and epithermal neutrons

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 105, NO. E8, PAGES 20,347-20,363, AUGUST 25, 2000 Chemical information content of lunar thermal and epithermal neutrons W. C. Feldman, D. J. Lawrence, R. C. Elphic, D. T. Vaniman, D. R. Thomsen, and B. L. Barraclough Los Alamos National Laboratory, Los Alamos, New Mexico S. Maurice Observatoire Midi-Pyrdndes, Toulouse, France A. B. Binder Lunar Research Institute, Tucson, Arizona Abstract. Simulations of equilibrium thermal and epithermal neutron flux spectra for the Moon have been studied to determine their chemical information content. Most of this information resides in a single parameter, the ratio of macroscopic absorption to energyloss cross sections. Although this parameter cannot specify the chemistry of lunar soils uniquely, it provides an index that can be used to quantitatively separate anorthositic from mafic chemistries. Hydrogen abundances can best be derived from measurements of the epithermal neutron flux, which is strongly related to its macroscopic energy-loss cross section. The ratio of thermal to epithermal neutron flux measured by Lunar Prospector is shown to agree quantitatively with simulations. This agreement is used to show that the highlands terrane on the farside of the Moon is anorthositic, containing high percentages of plagioclase and possibly a range of Mg-suite minerals with a high Mg/(Mg + Fe) atomic ratio. Our best estimate of the abundance of FeO is 2%, with an upper limit of 5%. 1. Introduction Measurements of lunar neutrons were first suggested by Lingenfelter et al. [1961] as a tool for gaining information about the chemical composition of the Moon. They concluded that leakage neutron fluxes from the Moon could provide a sensitive measure of the near-surface hydrogen abundance. A determination of the abundances of other elements from neutron observations alone would be more ambiguous. The first measurements of lunar neutrons determined the depth profile of thermal neutrons at the Apollo 17 landing site [Burnett and Woolum, 1974; Woolum et al., 1975]. A comprehensive set of neutron measurements giving the global distri- 2. Neutron Moderation Theory bution of thermal, epithermal, and fast neutrons has just been completed aboard Lunar Prospector [Feldman et al., 1998a, b; Neutrons are produced on the Moon by interactions between galactic cosmic rays (GCRs) and the nuclear constitu- Maurice et al., this issue. These data are ideal for addressing ents of lunar material. Production rates are determined by the the original goal of Lingenfelter eta!. [1961], to evaluate the GCR flux and the composition of the near-surface layers [Linchemical information content of neutrons that leak from the genfelter et al., 1961;Armstrong and Alsmiller, 1971; Kornblum et lunar surface. We concentrate on the thermal (E < 0.4 ev) al., 1973; Dagge et al., 1991; Masarik and Reedy, 1994; Gasnault and low-end fraction of the epithermal (0.4 ev < E < 1 kev) et al., 2000]. After production the neutrons moderate to lower energy ranges in the present study and refer to Maurice et al. energies through elastic scattering collisions with atomic nuclei [this issue] for a discussion of the fast neutron energy range, 0.6 at all energies and through inelastic nuclear reactions at ener- MeV < E < 8 MeV). gies generally above 0.5 MeV. This inelastic scattering thresh- A quantitative comparison of neutron simulations with the old of 0.5 MeV defines the upper limit of the energy range of Lunar Prospector neutron measurements shows that useful epithermal neutrons. The thermal range is defined by that petrologic composition information, in addition to a sensitive energy below which energy transferred to neutrons from elastic collisions with lunar nuclei first becomes noticeable in neutron determination of the hydrogen content of surface layers, is flux spectra (Ec = 0.4 ev). indeed possible [Feldman et al., 1998a, b]. This information is Copyright 2000 by the American Geophysical Union. Paper number 1999JE /00/1999JE ,347 contained in the value of one parameter, the ratio of the macroscopic absorption cross section 5;aO to the macroscopic energy-loss cros section { 5;s. As will be shown, this parameter provides a sensitive discriminator of the total Fe and Ti content of lunar soils. A quantitative comparison between the measured ratio of thermal to epithermal neutron fluxes in the highlands with the simulated ratio indicates that the composition of highland soils is ferroan anorthositic (FAN), possibly mixed with Mg-suite minerals that have a high magnesium atomic number, [Mg/(Mg + Fe)]. Neutrons can be absorbed at all energies, either through the thermal absorption mechanism, which has a cross section that varies as E -o.s, or through nuclei-specific resonances. These resonances occur at ever lower energies as the nuclear mass

