The lunar neutron flux revisited

EARTH AND PLANETARY SCIENCE LETTERS 16 (1972) 355-369. NORTH-HOLLAND PUBLISHING COMPANY

[] THE LUNAR NEUTRON

FLUX REVISITED*

R.E. LINGENFELTER Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90024, USA E.H. CANFIELD and V.E. HAMPEL Lawrence Radiation Laboratory, Livermore, California 94551, USA Received 24 July 1972

Cosmic ray-produced neutron equilibrium spectra are calculated for a variety of lunar surface compositions. From these spectra production rates of 80 Kr, 82 Kr, 114Cd, 131Xe, 150Sin, 152Sm, 152Gd, is6 Gd, 158Gd and 187Re due to neutron capture on 79Br, 81 Br, 113 Cd, 130Ba, 149Sm, 151Eu, 155Gd, 157Gd and 186W are determined and compared with measurements.

1. Introduction Ten years ago we [1] calculated the cosmic ray produced neutron flux at the lunar surface for a variety of assumed surface compositions in order to estimate the potential usefulness of lunar neutron flux measurements in determining the surface composition. It proved not to be a useful technique, and since then the Apollo astronauts have brought back samples of lunar surface material for extensive direct analysis. Among these analyses are the measurements of Lunatic Asylum [2] which show anomalous abundances of the isotopes 158 Gel through 155 Gd. These anomalies can be attributed to excess 158 Gd and 156 Gd produced by the capture of cosmic ray neutrons on 157 Gd and 155 Gd which have enormous resonance cross sections at thermal energies and are depleted. Epithermal neutron capture has been suggested for the anomalous abundances of 80 Kr and 82 Kr by capture on 79 Br and 81 Br [3], 187 Re by capture on 186 W [4] and 131 Xe by capture on 130 Ba [5, 6]. To study these and related processes in detail we have recalculated the cosmic ray neutron flux spectrum in lunar surface material and determined the production rates of the isotopes, 80 Kr, 82 Kr, 114 Cd, * Publication No. 985, Institute of Geophysics and Planetary Physics, University of California, Los Angeles.

131 Xe, 150 Sm, 152 Sin, 152 Gd, 156 Gd, 158 Gd and 187 Re as a function of depth in lunar material, having a range of compositions and temperatures. From these studies we find that measurable anomalies should also be found in the abundance ratio of isotopes 150 Sm/ 149 Sm from neutron capture on 149 Sm and 114 Cd/ 113 Cd from capture on 113 Cd. The predicted Sm anomalies have recently been confirmed by Russ et al. [71. Armstrong and Alsmiller [8], as a part of a more general calculation of cosmic ray interactions in the lunar surface material, have calculated the equilibrium intensity of lunar neutrons but, since they did not calculate the spectrum at energies < 0.4 eV, they were not able to make any meaningful estimate of the thermal neutron capture rates.

2. Transport calculation The equilibrium neutron flux spectrum in lunar surface material was calculated using the neutron transport equation. The multi-group transport equation for the neutron angular flux as a function of energy group, i, and depth x (g.cm "2) in a one-dimensional slab may be written

R.E. Lingenfelter et al., Lunar neutron flux

356

/2 ff-X + Nti

)

~oi(/2,x ) = S i ( x ) +

+ ~ }(2l+1)P/(/2)~) Zl, j_+i¢lj(X) t=0

(1)

j

In equilibrium the neutron losses (left hand terms) from energy group i, angle d/2 at/2 and depth dx at x by transport and by nuclear interactions balance the sources (right hand terms) to that group from neutron production and from scattering into that group and angle from all groups/. The individual terms are: /2 = cosine of the angle with respect to x, PI (/2) = Legendre polynomial, S i (x) = group source (neutrons • g-t . sec-t), ~0i (/2, X) = group angular flux, neutrons • cm "2 "sec-1 with d# in the direction/2, 1 ~Oli(X) = f dgPl (/2)~oi(/2,x) = Legendre moment -I of the angular flux. For example: S0oi(x) is the group scalar flux equal to q0i in diffusion theory and qOli(X) is the group current density equal to -OiOqoi/Ox in diffusion theory, Nti = Nat. + N si = group total macroscopic cross section (cm 2 • g-1 ), ]~ai = group macroscopic capture cross section, ~dE, 1 Nsi=TLoifdE%(E) j f-1 d/2'N(E-+E',/2'), i 0

Nl, j-~i = 1

fdE ,,(E)f-1 d/2'PI(/2')N-,(E-+E',/2)

_ 1 fdE' eli i j

= Legendre moment of the macroscopic energy transfer matrix, Y~ (E-~E',/2') = differential macroscopic cross section for scattering from energy E into dE' around E'through an angle whose cosine is within d/2' around/2'. In these calculations we used not only the usual l=0 transfer matrix [9] but also the l= 1 matrix to account for anisotropies in the neutron scattering in the keV and MeV range. These equations can be solved by the ANISN code [10], which uses difference equations based on dis-

crete meshes in x and/2. Our calculations were of the $4 type which have four angular intervals. The energy spectrum from 10 MeV to 0 eV was divided into 25 energy groups. Eleven groups of equal logarithmic intervals were used to give good spectral detail in the energy range from 1 eV to 0.00178 eV where the Gd and Sm capture cross sections are important. The lunar surface was considered to be a homogeneous slab. The calculations were made for lunar surface material having the composition of the Apollo 11 lunar fines and for a wide range of compositions around that, which span that of other samples from Apollos 11, 12, 14 and 15. The abundances of the major elements in the Apollo 11 lunar fines were taken from the analysis by Wiik and Ojanpera [I 1]. The trace abundances of 79 Br,81 Br, 113 Cd, 130 Ba, 149 Sm, 151 Eu, 155 Gd, 157 Gd and 186 W are taken from the analyses by Gast and Hubbard [12] and Keays et al. [13], assuming isotopic abundances of 50.54% for 79 Br, 49.46% for 81 Br, 12.26% for 113 Cd, 0.101% for 130 Ba, 13.83% for 149 Sm, 47.82% for 151 Eu, 14.73% for 155 Gd, 15.68% for 157 Gd and 28.41% for 186 W. This composition is summarized in table 1, together with the microscopic and macroscopic neutron capture cross sections at a reference energy of 0.0253 eV. At thermal and epithermal energies ( < 1 keY) all of the major elements have 1/v-dependent capture cross sections and essentially constant scattering cross sections which are elastic and isotropic in the center of mass. On the other hand, all of the trace elements considered show strong resonance capture at these energies and thus are not simple 1/v absorbers. The energy dependent capture cross sections for these isotopes (except 130 Ba) were calculated from the Breit-Wigner resonance parameters given in table 2. The 130 Ba resonances have not yet been identified, but the average capture cross section in the range from leV to lkeV has been found [5] to be 212 b. The capture cross sections at 0.0253 eV are also shown in table 1, but because of the resonances those values are not representative of their capture efficiency relative to the 1/v cross sections. This will be discussed in detail below. The magnitude of the macroscopic thermal capture cross section strongly affects the thermal neutron spectrum and the neutron capture rates. From the macroscopic cross sections in table 1 we see that the

