Measurement of the neutron capture cross-section on argon

TL;DR

This paper presents a precise differential measurement of the neutron capture cross-section on argon using a Time-Of-Flight neutron beam, addressing previous discrepancies and providing critical data for neutrino and dark matter experiments.

Contribution

It provides the first differential measurement of neutron capture on argon over a specific energy range, improving accuracy for experimental applications.

Findings

Measured cross-section: 673 ± 26 (stat.) ± 59 (sys.) mb

Differential cross section fitted assuming 1/v dependence

Addresses previous measurement discrepancies

Abstract

The use of argon as a detection and shielding medium for neutrino and dark matter experiments has made the precise knowledge of the cross section for neutron capture on argon an important design and operational parameter. Since previous measurements were averaged over thermal spectra and have significant disagreements, a differential measurement has been performed using a Time-Of-Flight neutron beam and a $\sim$4$\pi$ gamma spectrometer. A fit to the differential cross section from $0.015-0.15$\,eV, assuming a $1/v$ energy dependence, yields $\sigma^{2200} = 673 \pm 26 \text{ (stat.)} \pm 59 \text{ (sys.)}$\,mb.

Tables

Table 1. Table 1: Summary of the contributions to the final error of the cross section.

Error	Stat. (%)	Sys. (%)
$\delta \rho /\rho$	0.0	0.3
$\delta L/L$	0.0	2.2
$\delta \epsilon /\epsilon$	0.3	0.9
$⟨\delta G_i/G_i⟩$	2.0	0.0
$⟨\delta N_i/N_i⟩$	1.6	5.8

Equations

$$D^S=T_0^{S}R.$$

$$D^V=T_0^{V}R+{\Phi }^V{\sigma }_b.$$

$$D^A=T_0^{A}R+{\Phi }^A{\sigma }_b+{\Phi }^A{\sigma }_a.$$

$${\Phi }^A{\sigma }_a=D^A-\frac{T_0^A}{T_0^S}{D}^S-\frac{{\Phi }^A}{{\Phi }^V}\left(D^V-\frac{T_0^V}{T_0^S}{D}^S\right).$$

$$\sigma (v)=\frac{{\sigma }_{mp}{v}_{mp}}{v}$$

$$v_{mp}=\sqrt{2kT/m}$$

$${\sigma }_i=\frac{A}{a_{40}\rho L{N}_A}\frac{G_i}{\epsilon N_i}-{\zeta }_i$$

Full text

I Introduction

Argon is a common detection medium used in many particle physics experiments. As a noble element, it has a low affinity for electron absorption and can therefore be used in Time Projection Chambers (TPC) or other applications where long distance electron or ion drift is desirable. Due to its low cost compared to other noble elements, such as xenon or neon, it has been used in very large neutrino detectors including ICARUS Antonello:2013ypa , MicroBooNE Acciarri:2016smi , and protoDUNE Abi:2017aow . A large liquid argon TPC is also planned for the DUNE experiment Acciarri:2016ooe . Argon is also an excellent scintillator and can be made very radiologically clean, thus it is also used as a target in dark matter experiments, for instance DarkSide Aalseth:2017fik , and as a shield for neutrinoless double beta decay experiments such as GERDA Ackermann:2012xja and LEGEND Abgrall:2017syy .

All these applications rely on having a complete understanding of the transport of neutrons through liquid argon and the physics of the (n,$\gamma$) capture process on natural argon. There has been only three measurements of the thermal-neutron capture cross section, and these have yielded inconsistent results Koehler:196318a ; French:1965225 ; RANAKUMAR1969333 . All were done by activating samples of argon in a nuclear reactor, counting the beta decay of the 41Ar daughter in a gamma spectrometer, and then making appropriate corrections to convert the reactor spectral averaged cross section to the standard thermal cross section ($\sigma^{2200}$). In this paper we report the results of a differential measurement of the neutron capture cross section on argon in the thermal energy range using the Detector for Advanced Neutron Capture Experiment (DANCE) at Los Alamos National Laboratory.

