Space-based Measurements of Neutron Lifetime: Approaches to Resolving the Neutron Lifetime Anomaly

Free neutrons have a measured lifetime of 880 s, but disagreement between existing laboratory measurements of ~10 s have persisted over many years. This uncertainty has implications for multiple physics disciplines, including standard-model particle physics and Big-Bang nucleosynthesis. Space-based neutron lifetime measurements have been shown to be feasible using existing data taken at Venus and the Moon, although the uncertainties for these measurements of tens of seconds prevent addressing the current lifetime discrepancy. We investigate the implementation of a dedicated space-based experiment that could provide a competitive and independent lifetime measurement. We considered a variety of scenarios, including measurements made from orbit about the Earth, Moon, and Venus, as well as on the surface of the Moon. For a standard-sized neutron detector, a measurement with three-second statistical precision can be obtained from Venus orbit in less than a day; a one-second statistical precision can be obtained from Venus orbit in less than a week. Similarly precise measurements in Earth orbit and on the lunar surface can be acquired in less than 40 days (three-second precision) and ~300 days (one-second precision). Systematic uncertainties that affect a space-based neutron lifetime measurement are investigated, and the feasibility of developing such an experiment is discussed.


Introduction
Free neutrons are unstable and have a mean lifetime, tn, of ~15 minutes for beta decay (via the weak interaction) into a proton, electron, and antineutrino. Knowledge of the neutron lifetime is important because its precise value provides constraints to both fundamental physics and Big-Bang nucleosynthesis. There currently exist two types of laboratory experiments -"beam" and In light of this discrepancy, a third technique of space-based neutron spectroscopy was put forward by Feldman et al. [2] to measure neutron lifetime. This technique measures neutrons from planetary surfaces or atmospheres that are generated by nuclear spallation reactions when galactic cosmic rays (GCRs) impact the planets. The primary spallation neutrons have initial energies, En, greater than 1 MeV, but a fraction of them are down scattered in energy via inelastic scattering collisions with atmospheric and/or surface material prior to escaping into space. The resulting energy spectrum for neutrons that escape into space consists of a power law shape for energies in the range of a few eV to ~500 keV (epithermal neutrons), and a Maxwellian shape for the lowest energy (thermal) neutrons that are in thermal equilibrium with the surrounding material (e.g., [3] and Figure 1). For large enough planetary bodies (e.g., like the Moon or bigger), thermal neutrons are gravitationally bound and have a surface-to-surface time-of-flight that is comparable to the neutron lifetime. Large asteroids have masses that are two orders of magnitude smaller than the Moon, and thus cannot gravitationally trap even the slowest neutrons (see Section 2.1).
The first measurement of neutron lifetime using this space-based technique was reported by Wilson et al., [4] using neutron data collected by NASA's MESSENGER mission during flybys of Venus and Mercury in 2007 and 2008. While the lifetime measurement using these data of 780±60 stat ± 70 syst s does not have an uncertainty low enough to be competitive with existing laboratory measurements, it nevertheless demonstrated the feasibility of the space-based technique. Another study using data from the Lunar Prospector mission at the Moon has reported an independent measurement of neutron lifetime 900 !"# stat ()# ± 17 syst s [5]. Additional spacebased data from Mars, Mercury and the Moon [6,7] exist with which further measurements of tn may be attempted. However, none of these existing datasets were generated with instruments designed for the purpose of a neutron lifetime measurement. These experiments therefore have constraints that limit their usefulness for neutron lifetime measurements, either because of limited statistical precision and/or large systematic uncertainties. With the knowledge gained by planetary neutron measurements in recent years, we have better information for how a space-based neutron lifetime experiment could be realistically designed and built within the constraints of a small-tomoderate space mission.
A number of factors need to be considered when planning such a mission. Measurement constraints such as the host planet and measurement configuration (e.g., circular orbit, elliptical orbit, landed) have a primary importance for how to carry out a measurement with the optimum statistical precision, as well as minimizing and mitigating systematic uncertainties.
Implementation factors, such as instrument heritage and the ability to reach a given location, affect the practicality of accomplishing a mission scenario. Finally, detector considerations such as type ( 3 He gas, lithium glass, borated plastic, etc.), geometry, and number of detectors also play an important role. Within these constraints we investigate two types of measurements: planetary orbital and planetary landed. For orbital missions, we consider the Earth, the Moon, and Venus.