R.E. Lingenfelter et al., Lunar neutron flux

357

Table 1 Composition of Apollo 11 lunar fines. Neutron Capture Cross Section at 0.0253 eV Element

Abundance

Microscopic

Macroscopic

(1024 atoms • g-1 )

(b)

(cm 2 ° g-1 )

0

1.58 x 10 -2

< 2

Si

4.23

X 10 -3

1.6 X 10 -1

6.8 × 10-4

A1

1.63 × 10 -3

2.3 X 10"1

3.7

Fe

1.32 X 10-3

2.53 × 10 o

3.3 X 10 -3

Ca

1.29 X 10 -3

4.3

5.5

Mg

1.19× 10-3

7.5 × 10-5

Ti

5.70 x 10-4

6.3 × 10-2 o 6.1 x 10

lSTGd

1.03X 10-8

2.4 X 105

2.4× 10 -3a)

155Gd

9.8 × 10 -9

5.8 × 104

5.7X 10 -4 a)

149 Sm

7.3

X 10 -9

4.08 × 10 4

3.0 × 10 -4 a)

151Eu

3.4 × 10 -9

7.8 × 103

2.6× 10-5 a)

13o Ba

1.0 × 10-9

8.8 × 10 o

8.8 X 10-9 a)

79 Br

7.5 × 10-lO

1.14 × 10 1

8.5 × 10-9 a)

81 Br

7.5

3.2

2.4 X 10 -9 a)

× 10 -lO

x

10 -4

X 10 -1

× 10 o

< 3

× 10 -6

×

10 -4

X 10 -4

3.5 × 10-3

186 W

2.3 × 10-1°

4.0 × 10 1

9.2

113Cd

2.6

2.0 × 10 4

5.2X 10-Ta)

× 10 "11

× 10 -9 a)

a) The effective capture cross sections differ from these values because of resonance capture, see table 4 and fig. 6. bulk of the thermal 1/v-dependent capture is in titanium and iron. The abundances o f these two elem e n t s vary significantly with rock type and locality in A p o l l o samples taken so far. On the other hand, the total n e u t r o n p r o d u c t i o n rate, the elastic scattering cross section and the energy loss distribution ~; (E-~E ',/a' ) of n e u t r o n s in the lunar material is determined almost wholly by the m o s t a b u n d a n t elements, o x y g e n and silicon. The abundances of these two elements do n o t show i m p o r t a n t variations with rock type or locality in the A p o l l o samples. Thus, for the purpose of the n e u t r o n equilibrium flux calculation, all c o m p o s i t i o n variations m a y be reduced to variations in the macroscopic 1Iv capture cross section, provided that corrections are m a d e for the variations caused by changes in the trace e l e m e n t abundances. We have carried out calculations for c o m p o s i t i o n s which have 0.25, 0.5 and 2 times the macroscopic

1/v-dependent capture cross sections of the A p o l l o 11 fines. F r o m these it is possible to estimate capture ratios for a variety o f nuclei in the whole range o f lunar compositions. The group-averaged cross sections in the energy range (10 MeV ~> E ~> 3 eV) are obtained from the C L Y D E code [ 14] using the cross section data compiled and evaluated by H o w e r t o n [15]. F o r these groups, b o t h the l = 0 and transport corrected I = 1 transfer matrices were used. The cross sections were avel;aged over each energy group by a flux weighting spectrum p r o p o r t i o n a l to Ee "E for E > 2 MeV and to

1/E for E < 2 MeV. The calculation of the group cross sections at energies < 3 eV requires assumptions a b o u t the thermalization process of low energy neutrons. However, the narrow energy groups chosen in this range greatly reduce the possible errors resulting from such assump-

R.E. Lingenfelter et al., Lunar neutron flux

358

Table 2 Breit-Wigner Resonance Parameters. E o (eV) xss Gd (n, 7) 156 Gd

F7(eV)

I'n(eV)

I

J

0.0268

0.108

0.000095

~3

2

2.008

0.110

0.00037

2.568

0.111

0.00198

53 3 ~-

2

6.3

0.106

0.00251

7.73

0.140

0.00154

0.109 0.106

10.1 ls7 Gd (n, 7) 158 Gd

149 Sm (n, 7) lSO Sm

113 Cd (n, 7) 114 Cd

lsl Eu (n, 7) 152 Eu

186 W (n, 7) 187 W

0.0314

1

0.00018

3 ,~ 3 -2 3 ~-

3 ~-

0.000472

? ~-

4 4

2 3

2.85

0.097

0.00035

7 ~

0.0976

0.063

0.00050

7 ~-

4

0.87

0.060

0.00073

7

4

4.93

0.067

6.48

0.062

0.00080

8;9

0.062

0.00800

7 ~7 ~7 ~-

O. 178

O. 113

0.00065

~1

1

1

1

0.00201

18.5

0.115

0.00028

64.0

0.080

84.9

4 7 ~4

~-

0.00666

~1 ~-

0.115

0.022

]-

1

1

0.321

0.0795

0.0000557

5 5-

3

0.460

0.087

0.000648

s ~-

3

1.06

0.085

0.000201

5 ~-

3

1

~-

1.83

0.091

0.000035

5

5

2.46

0.092

0.000197

s ~-

3

3.37

0.092

0.00222

2

3.71

0.088

0.00074

ys 5 ~5

5

4.85

0.091

0.00010

5.47

0.091

0.00014

6.00

0.091

0.00036

7.25

0.091

0.0021

S 5 T

7.44

0.091

0.0022

5 ~-

9.06

0.091

0.0010

{

0.266

0.045

0

171.0

0.0235

0.056

0

~-

221.0

0.55

0.046

0

1

18.8

~ 5 ~-

5

5 ~5 "2 5 5

1

R.E. Lingenfelter et al., Lunar neutron flux

359

Table 2 (continued) Breit-Wigner Resonance Parameters.

