences on the geometrical configurations of the three atoms. The nonadditive interactions start to appear in second-order. To demonstrate the results and for applications, the obtained coefficients
Cn are evaluated with highly accurate variationally generated nonrelativistic wave functions in Hylleraas coordinates for $\text{He}(1{\phantom{\rule{0.16em}{0ex}}}^{1}S)\text{\ensuremath{-}}\text{He}(1{\phantom{\rule{0.16em}{0ex}}}^{1}S)\text{\ensuremath{-}}\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{1}S)$, $\text{He}(1{\phantom{\rule{0.16em}{0ex}}}^{1}S)\text{\ensuremath{-}}\text{He}(1{\phantom{\rule{0.16em}{0ex}}}^{1}S)\text{\ensuremath{-}}\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{1}P)$, $\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{1}S)\text{\ensuremath{-}}\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{1}S)\text{\ensuremath{-}}\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{1}P)$, and $\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{3}S)\text{\ensuremath{-}}\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{3}S)\text{\ensuremath{-}}\text{He}(2{\phantom{\rule{0.16em}{0ex}}}^{3}P)$. The calculations are given for three like nuclei for the cases of hypothetical infinite mass He nuclei, and of real finite mass
4He or
3He nuclei. The special cases of the three atoms in equilateral triangle configurations are explored in detail, and for the cases in which one of the atoms is in a
P state, we also present results for the atoms in an isosceles right triangle configuration or in an equally spaced collinear configuration. The results can be applied to construct potential energy surfaces for three helium atom systems.
Abstract The energy of interaction of a normal helium atom and one excited to the first triplet or singlet metastable state is calculated over a range of nuclear separations from a0 to 12a0. The Heitler-London method is followed, with inclusion of all non-orthogonality integrals, and using analytic wave functions. Because of identity of the nuclei, g and u states of interaction occur, the energy of the u state having a minimum at about 2·1a0, and a positive maximum of 0·29 and 0·26 eV (for triplet and singlet states respectively) at about 4a0; the g state is entirely repulsive. Comparison is made with experimental evidence for the binding energy of normal and metastable (triplet) atoms. An estimate is made of the second-order dipole-dipole interaction for large separations, and it seems certain that the first-order interaction dominates at least to 12a0. Methods of calculating the necessary integrals are discussed in an appendix.
The long-range interaction between an antiprotonic helium atom
pHe+ and helium atom in its ground state is studied. We calculate the dispersion coefficients
C6 using the complex coordinate rotation (CCR) formalism in order to comply with the resonant nature of metastable states of the antiprotonic helium. We present as well numerical data on static dipole polarizabilities of antiprotonic helium states. The obtained coefficients
C6 may be used to estimate the collisional shift and broadening of transition lines in a low-density precision spectroscopy of the antiprotonic helium.