Each of these bodies are large enough to have sufficient gravity to make neutron lifetime measurements, and all are reasonably accessible with standard space launch capabilities. For landed measurements, we consider the possibility of neutron lifetime measurements made from a single location on the lunar surface. A primary reason for investigating measurements from the lunar surface is that a renewed effort to place low-cost instrumentation on the Moon might enable a neutron lifetime experiment to be feasibly emplaced there.
The organization of this paper is the following. Section 2 discusses orbital neutron measurements, provides a baseline instrument design, and describes the expected performance of orbital neutron lifetime measurements at the Earth, the Moon, and Venus. Section 3 describes how a neutron lifetime measurement could be made from the lunar surface. Section 4 gives a general discussion of the systematic uncertainties associated with all space-based neutron measurements. Section 5 gives a summary of these results and discusses the next steps needed for fielding a realistic neutron lifetime mission.

Principal of Technique
Planetary neutron measurements have been made at seven different planetary bodies, which include: the Moon, Mars, Mercury, Venus, asteroids 4 Vesta and 1 Ceres, and the Earth.
For the non-Earth measurements, neutrons have been used to quantify surface or atmospheric composition [e.g., 7,8,[9][10][11]. Based on these measurements and the modeling carried out to support these measurements [e.g., 7], there is a good understanding of the effects of planetary neutron generation, transport, and detection by orbital instruments, as well as the neutron flux dependence on surface and/or atmospheric composition. Figure 1 shows modeled neutron energy flux spectra for the Moon, Earth, and Venus. These spectra were generated using the particle transport code MCNPX, which simulates GCR-induced neutron production and transport, including effects from surface and/or atmospheric composition, surface temperature, and gravitational binding. For the Moon, two spectra are shown -one for lunar highlands materials that have low abundances of thermal-neutron absorbing materials Fe, Ti, Sm, and Gd; and one for lunar maria materials that have high abundances of these elements. The effects of these abundance differences are seen primarily for thermal energies (En<0.4 eV), where the maria materials have substantially fewer thermal neutrons than highland materials due to neutron absorption. These and other compositional effects have been quantitatively validated using orbital measurements [e.g., 3,12]. The neutron spectra for Earth and Venus were generated using a 50-layer atmosphere model that accounted for density and temperature in each layer, as well as standard compositional values [13]. The neutron flux for the Earth is significantly lower than either the Moon or Venus because Earth's atmosphere is dominantly composed of nitrogen (78%), which is a relatively strong neutron absorber. In contrast, Venus' atmosphere is dominated by carbon and oxygen (96.5% by volume CO2), and both those elements have a relatively small thermal-neutron-absorption cross section. As a consequence, at the peak energy of 0.04 eV, the thermal neutron flux at Venus is almost a factor of 150 larger than that of Earth.
Neutron lifetime measurements are performed via measurements of thermal neutrons, which follow trajectories that are significantly influenced by the planet's gravitational field, with sufficiently low-energy neutrons being gravitationally bound to the planet. Feldman et al. [14] derived the time required, Dt, for a neutron to leave and then return to a planetary surface: where, and = (2 ⁄ − 1), for ⁄ < 1 (2).
In this expression, the neutron kinetic energy is K (in eV), the planetary radius is RM, neutron mass is m, and the neutron launch direction is µ = cos(q), where q is the angle relative to the surface  eV and 1 x 10 -5 eV, respectively; thus, thermal neutrons are not gravitationally bound to these and smaller bodies.

Measurement Implementation
There are multiple ways to make space-based neutron measurements. These include using 3 He gas proportional counters [15] and different types of scintillators such as borated plastic (BP) and Li glass (LG) [16]. In addition to different sensors, there are different methods for separating thermal from higher energy neutrons. A straightforward energy discrimination is to cover neutron sensors with thermal-neutron absorbing materials (e.g., Cd) that enable count-rate differences between thermal and non-thermal-neutron detecting sensors to be a measure of thermal neutrons [15]. Another method for discriminating neutron energies with orbital neutron measurements is the Doppler filter technique [17]. This technique takes advantage of the similarity in velocity between typical spacecraft in orbit about a planet (few km/s) and thermal neutrons (a thermal neutron with energy of 0.025 eV has a velocity of 2.2 km/s). An enhancement of thermal neutrons is measured when the spacecraft velocity vector is parallel with the sensor normal vector; a relative decrease in thermal neutrons occurs when the spacecraft velocity vector is anti-parallel to the sensor normal.