II EXPERIMENTAL SETUP

DANCE is located on Flight Path 14 at the Lujan Neutron Scattering Center LANSCEBeam:1990 at a distance of $20.25$ m from the upper-tier water moderator of the accelerator-driven pulsed neutron source. The neutrons are produced via spallation reactions caused by an $800$ MeV proton beam, impinging on a tungsten target, with a typical beam current of $80$ $\mu$A. A mercury shutter can be used to prevent neutrons reaching the target, allowing different run types to be performed as described in Sec. IV. The gamma detector is a nearly 4$\pi$ gamma ray calorimeter composed of a spherical array of 160 BaF2 crystals, each with a volume of $734$ cm3 and monitored by a photomultiplier tube (PMT). Adjacent to the crystals’ inner face and surrounding the evacuated beam pipe where neutrons are traveling from the moderator, a $6$ cm thick 6LiH shell has been installed to attenuate the rate of scattered neutrons capturing on the BaF2 crystals. A detailed description of the DANCE setup can be found in Refs. Heil:2013oua ; MOSBY201475 . This Time-Of-Flight (TOF) system is capable of measuring neutron energy in the thermal range with a few meV accuracy.

The Argon Capture Experiment at DANCE (ACED) consists of a target volume of argon gas located at the center of the DANCE spectrometer. This target consists of a hollow aluminum cylinder that is $2.9$ cm long, $3$ cm in diameter, sealed by two $0.0762$ mm thick Kapton windows spaced apart by $2.30\pm 0.05$ cm. This uncertainty is estimated from the dimensional tolerances specified on the target blueprints. These Kapton windows allow neutrons to pass through while minimizing scattering. The same apparatus was used for a previous measurement of the 136Xe neutron capture cross section PhysRevC.94.034617 . The target volume was filled with high purity ($99.999$ % Ar) gaseous natural argon and pressurized above the local atmospheric pressure throughout the data taking period. As described in Sec. III, background measurements were taken with the target fully evacuated and kept at the same vacuum level as the surrounding beam pipe.

A detailed schematic of the ACED gas system is displayed in Fig. 1. An electronic regulator was used to control the absolute pressure in the target, which was monitored, along with the temperature, by two temperature compensated gauges (Additel 681-02) located upstream and downstream of the vessel. A buffer volume was used to smooth out small pressure fluctuations in the system. As a result, during the data taking periods the average pressure and temperature of argon were $1.0987\pm 0.0005$ bar absolute and $296.7\pm 1.0$ K, respectively. These values yielded an average density of $\rho=(1.779\pm 0.006)\times 10^{-3}$ g/cm3. The uncertainty in temperature was derived from the observed temperature fluctuation in the experimental hall. The error on the average density takes into account the intrinsic accuracy of the gauges, the difference between the upstream and downstream gauges, and the stability of the pressure and temperature over the duration of each run.

III MEASUREMENT STRATEGY and RUN DESCRIPTION

Events in DANCE are recorded in a $15$ ms acquisition window triggered by either a beam spill or an external pulser - provided the energy deposit is above $150$ keV.

Data undergo several stages of processing. Initially the intrinsic alpha-induced background present in the BaF2 crystals111The intrinsic radioactivity of BaF2 originates from the $\alpha$-decay chain of the chemical homologue 226Ra (typically $0.2$ Bq/cm3 Heil:2013oua ). Most of the DANCE crystals have an intrinsic alpha activity ranging between $150$ and $250$ Hz. is removed on a crystal-by-crystal basis by applying a time profile discrimination cut. This selection is based on the difference in intensity ratio between the fast and slow components of the BaF2 scintillation light Reifarth:2013xny as a function of the radiation type in this case, between alphas and gammas. Next, individual gamma rays are reconstructed via a nearest neighbor clustering algorithm, in which all adjacent crystals, contributing to a single event, are grouped into a cluster. The number of such clusters gives the reconstructed cluster multiplicity of that event; the energy of the cluster provides the individual reconstructed gamma energy, with the summed energy of all clusters yielding the total reconstructed event energy. The need for such an algorithm is necessitated by gammas undergoing multiple Compton scatters and depositing energy in adjacent crystals.

The ACED data taking period ran from the 2nd to the 14th November 2018 and was split into 6 distinct non-calibration run types intermittently spaced throughout this period. Each run type was designed to allow a full understanding of the detector conditions, response, and backgrounds. This included four “beam on” run types where the target was either filled with argon, or completely evacuated, and with the beam shutter open or closed. Additionally, there were two “beam off” runs in which the target was either filled with argon, or completed evacuated.

