Theory of alpha recoil effects on radon release and isotopic disequilibrium

Theory of alpha recoil effects on radon release and isotopic disequilibrium ROBERT L. FLEKCHER Genend Electric Research & Development Center, Schenectady, New York 12301

(Received May 25, 1982; accepted irr r~~sed~rrn January 1I, 1983) Abstract-Using the present unde~ding of the mechanisms of release from rocks and soifs of recoiling products of alpha emission, physical predictions can be made of the fraction of these nuclei that are directly freed and the fraction that can subsequently be freed by the action of water. The fractions depend on the size and nature of the grains in which the recoiling nuclei originate, the size and shape of the pore spaces, the nature of tbe surrounding grains, the decay lifetime of the recoiling nuclei, and the time sequence of the presence of water. For simplified assumptions quantitative predictions are made of Rn emanation ratesand of isotopic disequilibrium. INTRODUCTION

BA!SIC MODELS

RELEASEOF products of alpha decay from rocks and soils in nature is a common phenomenon. Emana-

Before attempting to assess the overall release of alpha mcoihng nuclei, individual physical and geometrical steps in the process must be considered. First the fraction of alpha recoils that exit a gram is evaiuated; then for a given pore space geometry the fmction of those exiting one gram that enter the adjacent grain is calculated (and therefore the fraction that is stopped in the pore space). Using these results the overall expectations are evaluated for different conditions.

tion of 222Rn from the ground is one example. Another is the striking variability of 2wU/z38U ratios on earth (for example, see the brief summary by SZABO, 1969). The 2wU/23sU activity ratios make it clear that the presence of water is of critical importance. Water in general has higher 2MU/238Uactivity than the rocks it has permeated, a result that is generally interpreted in terms of the locations of 2yU atoms being associated with recoil and radiation damage from the 238U decay by alpha emission. The fact that such disequilibrium is not found on the moon, where water has not been present (ROSHOLT and TATSUMOTO, 1970, 197 I ) bolsters the case that water is of critical importance. There is evidence for two roles of water. The first is purely as a stopping material for ejected recoil nuclei (KK?OSHI, 197 I; FLEISCHERand RAABE, 1978). The presence of water in pore spaces prevents ejected nuclei from penetrating adjacent grains. The second action of water is as an etchant, which allows imbedded recoil fragments that are part of the alpha recoil damage to be released into the water (FLEISCHER, 1975, 1980, 1982a, 1982b; FLE~SCHERand RAABE, 1978). This action could immediately affect recoils that cross very narrow wet pore spaces and would eventually release recoils that cross dry porosity, provided that water su~uen~y enters. The purpose of this work is to identify and evaluate the considerations that determine the extent of replease of alpha recoil nuclei from a solid, and hence to better understand ( 1) isotopic disequilibrium associated with alpha emitters and (2) radon emanation. The discussion is also relevant to proper disposal of solid nuclear waste that contains alpha emitters. The number of parameters that enters is high enough and sufficiently difficult to measure that in most real cases they arc not known. Nevertheless some assumptions will be made to allow consideration of iliustrative examples.

Fractional escape of recoils Escape from a sphericai grain. For convcnicna of Calculation a spherical gram is wnsidemd. Although gtains are in fact only occasionally spherical (lunar glass soils are examples), a sphere is a reasonable a~xi~tion to equiaxial grains. Consider as sketched in Fig. 1a point P located at distance r from the center of grain of diameter D. If alpha docays produce recoils of range R, isotropically around the point., the recoils exit the grain if oriented into the portion of the sphere of radius R, about P that lies above the plane AR The fraction fe escaping the solid angle in that spherical cap is (R, - x)/2R,, and x as a function of r can be found from noting that Rf - x2 = (O/2)2 - (r + x)‘. It follows that f, = [(2&/D + 2r/D)2 - l~/(~6r~/D2) The fraction F, for the whole grain is obtained by int~ting over the volume:

where a = 2RJD, a result derived by FLUCGEand ZIMENS (I 939). As shown in Fig. 2 (“SINGLE GRAIN”) this expression correctly approaches zero for small R, (4D), being proportional to 3RJ2D (FLEWHER, 1975); and it becomes unity for R, 2 D, since even recoils starting at one surface cross the grain. The preoseding applies for R, < D/2. For D 2 R, > D/2 the expression just given for fe applies only

where *, = XdDHIE:, i’hls result ISgven m FIB. 3 jLn?{Ul”‘). The results on a linear scale are shown III Fig. 3. Because there are always large grams In this distribution. complete escape 1snever possible. It is. however. closely approximated for small DMIN, since most of the grains in this case. are small relative to the recoil range. The results given

Ln Figs. 2 and 3 represent

the

grain or an assemblage of grains by recoil effects. Not all of the ejected recoils will be accessible to interstitial fluids. The next section considers what tiactions of the ejected recoils will be (I) stopped in pores and (21 injected into adjacent grains. maximum

loss from

a

Stopping of recoils ul pore spaces Recoils that leave grains either are stopped in pore spaces or enter adjacent grains. First consider a planar

FIG. 1. Recoil fragments leaving a spherical grain. In a grain of diameter D the recoils of range & leave the grain

from point P if their direction takes them through the piane AB. for r 1 R, - D/2, and ]e is unity for 0 4 r 5 R, - Dj2. The integration then yields the same result as in Eqn. ( 1). Releasefrom an assemblage o/grains. Most material contains a disttibution of grain sizes, so that the fraction exiting is an average over the grain size distribution. Figure 3 shows the result for a number distribution, n,(D), that corresponds to a constant number of grains of each diameter up to a limiting diameter I&x. (n,(D)AD is the fraction of grains whose size lies in the diameter range ilD.) For =&ix &(M

Ffel’= I” n,(D)F&. 0 gives f2)

where B = 2R,jDMAx. This uniform distribution by number is strongly peaked by volume near the maximum grain diameter. It may be a reasonable description of a rock in which most of the volume is occupied by larger grains, but in which smaller grains of accessory minera& are present. The non-uniform distribution of the afpha-emitting nuclei is a funher complication. Equation (2) is given in Fig. 2 (“n,(D)“). A second ~~bution of grains that is useful to consider is more descriptive of a soil or of a powder that results from comminution. Two such distributions are noted by FLESCHER and RAABE (1978). For the present purposes they can be represented by a function n&D), where =&,INID

D 2 DWN

=o

/I

KS

!R,--vi/R< =

D ’ DMAX

=(3@/4) In (2/B) + 3/3/g + @/32.

The fraction jt; 01 the recoils that enter the 2~ solid angle toward the pore and are stopped in the fluid is

and

D < &AX

i =o

pore space of width W. as sketched in Fig. 3. If the range of the recoiling nucleus IS Rs in the solid and RF in the fluid (air or water) that fills the pore space, it is usefui to replace the width w with a reduced width. wRJ&, the thickness it would have if the fluid in the pore had the Same stopping power as the solid. Then the construction given. a sphere surrounding 3 point P at depth .Yfrom the surface, allows the fraction of recoils exiting from that depth to be found and separated into those that stop in the fluid and those that are imhedded in the adjacent solid.

t/H,:for

R, - v < wRJF~.

corresponding to the geometries I and 2 respective& in Fig. 4. Geometry I of Fig. 4 gives a resutt that is independent of X. The reason is that a segment of a sphere (the portion between two parallel planes that cut the sphere) has an area that depend only on the spacing of the two planes.