We posit a baseline neutron lifetime instrument design based on experience with the MESSENGER Neutron Spectrometer (NS). Figure 3 illustrates the MESSENGER NS, which measured a range of neutron energies using a BP scintillator and two LG scintillators. The BP sensor was a 10 cm 3 cube of plastic scintillator. The two LG sensors were 10 cm by 10 cm by 4 mm LG plates placed on two opposite sides of the BP sensor. Each sensor was read out by separate photomultiplier tubes (PMTs). Thermal and epithermal neutrons were measured with the two LG sensors using the Doppler filter technique [18]. periapsis altitude from Mercury of a few hundred km, and an apoapsis altitude of ~10,000 km [19].
Note that for the MESSENGER mission, each 12-or 8-hour orbit had a large variety of pointing attitudes in order to satisfy the various observational requirements of the mission's seven different instruments [19]. The neutron count rate from the LG2 sensor is shown in Figure 4c, where the increasing count rate is due to the larger neutron flux at close distances to Mercury's surface. Due to the fact that the neutron sensors are largely hemispherical detectors, measured neutron counts are statistically significant when the detector is within one-body radius (2438 km) of Mercury's surface. The altitude and velocity-direction dot product with the spacecraft x-axis direction are shown in Figure 4a and 4b, respectively.
For the orbit shown in Figure 4, the spacecraft executed a rotation near the periapsis such that the velocity direction went from being aligned with the normal to the LG2 sensor to being anti-aligned with the LG2 sensor. This rotation is illustrated in Figure 4b with the vector-velocity dot product with the spacecraft x-axis (which is aligned with the LG2 normal vector). The effect of the rotation is seen where there is a relatively large thermal-neutron count rate prior to the rotation, and a count-rate drop after the rotation. Note that the spacecraft velocity of 3.5 km/s at periapsis corresponds to a neutron energy of 0.065 eV.
The effects varying neutron lifetimes would have on the neutron count rate is shown by simulated count rates (colored traces) in Figure 4c. The details of how these simulated count rates were implemented is described in various prior studies [4,7,11,18,20,21], with the foundational algorithms given by [14]. Neutron lifetime effects manifest as count-rate variations for different tn values when thermal neutrons are detected prior to the rotation. Specifically, short lifetimes yield lower count rates and long lifetimes yield higher count rates. In contrast, post-rotation lifetime-derived variations are suppressed since the LG2 sensor only measures higher-energy epithermal neutrons that are not noticeably affected by lifetime. The relative count-rate difference between pre-and post-rotation measurements therefore provides a measure of tn. We note that while this particular orbit provides an optimum configuration for a tn measurement (and well illustrates the technique), many similar such orbits are needed to achieve a statistically significant measurement.
Based on this one-orbit scenario, Figure 5 shows a notional detector arrangement that could carry out a sequence of orbits to achieve a statistically significant neutron lifetime measurement.
This design uses four 100 cm 2 by 4 mm thick LG detectors arranged around an axis of rotation that is perpendicular to the spacecraft velocity direction around a planet. For an appropriate rotation speed (e.g., one rotation per few minutes), each detector will cycle through measurements ranging from thermal to epithermal energies. The four detectors provide an increase in statistics over a single detector, as well as redundancy if a detector fails. The four identical detectors in a constant rotation also allows a consistent detector-to-detector normalization to account for time dependent count-rate changes, such as from time variable cosmic ray flux variations (see Section 4).
In regards to engineering considerations, this baseline design has a number of benefits.
Most important, the sensor technology has very high spaceflight heritage, as the identical scintillator and photomultiplier tubes used for MESSENGER could be used here. The four-sensor configuration is ideally suited for existing four-channel electronics systems being used on planetary neutron gamma-ray and neutron experiments planned for launch in the near future [22,23]. Finally, this sensor arrangement is appropriate for implementation on a small satellite, which can reduce neutron background and systematic measurement effects (see Section 4), as well as lower satellite design and launch costs.