2 20,348 FELDMAN ET AL.: CHEMICAL INFORMATION IN LUNAR NEUTRONS increases, extending down to the kev range for the transition where H is proportional to the neutron injection rate to lower metals such as Fe and Ti. In addition, elastic-scattering cross energies at E H = 1 kev, /3-2A(Eo/E) ø', 13 = sections for all nuclei are generally constant at energies below (g sad) -, and these resonances. These facts simplify greatly a description of the mechanisms that shape neutron flux distributions at ener- A -- (. ao/. s) ' (5b) gies below -1 kev. This energy range is covered by the two Inspection of (5a) shows that if both neutron absorption is 3He gas-proportional counters aboard Lunar Prospector (LP) negligible (/3-0) and loss to space is negligible (8 = 0) in the [Feldman et al., 1999]. We will therefore concentrate on this epithermal energy range, then Fepi(E ) is proportional to 1/E. range in the present study. The effect of neutron absorption is the exponential multipli- In order to develop intuition regarding the information con- cative factor having an exponenthat varies as E -ø'5 and that tent of low-energy neutrons (E < 1 kev), we follow the of neutron escape is to raise the power-law exponent of E from development presented by Fermi [1950]. The current of neu- -1 to-(1-8). trons in the epithermal energy range in log-energy space due to Following the same development, the current of neutrons elastic scattering, q(e), is constant because the average frac- that scatter to lower energies across the threshold energy E c tional energy loss per elastic-scattering collision, s c = AE/E = that separates the thermal from the epithermal neutron popd[ln (E)] = de, is constant. This neutron current within ulations must equal the rate at which neutrons are absorbed log-energy interval, de, is given by the rate of nuclear elastic below E c. It then follows that scattering collisions per gram of regolith times the fractional energy loss per collision: Ec[N(Ec) Vc] 5;s = N(E) V a de df, (6) q(e) = n(e)v 5;s = Q, (la) where n(e) is the neutro number density in In (E) interval where d f is the differential solid angle of the neutron velocity de, V is the neutron speed, Es is the constant macroscopic vector. Noting that V a is a constant, VoS;aO, and that Nc -- crossection for elastic scattering, and Q is a constant, giving f * N(E)dEdf is the neutronumber density for energies the injection rate of neutrons into the low-energy portion of below E c, we find that the ratio of thermal flux, which is the equilibrium neutron flux distribution from energies >1 proportional to NcV o and to the epithermal flux F c = kev. Throughouthis paper, the macroscopic cross sections F(Ec) = N(Ec)V c at energy E = Ec, is given by are given by Ftherm/Fepi = NcVo/Fc = Ec( s/ ao) = Ec/ A. (7) 5; = 5;j[f tr/10/aj], (lb) We note that the ratio of thermal to epithermal neutron flux depends on only one parameter, A, which is derivable from the where the sum is over all elements, j, with mass fraction f., chemistry of the lunar soil. Because it will turn out that/3 is very crossection try, and atomic mass Ai, and A o is Avagadro's small (i.e., the neutron loss rate to space is not important), (5a) number. The units for these cros sections are cm 2 g-. Mulshows that this same parameter, A, is also a contributing factor tiplication by the density changes the units to an inverse scattering or absorption length, in cm-. of the epithermal neutron flux. We note, however, that Fep i should also depend on the injection rate from the fast neutron Loss of neutrons due to absorption, leading to a reduction in energy range (through H), which varies over a range of -30% the neutron current in energy interval de, is given by for the Moon [Feldman et al., 1998a; Mauricet al., this issue]. dq = rt(e)v ade, (2) 3. Neutron Simulations where 5; a is the macroscopic neutron absorption crossection. Near the surface of the Moon there is an additional loss mechanism due to the spatial diffusion of neutrons to the surface The relationships developed in section 2 were derived using from below followed by their escape to interplanetary space. only general nuclear properties of the nuclei having masses up Applying kinetic theory, this loss rate is proportional to the through Fe. Exceptions can be found. More accurate simulaupward directed spatial current of neutrons at the surface tions of equilibrium neutron flux spectra can be, and have divided by their spatial diffusion length A a in the near-surface been, made using Monte Carlo and Boltzmann transport codes regolith. The reduction in neutron current in energy interval, coupled to comprehensive nuclear cross-section libraries [Linde, due to escape to space is then genfelter et al., 1961, 1972; Armstrong and Alsmiller, 1971; Kornblum et al., 1973; Drake et al., 1988; Dagg et al., 1991; Masarik dq = n(e)vde/(gaa), (3) and Reedy, 1994; Feldman et al., 2000]. Because the trends evident in the simple approach are very useful to guide intuwhere g is some proportionality constant and A a has units of ition prior to embarking on an extensive set of neutron simug cm -2 in (3). Assembling all of the parts, the excess of q at lations, they are calibrated against a select set of simulations in e + de over q at e is given by this section. Of course, our ultimate goal is to develop and d[n(e)v s] : [n(e)v/(gad)]de + [n(e)viea]de. (4) Rearranging terms and noting that SC s is independent of e, 5;a = 5;ao(Eo/E) ø'5, where 5;ao = 5;a(Eo), E o = ev, and the neutron flux, F(e) = n(e)v = EF(E), we get Fepi(E) = H exp - (13)/E( - ), (5a) 3.1. General fo Ec calibrate a set of neutron measurables that can be used to provide chemical information about the lunar surface. The most useful set of measurables found from our simulations is summarized in Table 1. In order to implement this calibration, we choose the set of soil compositions obtained from samples returned by the Apollo and Luna missions. Average chemical abundances for

3 Table 1. Information FELDMAN ET AL.: CHEMICAL INFORMATION IN LUNAR NEUTRONS 20,349 Neutron Measurables That Provide Chemical Depth Profiles e-folding depth (neutron scattering length) Z, = 0.084Aa g cm -2 Peak neutron flux intensity zx = 0.68[Peak(Fthorm/Fop,)]- ": [ 7Z,] = [Peak(Fep,)] -l' Neutron flux intensities Figure Figure 4a Figure 5a Figure 5b Figure or Equation Epithermal/thermal neutron flux ratio A = 0.54[Fepi/Fthcrm(Sim)] equation (14) Epithermal neutron flux intensity constant (from graphs by Gatbet and Kinsey [1976]). Effective s = 0'0032[Fcp,] - '2 Figure 9 (l/l/) absorption cros sections for Gd and Sm were taken from Lingenfelter et al. [1972]. According to the results of the simplified treatment of neutron moderation presented in section 2, the dominant paramsoils and regolith breccias from Apollo 11, 12, 15, 16, and 17 eter that shapes the equilibrium neutron flux spectrum is A = and from Luna 16, 20, and 24 are given in Table 8.1 of Haskin E a0/{ Ex. Inspection of column 5 of Table 2 shows that this and Warren [1991]. Average chemical abundances for Apollo parameter varies over a factor of 2.9 for the compositions of 14 regolith are given in Table 7.15 ofmckay et al. [1991]. These the returned lunar soils, from for the AP16 soil to 1.14 compositions were augmented to include ferroan anorthosite for the APll soil. This range is due mainly to variations in the (FAN), norire (NOR), and a high-ti Apollo 17 basalt in order macroscopic absorption crossections, as the energy-loss cross to extend the range of A in our sample. We also include the sections are nearly constant, ({ Ex) = _ cm 2 potassium, rare earth element, and phosphorous (KREEP) g-. If we increase our sample to include FAN and the Apollo basalt compositions with and without Gd and Sm (designated 17 high-titanium basalt, this range extends from to 1.41, by KBR and KBN, respectively) that were used by Feldman et yet the value for ({ Ex) does not change materially. This last al. [1991] in order to illustrate the effects on the energy struc- property does not hold if H20 is mixed into the soil. Here, ture of the equilibrium flux distribution caused by non-(1/v) increases from for pure FAN to 1.35 for pure H20, as absorbers. seen in Table 3. Concurrently, the parameter A = Macroscopic cros sections were calculated for each of the drops from to , which is a factor of 20. compositions and are collected in Table 2. Also included are A fact worth noting from Table 4 is that the sensitivity of the ratios of epithermal-to-thermal neutron fluxesimulated thermal and epithermal neutrons to composition extends to an altitude of 30 km, Fepi/Fther m. The same information that of the mineral composition through the magnesium nummixed FAN and various percentage H20 compositions is col- ber, given by the atomic ratio, mg = Mg/(Mg + Fe). While the lected in Table 3. (Throughout this paper, FAN is defined by cross section ratios of the two end-members for plagioclase FAN + 0% H20. ) (albite and anorthite) are very close to one another (0.27 and The cross sections for key minerals that have been promi- 0.29, respectively) and to FAN (0.334), the Mg-Fe endnently identified in returned lunar samples are given in Table members of all solid-series solution mafic minerals diverge 4. Absorption cross sections were evaluated at a room- radically. For example, the cros section ratios of the two Mg temperature thermal energy of ev [Mughabghab et al., and Fe end-members of olivine (forsterite and fayalite) are 1981], and elastic scattering cros sections were evaluated at and 1.85, respectively, those of orthopyroxene (enstatite 100 ev, in the range where these cross sections are nearly and ferrosilite) are and 1.38, respectively, and those of the Mg and Fe end-members of clinopyroxene are and 0.925, respectively. These divergences are driven solely by the Table 2. Macroscopic Cross Sections for Lunar Soils relative atomic abundances of Mg and Fe in the minerals. The Composition Es Es Eao EaO/ Es Fepi/Ftherm APll AP AP AP AP API LUN LUN LUN FAN NOR KBN KBR API7 high-ti basalt Table 3. Macroscopic Cross Sections for FAN + P% H20 Percent H20.5,,., Ea0 EaO/ E, Fcp,/Fti... FAN + 0% H FAN % H FAN + 0.1% H FAN + 1% H FAN + 3% H FAN + 10% H FAN + 30% H % H All cros sections are in units of cm 2 g Table 4. Macroscopic Cross Sections for Key Minerals Mineral Es Es EaO EaO/ Es Forsterite Enstatite Cristobalite Mg-CPX Albite Anorthite Fe-CPX Ferrosilite Fayalite Chromite Ilmenite All cross sections are in units of cm 2 g-1. All cross sections are in units of cm 2 g-1.

