Exact analytical expressions for the matrix elements of the Uehling potential in a basis of explicitly correlated exponential wave functions are presented. The obtained formulas are then used to compute with an improved accuracy the vacuum polarization correction to the binding energy of muonic and pionic molecules, both in a first-order perturbative treatment and in a nonperturbative approach. The first resonant states lying below the $n=2$ threshold are also studied, by means of the stabilization method with a real dilatation parameter.Exact analytical expressions for the matrix elements of the Uehling potential in a basis of explicitly correlated exponential wave functions are presented. The obtained formulas are then used to compute with an improved accuracy the vacuum polarization correction to the binding energy of muonic and pionic molecules, both in a first-order perturbative treatment and in a nonperturbative approach. The first resonant states lying below the $n=2$ threshold are also studied, by means of the stabilization method with a real dilatation parameter.

arXiv:1211.7234Physical Review AJan 14, 20133 citations

Many-body phsyics with ensembles of atoms in resonant interactions

Antoine Browaeys

Mar 1, 20220 citations

Fine and quadrupole structure of the weakly bound systems (dtμ)11dee and (ddμ)11dee

D. Bakalov, K. Bakalova, V. I. Korobov +2 more

The interaction of the quadrupole electric moment of the muonic molecules with the Coulomb field of the embedding ${\mathrm{D}}_{2}$ molecule gives rise to corrections to the energy levels that depend on the spin and significantly modify the muonic molecule fine structure. We present the first-order calculation of the fine and hyperfine structure of the energy levels of the weakly bound states $(dt\ensuremath{\mu}{)}_{11}$ and $(dd\ensuremath{\mu}{)}_{11}$ that accounts for the quadrupole finite-size corrections as well. The reported results are of interest for the upcoming high-precision measurement of the energy levels and the formation rate of the muonic molecules $\mathrm{dt}\ensuremath{\mu}$ and $\mathrm{dd}\ensuremath{\mu}$.The interaction of the quadrupole electric moment of the muonic molecules with the Coulomb field of the embedding ${\mathrm{D}}_{2}$ molecule gives rise to corrections to the energy levels that depend on the spin and significantly modify the muonic molecule fine structure. We present the first-order calculation of the fine and hyperfine structure of the energy levels of the weakly bound states $(dt\ensuremath{\mu}{)}_{11}$ and $(dd\ensuremath{\mu}{)}_{11}$ that accounts for the quadrupole finite-size corrections as well. The reported results are of interest for the upcoming high-precision measurement of the energy levels and the formation rate of the muonic molecules $\mathrm{dt}\ensuremath{\mu}$ and $\mathrm{dd}\ensuremath{\mu}$.

Physical Review AMay 1, 19989 citations

Many-body physics with atoms in resonant interaction

Antoine Browaeys

Aug 1, 20220 citations

Many-body physics with ensembles of atoms in resonant interactions

Antoine Browaeys

Mar 1, 20220 citations

n=2

threshold are also studied, by means of the stabilization method with a real dilatation parameter.

The interaction of the quadrupole electric moment of the muonic molecules with the Coulomb field of the embedding

{\mathrm{D}}_{2}

molecule gives rise to corrections to the energy levels that depend on the spin and significantly modify the muonic molecule fine structure. We present the first-order calculation of the fine and hyperfine structure of the energy levels of the weakly bound states $(dt\ensuremath{\mu}{)}_{11}$ and $(dd\ensuremath{\mu}{)}_{11}$ that accounts for the quadrupole finite-size corrections as well. The reported results are of interest for the upcoming high-precision measurement of the energy levels and the formation rate of the muonic molecules $\mathrm{dt}\ensuremath{\mu}$ and $\mathrm{dd}\ensuremath{\mu}$.