1000

GRAIN RADIUS/RECOIL RANGE D/2& I IO 0.1 100

0.001

0.01

0.01

n20)

i

i

DM(rN

If this function is integrated in the analogous manner to n,(D), m p2, c

=

scl

&DFD

I

0.1

IO

100

2R,/D RECOIL RANGE/GRAIN RADIUS FIG. 2. Fraction of recoils leaving spherical grams for a single gram and for two distributions of grain sizes. n, is a constant number distribution up to a limiting diameter D1,4,, and n: is a D,,,/d dist~bution. repenting a soil i)r fragmental matenai

Alpha recoil and Rn retease Integrating over 0 zz x 5 &, i.e. all V&W of x for which some recoiis escape the grain, the av* fraction stopping intheporeis f~ = a(2 - 6)/2,

where

781

GEOMETRY 1

d = W/RF

Similarly the fraction _fi injected in the adjacent grain is obtained by averaging (1 - x/& - 6) over the interval 0 s x s Rs( I - w/RF) in which some recoils enter that grain. f, = % - 6 + 6’12. Note that fi + fE = Ih, so that half of the recoiIs that move toward the surface from witbin a distance & of it stop in the gmin of origin and half are cja%ed (as shown for example by Fig. 2-8 in i%ESCHER et al. (1975)). Themfore the f’raction FFof those that are ejected that stop in the pore space is 2fF and the fraction of those that are ejected that enter the adjacent grain F, is 2&, i.e. FF = 215- 6” F, = 1 - 26 + 6’

(4)

lf6r l,FF= l,i.e.allrecoilsthatareejectedstopinthe interstitial fluid. Distributions of pore widths. In generaI there will be a distribution of pore sizes. Two such distributions n(w) wiil be considered. An exponential distzibution w$ exp(-w/we) has many more narrow pores than iarge pores and might be thought of as a representation of the porosity in a rock. A constant lotion (n(w) = w$. w < wo; n(w) = 0, w > ~0) might approximate the openings in a soil or coUection of grains. Fi = ~0”~(w)F&wthen is the &action of ejected recoti that arc injected into adjacent grains. For the exponential distribution

Fi = (1 - 2~) + 22( 1 - e-l’*), c = wO/RF and for the constant distribution =1-t+&3

Ei

r -(3c)_’

(5)

f< 1

(6) ?L> 1.

The three results (Eqns. 4 to 6) are presented in Fig. 5. For the two ~butions of pore sizes there is some implantation for all values of we, since tbcre are always some ponswhichare~~caoughthatancoilcancross.~e fmctionstoppedintheponsis 1 - Fi.

FIG. 4. Geometry of recoil fmgments of rangz Rs in the &id, ejected into a pore space of width w, containing a t&id in which the recoil range is RF. If the pore space is reduced to a width wWRF, tk stopping locations as a function of angle from a point P is given by a spherical surface.

N = * P exp(-t/r)dt

= F+[ I - exp(-td/r)]

(7)

For short times (t,, 4 z), N, (==&) is linear in time and for long times (td # T) N, is constant (==I+). For many of the significant mdionuclides the times of intmr* will be short relative to the mean decay time, so that Linear impiantation with time can be used to infer the density of implanted atoms. =Rn is an exception because of its 5.5 day mean life. Efkct @finite leaching rate The rate at which recoils are removed by 24-hour leaching has been studied for a number of minerals but only for

Effect offinite life of recoil nuclei Since most of the recoil nuclei of interest are radioactive, the fraction of those imbedded in adjacent grains that are available for r~iease by leaching varies with time. If an initially recoil-f&e surface is implanted at a rate of P atoms/ cm%ec of mean decay life t, the number present after a dry storage time td is

CHARACTERISTIC REDUCED PORE WIDTH

0

0.5 RECOILRANGE/GRAIN

1.5 RADIUS

FIG. 3. As in Fig. 2 except that the scale is linear.

2.0

FIG. 5. Fraction of recoils leaving a grain that is injected into the adjacent grain. Calculated for planar pore of width wn and for exponential and constant distributions of pore widths, thought to be descriptive of rocks and soils respectively.

