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

TL;DR

This work reports the first direct measurement of the neutron incoherent scattering length for $^{199}$Hg using a Ramsey-type approach with stored ultracold neutrons in the PSI nEDM setup. By exploiting the pseudo-magnetic field generated by polarized Hg nuclei and tracking the neutron Larmor frequency shift across varying Hg densities and polarizations, the authors extract the slope $\partial(\Delta f_n)/\partial(\rho P)$ and deduce $b_i$ via $b_i = \frac{m_n}{2 \hbar} \sqrt{\frac{I+1}{I}} \frac{\Delta f_n}{\rho P}$. They determine $b_i = (-16.2 \pm 2.0)$ fm, establishing the sign and aligning the magnitude with literature values, thereby refining systematic uncertainty budgets in nEDM experiments using Hg as a co-magnetometer. The result highlights the importance of simultaneously measuring Hg polarization and density in future neutron EDM searches and has implications for other co-magnetometer systems such as $^{129}$Xe.

Abstract

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 $b_\textrm{i}$ 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 $b_\textrm{i}= (-16.2 \pm 2.0)\,$fm agrees in magnitude with previous determinations and provides the so-far unknown sign of the quantity.

Figures (6)

• Figure 1: (Color online) a) A sketch of the Ramsey apparatus to measure the neutron EDM at the Paul Scherrer Institute. The small green spheres represent the neutrons and the large pink spheres the mercury atoms. The incoming ultracold neutrons (UCN) are transported from the source (U) to the switch (S), which guides them to the precession chamber (C) via neutron guides (G). After a certain storage time, the UCN are eventually transported from the precession chamber to the switch, and the detectors for spin-up and spin-down neutrons (D1, D2). The mercury system, indicated in pink colors, consists of the source (H) and a polarization cell situated below the precession chamber, the read-out laser (L) on one side, and a photo-detector (PD) on the opposite side. The blue dashed line represents the volume where the magnetic field $\lvert \vec{B}_0\rvert \approx 1\,$µ T is applied, and the blue arrow represents its orientation. This volume is shielded from the ambient magnetic field by four cylindrical layers of mu-metal, not shown for clarity. The neutrons and mercury atoms are represented with their spin (black arrow) during the free precession. The coils used to perform the spin flips are not depicted for clarity. b) A simplified representation of the DC signal recorded by the photo-detector (PD) for one measurement cycle as a function of time. The characteristic times $t_0$, $t_1$, and $t_3$ are related to the measurement sequence of the mercury and correspond to the points in time when the chamber starts to be filled with mercury, when the free precession of the mercury spins starts, thus, creating an associated oscillating signal, and when the emptying process of the chamber begins, respectively. Below the spin states of the mercury nuclei and the neutrons are shown when the neutron Ramsey technique is exactly on resonance and for a $\frac{3}{4}\pi$ mercury spin flip configuration. The spin flip pulses are indicated by the color shaded areas in the diagram. The duration of the mercury spin flip pulses are listed in Table \ref{['Table:Batches']} and the neutron spin flips pulses have a length of $T_{SF}=2$ s.
• Figure 2: Example of asymmetry $A$ vs. $\Delta \nu$ plot from batch 3. Here, only ten data points are used for the fit with Eq. (\ref{['eq.sinFit']}) (red curve) due to the selection criteria described in Sec. \ref{['DataSelection']}.
• Figure 3: a) Example of a DC-coupled signal of the ${}^{199}$Hg co-magnetometer for a $\frac{3}{4}\pi$ spin configuration. The $DC(t)$ values are represented by red squared dots for the times $t_0$, $t_1$, and $t_2$. b) Detailed view of the green framed region in Fig. 3a. The first part of the signal corresponds to the mercury spin flip and is fitted by a double sinusoidal function indicated in pink (fast sinusoidal oscillation multiplied with a sinusoidal envelope). The value of $DC(t_1)$ is determined from this fit. The green line is a guide for the eyes to see the oscillating signal caused by the free precession of the mercury spins. c) An example of the AC-coupled filtered signal between $t_1$ and $t_3$ (black curve) of the photo-detector of the same cycle. The red curve is a representation of the decay sinusoidal function used to fit the data but with its period scaled by a factor of 100 so that the oscillations become visible. For this cycle, the amplitude is $a_s(t_1)=0.36\,$V, the running averages of the light signal are $DC(t_0)=-5.48\,$V, $DC(t_1)=-3.28\,$V, and the decay time constants are $T_2 = 101\,$s and $T_3=810\,$s.
• Figure 4: a) Pull distribution of $DC(t_1)$ as defined in Eq. (\ref{['eq:PullDC']}). The red dashed lines represent the exclusion limits. Note, the vertical axis is in log-scale for a better visibility. b) Pull distribution from Eq. (\ref{['eq:PullCos']}). The red dashed lines represent the exclusion limits and the continuous red line is a Gaussian fit to the distribution. c) Pull distribution of the product of the mercury number density and polarization as defined in Eq. (\ref{['eq:PullrhoP']}). The red dashed lines represent the exclusion limits and the continuous red line is again a Gaussian fit.
• Figure 5: An example of linear regression for one polarization group using the same group of data as in the previous figures \ref{['Fig:CosFit']} and \ref{['Fig:PMT']}. A positive (negative) value of $\rho P$ corresponds to the $\frac{3}{4}\pi$ ($\frac{7}{4}\pi$) mercury spin configuration.