79 Br (n, q,) 8o Br

E o (eV)

I'3,(eV)

Fn (eV)

I

J

35.83

0.3265

0.04032

~3

2

0.3915

0.03427

3

~

1

0.3664

0.08219

~

1

3

53.72 189.4

81 Br (n, "r) 82 Br

238.5

0.3004

0.5864

~

2

101.0

0.2716

0.1546

~3

2

3

135.5

0.3218

0.4101

~

1

205.0

0.3788

0.01764

~3

2

tions. In lieu of satisfactory models for chemical binding and crystalline effects we treated the lunar material (below 3 eV) as a monatomic Maxwell gas of atomic weight, .~ = 20. This value was chosen by requiring that the average logarithmic energy loss per scatter be the same for the gas as for the mixture. The average logarithmic energy decrement [16] is A+t ~"= 1-~ ( A - l ) 2 in (~---~),

(2)

We require that

(t- z s ) gas =

Zsj,

(3)

The 'hardened' Maxwellian changes smoothly to a lIE dependence at 2 k T (hard) = 0.167 eV. For these low energy groups only the t = 0 transport-corrected transfer matrix was used. The group-averaged capture and total cross sections were generated with the SOPHIST-3 code [ 18] using the same weighting flux. The energy and spatial distribution of the neutron production in the lunar material assumed in this calculation has the same functional form as that used by Lingenfelter et al. [1], but the values of some of the parameters are changed:

S (E,x) = SoE exp {-E/O)exp { - x / A )

(5)

1 where the sum is over the elements of the mixture. This yields a value o f . 4 = 20.3. The transfer matrices for these low energy groups were calculated with the SOPHIST-1 code [17] for three moderator temperatures T (hot) = 400K, corresponding to the maximum lunar surface temperature, T (med) = 200K, and T (cold) = OK. The same flux weighting spectrum was used in each case: a 'hardened' Maxwellian for low energies which changes smoothly to a lIE dependence for higher energies. The 'hardened' temperature [ 16] is obtained from values of the absorption and scatter cross sections evaluated at an energy corresponding to the temperature of the lunar material ; i.e. E = k T ( h o t ) = 0.0351 eV

k T (hard) = (1 + 0.7 A Za/Es) kT(hot) = 0.0835 eV

(4)

where 0 is the evaporation temperature in MeV and A is the attenuation length in g • cm'2: In the calculations S O was normalized so as to give a total neutron production of 1 neutron • sec "1 under each cm 2 of the lunar surface. The absolute normalization of the neutron production can be derived from the cosmic ray neutron production in the earth's atmosphere, as was done in Lingenfelter et al. [ 1], considering also more recent studies of the atmospheric neutron intensity [ 19]. The production rate of neutrons at the lunar surface should be larger than that in the earth's atmosphere for three reasons: the higher average cosmic ray intensity at the lunar surface, the higher average atomic mass of lunar material, and the added neutron production due to ~r mesons. The cosmic ray intensity at the surface of the moon is larger than that in the upper atmosphere of the earth

360

R.E. Lingenfelter et al., Lunar neutron flux

because the moon has a negligible magnetic field. In fact lunar surface intensity should be the same as that above the poles of the earth, where exclusion of cosmic rays by the geomagnetic field becomes negligible. This intensity varies over the solar cycle from a value of about 8.4 neutrons • cm -2 . sec "1 at solar minimum to about 5.6 neutrons • cm 2 - sec "1 at solar maximum and the average over the last solar cycle is 7.1 neutrons, cm -2 - sec "l [19]. The cross section for the production of neutrons ( < 10 MeV) is roughly proportional to the one half power of the atomic number, A I [20, 21]. The Apollo 11 fine composition, listed in table 1, corresponds to an average A = 23 compared to A = 14.5 for the earth's atmosphere. Thus the average neutron production cross section for lunar material would be ~ 1.26 times that at polar latitudes in the earth's atmosphere. This gives an average lunar neutron production rate of 9.0 neutron • cm -2 . sec "1 by cosmic ray nucleons in evaporation and knock-on processes. Of these about 20% are produced at energies greater than 10 MeV and about half of these escape or are captured before scattering down below that energy. Thus the effective production rate of neutrons of energy < 10 MeV by these processes is about 8.1 neutrons • cm -2 • sec -1, with an uncertainty of about 25%. The estimate of the neutron production by pion interactions is the same as that made previously [ 1]. Pions made by cosmic ray interactions nearly all decay with a half-life of 2 × 10-8 sec before capture in the earth's diffuse atmosphere. However, in the much denser lunar material, the bulk of the n- mesons will be captured, releasing on the average 4 neutrons of E < 10 MeV. Because of Coulomb repulsion the ~r+ mesons are not captured by nuclei. Cosmic ray and bevatron data show that about one n" meson would be produced per incident proton. Assuming the incident proton flux at the lunar surface to be the same as at the earth's poles, about 2 protons • cm -2 • sec"l, we expect 8 + 3 neutrons • cm -2 • sec "1 from (rr', n) events. Combining the evaporation, knock-on, and n" components, we then estimate the total production rate of neutrons of energy < 10 MeV on the moon to be 16 + 5 neutrons • cm -2 • sec -1. This estimate is consistent with a much more detailed calculation of cosmic ray neutron production by Armstrong and Alsmiller [8], using Monte Carlo technique, which gives a pro-

duction rate of neutrons of energy < 15 MeV in lunar material of 17.5 neutrons • cm "2 • sec"1 . The evaporation temperature 0 was chosen to be 1 MeV which is consistent with the evaporation spectrum measurements [21] and calculations [22]. The attenuation length, A, was taken to be 165 g/cm 2, which is the measured value in the earth's atmosphere at polar latitudes [23] where there is no geomagnetic cut off in the incident cosmic ray spectrum. Armstrong and Alsmiller [8] calculate a neutron production rate which is essentially constant to a depth of "~ 150 g. cm -2 and then decreases exponentially with a A ~ 200 g • cm "2. This form is similar to that measured in the earth's atmosphere at lower latitudes, where cosmic rays of energy less than a few GeV are excluded [23] but such flattening and larger A seem inconsistent with the polar measurements which should be a better approximation to the full cosmic ray spectrum incident at the moon. On the other hand, this difference may result from the added neutron production by pions in dense material which was not important in the earth's atmosphere. To determine the significance of this difference we have also made an equilibrium calculation using a source distribution similar to that generated in the Monte Carlo calculations. This distribution gives thermal capture rates which are about 10% higher than those for a simple exponential. Thus the uncertainty resulting from this is less than that in the absolute normalization although the peak intensity is shifted to slightly greater depth.