4 20,350 FELDMAN ET AL.: CHEMICAL INFORMATION IN LUNAR NEUTRONS (a) -- HeSn I i X = HeCd I 1 05 :::) (b) o Simulation [] Measured v x U_ 100- z o l z '?... i I... i Energy (ev) oo Neutron Energy (ev) Figure 1. (a) The calculated efficiencies at normal incidence of the tin-covered (HeSn) and cadmiumcovered (HeCd) gas proportional counters aboard Lunar Prospector. The difference between the two efficiency curves (HeSn-HeCd) gives the efficiency for thermal neutrons, and the HeCd efficiency curve is used tu uc,,,e cljitnciinm neutrons. to) Simulated and measured neutron flux energy spectra generated using the 9Be(d, n) reaction followed by moderation using a graphite block surrounded by a 2.5-cm-thick polyethylene veneer as explained by Feldman et al. [1995]. magnesium number of a mineral [Mg/(Mg + Fe)] is therefore most important in determining the equilibrium neutron energy spectrum. Finally, we note that the maximum ratio of cross sections corresponds to ilmenite, because this mineral has equal amounts of Fe and Ti, both of which have relatively high absorption cross sections. and epithermal portions of neutron flux spectra. This result is shown clearly in Figure lb, which presents an overlay of the laboratory-measured spectrum of fast neutrons generated by the 9Be(d, n) reaction that were thermalized in a block of graphite moderator covered with a 2.5-cm-thick veneer of CH2, with the spectrum calculated using a Monte Carlo 3.2. Simulations of Equilibrium Flux Spectra (MCNP) simulation [Feldman et al., 1995]. Other examples of similar spectra measured in laboratory simulations of planetary Simulations of equilibrium neutron flux spectra at the lunar surface were made for all of the compositions given in Tables 2 and 3 using the ONEDANT code [Alcouffe et al., 1995]. Gravitational boundary conditions for the Moon were included [Feldman et al., 1989], and Liouville's theorem was used to propagate the surface spectra to the altitude of Lunar Prospector during the low-altitude phase of its mission, 30 km (see Feldman et al. [1993] for details of the procedure). The depth dependence of the neutron number density, the thermal flux, and the epithermal flux were also calculated for each of these compositions. The neutron number density was calculated by integrating the simulated neutron flux divided by the neutron neutron-flux leakage spectra are given by Drake et al. [1994]. Note that the computer simulation agrees very well with the measured spectrum over the full energy range spanning ev. This agreement is particularly significant for energies less than ev because the cross-section library that was used in the MCNP simulation shown in Figure lb (and that is used exclusively in all ONEDANT simulations presented later) assumes the scattering medium is composed of a monatomic gas of atoms having a chemistry prescribed by the user. This assumption does not hold for neutron energies less than molecular and mineral binding energies, which are typically of the order of, or less than, ev. The agreement between the flux speed over all energies. The thermal and epithermal fluxes simulations and measurements must mean that neutronwere calculated by integrating the product of the respective nucleus collisions occur on timescale so short compared with Lunar Prospector neutron spectrometer (LPNS) efficiency atomic relaxation times that they appear as individual nuclei functions and the simulated neutron flux over all energies. A description of the Lunar Prospector neutron spectrometer is given by Feldman et al. [1999]. interacting with the incident neutrons. Subsequent relaxation must then proceed by coupling postinteraction translational energies of the nuclei to longitudinal and transverse waves in the The efficiency functions calculated for neutrons incident on medium. Rotational motions are not allowed in solid assemblies. both of the LPNS sensors perpendicular to their cylindrical axes are shown in Figure la. The difference in efficiencies for 3.3. Depth Profiles the Sn-covered and Cd-covered sensors is used to define the Starting first with the neutron number densities, variations thermal neutron flux, and the efficiency of the Cd-covered of depth profiles with the water content of a ferroansensor is used to define the epithermal neutron flux. Note that anorthositic composition (FAN) are illustrated in Figure 2a. they cross over at ev. It turns out that this crossover Inspection shows that the depth at which the profiles reach energy provides a very clean delineation between the thermal their maximum decreases monotonically toward the surface as

5 FELDMAN ET AL.' CHEMICAL INFORMATION IN LUNAR NEUTRONS 20,351 (a) 5 I I I 3.5 (b) O 0% U20 o FAN [] 1 ø,/o H20 3 [] NOR ß 24 4_1 o 3O/oH20 [_ >o( Luna20 \\ x 10%H0 2.5, Apo,o14, 300,0 / ß Apo,o11 Apollo 17 ;; 1.5 Z Depth (g cm '2) Depth (g cm '2) Figure 2. (a) The depth profile of neutron number density for a FAN composition containing various mass fractions of H20. (b) The depth profile of neutron number density for a selection of soil chemistries estimated for a variety of Apollo and Luna landing sites, as well as for model ferroan anorthosite (FAN) and norite (NOR). the water content increases, in agreement with the results of Lapides [1981]. In contrast, the peak densities do not vary monotonically. Instead, the peak density maximizes at a water mixture of-- 3% by mass. This behavior does not hold for variations with respect to composition when the hydrogen abundance is zero. A sample of the depth profiles for compositions that are characterized by a range of A =. ao/. s is shown in Figure 2b. Inspection shows that they all peak at about the same depth, although their peak amplitudes decrease with increasing values of A (which, as seen in Table 2, is largely due to variations in 5;a0 ). The foregoing two effects need to be quantified in order to explore the information content of thermal and epithermal neutron flux spectra below the lunar surface. Starting first with the depth dependence of neutron number density, all depth profiles given in Figure 2a were parameterized using a function of the form N(d) = B - C exp [-d/ad], (8) where N is the neutron number density, B and C are constants, d is the depth in g cm -2, and Ad is the e-folding depth, which is a neutron diffusion length. This form was chosen because an exponential function is a solution of Laplace's equation, which is a limit of the diffusion equation when the diffusion coefficient, D = (3Ad)- is constant. Samples of the quality of fits are shown in Figure 3 for the two end-member H20 concentrations in our FAN + P% H20 series of simulations. Inspection leaves little doubt that (8) provides a very good representation of the simulations. The dependence of this diffusion length on the macroscopic scattering length in the watercontaining FAN soils is shown in Figure 4a. The strong and monotonic dependence of this scattering length on the abundance of H20 in the soil (effectively its hydrogen content) leads to the conclusion that A d provides a good measure of the A d = 141 g c 2, 100% H g c Depth (g crn -2) Depth (g cm -2) Figure 3. Fits of an exponential to a sample of neutron number density profiles for a FAN composition containing (a) pure FAN and (b) pure H20.