Neutron Lifetime Measurements at the Earth, Moon, and Venus: Statistical Uncertainty and Required Measurement Time
Here we explore mission scenarios using the detector arrangement in Figure 5 to estimate the statistical performance for possible measurements at the Earth, Moon, and Venus. Earth orbit is the most easily accessible location for a space-based neutron detector, and was the location assumed by Feldman et al. [2] in the initial study that proposed space-based neutron lifetime measurement. While not as accessible as low-Earth orbit, lunar orbit is visited by many spacecraft, and with renewed interest in lunar exploration will likely be a more frequent destination by spacecraft. Finally, while Venus orbit is more difficult to reach than Earth or lunar orbit, it is nevertheless visited with some frequency either for dedicated missions or gravity assist flybys.
For any of these locations, a neutron lifetime mission could be flown as a stand-alone mission or as a hosted payload for another mission.
To understand the fundamental statistical performance of a detector in orbit about these planetary bodies, we first simulated a circular orbit about each planet. For Earth and Venus, we assume an altitude of 500 km; for the Moon due to its smaller size, we assume an altitude of 50 km. These are straightforward altitudes to obtain for orbiting spacecraft around these bodies. We also simulated elliptical orbits at Venus with periapsis and apoapsis altitudes of 250 km and 750 km, respectively. This orbit keeps approximately the same average 500-km altitude as the circular orbits. For this simulation, we assumed the four sensors are rotating around the sensor center line with a rate of 0.5 rotations per minute. Figure 6a shows the simulated count rates for one orbit using one of the four sensors with different assumed tn values. The longer time scale (zero to 50minute) count-rate variation is due to the altitude-dependent count rate. The higher time frequency count-rate changes are due to the sensor rotation that constantly varies from Doppler-enhanced, with a larger fraction of thermal neutrons, to Doppler-suppressed, with a larger fraction of epithermal neutrons. Figure 6b focuses on 20 minutes of the orbit where the count rates from two of the opposing sensors are shown.
To estimate the statistical precision for each planet and orbit type, a c 2 value was calculated comparing each of the models to a 900-s reference model, which was used as a proxy for the measurements, and assuming Poisson statistics on the 'measurement'. Given the c 2 estimate for one orbital period T, the expected c 2 value after a total measurement time t was calculated by scaling with a proportionality factor . ( ) = ⁄ . ( ). Thus, the expected value of tn that is distinguishable from the reference lifetime 2 3## after a total measurement time t is given by

Surface Based Neutron Lifetime Measurements on the Moon
There is a recent effort with international space agencies to return people as well as scientific and engineering instrumentation to the lunar surface. With the recognition that this "return to the Moon" strategy provides an opportunity to place a neutron lifetime experiment on the lunar surface, here we investigate a notional experiment and how well it could measure tn.
In keeping with the sensor architecture of the orbital experiment, here we suggest a four- Gd, and Sm, thus providing the highest fluxes of thermal neutrons on the Moon [3]. Figure 9 shows the respective upward and downward neutron fluxes for an experiment placed on a location with low abundances of neutron absorbing materials. Since the Moon's gravity only traps a fraction of the thermal neutrons escaping from the lunar surface, this downward flux is relatively small compared to the upward flux.
With this sensor arrangement, we have determined the statistical precision that can be achieved for measuring tn as a function of accumulation time using the same procedure that was described in Section 2.3 for orbital measurements. The black dashed line in Figure 7 shows the results, where a landed lunar measurement is statistically similar to an Earth orbiting measurement.
The primary reasons for the improvement in statistical precision over that of a Moon orbiting measurement are the increase in count rate due to being closer to the planet and the clean isolation of low-energy, gravitationally bound, neutrons. For one lunar sunlight period (half a lunar day, or 15 Earth days), a measurement precision of ~4 s could be achieved, with slightly better than 3 s in a full lunar day. Longer-term (multi-month) operation on the lunar surface will require accommodations to survive the cold lunar night. However, if such a detector were accommodated with multi-month operation, then a 1-s-precision measurement could be acquired in less than a year of accumulation time. We therefore conclude that a landed lunar measurement is feasible within existing technologies.

Expected Systematic Uncertainties
In Section 3, we showed that it is possible to make high-precision measurements of tn with both orbital and landed lunar measurements. However, the driving factor for achieving a competitive tn measurement is likely not statistical precision, but systematic uncertainties.
