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Mass scaling and non-adiabatic effects in photoassociation spectroscopy of ultracold strontium atoms

We report photoassociation spectroscopy of ultracold $^{86}$Sr atoms near the intercombination line and provide theoretical models to describe the obtained bound state energies. We show that using only the molecular states correlating with the $^1S_0$$+$$^3P_1$ asymptote is insufficient to provide a mass scaled theoretical model that would reproduce the bound state energies for all isotopes investigated to date: $^{84}$Sr, $^{86}$Sr and $^{88}$Sr. We attribute that to the recently discovered avoided crossing between the $^1S_0$$+$$^3P_1$ $0_u^+$ ($^3Π_u$) and $^1S_0$$+$$^1D_2$ $0_u^+$ ($^1Σ^+_u$) potential curves at short range and we build a mass scaled interaction model that quantitatively reproduces the available $0_u^+$ and $1_u$ bound state energies for the three stable bosonic isotopes. We also provide isotope-specific two-channel models that incorporate the rotational (Coriolis) mixing between the $0_u^+$ and $1_u$ curves which, while not mass scaled, are capable of quantitatively describing the vibrational splittings observed in experiment. We find that the use of state-of-the-art ab initio potential curves significantly improves the quantitative description of the Coriolis mixing between the two -8 GHz bound states in $^{88}$Sr over the previously used model potentials. We show that one of the recently reported energy levels in $^{84}$Sr does not follow the long range bound state series and theorize on the possible causes. Finally, we give the Coriolis mixing angles and linear Zeeman coefficients for all of the photoassociation lines. The long range van der Waals coefficients $C_6(0_u^+)=3868(50)$~a.u. and $C_6(1_u)=4085(50)$~a.u. are reported.