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Hyperfine structures of $^{211}$Fr due to the interactions of magnetic dipole($\mu$), electric quadrupole ($Q$) and magnetic octupole ($\Omega$) momentswith the electrons are investigated using the relativistic coupled-cluster(RCC) theory with an approximation of singles, doubles and important valencetriples excitations in the perturbative approach. Validity of our calculationsare substantiated by comparing the results with their available experimentalvalues. Its $Q$ value has also been elevated by combining the measuredhyperfine structure constant of the $7p \ ^2P_{3/2}$ state with our improvedcalculation. Considering the preliminary value of $\Omega$ from the nuclearshell-model, its contributions to the hyperfine structures up to the $7d \^2D_{5/2}$ low-lying states in $^{211}$Fr are estimated. Energy splittings ofthe hyperfine transitions in many states have been assessed to find outsuitability to carry out their precise measurements so that $\Omega$ of$^{211}$Fr can be inferred from them unambiguously.

Appraising nuclear octupole moment contributions to the hyperfine structures in $^{211}$Fr