3. Neutron equilibrium spectra and capture rates By the procedures thus discussed, we calculated the spatial and energy distributions of the equilibrium neutron flux and capture rates for various assumed lunar surface material compositions, temperatures and fast neutron production distributions. First we studied the effects of the temperature of the lunar surface material and the depth dependence of the neutron production on the equilibrium neutron spectra and trace isotope capture rates in Apollo 11 fines. The gross effects of the variations in the temperature and the neutron production distribution may be seen in the neutron demography table 4, obtained by spatial and energy integrations of equilibrium

361

R.E. Lingenfelter et al., Lunar neutron flux

distributions. The temperature of the lunar material affects only the relative capture rates in the trace isotopes whose thermal capture cross sections differ from a 1/u dependence. A higher lunar material temperature shifts the thermal flux spectrum to higher energy as can be seen in fig. 1 from the temperature dependence of the depth-integrated neutron flux epi/zXE 1 , where

10 4

(b i = ;

~_-a~ iO~ c23 m ~,~

~'~ E~

Ii

o_

Ni

tO~ 10-3

i0-~

i0-~

10~

i0 o

NEUTRON

( n e u t r o n s " g- c m "4 • sec -1) (6)

If all of the capture cross sections were 1/o-dependent then the relative capture rates would be independent of the spectral shape. But because of thermal and epithermal resonances the capture cross sections of most of the trace isotopes which we consider, differ markedly from 1/v and from each other as can be seen in fig. 2 for 157Gd and 149 Sm. Thus as the spectrum shifts to higher energy the capture rates of 157 Gd and 155 Gd, which have the lowest resonances, decrease while those of 149 S m l S 1 Eu and 113 Cd which have strong resonances at slightly higher energies increase, and those of 130 Ba> 186 W, 79 Br and 81 Br, whose principal resonances are far above thermal energies, are independent of temperature effects. For the range of possible lunar material temperatures, however, this is only a relatively small effect. The 157 Gd and 155 Gd capture rates decrease by only 20% as the temperature increases from OK to 400K, while those of 149 Sin, 151 Eu and 113 Cd increase by only 5% to 15%. There is no significant change in the depth dependence of the capture rates for this

APOLLO'II FINES

~ 10~

d x t0oi ( x )

o

I0 2

E N E R G Y (ev)

Fig. 1. Depth-integrated neutron flux spectra in Apollo 11 fines at OK and 400K. I0-~

Sm 149

Gdmr 104

10-2

10.3

L ]\

t2:

o~

10-5

t0-6 l0-~ t.~ .ff

IO-r

~ I0 2

%~ ~_~

{-~ 03 10-3 E

i0-~

I0 'I0 3

~

*

I0 -2

I0 -i

PO°

10-2

I0 P

104 I0 °

NEUTRON ENERGY (evl

Fig. 2. Energy dependent capture cross sections and rates for is7 Gd and 149

S m in

Apollo 11 fines at OK and 400K.

362

R.E. Lingenfelter et al., Lunar neutron flux

temperature variation. Thus surface temperature variations during the lunar day, which range from about 120I( to 400K, do not greatly affect the capture rates in these elements. The effect of a possible flatter depth dependence of the neutron production distribution near the lunar surface was also studied. The equilibrium capture rates were calculated for a simple exponential production distribution (eq. 5) with A = 165 g • cm -2 and for a flattened distribution with A = oo for 0 ~< x ~< 165 g. cm -2 and A = 165 f o r x > 165 g . cm "2. Both were normalized to a total neutron production rate of 16 neutrons, cm -2 • sec "1. The principal effect of a flatter distribution is to reduce the neutron leakage and hence increase the fraction of neutrons captured in the material. As can be seen in table 4, the leakage current is 30% lower for the flattened distribution than for the simple exponential, while the capture rates are all 15% higher. The increased capture, however, is not uniformly distributed in depth. A t depths less than about 150 g • cm -2, where the equilibrium neutron distribution is determined principally by the transport, scattering and capture properties of the lunar material, the capture rates are essentially the same for both production distributions. At greater depths, where leakage is negligible, the capture rates directly reflect the higher neutron production rate, becoming higher for the flatter distribution than for the simple exponential. The depth dependence of the 157 Gd capture rates and the neutron production rates for these two cases are shown in fig. 3. This variation produces no significant change in the shape of the neutron spectrum at thermal energies. Thus the uncertainty in the depth dependence of the neutron production also does not greatly affect the capture rates in the trace elements which are considered. Next we shall consider the expected relative magnitudes of the Sin, Gd, Cd, Re, Kr and Xe isotopic abundance anomalies produced by neutron capture processes in the Apollo 11 fines. The thermal resonance capture reactions together with the abundances, f, of the target nuclei relative to the product nuclei are listed in table 3. It should be noted that 152 Eu decays roughly 45% of the time by/3- emission to stable 152 Gd and the remaining fraction of the time by electron capture to stable 152 Sin, and that 80 Br

~

/~POLLO

II FINIS

1 j

~,

~

~

0

I00

200

PRODUCTtOt~

~EUTROt~

300 400 DEPTH (gin crn2)

500

700

600

Fig. 3. Effect of the assumed neutron production distribution on the depth dependence of neutron capture on 157 Gd. decays 92% of the time by/3- emission to stable 80 Kr and the remainder of the time by either/3 + emission or electron capture to stable 8O Se. These capture reactions cause anomalous decreases in the abundance of the target nuclei and anomalous increases in the abundances of the product nuclei. The relative magnitudes of the anomalies in the target nuclei are simply proportional to the neutron-flux averaged capture cross sections for those nuclei, Oeff ; and the relative magnitudes of the anomalies in the product nuclei are proportional to the product of the averaged capture cross sections and the abundance of target relative to the product nuclei, f%ff.. The flux-averaged resonance capture cross sections may be defined in several ways. For the purposes of comparison we shall define an effective 1/v-dependent cross section for resonance capture in each isotope which gives the same total capture rate as the actual sum over group cross sections: °eft--

~

i

~i Oai / ~ 6Pi( Vo/U )i i

'

(7)

where aeff is the value of the 1/v-dependent capture cross section at 0.0253 eV which gives the same total capture rate as the exact resonance capture cross section Oa/when summed over the energy flux spectrum, dPi . The effective capture cross sections at 0.0253 eV

R.E. Lingenfelter et aL,

Lunar neutron

363

flux

Table 3 Relative magnitude of isotopic abundance anomalies in Apollo 11 lunar soil samples. Reaction

Target

Measured

Effective

Product f

Oa (b)

°eft (b)

foeff

Oeff(l+f )