6 20,352 FELDMAN ET AL.: CHEMICAL INFORMATION IN LUNAR NEUTRONS (a) FAN + P% H20 i i 1 i 1 0% o lo% oooo x Thermal (b) / ) R na 20 ithermal Lun24 o ollo 11 Apollo 17 High-Ti Basalt o loo% o.1 I I Scattering Length (gcm-2),y--, a o Figure 4. (a) The dependence of e-folding depths (effectively the neutron spatial diffusion lengths) determined from fits of an exponential to the density depth profiles in Figure 2a, on the neutron scattering length, Er. (b) The dependence of thermal and epithermal neutron fluxes at the peaks of the depth profiles shown in Figure 2b, on E ao. hydrogen abundance. A similar result is obtained by using the macroscopic energy-loss cross section, seer, which also increases monotonically with the hydrogen abundance. On the other hand, the peak intensity of thermal neutron shown) is double valued as a function of hydrogen abundance, yet the macroscopic absorption cross section increases monotonically with increasing water content, as seen in column 4 of Table 3. However, a unique representation of peak thermal flux beneath the surface provides a measure of the composition and epithermal flux intensities is possible using/x and seer, as of dry soils through the macroscopic absorption cross section, E a0, as shown in Figure 4b. Indeed, the neutron flux intensity at the peak of the depth-dependenthermal neutron profile shown in Figures 5a and 5b. The ratio of peak thermal-toepithermal flux intensities is seen in Figure 5a to closely follow a power law function of A, given by follows the power lawaep, o quite closely, where A = and p = In contrast, the dependence of the peak Peak[Ftherm/Fepi] : A [ ao/ ] s] p, (9) intensity of the epithermal neutron flux with depth also follows where A = 0.7 and p = This result is very close to a power law, but with an index that is an order of magnitude that predicted (p = - 1) by the simplified theory of neutron lower, p = , as shown in Figure 4b. moderation given by (7). Additionally, the peak epithermal The foregoing presentation fails to provide a unique measure of composition when hydrogen is present. This result is seen clearly in Figure 2a. Here the peak neutron number density (as well as the thermal neutron flux, which is not flux follows a similar power-law function of the macroscopic energy-loss cross section seer, where A = and p = -0.85, as shown in Figure 5b. The cluster of points in the top left-hand corner of Figure 5b gives the peak epithermal fluxes x 10- o Apollo High Ti Basalt A' oollo 11 FAN + P% H20 14 Luna 24,a 20 (a) P 10 3o loo x (b) P, 30 FAN + P% H { s (g cm'2) Figure 5. (a) The dependence of peak values of Fepi/Ftherm on/x = E,o/seEr. (b) The dependence of peak values of Fep i on r'

7 FELDMAN ET AL.: CHEMICAL INFORMATION IN LUNAR NEUTRONS 20,353 FAN [] KBN, o KBR - (1) x AP17 'E X (D z 10 '5,,,,,,,i,,,,...,,...,,,,,,,,i...,,,,,,, Energy (ev) Figure 6. A sample of neutron flux spectra simulated at 30-km altitude for FAN, KREEP basalt containing no Gd or Sm (KBN) and containing Gd and Sm (KBR), and the Apollo 17 high-ti basalt compositions. for all of the Apollo and Luna soil compositions without H20. The vertical width of this cluster then represents the systematic uncertainty in estimating H20 abundances from measurements of the peak epithermal flux alone. Although not shown here, the fit of a power law in energy to the FAN flux spectrum divided by exp (-/3) (from equation (5a)) in the energy range between I and 1000 ev is given by the power-law index, p = Comparison with the results of the simple theory of neutron moderation given by (5a) yields 8 = The fact that 8 << 1 indicates that the loss of neutrons to space is indeed a small effect. Using see,. = from Table 2 and Ad = 141 gcm -2 from Figure 3a yields # = Applying this value of # to the case of pure H20 (from Figure 3b) yields 8 = andp = This value compares favorably with the fit of a power-law dependence on energy to the simulated flux spectrum for H20 giving p Two other observations are worth noting in Figure 6. First, the effect of the rare earth elements on the equilibrium flux spectrum is most noticeable at energies below -0.2 ev, as seen by comparing the KBN and KBR flux spectra. This behavior is to be expected because the resonances that contribute most to the very high thermal-absorption cross sections for both Gd and Sm are at or below 0.1 ev. Second, the flux spectra of KBN and API7 both fall below that of FAN by factors that increase with decreasing energy. This behavior is predicted by the sim- ple theory of neutron moderation to reflect absorption in the bulk regolith, as given by the exponential term in (5a). In order to quantify the validity of (5a), all simulated flux spectra at 30-km altitude were fit by a function of the form F(E) = Ftherm(E ) -t- FeN(E), (10) 3.4. Neutron Flux Spectra Ftherm(E ) = A (E/Er) exp [-E/Er], (11) Simulations of neutron flux spectra at 30-km altitude were made for all compositions listed in Tables 2 and 3. A sample of these spectra that cover the full range of A is presented in FeN(E) = H exp [-13](E/Eep )l'ø6/[l + (E/Eepi)2], (12) Figure 6. The values of A are 0.334, 0.591, 1.042, and 1.41 for the FAN, KBN (KREEP basalt with no Gd or Sm), KBR (KREEP basalt that includes the rare earth elements Gd and where H = 0.11, /3 = 2A(Eo/E) ø's, and Eep i ev. Similar functional forms were shown previously [Drake et al., 1988; Dagge et al., 1991] to provide adequate fits to simulated Sm), and the AP17 high-ti basalt compositions, respectively. neutron flux spectra. Inspection shows that (12) provides a Inspection shows that although all four flux spectra approach a common power law at energies above -10 ev, they differ markedly at lower energies. close approximation to (Sa) at energies greater than a few ev, with 8 = 0.06, while providing a smooth transition to the thermal flux function given by (11), at lower energies. Result- 0,1- (a) 0.01 LI_ v x r- o.ool - o z , s,,,,,,,,,,,... i... i,,,,,,,,i, 1 0 's Neutron Energy (ev) Neutron Energy (ev) Figure 7. Samples of fits to two neutron-flux spectra that are characterized by widely different values of A (corresponding to FAN and Apollo 17 soil samples) to equations (10), (11), and (12). In each sample the circles give the simulated spectra, the solid lines delineated by diamonds give the thermal fit, those delineated by crosses give the epithermal fit, and those delineated by squares give the total fit.