R. L. Flewher

‘82

iron can readily be adjusted to include the fraction of imbedded recoils that is released by different phases. Zero leaching of ‘3*U is assumed. If the grains

1

o%ool0.0, LI

-

0.1

I

IO

100

TIME t/~

FIG. 6. Radon released and Integrated track density ior leaching of implanted “‘Rn. The release pattern of Eqn. 8 is assumed, with radioactive decay lifetime of 5.5 days IT) included.

muscovite has It heen measured over longer rimes.. up to 120 days (FLEISCHER, 1982a). Although there is considerable scatter in the results. they are consistent with the relation < = (t,lr#J I, - I. (8) where { is the fraction of recoils removed. I, is the leachmg time, and to is a constant (equal to I year). There is no theoretical hasis for this equation, and further experimental work will very likely lead to a better description. To the extent that this equation is valid. however. it implies that leaching is complete within a year, a time that is a small fraction of the decay lives of such relevant nuclides as ‘%. ?“‘Th, and 2Z6Ra. Complete leaching however requires a time that is long relative to the mean life of ***Rn. The consequence of the effects that lead to Eqns. (7) and (8) is that a surface which initially is implanted with “*Rn and then leached gives rise to an extended pulse of radon being released into the solution, the number of atoms being governed by the release kinetics (Eqn. 8) and by the radioactive decay of the radon. If a surface has N, atoms implanted just before water is introduced, the number released (and still undecayed) is N, exp(-r/r)(t/t&‘4, which is shown in Fig. 6 as the dashed curve. Integrating track detectors placed at time t = 0 into the space where the radon is released will record the signals given hy the solid curve in Fig. 6. “C,” is a proportionality constant that depends on the detector calibration (FLEISCHERer al., 1980). and V is the volume of the &pace in which the radon is collected. The particular power law in Eqn. (8) results in the maximum concentration of radon being reached after a time of +/4. approximately 33 hours. CONSEQUENCES

FOR

ISOTOPIC

EQUILIBRIUM

It would be useful to be able to predict the state of 234U/2’*U disequilibrium for a particular rock or soil. Unfortunately the information needed is not generally available for real cases. Therefore this discussion will be confined to describing how such predictions can be made. with illustrations using assumed size-distributions of grains and of pore-spaces. The extent of zwU/238U disequilibrium is directly

derivable from curves such as are given in Fig. 2. This is true if the extrapolation made earlier of the leaching behavior of mica is valid in inferring that all of

the implanted recoils can be released by leaching and if that inference is valid for all minerals. These assumptions are made in what follows. If later work shows that only partial leaching occurs. the calcula-

themselves are soluable, both “*U and ‘3JU will be put into solution. Since under these assumptions all of the ““Th recoils f the progenitors. once removed, of ‘3JU1 that leave a grain are either stopped in the interstitial space. or later released into it by interstitial liquids, the fractional depletion of the solid in ‘34U is given directly by the ordinate in Figs. 2 and 3. For example of the material of interest is a tine sand described by nl(DMAx), with DMAX = 100 grn and R, = 200 A. ?R,/DvAx = -I.IO-? a fraction of recoils of 0.002 is released, and therefore the ‘34U/238U activity ratio of 0.998 is expected In the soil. If the uranium was located mostly in submicron uranium-rich minerals described by nl(DMAx)with DMAX = 0.1 pm. 1R,) DMAx = 0.4and the activity ratio would have a much lower value, 0.36 !read from Fig. 3). The lost z34U activity is transferred into the water m the pore spaces. Its concentration there depends on the volume of pore space it occupies and the extent to which its composition is altered by recharge or concentrated by evaporation. The fact that large disequilibria are sometimes observed in materials of relatively large grain size is a likely indicator of nonuniform uranium location. an appreciable fraction being present in minute grains from which the escape of recoils is more abundant. Examples of small secondary crystals within a larger-grained matrix are given by RIESE er (II. ( 1980). It is also of interest to evaluate the relative Importance of the two known mechanisms of effecting disequilibrium-stopping recoils in the interstitial space and leaching of implanted recoils. Stopping is enhanced by the presence of water and implantation by its absence, so that it is necessary to consider the dry and wet cases separately. The overall result will depend on the fraction of the time that the pore spaces are water-filled. The following assumptions are made: The recoils have a range of 50 pm in dry pore space and 500 A In water, (approximate numbers from the method of LINDHARD and SCHARFF. 1961) and all implanted recoils are ultimately released by water. Figure 5 allows the wet and dry fractions to be calculated for the pore size distributions that have been considered. If we represent the pore size distribution in the so11 considered previously (n,( 100 pm)) as the constant distribution n(w,) with M/) = 30 pm. then we/RFis 600 when