149 Sm (n, 3`) 15o Sm

1.86

4.18 X 104

5.6 X 104

1.0 x 105

1.6 x 105

157 Gd (n, 3`) 158 Gd

0.63

2.41 x l 0 s

9.0 X 104

5.6 x 104

1.5 x I0 s

0.72

5.8

X 104

2.2 x 104

1.6 x 104

3.7 x 104

3.5

X 10 3

3.5 x 10 3

8.0 x 104

8.3 x 104

155 Gd (n, 3`) 156 Gd lSl Eu (n, 7) 152 Eu ( y ) 152 Gd

22.8

151 Eu (n, 3') 152 Eu (e) 152 Sm

0.18

4.3

X 10 3

4 . 3 x 10 3

7 . 8 x 102

5 . 1 x 10 3

1 1 3 C d ( n , 3") 114Cd

0.425

2.0

X 104

3.9 X 104

1.7 X 104

5.6 X 104

X 10 0

81Br (n, 3') 82 Br ~ - ) 82 Kr

~ 4 X 102

3.2

6.5 X 101

2.6 X 10 4

2.6 X 10 a

79 Br (n, 3") 80 Br (/3") 80 Kr

~ 2 X 10 3

1.14 X 101

1.5 x 102

3.0 x 10 s

3.0 X l 0 s

1 8 6 W ( n , ' y ) l S T w (,8-) 187Re

~ 3 X 103

3.5

X 101

6.0 X 10 2

1.8 X 10 6

1.8 X 10 6

13o Ba (n, 3") 131 Ba (2e) 131 Xe

~1 X 104

8.8

X 10 °

1.9 X 10 3

1.9 X 10 7

1.9 X 10 7

for the Gd, Sm, Eu, Cd, W, Br and Ba isotopes, determined from the calculated neutron equilibrium flux in Apollo 11 fines, are shown in table 3. The measured values of the capture cross sections at 0.0253 eV are also shown for comparison. The effective capture cross sections for 157 Gd and 155 Gd, which have gamma emission half-widths, F3(, greater than the resonance energy, Eo, (see table 2), are about 65% lower than the 0.0253 eV values, while the effective cross sections for the other isotopes, which all have ['7 < E o ' are comparable to or greater than the measured 0.0253 eV values. We see from Oeff that the largest negative abundance anomaly produced by neutron capture is in 157 Gd and the second largest is in 149 S m . On the other hand we see from the product of f and Oeff, that the largest positive abundance anomaly is in 131 Xe and the second largest is in 187 Re. These result principally from the large ratio of target to product isotope abundances, rather than from large effective capture cross sections. The neutron capture rates on the various trace isotopes in captures per target atom per aeon (109 yr) in Apollo 11 fines at OK are shown in fig. 4 as a function of depth in g. cm 2 beneath the lunar surface. The capture rate for a simple 1/v-dependent absorber with a 100 b cross section at 0.0253 eV is also shown for comparison. All of the capture rates show a rather broad peak at a depth of about 150 g • cm "2. The relative

10 2 157Gd

ZeCf= OI crn2 gm-I

?%rn "

F

10-3 o

t

lO-a

%

d 105 cd

% /

• tO G

107

0

100

200

300

400

500

600

700

DEPTH (gin cm 2) Fig. 4. Neutron capture rate (captures • atom -l • aeon "l ) for 157 Gd, 149 Sin, 113 Cd, 155 Gd, 151 Eu, 130 Ba, 186 W, 79 Br, 81 Br, and a 100 b 1/o-dependent absorber in Apollo 11 fines at OK as a function of depth (g • cm -2) beneath the lunar surface.

depth dependences of the capture rates for a 1/v-dependent cross section and for the various isotopes with thermal capture resonances 157 Gd, 149 S i n , 113 Cd, 155 Gd and 151 Eu are all very similar, differing only by less than + 5% over the range of depths

2.2 × 104 2.9 × 104 3.5 × 104

9.0 × 104

1.2 × 105

1.4 × 105

2.4 × l0 s

0.0085

0.00425

0.00212

Measured o at 0.0253 eV 5.8 X 104

1.3 × 104

6.0

5.2 x 104

4.7

6.1

0.0170

5.3

0.00212

4.7

6.1

6.2

2.39

1.34

0.56

0.18

157 Gd

4.1 × 104

5.4 × ! 0 4

5.7 X 104

5.6 × 104

4.6 × 104

149 Sm

Captured at E > 3eV

ls5 Gd

5.2

0.00425

4.7

Captured at E > e ¥

4.7

7.0

6.1

6.1

Captured at E > 3eV

0.65

0.56

0.45

is7 Gd

0.15

0.13

0.10

15s Gd

0.29

0.25

0.26

149 Sm

0.018

0.016

0.018

is1 Eu

0.00072

0.00062

0.00072

113 Cd

0.0014

0.0012

0.0012

13°'Ba

0.00010

0.00009

0.00009

186 W

0.62

0.43

0.25

0.11

149 Sm

0.024

0.020

0.016

0.011

l s l Eu

7.8 X 103

4.6 X 103

5.9 × 103

7.8 X 103

1.0 X 104

~sl Eu

2.0 X 104

3.3 X 104

3.6 X 104

3.9 × 104

3.9 X 104

113 Cd

Table 6 Effective cross sections (b).

0.53

0.30

0.13

0.04

15s Gd

0.00121

0.00120

0.00119

0.00118

130 Ba

8.8 × 10 °

7.5 × 102

1.2 X 103

1.9 × 103

3.5 X 103

13o Ba

0.00136

0.00097

0.00062

0.00032

113 Cd

Captured in

3.5 × 101

2.6 × 102

3.7 × 102

6.1 × 102

1.1 × 103

186 W

0.000092

0.000088

0.000085

0.000083

186W

0.00008

0.00007

0.00007

79 Br

1.1 × 10 ~

6.4 × 10 ~

9.4 × 101

1.5 x 102

2.8 × 102

79 Br

0.000073

0.000070

0.000068

0.000067

79 Br

Table 5 Lunar n e u t r o n demography for variation in thermal capture cross section (unit: neutrons cm 2 column sec).

5.3

4.7

4.7

Captured at E >3eV

is7 Gd

5.2

0.0085

3.7

5.2

5.2

Leakage current

X (l/v) at 0.0253 eV (crn 2 . g-l)

5.1

~/165

0

0.0170

165

0

Leakage current

165

400

(l/o) at 0.0253 eV (cm 2 . g - l )

A (g. cm -2)

T

(°K)

Captured in

Table 4 Lunar neutron demography for Apollo 11 fines with variations in temperature and n e u t r o n production distribution ( unit: n e u t r o n s / c m 2 column sec).

