Precision Calculation on Many Body Atomic Systems

The long-range interactions among two- or three-atom systems are of considerable importance in the cold and ultracold research areas for many-body systems. For an ion and an atom, the long-range interaction potential is dominated by the induction (or polarization) potential resulting from the (classical) effect of the ion's electric field on the atom and the leading term of the induction potential is much stronger than the (quantum mechanical) dispersion (or van der Waals) interaction. The present paper focuses on the long-range interaction of the $\mathrm{Li}(2\phantom{\rule{0.16em}{0ex}}^{2}S)\ensuremath{-}\mathrm{Li}(2\phantom{\rule{0.16em}{0ex}}^{2}S)\ensuremath{-}{\mathrm{Li}}^{+}(1\phantom{\rule{0.16em}{0ex}}^{1}S)$ system, to see what changes this induction effect (originating in the electric field of the ${\mathrm{Li}}^{+}$ ion) yields in the long-range additive and nonadditive interactions of this three-body system. Using perturbation theory for energies, we evaluate the coefficients ${C}_{n}$ in the potential energy for the three well-separated constituents, where $n$ refers to the corresponding order in inverse powers of distance, obtaining the additive interaction coefficients ${C}_{4}, {C}_{6}, {C}_{7}, {C}_{8}, {C}_{9}$ and the nonadditive interaction coefficients ${C}_{7}, {C}_{9}$ . The obtained coefficients ${C}_{n}$ are calculated with highly accurate variationally generated nonrelativistic wave functions in Hylleraas coordinates. Our calculations may be of interest for the study of three-body recombination and for constructing precise potential energy surfaces. We also provide precise evaluations of the long-range potentials for the two-body $\mathrm{Li}(2\phantom{\rule{0.16em}{0ex}}^{2}S)\ensuremath{-}{\mathrm{Li}}^{+}(1\phantom{\rule{0.16em}{0ex}}^{1}S)$ system. For both the two-body and three-body cases, we provide results for the like-nuclei cases of $^{6}\mathrm{Li}$ and $^{7}\mathrm{Li}$ .The long-range interactions among two- or three-atom systems are of considerable importance in the cold and ultracold research areas for many-body systems. For an ion and an atom, the long-range interaction potential is dominated by the induction (or polarization) potential resulting from the (classical) effect of the ion's electric field on the atom and the leading term of the induction potential is much stronger than the (quantum mechanical) dispersion (or van der Waals) interaction. The present paper focuses on the long-range interaction of the $\mathrm{Li}(2\phantom{\rule{0.16em}{0ex}}^{2}S)\ensuremath{-}\mathrm{Li}(2\phantom{\rule{0.16em}{0ex}}^{2}S)\ensuremath{-}{\mathrm{Li}}^{+}(1\phantom{\rule{0.16em}{0ex}}^{1}S)$ system, to see what changes this induction effect (originating in the electric field of the ${\mathrm{Li}}^{+}$ ion) yields in the long-range additive and nonadditive interactions of this three-body system. Using perturbation theory for energies, we evaluate the coefficients ${C}_{n}$ in the potential energy for the three well-separated constituents, where $n$ refers to the corresponding order in inverse powers of distance, obtaining the additive interaction coefficients ${C}_{4}, {C}_{6}, {C}_{7}, {C}_{8}, {C}_{9}$ and the nonadditive interaction coefficients ${C}_{7}, {C}_{9}$. The obtained coefficients ${C}_{n}$ are calculated with highly accurate variationally generated nonrelativistic wave functions in Hylleraas coordinates. Our calculations may be of interest for the study of three-body recombination and for constructing precise potential energy surfaces. We also provide precise evaluations of the long-range potentials for the two-body $\mathrm{Li}(2\phantom{\rule{0.16em}{0ex}}^{2}S)\ensuremath{-}{\mathrm{Li}}^{+}(1\phantom{\rule{0.16em}{0ex}}^{1}S)$ system. For both the two-body and three-body cases, we provide results for the like-nuclei cases of $^{6}\mathrm{Li}$ and $^{7}\mathrm{Li}$.