the soil is wet and 0.6 when dry. which from Fig. 5 gives fractions implanted of 0.0054 and

0.52 respectively. While the material is wet. more than 99% of the disequilibrium that ultimately results IS due to stopping recoils: when dry 48% of it is: and If fw IS the fraction of the time the soil IS wet the Ljverall fraction of the effect that is due to ImpIantation plus leaching is 0.52( 1 - jw)f 0.0054 jw This result means that implantation plus leaching is the

Alpha recoil and Rn release dominant mechanism only if the fractional time that the sand is wet is less than 3.9%. In the second example given-where the uranium resides in 0.1 pm grains, the pore space parameter wo is taken as 0.03 pm, and one calculates wO/RF to be 0.6 (wet) and 0.0006 (dry), and the fraction implanted is 1.Ot 1 - fw) + 0.52fw (= 1 - 0.48fw). For all values of fw implantation-plus-leaching is the major mechanism of 2wU release. Since rocks usually have porosities that are much lower than soils, the characteristic pore widths w. will tend to be smaller than for soils of similar grain sizes. If w. = 0.1 pm for a rock which is described by the exponential n(w) distribution, the fractional contribution from leaching is 1 - 0.85fw.

CQNSEQUE?XES

-WET---_tDRY+ETWlT 4 l4.8cm i WET BARRIER (WATER)_

‘I n(u)=w~8x&w/w,) w,=lO%m 1,

FOR RADON EMANATION

Radon emanation into the atmosphere is controlled by the same factors as were just described for *W/*W activity ratios with the addition of two further effects. One is the influence of time considered in the section entitled “Effect of finite leaching rate” as described by Fig. 6. If the decay life of the implanted nuclide is comparable with the time needed to release it by leaching, the precise timing and duration of wet and dry periods becomes important. The second effect is the slow diffusion of U2Rn in water, which means that release from the pore spaces into the atmosphere is attenuated. Although usually the release into the atmosphere is the measured quantity of interest, for this discussion it is useful first to consider only release into interstitial space and then note the additional decrease which results from decay during diffusion through water or gas out of the rock or soil into free air. Effects of non-uniform distribution of 226Ra are ignored.

Dry emanation

When the sample is dry the emanation is solely by stop ping in the interstitial gas. For most particle-size and poresize distributions less of the radon that is ejected from the grains is stopped in the interstitial space than would be in the case for water-filled pores. In the two examples of soils considered earlier 48% and 0.06% of the escaping recoils were stopped rather than implanted, and 0.12% were stopped in the example of rock. In short only for large pores is this a major fraction.

TABLE 1

RADON FOR

783

RRLEABRD INTO PORESPACES TRREEMODEL MATERIALS

I I I 20 30 40 50 TIME[DAYS]

/ 60

70

FIG. 7. Radon release for a rock model, wet and dry. Water increases the release into pore spaces but attenuates its escape from the rock.