3.2 × 10 °

2.7 × 10 ~

3.9 X 10 ~

6.5 × 10 ~

1.2 × 10 z

81 Br

0.000031

0.000030

0.000030

0.000029

81Br

0.00004

0.00003

0.00003

81 Br

-n

9"

t~

365

R.E. Lingenfelter et al., Lunar neutron flux

from 0 to 750 g • cm "2. The relative rates for the isotopes with epithermal capture resonances, 130 Ba, 186 W, 79 Br and 81 Br are also very similar to one another but these rates, compared to those of the isotopes with thermal capture resonances, are about 20% higher near the surface and about 20% lower at depths below the peak. Finally we shall consider the effects of composition on the neutron equilibrium spectra and capture rates. The greatest variations which we find in both the spectra and neutron capture rates are those resuiting from the variations in the lunar surface material composition which change the total macroscopic capture cross section at thermal and epithermal energies. Nonetheless, for a constant capture cross section, the spectra and capture rates are essentially independent of the detailed composition of the elements contributing to the 1/v-dependent macroscopic capture cross section, as long as the abundance of the principal elements responsible for neutron scattering, O and Si, are not significantly changed. Since the total macroscopic capture cross section varies significantly with rock type and locality for the Apollo samples, we have calculated the equilibrium neutron spectra and capture rates for a range of this cross section reflecting a great variety of possible variations in the composition. In general the capture rates in trace isotopes are roughly inversely proportional to the total macroscopic capture cross section, as can be seen from the neutron demography in table 5. In the examples considered, the compositions of the trace isotopes were held constant at their values in the Apollo 11 fines, while the 1/v-dependent contribution to the total macroscopic capture cross section at 0.0253 eV was varied from 0.25 to 2 times the Apollo 11 fines value of 0.0085 cm 2. g-1. The strong dependence of the capture rate for a fixed trace isotope abundance on the total macroscopic capture cross section arises from two effects. First, the equilibrium number density, and hence the flux, of thermal neutrons is directly proportional to their mean life for capture, which is inversely proportional to the total macroscopic capture cross section (see fig. 5). Thus the capture rate on a trace isotope of constant abundance is inversely dependent on the total capture cross section. Secondly, the shape of the thermal neutron spectrum is also dependent on the

,o,L g

Z~eH cm2 grn I :

-

~ q

It:

%

-~

ZzZ

0035

0025 0092

~ -

103

C °t

E

--I

10 2

I0 ~ 400 °/<

;o4l ~d IO3 t~

IOZkl

I

~

10q IO 3

J

tO 2

i0-~ NEUTRON

i0 o

i0 ~

iO z

ENERGY (ev)

Fig. 5. Depth-integrated neutron flux spectrum at OK and 400K as a function of the effective total macroscopic capture cross section of the lunar surface material. total capture cross section with the peak energy being roughly proportional to the total capture cross section in the OK case and less strongly dependent in the 400K case (see fig. 5). The effects of variations in the abundance of the thermal and epithermal resonance capture nuclei on the spectra can also be approximated by the effective 1/v-dependent capture cross sections, defined in eq. (7). The effective capture cross sections at 0.0253 eV calculated from eq. (7) for the Gd, Sm, Eu, Cd, Ba, W and Br isotopes are given in table 6 for the four examples described above at OK. An effective total macroscopic capture cross section £ e f at 0.0253 eV may thus be calculated using the effective capture cross sections for the trace isotopes and the measured 1/v-dependent capture cross sections for the other elements. To a first approximation the effective total cross section then, characterizes the medium and determines the equilibrium thermal neutron spectrum, independent of the detailed composition of the elements contributing to the thermal capture. This approximation breaks down of course when the effective resonance capture exceeds the 1/u-dependent component, but

366

R.E. Lingenfelter et al., Lunar neutron flux

this situation has not occurred in the lunar sanlples collected so far. Thus a variety of composition variations can be represented simply by variations in a single parameter, the effective total macroscopic capture cross section, Neff', and the effects of composition variations on the neutron equilibrium spectrum and neutron capture rates can be correlated with this effective cross section. The determination of Yeff for a particular composition involves a slight iteration since the effective resonance capture cross sections, Oeff, are themselves dependent on the neutron spectrum as influenced by Zeff. The dependences Of Oeff for 157 Gd, 149 Sm, 113 Cd, 155 Gd, 151 Eu, 130 Ba, 186 W, 79 Br and 81 Br on Yeffare shown in fig. 6a. For a particular composition we must first calculate the l/v-dependent contribution to the total macroscopic capture cross section. Using this value as a first estimate of Yeff, we then determine the Oeff's for the trace isotopes and, adding their contribution to the total macroscopic capture cross section, we make a second estimate of 2;eff. From this we reevaluate the Oeff's and revise the estimate of ~2eff, at which point the value has usually converged to within a few

'

'

.....

fo)j to 2

tO5

wE

~ g o

...>.-%

,,

103

104

g

5

,_,

."x '3co

~

103

aoBa 10-a

'g g g G ~0~

IOOb o-(m/v)

T 10-5

L~

.

3x10-3

lO-2

3xl0 4 ~eff {cr°2qm- t l

2xlO 2

SlBR

iO-Z

2x10-2

Fig. 6. Effective resonance capture cross section (a) and the peak (~ 150 g • cm-2) neutron capture rate (b) for 1s7 Gd, 149 Sm, 113 Cd, 155 Gd, i s 1 Eu, 1;30 Ba, 186 W, 79 Br and

81 Br at OK and 400K as a function of the effective total macroscopic capture cross section Zeff.

percent. For the Apollo 11 fines Neff is 0.0103 cm 2" g-1. The effects of composition variations on the neutron capture rates in these isotopes can also be seen in fig. 6b where these rates per atom per aeon at the peak ( ~ 150 g- cm -2) in the depth distribution are shown as a function of Y'eff" The relative shape of the depth dependence for each of these capture rates is essentially independent of Yeff and thus the depth dependence of these rates for a particular value of Y eft can be determined simply by scaling the value plotted in fig. 4 for a Yeff of 0.010 cm 2 • g-1 by the peak ( ~ 150 g • cm "2) rate shown in fig. 6b.

