Feasibility study to use neutron capture for an ultralow energy nuclear-recoil calibration in liquid xenon

The feasibility of an ultralow energy nuclear-recoil measurement in liquid xenon using neutron capture is investigated for a small (subkilogram) liquid xenon detector that is optimized for a high scintillation gain, and a pulsed neutron source. The measurement uses the recoil energies imparted to xenon nuclei during the deexcitation process following neutron capture, where promptly emitted $\gamma$ cascades can provide the nuclei with up to $0.3{\mathrm{keV}}_{\mathrm{nr}}$ of recoil energy due to conservation of momentum. A successful calibration of scintillation photon and ionization electron yields below this energy will contribute to a greater sensitivity for liquid xenon experiments in searches for light weakly interacting massive particles.

Figure 1

Nuclear recoil spectrum due to neutron interactions simulated in the MiX detector. The shaded light green histogram (140,000 counts) shows all recoil events due to neutron captures, while the shaded dark green portion (20,000 counts) only retains those where all of the $\gamma$-rays from the nuclear deexcitation process escape the active volume. The concentration of signals below about $0.3{\mathrm{keV}}_{\mathrm{nr}}$ provides an opportunity for a measurement of quanta in this energy region. Also shown are the recoil events due to elastic (dashed magenta) and inelastic (dashed-dot blue) neutron scatters. All inelastic scatters are shown, regardless of whether their deexcitation $\gamma$-products escape the TPC.

Figure 2

Top: NR spectrum due to thermal neutron capture in LXe simulated using geant4. The gray uncertainty band represents the total uncertainty, which incorporates discrepancies in the $\gamma$ spectra between the ENSDF and the EGAF files. Bottom: the error band in the top panel is presented as percent uncertainty for clarity.

Figure 3

3D model of the MiX detector. The inner cryostat encloses the LXe space that partially submerges the TPC assembly, and thus the TPC contains only a small fraction of the LXe in the system. The thickness of the water tank shown here is 5 cm.

Figure 4

Kinetic energy distributions of neutrons as they enter the TPC after being moderated by the water tank, shown for various thicknesses of the tank.

Figure 5

Distributions of the NR energy transferred to xenon in the TPC by neutron scattering before capture, shown for various thicknesses of the water tank.

Figure 6

Top: neutron capture locations in the TPC (left), and signal event locations (right), each normalized to unity. The neutrons enter the water tank from the right, which causes the higher concentration of captures on the right edge. The white circle on the right plot indicates the fiducial radius defined in the MiX detector [27]. Only 20% of signal events fall outside its radius. Bottom: radial positions of capture (light green) and signal (dark green) events. The signal population scaled to the total counts of captures is also shown (dashed) to demonstrate the higher concentration of signal events near the walls of the TPC.

Figure 7

Recoil energy of the xenon atoms at the time the neutrons were captured for ${10}^5$ neutron captures. The simulation corresponds to a 5 cm water tank and a $30\mu \mathrm{s}$ pulse width. A small fraction of neutrons, shown in the top left quadrant, reaches the TPC early with enough energy to cause collisional recoil energies noticeably greater than the $0.3{\mathrm{keV}}_{\mathrm{nr}}$ possible by the $\gamma$ cascades alone. The time of flight of these events is $\mathcal{O}(100\mathrm{ns})$, so they abruptly cease shortly after the pulse ends at $30\mu \mathrm{s}$.

Figure 8

Time distribution of the neutrons that interact with the active LXe volume in the TPC, from a simulation done for a 5 cm water tank and $w_n=30\mu \mathrm{s}$. The total counts due to neutron capture (light green) and elastic scattering (dashed magenta) are normalized to unity. Inelastic scattering events are omitted from this plot for clarity as their rate is a hundredfold less than the elastic rate. All events shown here deposit less than $1{\mathrm{keV}}_{\mathrm{nr}}$. The dark green histogram shows all signal events, and the hatched portion shows the signal events that occur after the last scattering time. Visual checkpoints for when 50% and 90% of all signal events occur are shown with the vertical dashed and dotted lines, respectively.

Figure 9

Recoil energy distributions of the signal events inside the signal window (solid) and before the signal window (dashed) for $w_n=30\mu \mathrm{s}$ and a 5 cm water tank moderator. Waiting until the last scatter occurs ensures that the capture of fast neutrons, which are associated with larger recoil energies, are not included in the analysis.

Figure 10

Simulated metrics as a function of neutron pulse width for ${10}^9\mathrm{n}/\mathrm{s}$ and various water tank thicknesses. Top: number of signal events falling inside a signal window. Center top: width of the signal window, which begins after the last scattering event and ends when 99% of signal events have been produced after the last scatter. Center bottom: ${\mathrm{N}}_{\text{signal}}$ for events that deposit less than $1{\mathrm{keV}}_{\mathrm{nr}}$ in the TPC. Bottom: ${\mathrm{T}}_{\mathrm{NR}}$ for events that deposit less than $1{\mathrm{keV}}_{\mathrm{nr}}$ in the TPC.

Figure 11

Deposited energy spectrum due to the internal (dotted) and external (dashed) ER background below 0.5 keV without clustering applied, for a 5 cm water moderator. Also shown is the corresponding recoil spectrum due to the neutron capture signals. This simulation assumes a 1.2 day exposure with a $30\mu \mathrm{s}$ pulse width and 60 Hz pulsing frequency, resulting in 20,000 neutron capture signal events. The number of ER counts below 0.5 keV is less than 0.1% of the number of NR signal counts.

Figure 12

Distribution of high energy ER deposits in the TPC as a function of time elapsed since the beginning of a neutron pulse of width $30\mu \mathrm{s}$. Simulated for a 5 cm water tank, ER events resulting from 3000 pulses are shown, corresponding to about 12 signal events. Shown in orange is the signal window for this configuration, presented in the center top panel of Fig. 10.

Figure 13

Probability $P$ of obtaining a clean signal window where no signal event is accompanied by an ER deposit, as a function of neutron pulse width $w_n$. Curves are shown for a representative set of water tank thicknesses.

Figure 14

The projected 90% sensitivities for a generic background-free LXe experiment with a full LUX-like exposure are shown for different energy thresholds in solid maroon, red, and orange curves. The limits are generated using the NEST 2.0.1 default yield models [51]. The searches use both ionization and scintillation channels with no PMT coincidence requirement and a two extracted-electron threshold. A 0% signal acceptance is enforced for recoil energies below the indicated values. The solid and dashed blue curves verify that the LUX result is fairly reproduced [55]. Also shown are limits from LZ (dashed black) [56], XENON1T (dashed green) [57], and DarkSide-50 [58] (dashed purple).

Figure 15

Nuclear recoil spectra for 500,000 neutron capture events produced by the geant4 simulation and reconstruction for ${}^{129}\mathrm{Xe}$, ${}^{130}\mathrm{Xe}$, and ${}^{131}\mathrm{Xe}$. The reconstructed recoil energies skew slightly lower than the geant4 simulation, but the spectra match well above $0.13{\mathrm{keV}}_{\mathrm{nr}}$.

Figure 16

Nuclear recoil spectra for 500,000 neutron capture events produced by geant4 simulation, geant4 reconstruction, and reconstruction using the EGAF database. The uncertainty in the EGAF NR spectrum (purple band) is calculated by varying the width of the Gaussian $\gamma$ multiplicity distribution for each isotope. The EGAF reconstruction matches the geant4 simulation closely for energies greater than $0.13{\mathrm{keV}}_{\mathrm{nr}}$.