IV RUN SELECTION and CALIBRATION

Data quality cuts (e.g. run duration, expected crystal occupancy, sufficient number of alpha events to perform calibration) are applied to ensure good detector performance. This reduces the overall data-set by about $25$ %. Furthermore, of the 160 crystals three did not show satisfactory results due to their low gain, hence were removed from the analysis.

The energy calibration of DANCE, using 22Na, 88Y, 60Co, and 239Pu-9Be radioactive sources, was performed before and after the argon target runs. Each crystal’s energy response was found to be linear to within $2.4$ %. The energy scale is accurate to within $1.4$ % in the energy range of interest ($<6$ MeV). This was deduced by comparing the reconstructed to nominal energies of the calibration sources. Moreover, the stability of the energy scale throughout the data taking period was assessed. This was achieved by looking at the energy deposited by the most energetic, fully-contained alpha from the intrinsic radium contamination, and was found stable to within $1$ %.

A total energy cut is applied in order to select events from neutron captures on 40Ar. Given the Q-value of $6.0989$ MeV, events need to deposit a total energy of $6.1^{+0.5}_{-0.9}$ MeV in the detector. Here, the energy window accounts for: the $150$ keV hardware threshold, the energy scale uncertainty, and the $4$ % resolution of the detector at this energy (measured using the calibration data). In addition, we require more than one reconstructed cluster - this is motivated by the fact that a neutron capture on an s-state for a $0^{+}$ nuclei will produce multiple gammas. This is confirmed in the CapGam database Hardell:1970tncna ; Nesaraja:2016ktw . Moreover, requiring multiple clusters in an event suppresses the constant-in-time (CIT) background due to natural radioactivity within the crystals and from outside of the detector Reifarth:2013xny .

To assess the efficiency of measuring the 41Ar gamma cascade, a Geant4-based Agostinelli:2003250 ; Allison:2016186 ; Jandel:2007ge simulation was performed. This modelled, on a crystal-by-crystal basis, the energy resolution and the minimum detectable deposited energy - along with their uncertainties ($0.6$ %). Furthermore, it accounted for the uncertainty in the intensities of the major gamma lines Hardell:1970tncna ; Nesaraja:2016ktw in the 41Ar gamma cascade ($0.7$ %). Finally, it included the combined effect of the Q-value and cluster multiplicity cuts. This approach yielded a result of $\varepsilon=98.9\pm 0.3\text{ (stat.)}\pm 0.9\text{ (sys.)}$ %.

Two beam monitors, 6Li and 3He, located downstream of the target volume, were used to understand the neutron beam flux as a function of energy. These utilize the known neutron capture cross sections for the 6Li(n,$\alpha$)3H and 3He(n,p)3H interactions, respectively. This, combined with the neutron beam size being smaller than both the argon target volume and the beam monitors, allowed the determination of the total neutron flux. In this analysis, we used the 6Li monitor to measure the beam flux with the 3He monitor providing an essential consistency check. The absolute calibration of the beam monitor was obtained using the controlled activation of a sodium sample, which was placed in the neutron beam at the same location as the argon target volume. The activated sodium target was later counted on a HPGe detector to determine the neutron flux at DANCE. Using the energy profile of the beam monitors, only thermal neutrons ($<0.2$ eV) were selected and their contribution to the total flux was calculated. A detailed description of this method can be found in Ref. SodiumPaper . This procedure has an uncertainty of $5.8$ % when combined with the detector stability over time and is the dominant uncertainty in the experiment (see Tab. 1).

In order to quantify events coming from neutron captures on argon it is necessary to perform a background subtraction. To do this the following three data-sets are used: beam incident on the argon filled target (A), no beam incident on the argon filled target (S), and beam incident on the target under vacuum (V).