8 20,354 FELDMAN ET AL.' CHEMICAL INFORMATION IN LUNAR NEUTRONS x (a) Apollo High-Ti Basalt OR 3// FAN + P% H X 2.4 ) Apollo / -, Apollo Luna 16 /g' Apollo Apollo 15 _ /'/ Apollo 17// Luna / - / /Luna LAp16 ' / NO. 0.81,,, I,,, I,, I,,, I,,, / _ A A Figure 8. The dependence on A -- EaO/ s of epithermal-to-thermal flux ratios. The straight line at the left is the best fit power law to all simulated chemistries, given by Fepi/Fther m A ø'75. The straight line at the right is the best linear fit to the subset of all simulations that ar e for the Apollo and Luna soil samples and is given by Fepi/Fther m = A. ant fits to simulated spectra are given in Figure 7 for two the case of the peak neutron flux below the surface, the epiend-member compositions having values of A that represent thermal neutron flux above the surface decreases with increasthe full range of values given in Table 2. The fits are seen to be quite good, again confirming the adequacy of the simple approximation to neutron moderation given by (5a). A check on the validity of this model can be made by comparing the "hardened temperature," E r, determined from ing hydrogen abundance in response to the consequent increase in SeEs. Inspection shows that the effect is quite large, about two orders of magnitude. This amount is to be compared to variations in the epithermal neutron flux caused by changes in the composition (amounting to -14%). These compositionthese fits with those estimated using the relation from Weinberg driven variations are shown in Figure 9 for the simulations of and Wignet [1958, p. 340], Er = E0(l + ha), (13) all Apollo and Luna soil samples by the cluster of circles at the top left. The width of this cluster provides a measure of the systematic uncertainty in determining the hydrogen abundance where h is some constant. Although not shown here, the fits to (10) and (11) are quite good (correlation coefficient R = 0.89), yielding best fit values of Eo = and h = 1.30 from (13). We note that the value of h is in the range determined for reactor moderators, 1.20 < h < 1.84, given by Weinberg and Wignet [1958, p. 340]. Another check is possible by correlating the ratio of thermal to epithermal amplitudes, A/H, with A. Again, although not shown here, the correlation is quite good (correlation coefficient R = 0.999) and can be represented by a power law in A having indexp = Simulated Counting Rates from measurements of the epithermal flux alone. 4. Comparison Between Lunar Prospector Observations and Numerical Simulations 4.1. General Analyses of all simulations presented in section 3 showed that the chemical information content of thermal and epither- The foregoing simulated neutron flux spectra at 30-km altio P=3% tude were translated to LPNS counting rates using the sensor 0.1- efficiencieshown in Figure la. They, like the peak flux intensities below the lunar surface (given in Figure 5a), are well organized by a power-law function of A, as shown in Figure 8a. o P=10% Here the power-law index is 0.75, which is somewhat smaller than the index that best represents the peak fluxes below the surface, given byp However, the relationship between the ratio of epithermal-to-thermal counting rates and A can be approximated by a straight line when the compositions are confined to those of the Apollo and Luna soil samples, as FAN + P% H20 o p = 30% 100% H20 shown in Figure 8b. We note for later use that the simulated epithermal-to-thermal counting rates for these soils range between and 2.35, which differ by a factor of {Zs 1 For completeness, the dependence of the epithermal neu- Figure 9. The dependence of simulated epithermal neutron tron flux simulated at an altitude of 30 km on the macroscopic fluxes at 30-km altitude on SeEs. Note the very small percentage energy-loss cross section SeEs is shown in Figure 9. Just as for variations of simulated fluxes in all dry soils. E P = 0.1% o P=1%

9 FELDMAN ET AL.: CHEMICAL INFORMATION IN LUNAR NEUTRONS 20, / p Epis # Epis' Fast [ I t I 1 Epis errns I... I Counts Figure 10. Histograms of the thermal, epithermal, and fast neutron fluxes for the low-altitude portion (30 kin) of the Lunar Prospector mission. Also shown are combinations of the measured epithermal and thermal fluxes given by Fep i = Fep i Fther m and Fe5 i = [Fep i Ftherm]. mal neutron fluxes resides mostly in the magnitude of a single measured and simulated fast neutron fluxes from the Moon parameter, A = E,o/ Es. Furthermore, A is simply related to [Feldman et al., 1998a; Maurice et al., this issue; Gasnault et al., the ratio of the epithermal-to-thermal neutron flux (Fepi/ 2000] show that the intensity of these neutrons vary by as much Ftherm(Sim)) at 30-km altitude by inverting the regression as -30%. shown in Figure 8b: 4.2. Range of Flux Intensities A = 0.539[Fepi/Ftherm(Sim)] ( 4) Before proceeding to apply this relation to neutron fluxes measured using Lunar Prospector, we must first evaluate how well the LPNS observations agree with predictions of the simulations. This task requires use of the ratios of fluxes because the simulations presented earlier are all normalized to the fast neutron input to the ONEDANT code. Analyses of both the 400 3OO Thermal/Ep thermal Neutrons Figure 11. Histograms of Ftherm/Fepi (dashed line) and (Ftherm/Fepi) - (Ftherm/Fepi)... solid line. See the text for discussion. Histograms of the several components of neutron flux intensities at 30-km altitude within pixels of all quasi-equal spatial areas on the Moon (equivalent in area to 2 ø x 2 ø latitudelongitude areas at the equator) are shown in Figure 10. We note that the thermal neutron distribution is broadest, with a full width at full maximum (FWFM) spanning a ratio of 3.1, that of the fast neutrons is next, with a FWFM spanning a ratio of 1.32 [see also Maurice et al., this issue], and that of the epithermal neutrons is least, with a FWFM spanning a ratio of Correspondence with the ONEDANT simulations requires knowledge of the ratio of thermal-to-epithermal (or, equivalently, epithermal-to-thermal) neutron flux. A histogram of this ratio is shown using a dashed line in Figure 11. Inspection of Figure 11 shows (1) a broad pedestal of occurrence rates that culminates in a modest peak at a thermal-to-epithermal flux ratio of -0.49, (2) a shoulder of increasing occurrence rates running from flux ratios that extend between about 0.7 and 0.9, (3) a relatively sharp peak centered at a flux ratio of -0.95, and (4) a shoulder on the high side of the peak that extends between flux ratios of about 1.07 and 1.2. We will address the correspondence between the various portions of this histogram and regions on the Moon in sections 4.5 and 5. However, for now, we note that the full range of observed thermal-to-epithermal neutron flux ratios matches closely that simulated for the different Apollo and Luna soil samples shown in Figure 8b. Whereas the measured flux ratio extends from about 0.4 to 1.2, corresponding to a factor of 3.0, the simulated flux ratios extend from for Apollo 11 to 1.17 for FAN, corresponding to a factor of 2.75.