4. C o m p a r i s o n w i t h m e a s u r e m e n t s

The general agreement between the calculated lunar neutron fluxes and the measured Gd anomalies was demonstrated [24] with the original flux calculations [ 1]. The present calculations are consistent with these calculations and simply extend them to give a more systematic treatment of composition variation. The largest uncertainty in the calculations is in the absolute normalization of the neutron production rate, and includes not only the + 30% uncertainty in the present rate but an added + 50% uncertainty at least in the time-averaged rate, dependent on the constancy of the galactic cosmic ray intensity and the effects of solar modulation and flare activity. This uncertainty forces an equal uncertainty on the absolute value of the various capture rates. Since the capture rates can be arbitrarily small, only the maximum capture rate and hence the maximum anomaly can give any measure of the reliability of the absolute normalization. One of the largest measured 158Gd/157Gd anomalies is in rock 10017 [7] where the ratio is 1.59849 + 0.00014 compared to the terrestrial average of 1.58660 + 0.00011. The anomalous 158 Gd due to neutron capture on 157 Gd then amounts to A -- (1.59849 - 1.58600) / (1 + 1.59849) = 0.00458 atoms of 158 Gd per initial atom of 157 Gd. From fig. 6b we see that the calculated peak ( ~ 1 5 0 g. cm "2 ) neutron capture rate on 157 Gd for this rock ( I ; etf = 0.0132 cm 2 • g-1 ) is 0.0029 per 157 Gd per aeon. Thus the measured anomaly is consistent with irradiation at depth of 100 to 200 g • cm "2 for 1.6 aeons.

367

R.E. Lingenfelter et aL, Lunar neutron flux

On the other hand if the rock was surrounded by lunar fines, such as 10084, Neff= 0.010 cm 2 • g-l, and was small enough that the neutron spectrum within it was not significantly modified from that in the surrounding fine material, then from the same figure we see that the peak capture rate on 157 Gd could have been as high as 0.0047. Under this condition irradiation at the same depth for only 1.0 aeon could have produced the measured 158 Gd/157 Gd anomaly. The rock was found on the surface but particle track measurements suggest that it could not have been there for more than 3 × 107 yr [25] which is consistent with either possibility. Thus even the largest measured anomaly is apparently in agreement with absolute normalization of the neutron production rate and places no restraints on it. The calculated 155 Gd anomaly is a constant 0.24 of the 157 Gd anomaly since the two capture cross sections have nearly identical shapes, so that the relative capture rates are essentially independent of the neutron spectrum. This is also in agreement with measurements [24]. The expected 152 Gd anomaly, due to neutron capture on 151 gu, is larger than that of either 158 Gd or 156 Gd but the precision of the measurements of this isotope is not sufficient to resolve the anomaly. These calculations predicted a measurable 150 Sm/149 Sm anomaly which has also been confirmed [7]. Since the principal resonance in 149 Sm is at higher energy than that in 157 Gd the ratio of the two anomalies is dependent on the neutron spectral shape and hence on composition and temperature. The ratio of the effective capture cross sections may be related to the measured anomalies by the following O149

[ ( 150Sm/149Sm)M . (150Sm/149Sm)0 ]

°157eff

[ (158Gd/157Gd) M . (158Gd/157Gd)0 ]

[ 1 + (158Gd/157Gd)M] × [1 + (150Sin/149Sm)M ] The calculated depth-averaged values and those determined from measurements [7,26] of Apollo and Luna 16 samples are shown in fig. 7. As can be seen both the magnitude of the ratio and the trend of the variation with Neff are in good agreement with the calculated values for temperatures between 200K and 400K.

.

.

.

.

.

.

Jo!

.

.

.

.

.

.

.

.

1~o4~ r4J63

.

-'

~oo~7~

2[ . . . . . . . . . . 0

005

OrO Zeff/crn2gm ~)

7

] O15

020

Fig. 7. Calculated and measured ratios of effective capture cross sections of 149 Sm to 187 Gd at 0, 200 and 400K as a function of the effective total macroscopic capture cross section. As can be seen from fig. 6b the composition dependence of the ratio of neutron capture in 157 Gd to that in 130 Ba and 186 W is even more pronounced than in Sm. In rock 10057 Reynolds et al. [27] find an excess of 131 Xe over that expected from spallation which may be due to neutron capture on 130 Ba [5]. This excess amounts to 1.7 + 0.3 X 10-5 atoms of 131 Xe per 130 Ba. For this rock (Neff = 0.0130 cm 2 • g-1 )we see from fig. 6b that the ratio of neutron captures per 130 Ba to neutron captures per 157 Gd is 1.15 X 10-4/2.9 X 10 -3 = 4.0 X 10-2 for a temperature of 0K and 1.15 X 10-4/2.3 X 10-3 = 5.0 X 10-2 for 400K. The measured [24] anomalous 158 Gd per 157 Gd in this rock is 2.5 + 0.6 X 10"4. Thus the calculated anomalous 131 Xe per 130 Ba would be 1.0 +- 0.3 X 10-5 for OK and 1.2 + 0.3 X 10-5 for 400K. Considering the uncertainties, this range of values is consistent with the measured anomaly. Anomalous 187 Re attributed to neutron capture on 186 W has been measured by Michel et al. [4] but the measurements suffer from large corrections due to additional 187 Re produced during neutron activation analysis. They find between 2.7 X 10-5 and 1.4 X 10-4 anomalous 187 Re atoms per 186 W atom in Apollo 14 fines 14163. For this material (Neff = 0.0088 cm 2 • g-1 ) we see from fig. 6b that capture per 186 W is between 7 X 10- 3 and 9 X 10 -3 of that per 157 Gd for temperatures of 0K to 400K. The measured [7] anomalous 158 Gd is 3.1 X 10- 3 atoms per 157 Gd and thus we should expect between 2.2 X 10 -5 and 2.8 X 10 -5 anomalous 187 Re atoms per 186 W. This is consistent with the low end of the measured

368

R.E. Lingen.ielter et aL, Lunar neutron flux

range, b u t clearly m o r e precise m e a s u r e m e n t s are required. N e u t r o n c a p t u r e - p r o d u c e d a b u n d a n c e a n o m a l i e s in 80 Kr a n d 82 K r have b e e n r e p o r t e d b y L u g m a i r and Marti [3, 28] in rock 14310. T h e y find a ratio o f anomalous 80 K r to a n o m a l o u s 82 Kr o f 2.6 -+ 0.4 w h i c h is c o n s i s t e n t w i t h the ratio o f 2.3 o b t a i n e d f r o m the calc u l a t e d p r o d u c t i o n rates (fig. 6 b ) and the relative abundance of the Br target isotopes. This ratio, as can be seen f r o m the same figure, is n o t sensitive to the comp o s i t i o n of the material. The a b s o l u t e a b u n d a n c e a n o n > alies are also in good a g r e e m e n t with the calculated values. L u g m a i r and Marti find an a n o m a l o u s 4.9 X 10 -13 g o f 80 K r p e r gram of m a t e r i a l which, for the r e p o r t e d Br a b u n d a n c e o f 0 . 2 3 5 p p m [29], w o u l d c o r r e s p o n d to 3.7 X 10 -6 a n o m a l o u s 80 K r a t o m s p e r 79 Br a t o m . We see f r o m fig. 6 b t h a t c a p t u r e per 79 Br is 1.25 X 10 -3 o f t h a t p e r 157 G d for this material ( Z e f f = 0 . 0 0 7 5 cm 2 - g-1 ), and f r o m the m e a s u r e d [28] a n o m a l o u s 158 G d o f 3.0 × 10 -3 we w o u l d t h u s e x p e c t 3.8 X 10 .6 a n o m a l o u s 80 K r a t o m s p e r 79 Br a t o m w h i c h is in very good a g r e e m e n t w i t h the m e a s u r e d value. The a b s o l u t e 82 K r a b u n d a n c e a n o m a l y also shows similar agreement. T h e c a l c u l a t e d 114 C d / l l 3 C d a n o m a l y is nearly as large as t h a t o f 158 Gd/157 Gd b u t n o isotopic abundance m e a s u r e m e n t s have been m a d e on Cd in the A p o l l o smnples.