Ultimately, the measurement of tn will be obtained by generating models of the expected count rates for given tn values, and then comparing these simulations with the measured data. The degree to which this model/data comparison can accurately measure tn depends on how well the simulations account for all the non-tn-dependent factors. Uncertainties in these factors are the systematic uncertainties that need to be understood in order to acquire a competitive tn measurement. Galactic cosmic ray (GCR) flux: GCRs initiate the interactions that generate neutrons, from which tn is measured. The GCR flux can vary in time by a significant amount (few to tens of percent) over time scales of hours to days to months [24,25]. Without accounting for these variations, they could easily mask any neutron lifetime measurement. There are multiple ways the GCR time variation can be taken into account. Separate GCR monitors could be included on an orbital or landed payload to make an independent measurement of GCR time variability.
Alternatively, the sensors making the neutron measurements can also monitor the GCR time variation. For the orbital package shown in Figure 5, GCR time variation can be monitored using the non-Doppler-enhanced epithermal neutron measurement. This is done by virtue of the fact that epithermal neutrons will respond to time variations in GCRs, but are not sensitive to tn.
Similarly, for the landed measurement scenario (Figure 8), GCR time variations can be monitored by virtue of one set of sensors measuring epithermal neutrons, and the other measuring thermal plus epithermal neutrons. We also note that for Earth orbiting measurements, atmospheric neutron production from the GCR varies as a function of latitude due to Earth's magnetic field, which cuts off lower-energy GCRs near the equator and allows lower-energy GCRs near the poles. Thus, GCR monitoring in an Earth-based measurement needs to account for this variability. A dedicated fast-neutron monitor is one way to measure such a latitude-dependent parameter [2].
A number of tasks need to be carried out to ensure GCR time variability introduces a small systematic uncertainty to a tn measurement. These include deriving the statistical uncertainty of an expected GCR count rate from an independent GCR monitor, if one is chosen for use on the mission. Alternatively, the statistical precision of epithermal neutron derived GCR rates, and the corresponding derived tn uncertainty can be determined in the different orbital and landed measurement scenarios. Such information can be determined using prior measurements of GCR variability with similar sensors [25].
Atmospheric/surface composition: Knowledge of the elemental composition of the gaseous atmosphere or solid surface is needed to derive a tn measurement. The reason is that different elemental compositions can cause variations in thermal neutron fluxes. At the Moon, the measured thermal neutron flux varies by over a factor of three over the entire lunar surface [26].
Gaseous atmospheres will likely have less spatial variability in thermal neutron flux due to their homogeneous nature; however, the elemental composition still needs to be known to derive tn.
Venus provides an ideal atmosphere as it has only two primary constituents of CO2 and N2, with trace amounts of other species. The impact that these trace elements may have on systematic uncertainties at the 1-to-3 s precision level needs further investigation. In contrast, the elemental composition of Earth's atmosphere is better known than Venus' atmosphere. But the Earth contains more dominant constituents (e.g., variable H2O that can affect the neutron flux), which may prevent knowing the atmospheric composition with sufficient precision to make a competitive tn measurement.   Figure S4 of [11]) can range from 200 K to ~350 K [13,30]. The temperature of Earth's atmosphere is well known (e.g., [13]).
Based on particle transport simulations [12,31], thermal-neutron count rates can vary by 4% to 6% from 100 K to 400 K. Since this variation is comparable to or larger than the variations for neutron lifetime, temperature variations either need to be limited and/or included in the modeling. Ways to limit temperature variations for orbital missions include using orbit parameters where temperature variations can be minimized, such as a sun synchronous orbit (e.g., always orbit over the dawn/dusk terminator). However, because the measured thermal neutrons will originate from a wide range of longitudes, this effect cannot be completely negated via orbit selection. Data can also be segregated into different temperatures when the data were gathered, and then corrections can be applied for these different temperatures. Such corrections can be carried out using first-principle corrections with known temperature variations, as well as empirical, datadriven corrections. In general, future work will use known temperature information, and after limitations are applied for a given mission scenario, investigate what level of uncertainties are caused by temperature variations, and the degree to which these variations can be corrected and/or included in the simulated count rates.