10 _ 20,356 FELDMAN ET AL.' CHEMICAL INFORMATION IN LUNAR NEUTRONS o:i 0.36 [ x I J_ Apollo 14 o / Luna 20 - o Z '.-- Apollo 1 4-' Apoll ol/ø Apollo 15../ o Luna16.. 0,31 - a o Luna 24 Apollo ApoIIo - with a significance given by the correlation coefficient R = In order to make the correspondence with Lunar Prospector observations, we must note that the foregoing simulations are normalized to the fast neutron input to ONEDANT, which does not hold in practice over the Moon [Feldman et al., 1998a; Maurice et al., this issue]. We correct approximately for this fact by constructing the correlation between epithermal and thermal neutrons, both normalized to the measured flux of fast neutrons in each equivalent 2 ø x 2 ø equal area pixel. This correlation is shown in Figure 13. The slope of the regression is 0.225, the zero offset is 1.11, and the correlation coefficient is R Comparison of these values with those in (15) shows the slopes and correlation coefficients are closely equal but the zero offset of the data is significantly larger than that for the simulations. This difference in zero offset is not mate- Thermal Neutron Flux (Simulated) rial to our comparison because the proxy we used for the fast neutron flux (the counts in the LP fast neutron detector) was Figure 12. The correlation between Fep i and Fther m simu- not normalized to the input required by the ONEDANT code. lated for all lunar soil samples at 30-km altitude. The straight However, the slope is important, and the observed and simuline is given by Fep i Fther m q- 0.28, with a correlation coefficient of R = lated slopes are seen to be closely equal. The similarity in correlation coefficients may or may not be significant, depending on whether or not the spread in observed flux ratios in 4.3. Correlation Between Epithermal and Thermal Neutrons The simplified theory of neutron moderation summarized in Figure 13 is dominantly caused by a breakdown in the assumpu cu tu uenve toa).,nebo assumptions are that YEa o E -ø's and Zs is constant throughout the epithermal energy range. (5a) and (7) shows that neutron absorption reduces the intensities of both thermal and epithermal neutrons. Although the Another way to test the correspondence between observaassumptions used to derive these equations do not strictly hold tion and theory is to compare histograms of the simulated over the full energy range spanned by epithermal neutrons (0.4 thermal-epithermal flux correlation, given by F½ i = [Fepi - ev < E < 500 kev), they are sufficiently accurate to account 0.23Ftherm], with that of the fast neutron flux. Both histograms for a correlation between epithermal and thermal neutron are shown in Figure 10. The overall match is seen to be reafluxes as measured using the LP neutron spectrometers. This sonably good. correlation for all Apollo and Luna composition simulated The facts that thermal and epithermal fluxes are related using ONEDANT is shown in Figure 12. It is given by through their common absorption by regolith nuclei and that they are both produced by galactic cosmic rays suggesthat we Fep, = 0.21Ftherm q- 0.28, ( 5) can try to make an empirical correction to observed epithermal 1.8 r I I ' 1.6 y- m,x + b m b R ':'/" '..":;?;½;..,;((.t½i '. "' ':.;...': :::.. ).. ',:t' :".::':"" ' m Thermal/Fas[ Figure 13. The correlation be een measured values of (F pi/ffa t) and (Fth m/ffa t). The straight line is given by (F pi/ffa t) = (Fth m/ffa t), with a correlation coefficient of R = 0.86.

11 FELDMAN ET AL.: CHEMICAL INFORMATION IN LUNAR NEUTRONS 20,357 Thermai/Epithermal Neutrons Thermol/Epithermol Residuol Plate 1. Colored maps at 2 ø longitude x 2 ø latitude resolution of measured values of (top) Ftherm/Fep i and of (bottom)(ftherm/fepi)residual. The (Ftherm/Fepi)residual are (Ftherm/Fepi) that are corrected for Gd and Sm abundances using the thorium abundances measured using the LPGRS, as detailed in the text.

12 20,358 FELDMAN ET AL.: CHEMICAL INFORMATION IN LUNAR NEUTRONS Epithermal/Thermal Neutrons Epithermal/Thermol Residuol Plate 2. Colored maps of (top)(fepi/fthcrm) and (bottom)(fepi/ftherm)residual in accord with the same procedure outlined in Plate 1 (essentially the inverse equivalent of Plate 1).

13 FELDMAN ET AL.: CHEMICAL INFORMATION IN LUNAR NEUTRONS Thorium Abundonce (ppm) Plate 3. The correlation between measured 2 ø x 2 ø samples of Fepi/Fther m and thorium abundance. See the text for details. fluxes from both effects by subtracting a fraction of the thermal flux. This procedure would then enhance the sensitivity of epithermal neutron observations to the abundance of hydrogen by suppressing the variance of the cluster of circles in the top left-hand corner of Figure 9. Although not shown here, the epithermal and thermal neutron fluxes measured at 30 km are found to be weakly correlated, with significance of R = We therefore define a hybrid epithermal neutron flux intensity, given by our "ground truth" knowledge of lunar composition. The correlation between measured and simulated epithermal-tothermal flux ratios at each of the Apollo and Luna landing sites is shown in Figure 14. An average over a 6 ø x 6 ø spatial pixel centered on each of the sites was used in constructing the measured ratio because the spatial response function of thermal neutrons is relatively broad. Inspection of Figure 14 shows the correlation is quite good. The straight line represents equality with no offsets or normalization constants. The coef- F *epi = F epi F therm' (16) ficient of correlation is R = The absolute agreement between measurements and simulations leads us to believe that A histogram of this hybrid quantity is shown in Figure 10. Comparison of the histograms for F ep i and Fep i shows that a small improvement in the form of a reduced width, and hence the less than perfect correlation seen in Figure 14 results from relatively small-scale heterogeneities in the composition of lunar soils at each of the sites. a reduced sensitivity to composition, is indeed possible. This improvement is more noticeable when comparing a global map 4.5. Correction for Gd and Sm of F epi to that of Fep i because most of the systematic variations A colored map of the ratio of thermal-to-epithermal neutron in Fep i due to variations in composition appear muted [FeMfluxes measured at 30 km is shown in Plate 1 (top). The highest man et al., 2000]. Of course, other techniques to eliminate values, which correspond to the right-hand part of the red nonhydrogenicomposition effects from the LP epithermal histogram in Figure 11, have yellow and white colors and are neutron flux observations are possible and are currently being seen to cover the highlands. The darker colors (black and deep investigated. purple) correspond to the left-hand part of the histogram and 4.4. Comparisons at Apollo and Luna Sites mark the frontside maria. A map of the inverse ratio (Fepi/ A more sensitive test of our ability to relate measured thermal and epithermal neutron fluxes with simulations is to use Ftherm), which helps delineate different compositions in the maria because the eye is most sensitive to orange, yellow, and