Wef emanation

Wet emanation has three components, steady-state stopping steady-state injection and leaching, and transient leaching of recoils that were implanted while the material was dry. Tbe steady-state stopping and injecte&and-leacbed fractions add up to all of the radon that is released. The calculated values for the three assumptions on rock and soil are given in Table 1. The peek in the transient, which is also listed, ranges from half to somewhat more than the steRdy_stRte value. The high transients are. the result of the (relatively) sudden release of radon that was impIanted efficiently when the pore space was dry. Because dry implantation is more efficient than wet, the implanted radon can be released by leaching more rapidly than the steady state rate for wet grains. The release from the rock or soil into air dcmases with the distance the =Rn must diffuse to escape, with a mean diffusion distance being 2.2 cm in water as discussed by FLESCHER and MOGRO-CAMPERO( 1978). The right-hand column gives the “critical” thickness of water to be diSused through that would reduce the wet emanation into the air to the value expected for dry emanation. An arbitrary example of the effect of wetting and drying for the hypothetical rock considered earlier is shown in Fig. 7. The wet rock releases into the pore spaces all of the radon ejected from grains; but if the thickness of water to be traversed is the critical value, the escaping fraction just equals the dry value in steady state conditions. If the value exceeds this critical value the release into the air when wet is less than the value when dry. Thus Fig. 7 can be used to rationalize some of the conflicting data on the sign of the effect of moisture on radon release. TANNER( 1964) describes the usual effect as positive: one example of a negative effect (accentuated, since *20Rn was studied) is given by GUEDALIAm al. (1970). If the release from solid grains into pore spaces is considered, the effect of moisture is to increase the emanation. But if, as is usual. the release into the surrounding air is measured, the result of wetting could be either to increase or decrease the radon release. depending on the distance radon must diffuse through water to enter the air.

R. L. Fktschttr

784

Two laboratory experiments demonstrate the mxease in radon emanation by water. The first set used 24 soil samples in small sealed systems such as that shown in Fig. 4 of FLEECHER and MOGRO-CAMPERO(1978). Twelve 100 gm samples with 5 to 50 gm of water added emanated over a 6 month-period 1.46 times that from 12 samples with 0 to 5 gm of added water. The second set of expenments utilized Coleman lantern mantles. which are composed of line filaments (20 pm fiber bundles. with fibers -0.5 pm diameter) of a material that contains Th02 and emanates ‘mRn. Three such sources were exposed dry for 2 weeks. three immersed in 20 gm of water forming a thin enough layer (-5 mm) that diffisionai escape was possible. The wet samples released 24 times the thoron that the dry ones did. The inference is that when dry most of the emitted 220Rntecoiis are imbedded in adjacent fibers. Whether the predicted radon transient has been observed is unclear. A possible example is given by CULLEN ( 19463, who observed elevated 222Rnexhalation from the earth after rainfalls. The average exhalation rate after 19 rainfalls was increased over the average value during seven months of observation by I .74 times. This increase is comparable with the I .5 to 2. I times for the model calculations in Table I. The data of MEGUMIand MAMURO (I 973) show mcreased radon exhalation afIer rainfalls of less than 2 cm and decreased radon for greater ones (which are more likely to create diffusional barriers).

DiSCUSSfON In choosing modets to evaluate quantjtatively~ two cases were selected where chemical effects are least important-2YU/238U disequilibrium (where both nuclides are of the same element and therefore are chemically the same) and radon emanation (where this inert gas is expected to be chemically inactive). The same primarily physical considerations as have been invoked here will also be important in considering other disequiiibria, such as 2qh/238U, 226Raf 238U, but in addition chemical effects will enter. Differential sotubiiities of diRerent elements in different solutions and a variety of tendencies to attach to a variety of surfaces will alter the predictions that would be derived from the present work. The similarities of uranium leaching by solutions of differing pH are remarkable (FLEISCHER, 1982a, 1982b); it is unlikely that such uniformity applies to all products of alpha emission. Because the range of geometries and of uranium and radium distribution in rocks and soils is immense and incompletely documented, the models used here are highly incomplete. The variety that exists in nature implies that the models are likely to approximate real systems, but it is not known as to whether they describe representative systems. Another approximation is that porosity has been described by openings with parallel surfaces, which approximate the geometry of cracks. in contrast, cylindrical porosity would require different, but straightforward analysis. CONCLUSIONS Models of the fate of nuclei that recoil from grains in rocks and soils into interstitial spaces and adjacent grains have been described and their implications derived for 234U/238U isotopic equilibrium and for r22Rn emanation. The ratio of direct stopping of re-