Physical Review AMar 16, 20203 citations

High accuracy many-body calculations on quantum computers

James K. Freericks, Jeffrey Cohn, Khadijeh Najafi +1 more

Bulletin of the American Physical SocietyJun 1, 20180 citations

Coupled rearrangement channel calculation of the fine and hyperfine structures of the antiprotonic helium atom

Nobuhiro Yamanaka, Yasushi Kino, Hiroshi Kudo +1 more

We precisely calculate the fine and hyperfine structure splittings of the $(v,J)=(1,35)$ state in the antiprotonic helium atom, where $v$ is the vibrational quantum number and $J$ is the total orbital angular momentum. The coupled rearrangement channel method is employed to efficiently describe correlation effects in the three-body system with atomic and molecular characters. An accuracy of better than ${\ensuremath{\alpha}}^{2}\ensuremath{\approx}50\mathrm{ppm}$ has been achieved. The result obtained is in good agreement with the previous calculation within $\ensuremath{\sim}200 \mathrm{ppm}.$ We also examine the correlation effects, in particular orbital polarization effects.We precisely calculate the fine and hyperfine structure splittings of the $(v,J)=(1,35)$ state in the antiprotonic helium atom, where $v$ is the vibrational quantum number and $J$ is the total orbital angular momentum. The coupled rearrangement channel method is employed to efficiently describe correlation effects in the three-body system with atomic and molecular characters. An accuracy of better than ${\ensuremath{\alpha}}^{2}\ensuremath{\approx}50\mathrm{ppm}$ has been achieved. The result obtained is in good agreement with the previous calculation within $\ensuremath{\sim}200 \mathrm{ppm}.$ We also examine the correlation effects, in particular orbital polarization effects.

Physical Review ADec 13, 200034 citations

Many-Body Perturbation Theory

Reiner M. Dreizler, Eberhard K. U. Gross

Springer eBooksJan 1, 19904 citations

{\mathrm{Li}}^{+}

ion) yields in the long-range additive and nonadditive interactions of this three-body system. Using perturbation theory for energies, we evaluate the coefficients

{C}_{n}

in the potential energy for the three well-separated constituents, where

n

refers to the corresponding order in inverse powers of distance, obtaining the additive interaction coefficients

{C}_{4}, {C}_{6}, {C}_{7}, {C}_{8}, {C}_{9}

and the nonadditive interaction coefficients

{C}_{7}, {C}_{9}

. The obtained coefficients

{C}_{n}

are calculated with highly accurate variationally generated nonrelativistic wave functions in Hylleraas coordinates. Our calculations may be of interest for the study of three-body recombination and for constructing precise potential energy surfaces. We also provide precise evaluations of the long-range potentials for the two-body $\mathrm{Li}(2\phantom{\rule{0.16em}{0ex}}^{2}S)\ensuremath{-}{\mathrm{Li}}^{+}(1\phantom{\rule{0.16em}{0ex}}^{1}S)$ system. For both the two-body and three-body cases, we provide results for the like-nuclei cases of

^{6}\mathrm{Li}

and

^{7}\mathrm{Li}

We precisely calculate the fine and hyperfine structure splittings of the

(v,J)=(1,35)

state in the antiprotonic helium atom, where

v

is the vibrational quantum number and

J

is the total orbital angular momentum. The coupled rearrangement channel method is employed to efficiently describe correlation effects in the three-body system with atomic and molecular characters. An accuracy of better than ${\ensuremath{\alpha}}^{2}\ensuremath{\approx}50\mathrm{ppm}$ has been achieved. The result obtained is in good agreement with the previous calculation within $\ensuremath{\sim}200 \mathrm{ppm}.$ We also examine the correlation effects, in particular orbital polarization effects.