Calculations of long range interactions for $^{87}$Sr Rydberg states*

A method for calculating the properties of Rydberg states and Rydberg-Rydberg interaction between two $^{87}$Sr atoms is described.[1] The method is based on a multichannel quantum defect theory (MQDT) description of the Rydberg states that accounts for the hyperfine splitting of the $^{87}$Sr$^+$ ground state. Results are given for the scalar and tensor polarizabilities and the eigenvalues of the $C_6$ matrix for the $5sns$ $F_T=9/2$ series. These results illustrate the new features that arise due to the hyperfine splitting of the thresholds. In particular, there should be several strongly coupled F\"orster resonances above $n=50$ unlike the case of $^{88}$Sr which has none. [1] F. Robicheaux, “Calculations of long range interactions for $^{87}$Sr Rydberg states,” J. Phys. B {\bf 52}, 244001 (2019).