14 20,360 FELDMAN ET AL.: CHEMICAL INFORMATION IN LUNAR NEUTRONS m mm m m 81! m,mm { mm mmmmm m mmm m ramrol mmmm m mm m m I m '",. m -, ",m-.,..m. ' '.m'.1'.... m,.,t 21.._ ß ß.. ß. : ',, ß ß, m_m. m mm 4'-'' ' : "" ' ß 'r.' -r ß :. _,. ß 'm m =, m..... m m.. -.".' mml ' '"'" '"" - -.r. - mmm lmmm ml mmmm ' Plate 4. A map of the thermal-to-epithermal neutron flux corrected for Gd and Sm abundances as detailed in the text. A six-element color code was chosen in accord with the classification scheme given in Table 5. white, is shown in Plate 2 (top). As shown in previous sections, these maps provide chemical information only through A, the ratio of macroscopic absorption to energy-loss cross sections. This ratio is affected significantly by contributions from Gd and Sm, which can, in places, mask the contributions from mafic elements such as Fe and Ti [Elphic et al., 1998, this issue]. In the spirit of exploring the limits of information about regolith chemistry from measured thermal and epithermal flux spectra, we have searched for a procedure to reduce the effects of Gd and Sm on these spectra in order to define better the composition of the major rock-forming elements. We have found that, indeed, these effects can be minimized (at least statistically) through use of the thorium abundance, which is 2 - Apollo 14 o /_ 1.8i / Apollo11 o _ also measured aboard Lunar Prospector using the gamma-ray spectrometer [Lawrenc et al., 1998, 1999, this issue]. A scatterplot of (Fepi/Fth...) as a function of thorium abun- dance using the low-altitude 2 ø x 2 ø quasi-equal area LP maps is given in Plate 3. It is seen to define a positive slope at the lower boundary of the distribution. This effect is expected qualitatively to result from Gd and Sm, which are known to correlate with Th [Haskin and Warren, 1991]. To explore this suggestion quantitatively, we parameterized the correlations between Th and Sm in samples returned by the Apollo program (given in Figure 8.9 of Haskin and Warren [1991] for highland material and in Figure 8.12 for mare material). The cosmic abundance ratio, Gd = 1.29Sm, was then used to estimate the Gd abundance. For the highlands, this procedure yields Gd = 4.24 Th ø'8i6 Sm = 3.29 Th ø'816. (17) Equation (17) should provide a good estimate of Gd and Sm abundances in the highlands because the correlation between Sm and Th is quite high there. The same procedure is more ambiguous for the maria. Here the correlation between Sm and Th is poor. The best that can be done is to provide lower, 1.6-[ Apollo 1% o Luna 16 - middle, and upper limit slopes that represent this correlation. 1.4 / / o Apollo Luna 21 _ We estimate these slopes to be rn = 5.3, 8.2, and 14.6, respectively, from the scatterplot presented in Figure 8.12 of 7L _ Haskin and Warren [1991]. They can be translated to values of (Fepi/Ftherm) through their known contributions to the macro- 08 b '"'l'111'' scopic absorption cross section using estimates provided by Lingenfelter et al. [1972]. These yield Z,0 = 31.7 x [0--6 Gd (in jug/g) and 57.1 x 10-6 Sm (in p g/g). If we choose the Epithermal/Thermal (Simulated) correction factors to (Fepi/Ftherm) for Gd and Sm to be zero Figure 14. The correlation between Fepi/Fther m measured when the abundance of Th equals zero, then the correction above each of the Apollo and Luna landing sites and the factor in the highlands is given by corresponding simulated flux ratios. The straight line represents equality. (Fepi/Ftherm)co r Th, (18)

