Measurement of the neutron incoherent scattering length of ${}^{199}$Hg using stored ultracold neutrons

We present the first direct measurement of the neutron incoherent scattering length of ${}^{199}$Hg. The measurement was performed with the Ramsey apparatus of the neutron electric dipole moment experiment located at the Paul Scherrer Institute. The incoherent scattering length $b_{\text{i}}$ was determined by investigating the pseudo-magnetic effect due to the strong interaction between the neutron spins and the nuclear spins of mercury atoms. The resulting frequency shift of the neutron Larmor precession frequency was determined for various ${}^{199}$Hg density and polarization values. The obtained value of $b_{\text{i}}=(-16.2\pm 2.0)$fm agrees in magnitude with previous determinations and provides the so-far unknown sign of the quantity.