Background signals: As in any experiment, background signals need to be minimized where possible, and corrected for when present. For space-based neutron detectors, backgrounds can be present as both non-neutron and neutron signatures. Non-neutron signatures are most likely due to charged particles and resulting photon radiation that deposit energy in the neutron sensor.
Li glass scintillators manifest a non-zero continuum background due to GCRs that needs subtraction from the measured neutron signature [18]. In contrast, 3 He sensors are relatively insensitive to charged particles and energetic photons (x-and gamma-rays), and thus typically exhibit a very low non-neutron background [15,26]. In addition to the nominal GCRs that are present at all times, there are also bursts of energetic particles that can cause large temporary backgrounds. These bursts come from solar energetic particle (SEP) events, and particle bursts from magnetospheric events within a planetary magnetosphere. For the locations considered here, all are susceptible to SEPs. However, Earth orbiting experiments might also need to contend with particle bursts depending on where in Earth's magnetosphere it is flown. In all these cases, particle bursts are usually dealt with by not using data acquired during the burst. Historically, removal of data contaminated by SEP and other particle events lead to a loss of approximately 15% calendar time of a given mission [24,25].
A second source of background are direct neutron backgrounds. GCRs produce highenergy fast neutrons (En > 0.5 MeV) via interactions with spacecraft and sensor materials, and these fast neutrons are routinely measured in space-based neutron experiments [32,33]. However, the amount of mass in most spacecraft is sufficiently low such that fast neutrons are not efficiently scattered to thermal energies [18,26]. Thus, the background thermal-neutron count rate is quite low. Even so, for a dedicated space-based neutron lifetime experiment, effort should be made to minimize the surrounding mass around the sensor, which will minimize the overall neutron background counts. This argues for a dedicated small-satellite mission, as opposed to a hosting a neutron lifetime instrument on a larger spacecraft. In terms of background corrections, these can be made to the data by peak fitting individually measured spectra. Orbital design can also be used such that an elliptical orbit with sufficiently high-altitude apoapsis allows for a regular cadence of background measurements that can then be subtracted from the primary planetary measurements.
The effect of such an elliptical orbit on the overall statistics is a trade that would need to be investigated. On one hand, a lower altitude periapsis would result in an increased count rate that could offset the loss in statistics from the lower count rate at higher altitudes. Alternatively, such an orbit could result in an overall loss of statistics where a "duty cycle" effect would need to be taken into account for the overall mission lifetime.
Sensor efficiency response: Knowledge of the angle and energy dependent sensor efficiency is needed to convert the measured count rate to a derived neutron flux, from which the neutron lifetime is determined. Uncertainties in the knowledge of this sensor response can potentially be a driving factor leading to unacceptably large uncertainties. Typically, a full sensor response is determined using a combination of particle transport modeling using codes like MCNPX or GEANT, and benchmarking to pre-launch calibration data. To accurately understand the response of these sensors to neutrons in space, all effective spacecraft material needs to be accurately modeled, and not just the sensor material. This modeling can be challenging for full sized spacecraft that have meter-sized dimensions or greater. In addition, for any given scenario, the exact spacecraft composition and mass distribution may not be fully known. Nevertheless, full simulations of MESSENGER NS data showed that relative uncertainties of ~<0.5% were achievable when neutron arrival angles were restricted to directions that did not travel through the full spacecraft material [7,18,20,21,34]. However, a dedicated space-based neutron lifetime experiment would strive to have a smaller spacecraft that is more easily modeled, thus achieving more uniform accuracies for all orientations. For landed experiments, missions that minimize nonsensor mass will enable more accurate modeling.

Discussion and Summary
Here, we provide a discussion and summary of the results given in Sections 3 and 4, and describe paths forward for planning and possibly accomplishing a space-based neutron lifetime measurement. Based on the statistical uncertainty results of Figure 7, Venus is clearly the best location for making neutron lifetime measurements. For the same observation time, Venus provides an almost order-of-magnitude better statistical uncertainty than an Earth orbiting or should be studied in more detail to assess their feasibility.
The next steps needed to assess the feasibility of a space-based neutron lifetime experiment are to work through all the expected systematic uncertainties given in Table 1 to determine the level to which they might unacceptably compromise a neutron lifetime measurement after all mitigations and/or corrections are carried out. In regards to the uncertainty categories in Table 1

Li glass scintillators
Spacecraft velocity

Rotating sensors
Planetary surface