coils m mterstitlai spaces to ~mpIan~tIon”foiiowedby-leaching is variable and depends on grain size, porosity geometry, and the presence or absence of water. Either of the two mechanisms can be dominant in different cases. REFERENCES C~JLLENT.

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FLEISCHERR. L.. PRICE P. 13.and WALKER R. M. ( lY75) Nuclear Tracks in Solids. Umv. of Calif. Press, Berkeley. FLEISCHERR. L. and MOGRO-CAMPEROA.f 1978) Mapping of integrated radon emanation for detection of iongdistance migration of gases within the earth: techniques and principles. .I. Ge0ph.v.x Rex 83, 3539-3549. FLEIXHER R. L. and RAABE0. G. t 1978) Recoiling atphaemitting nuclei-m~hanisms for uranium series disequilibrium. Geochim. Cnsmochim. Acta 42. 973-978. FLEISCHERR. L., GIARL) W. R., MOGR~-CAMPERO A.. TURNERL. G.. ALTERH. W. and GINGRICH J. E. ( 1980) Dosimetry of environmentai radon: methods and theory for lowdose intemated measurements. Health Phvs. 39. 957-962.

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FL&XX S. and ZIMENSK. E. (1939) Die bestimmung von korgr&sen und diffisionskonstanten aus dem emaniervermogen. Die theorie der emanier-methode (“The determination of grain size and diffusion constant by the emanation power. The theory of the emanation method”). Z. Phys. Chem. 342, 179-220. GUEDAL~AD., LAUREM J. L., FONTAN J.. BLANC I). and DRUILHET A. ( 1970) A study of radon 220 emanation from soiis. J. Geophys. Rex. 75, 357-369. KGOSHI K. f 197 1) Alpha-recoil ‘UTh: dissolution into water and the rHU/Z3SUdisequilibrium in nature. Science 173, 47-48. LINDHARDJ. and SCHARFT;M. ( 196 I ) Energy disslpatlon by ions in the KeV region. Ph~ps. Rev. 124, 128-l 30. MEGUMI K. and MAMURO T. (1973) Radon and thoron exhalation from the ground. J Geophys. Res. 78, 18041808. RIESE W. C., BR~~KINS D. G. and DELW VALLE R. S. ( 1980) Scanning-electron-microscope investigation of paragenesis of uranium deposits, Mount Taylor and eisewhere. Grants mineral belt. in Geology and Mneraf Technology of the Grants Uranium Region IX?? fed. C. A. Rautman) Memoir 38. New Mexico Bureau of Mines & Mineral Resources, p. 244-25 1. ROSHOLT J. N. and TATSUMOTO M. (1970) Isotopic composition of uranium and thorium in Apoiio 11 samples. Proc. .~pollo I1 Lunar Ser. Conf.‘. Geochim. Cosmochlm. km Suppl. I 2. 1499- 1502. ROSHOLTJ. N. and TATXJMOTO M. ( 197I j isotopic composition of thorium and uranium in Apollo 12 samples. Proc. .Ipollo I? Lunar Sci. Co& Geochim. Cosmochim. Acta. Suppi. 2 2, 1577-1584. SZABO B. J. (1969) Uranium-series dating of quaternary successions. Union. Inr. fbr Quat. Studies. 1’111 INQC!4 (hr$!/:, Paris, pp. 94 l-949. TANNER A, B. (1964) Radon mrgratlon In the ground. In The Nutural Radiation Envtronment feds. J. A. S. Adams and W M. Lewder) I-1.ofChicago Press. Ch. 9, lhl-iQff.