References [ i ] R.E. Lingenfelter, E.H. Canfield and W.N. Hess, The lunar neutron flux, J. Geophys. Res. 66 (1961) 2665. [2] Lunatic Asylum (A.L. Albee, D.S. Burnett, A.A. Chodos, O.J. Eugster, J.C. Huneke, D.A. Papanastassiou, F.A. Podosek, G.P. Russ Ill, tt.G. Sanz, F. Terra and G.J. Wasserburg), Ages, irradiation history, and chemical composition of lunar rocks from the Sea of Tranquillity, Science 167 (1970)463. [3] G.W. Lugmair and K. Marti, Neutron capture effects in lunar gadolinium and the irradiation histories of some lunar rocks, Earth Planet. Sci. Letters 13 (1971) 32. [4] R. Michel, U. Herpens, tt. Kulus and W. Herr, Isotopic anomalies in lunar rhenium, Proc. Third Lunar Science Conf. (1972) in press. [5] W.A. Kaiser and B.L. Berman, The average 13o Ba (n, 7) cross section and the origin of 131 Xe on the Moon, Earth Planet. Sci. Letters 15 (1972) 320. [6] P. Eberhardt, J. Geiss and H. Graf, On the origin of excess 131 Xe in lunar rocks, Earth Planet. Sci. Letters 12 (1971) 260.

[7] G.P. Russ III, D.S. Burnett, R.E. Lingenfelter and G.J. Wasserburg, Neutron capture on 149 Sm in lunar samples, Earth Planet. Sci. Letters 13 (1971) 53. [8] T.W. Armstrong and R.G. Alsmiller, Calculation of cosmogenic radionuclides in tile Moon and comparison with Apollo measurements, Proc. Second Lunar Science Conf. 2 (1971) 1729. [9] G. Bell and S. Glasstone, Nnclear Reactor Theory (Van Nostrand Reinhold, 1970) pp. 239 242. [10] W. Engle, ANISN, Oak Ridge National Lab. Report K-1693 (1967). [ 11 ] H.B. Wiik and P. Ojanpera, Chemical analyses of lunar samples 10017, 10072 and 10084, Science 167 (1970) 531. [12] P.W. Gast and N.J. Hubbard, Abundance of alkali metals, alkaline and rare earths, and strontium-87/strontium-86 ratios in lunar samples, Science 167 (1970) 485. [13] R.R. Keays, R. Ganapathy, J.E. Laul, E. Anders, G.F. lterzog and P.M. Jeffery, Trace elements and radioactivity in lunar rocks: implications for meteorite in fall, solar wind flux, and formation conditions of moon, Science 167 (1970)490. [14] R. Doyas, T. Michels, S. Perkins and R. Howerton, CLYDE, Lawrence Radiation Lab. Report UCID-15551 (1969). [15] R.J. Howerton, Tabulated neutron cross sections, Lawrence Radiation Lab. Report UCRL-50400 (1971). [16] A. Weinberg and E. Wigner, The physical theory of neutron chain reactors (University of Chicago, Chicago, 1958) pp. 282, 336. [17] E.H. Canfield, R.N. Stuart, R.P. Freis and W.H. Collins, Sophist-I, Lawrence Radiation Lab. Report UCRL-5956 (1961). [18] E.H. Canfield and J. Pettibone, Sophist-3, Lawrence Radiation Lab. Report UCRL-6912 (1962). [19] R.E. Lingenfelter and R. Ramaty, Astrophysical and geophysical variations in 14C production, in Nobel Symposium 12: Radiocarbon Variations and Absolute Chronology, ed. I.U. Olsson (Almquist and WikseU, 1970) 513. [20] E.R. Graves and L. Rosen, Distribution in energy of the neutrons from the interaction of 14MeV neutrons with some elements, Phys. Rev. 89 (1953) 343. [21] E. Gross, The absolute yield of low energy neutrons from 190MeV proton bombardment of gold, silver, nickel, aluminum and carbon, Lawrence Radiation Lab. Report UCRL-3330 (1956). {221 H.E. Mitler, Particle evaporation from excited nuclei, Smithsonian Inst. Astrophys. Obs., Special Rpt. No. 204 (1966). [23] R.E. Lingenfelter, Production of carbon 14 by cosmic-ray neutrons, Rev. Geophys. 1 (1963) 35. [24] O. Eugster, F. Tera, D.S. Burnett and G.J. Wasserburg, The isotopic composition of Gd and the thermal neutron flux in samples from Apollo 11, Earth Planet. Sci. Letters 8 (1970) 20. [25] G. Crozaz, U. Haack, M. Hair, M. Maurette, R. Walker and D. Woolum, Nuclear track studies of ancient solar radiations and dynamic lunar surface processes, Proc. Apollo

R.E. Lingenfelter et aL, Lunar neutron flux 11 Lunar Science Conf. 3 (1970) 2051. [26] G.P. Russ, III, D.S. Burnett and G.J. Wasserburg, Lunar neutron stratigraphy, Earth Planet. Sci. Letters 15 (1972) 172. [27] J.K. Reynolds, C.M. Hohenberg, R.S. Lewis, P.K. Davis and W.A. Kaiser, Isotopic analysis of rare gases from stepwise heating of lunar fines and rocks, Science 167 (1970) 545.

369

[28] G.W. Lugmair and K. Marti, Neutron and spallation effects in Fra Mauro regolith, Lunar Science llI (1972) 495. [29] J.W. Morgan, J.C. Laul, U. Kfiihenbilhl, R. Ganapathy and E. Anders, Major impacts on the Moon: chemical characteristics of projectiles, Proc. Third Lunar Science Conf. (1972) in press.