15 FELDMAN ET AL.: CHEMICAL INFORMATION IN LUNAR NEUTRONS 20,361 where Th is in /zg/g. We have used the relations between (Fepi/Ftherm) and A given in (14) as well as the facthat scs;s is nearly independent of all compositions when hydrogen is not present (see Table 2). The three slopes for the correlation between Sm and Th for the mare can then be translated to correction factors, giving (Fepi/Ftherm)cor: [0.296, 0.162, and 0.106] Th, (19) where Th is in /.rg/g. All four correction factors (one for the highlands and three for the maria) are presented in Plate 3 by the lines with zero intercepts. However, we expect that none of these lines will provide a correction for all terranes on the Moon. Instead, the bottom line (in green) will work best in the highlands, and the middle line (in red) will work best for the mare. For purposes of choosing a composite correction factor for all terranes, we define highlands material to have thorium abundances <3/zg/g and mare material to have thorium abundances >3/zg/g (see Th maps presented by Lawrenc et al. [1999]). The final correction is then given by the composite green and light blue lines at the bottom of Plate 3. The resultant histogram of corrected flux ratios is given by the solid-line histogram in Figure 11. The corresponding colored maps of (Fepi/ Ftherm)resi d and its inverse are shown in the bottom of Plates 1 and 2, respectively. Table 5. Ftherm/Fep i Classification of Lunar Soils Soil Sample (Ftherm/Fepi)resid* FeO, % TiO2, % Band 1 FAN white Color Band 2 NOR light blue Band 3 Apollo yellow Luna yellow Band 4 Apollo dark blue Band 5 Apollo green Apollo green Luna green Apollo green Band 6 Luna red Apollo red *The(Ftherm/Fepi)resi d were calculated by correcting the values of ix = 5;a0/ 5;s listed in column 4 of Table 1 for the contributions to a0 from Gd and Sm and then using equation (14) to derive Fepi/ Ftherm(Sim ) from ix. The break between bands 1 and 2 is 1.15, the break between bands 2 and 3 is 1.05, the break between bands 3 and 4 is 0.92, the break between bands 4 and 5 is 0.75, and the break between bands 5 and 6 is values of A for the end-member Mg-Fe solid-solution minerals, 5. Summary and Discussion listed in Table 4. For example, the end-members of the mineral olivine are forsterite and fayalite, which differ only in the Simulations of equilibrium thermal and epithermal neutron simple substitution of Fe for Mg, yet this substitution allows for flux spectra near the lunar surface were surveyed to determine values of A to range continuously between and their chemical information content. Two parameters relating to surface chemistry were found to be important: (1) the ratio of macroscopic absorption to energy-loss cross sections, A - Similarly, the end-members of orthopyroxine are enstatite and ferrosilite, which correspond to A between and Therefore derivation of a value of A , say, from mea- 5;a0/ 5;s, and (2) the macroscopic energy-loss cross section surement of the highlands thermal-to-epithermal flux ratio SeEs (or, almost equivalently, the elastic-scattering cros section could indicate a plagioclase-rich composition (e.g., FAN). Al- Es by itself). Whereas A is related monotonically the ratio of ternatively, it could also be consistent with pure olivine or epithermal-to-thermal flux intensities through (14), the energy- pyroxene having magnesium numbers higher than , or loss and scattering cross sections are related to the epithermal flux intensities as shown in Figures 4a and 9. The most comprehensive of the three parameters is A because it includes with a mixture containing, say, 50% plagioclase and 50% olivine or pyroxene having magnesium numbers higher than Another complication enters through the contributions to A information about hydrogen as well as of all the heavier ele- from Gd and Sm. These elements have been shown to be ments. The energy-loss and scattering cross sections provide information mainly about the abundance of hydrogen. All relations connecting chemical information to neutron measurables that were derived in this study from ONEDANT simulations are collected in Table 1. Comparison of the simulation results with the Lunar Prospector thermal and epithermal neutron observations reveals a close absolute agreement. This agreement allows us to conclude that the LPNS observations can be inverted to construct a map of A, which, in turn, provides a proxy for lunar composition. Inspection of Tables 2 and 3 shows that this proxy important both from simulations [Lingenfelter et al., 1972; Feldman et al., 1991] and from measurements [Elphic et al., 1998, this issue]. Nevertheless, the procedure developed at the end of section 4 demonstrated their credible, quantitative removal from highland terranes and their statistical removal from mare terranes using separate measurements of the Th abundance. Even in the maria, though, the improvement of the corrected flux ratio maps over the uncorrected maps is seen to be quite striking by noting the better definition of basaltic lava flows from interbasin highland areas. These interbasin highlands were shown by Lawrence et al. [1999, this issue] to support cannot generally be used to determine composition uniquely. relatively high Th abundances. A clear example of this im- The one exception is hydrogen, which is monotonically related to scs;s. All other elements are grouped together by their summed, weighted contributions to A. Nevertheless, certain elements such as Fe and Ti stand out because of their relatively proved definition is the ridge that separates Frigoris from Imbrium. In spite of this improvement, a quantitative interpretation of the different mare basalt deposits using the residual thermal-to-epithermal flux ratio map requires a combined large absorption cross sections. These elements are concen- analysis using other data sets (e.g., gamma rays, fast neutrons, trated in the mafic minerals so that A can effectively be used as an index that is lowest for the anorthositic compositions and highest for the mafic compositions. However, an ambiguity still remains, as can be seen by the and UV/VIS spectral reflectance data). Specifically, several elements provide strong and inseparable contributions to A. The farside highlands do not suffer from this problem. Indeed, the yellow and white colors in the residual map shown at

16 20,362 FELDMAN ET AL.: CHEMICAL INFORMATION IN LUNAR NEUTRONS the bottom of Plate 1 correspond to values of (Fepi/Ftherm)resi d for regolith dynamics, Geochim. Cosmochim. Acta, 2, , that rise above the level that marks FAN and the high mag- Dagge, G., P. Dragovitsch, and D. Filges, Monte Carlo simulation of nesium number end of the olivine and pyroxene mineral Martian gamma-ray spectra induced by galacti cosmic rays, Proc. groups. This result is most clearly demonstrated by classifying Lunar Planet. Sci. Conf. 21st, , compositions into discrete intervals (Ftherm/Fepi)resi d. The Davis, P. A., Jr., Iron and titanium distribution on the Moon from correlation shown in Figure 8b was used as a guide to choose orbital gamma ray spectrometry with implications for crustal evoluthe six discrete bands given in Table 5. A map of (Ftherm/ tionary models, J. Geophys. Res., 85, , Drake, D. M., W. C. Feldman, and B. M. Jakosky, Martian neutron Fepi)resi d color coded according to these bands is shown in leakage spectra, J. Geophys. Res., 93, , Plate 4. This map is quite striking. Areas color coded with red Drake, D. M., M. Drosg, R. C. Byrd, R. C. Reedy, D. A. Clark, P. A. J. and green represent the most Fe- and Ti-rich terranes, which Englert, J. F. Dempsey, S. G. Bobias, and L. Harris, Experimental delineate the frontside maria. Areas color coded with dark and numerical simulation of Martian neutron distributions, Nucl. blue form margins around the frontside maria and also delin- Instrum. Methods Phys. Res., Sect. B, 84, , Elphic, R. C., D. J. Lawrence, W. C. Feldman, B. L. Barraclough, eate the central portions of maria Humboldtianum, Smythii, S. Maurice, A. B. Binder, and P. G. Lucey, Lunar Fe and Ti abun- Marginis, Moscoviense, and Australis, as well as the Orientale and South Pole-Aitken Basins. The lunar highlands are predominantly white with a light blue border. The top two rows in Table 5 then indicate that the highlands are composed predominantly of ferroan anorthosite that grades gradually into a border having a more noritic composition. However, the composition for our FAN simulations had very low Fe and Ti abundances (FeO - 1.9% and TiO2 = 0.13%, as listed in columns 3 and 4 of Table 5). Our best estimate of the abundance of FeO in the highlands is therefore 2%. However, this estimate relies on a subtraction of the relatively small effect on A of Gd and Sm abundances in the highlands, as determined using the Th abundances derived from measured gamma-ray spectra. The analysis presented by Lawrence et al. [this issue] indicated that these Th abundances have a baseline uncertainty of ---2 ppm. This uncertainty translates to the horizontal offset between the high end of the neutron flux ratio histogramshown in Figure 11. Inspection of column 2 in Table 5 shows that this offset corresponds to a little less than the difference between FAN and NOR. We therefore conclude that the abundance of FeO in the lunar highlands is between 1.9 and 4.9%. This range contains the average FeO abundance derived from Clementine spectral reflectance data (FeO = 4.2% [Lucey et al., 1998] and <4.9% [Tompkins and Pieters, 1999; Pieters and Tompkins, 1999]) and from analyses of lunar meteorites (5.2% [Palme et al., 1991]). However, it is significantly less than that derived from Apollo gamma-ray data (FeO = 7.7% [Haines and Metzger, 1980; Davis, 1980]). Our result is consistent with a very high abundance of plagioclase in the highlands, which is predicted by the magma ocean theory of crustal evolution (see, e.g., the review by Warren [1986, and references therein]). However, this interpretation of LP neutron data is not unique. 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