In the following text, $T_{0}$ refers to the number of beam spills, $D$ is the number of events, $R$ is the rate of events, $\Phi$ is the neutron flux, and $\sigma_{a,b}$ are the neutron capture cross sections on argon and on the sum of surrounding materials, respectively. The number of CIT background events are measured in data-set S, given by:

[TABLE]

Analogously, in data-set V, $D^{V}$ is the sum of the background events due to the flux of scattered neutrons ($\Phi^{V}$) captured in the materials surrounding the target (e.g. the Kapton windows) together with CIT backgrounds:

[TABLE]

Furthermore, in data-set A, $D^{A}$ is comprised of CIT backgrounds, beam-related gammas passing through the shielding, background events due to captures on the surrounding materials, and neutron captures on 40Ar:

[TABLE]

The number of neutron captures on argon can then be calculated using Eqs. 1 to 3:

[TABLE]

Fig. 2 shows an example of this procedure, together with the energy spectra of the different ACED data-sets.

V RESULTS

Outside the resonance region ($<15$ eV for argon, see Ref. Brown:2018jhj ), the neutron absorption cross section follows the $1/v$ law Westcott:1960effective :

[TABLE]

where $\sigma_{mp}$ is the neutron absorption cross section at the most probable velocity:

[TABLE]

where $k$ is the Boltzmann constant, $T$ is the temperature of the moderator, and $m$ is the reduced mass of the argon-neutron system.

Inside the i-th neutron energy bin, the cross section can be evaluated as:

[TABLE]

where $A$, $a_{40}$ and $\varepsilon$ are the atomic mass of natural argon, the 40Ar abundance, and the efficiency to see the 41Ar gamma cascade after applying the selection cuts, respectively. $L$ is the length of the target, and $N_{A}$ is Avogadro’s number. $G_{i}$ is the number of neutron captures, detected by DANCE, for a given bin. $N_{i}$ is the number of neutrons seen by the beam monitor. Finally, $\zeta_{i}$ is a theoretical correction to account for the presence of 36Ar in natural argon. Natural argon consists of 36Ar ($0.3336$ %), 38Ar ($0.0629$ %), and 40Ar ($99.6035$ %) Wang:2014gja . We estimate the contribution from 38Ar to the cross section to be negligible ($<0.1$ %), but 36Ar does require a small correction. For this we use both the cross section for 36Ar$(n,\gamma)^{37}$Ar and the 37Ar gamma cascade from ENDF/B-VIII.0 Cameron:2012ogv ; Brown:2018jhj . Using $\zeta_{i}=\frac{a_{36}\,\varepsilon_{36}}{a_{40}\,\varepsilon}~{}\sigma^{36}_{i}$ gives on average a $1$ % correction in Eq. 7.

Fig. 3 shows the argon cross section as a function of the neutron velocity. The fit, from $0.015-0.15$ eV, using Eq. 5, yields $T=294\pm 36$ K and $\sigma_{mp}=670\pm 26\text{ (stat.)}\pm 43\text{ (sys.)}$ mb. Tab. 1 summarizes the contributions to the statistical and systematic uncertainties. $\delta N_{i}/N_{i}$ accounts for: the detector stability due to the difference in beam intensity between the argon and calibration runs ($3.1$ %), the consistency among the two beam monitors ($2.1$ %), and the uncertainties in the sodium calibration procedure ($4.4$ %). The systematic effect of the emission of internal conversion electrons was assessed using BrIcc Kibedi:2008etccub and was found to be negligible ($<0.5$ %).

After correcting for the average temperature of the moderator and the target, $\langle T\rangle=296\pm 36$ K, we obtain a result of $\sigma^{2200}=673\pm 26\text{ (stat.)}\pm 59\text{ (sys.)}$ mb for the standard thermal cross section. Moreover, Fig. 4 shows the differential cross section, from $0.015-0.15$ eV, re-scaled to $300$ K, alongside historical measurements Koehler:196318a ; French:1965225 ; RANAKUMAR1969333 and the evaluation from Ref. Brown:2018jhj .

In conclusion, we have measured for the first time the neutron capture cross section on 40Ar as a function of energy. These results can be used in the design of a new generation of dark matter and neutrino detectors using liquid argon as a detection medium and/or shield.

VI ACKNOWLEDGEMENTS

This work was supported by the U.S. Department of Energy (DOE) Office of Science under award number DE-SC0009999, and by the DOE National Nuclear Security Administration through the Nuclear Science and Security Consortium under award number DE-NA0003180. We gratefully acknowledge the logistical and technical support and the access to laboratory infrastructure provided to us by LANSCE and its personnel at the Los Alamos National Laboratory. We would also like to thank L. J. Kaufman for providing the target cell.

VII Bibliography