250 L E T T E R S T O T H E E D I T O R

2"x2"x6" Be TARGET 350"RADIUS | 1.63 Bev/c T T ' , + 5 '

* l f 2 f 3 f4=L IQUID SCINTILLATORS 3"DIA.

*5=LIQUID SCINTILLATORS 6"DIA. (SCHEMATIC)

s y > .ABSORBER ^ O f ^ . (SCHEMATIC)

FIG. 1. Experimental arrangement.

attenuation experiments may have an appreciable dependence on the angle within which secondaries from the interactions can cross the last counter, different experiments have been made with various geometries which we characterize by the rms value 0rms of the semi-aperture of the angular cone subtended by the last counter at the absorber. Table I shows the results obtained. The errors quoted include uncertainties other than the statistical error, such as those present in the muon contamination. By ob­serving the effect of thin Pb plates inserted between the slabs of the carbon absorber, the effect of the multiple Coulomb scattering in hydrogen was determined. The largest correction, ~3 mb, was found for the 0rms= 1.8° geometry. The large-angle, single Coulomb scattering in hydrogen was computed to be negligible. No such corrections are manifestly necessary for the D20—H20 difference.

Table I shows some probable dependence of the cross sections on 0rms, which could be interpreted as the result of secondary particles, possibly elastically scattered pions, projected close to the forward direction. Clearly, the value for 0rm3^2.5° can be taken for the total cross section; it is, after correction, cr(iT,p) = 34dr3 mb. In the same fashion, <r(ir~,d—p) = 29 ±3 mb. This latter value can be interpreted as approximately the cross section for negative pions on neutrons, <r(ir~,n) on the assumption that at these energies (X~2X 10-14 cm) and for values of the cross section quite smaller than ir(h/fxc)2=61 mb, aiiT^d) is close to the sum a(TT~,p)-\-(r(ir~)n). If one further assumes that charge symmetry holds, our measured value of a(ir~,d--p) could be considered as approximately equal to o-(ir+,p).

TABLE I. The total cross section of 1.5-Bev negative pions.

millibarns (uncorrected)*1

<T(TT ,p)

millibarns (corrected)a

<r(ir~,d—p) millibarns

7° 4.5° 2.5° 1.8°

30 ±2 33.7 ± 3 36 ± 3 35.5 ±3

34 ± 3 32.5 ± 3

25.6 ± 4

28.7 ± 3

a The values of column 1 are uncorrected for multiple Coulomb scattering loss of pions by hydrogen. The values of column 2 are corrected for this effect.

We are very grateful to Dr. G. B. Collins, Dr. G. K. Green, and to the entire Cosmotron Staff for their continuous coopera­tion and to Dr. H. S. Snyder for valuable discussions.

* Research performed at Brookhaven National Laboratory under the auspices of the U. S. Atomic Energy Commission.

t On leave from Johns Hopkins University, Baltimore, Maryland. 1 For increasing the pulse duration up to 20-30 millisec, we are especially

indebted to H. S. Snyder.

The Natural Tritium Content of Atmospheric Hydrogen*

A. V. GROSSE AND A. D. KIRSHENBAUM Research Institute of Temple University, Philadelphia, Pennsylvania

AND

J. LAURENCE KULP AND W. S. BROECKER

Lamont Geological Observatory, Columbia University, Palisades, New York (Received November 16, 1953)

R ECENTLY the existence of natural tritium in Norwegian surface waters was demonstrated.1 This was accomplished

by enriching the natural tritium content by electrolysis between 1 and 10 million-fold. Faltings and Harteck2 in Germany have approached this problem in a more daring manner by assuming that the molecular hydrogen, which is present in the air by about 0.5 ppm would contain cosmic-ray tritium in a much higher con­centration than in atmospheric water. They assumed that the tritons produced by cosmic radiation in the uppermost part of the atmosphere would be trapped essentially in molecular hydro­gen since at this altitude (~70 km) water is photochemically decomposed by ultraviolet radiation into atoms of hydrogen and oxygen. They were able to detect the natural tritium in a sample of hydrogen which was first isolated as water and then isotopically enriched. The effect due to the tritium, however, was only 10 percent above the counter background yielding an estimated T /H of 10~14.

With superior techniques at hand it was thought desirable to examine the tritium content of the molecular hydrogen in a sample of ground-level air in America. Thanks to the cooperation of Dr. G. O. Strother3 we were able to obtain 25 cc of water produced

L E T T E R S T O T H E E D I T O R 251

from atmospheric hydrogen in the neon-helium fraction of air which was taken 5 ft off the ground at the Buffalo, New York (lat. = 42.9°N) liquid air plant of the Linde Air Products Com­pany. The whole sample corresponded to 60 to 70 million liters of air. Part of the sample was isotopically enriched in T by stand­ard electrolytic methods by about a factor of 7. Both parts of the water sample were reconverted to hydrogen at Temple by pro­cedures described previously.1 For the measurement of the tritium concentration, which was done at Lamont, the hydrogen was re-purified over charcoal at dry-ice temperatures and placed in a three-liter GM counter 77 cm in length. The counting mixtures used were 2.6-cm ethylene, 2.8-cm argon, and 1-10-cm hydrogen which gave starting potentials of 1700-2000 volts and adequate plateaus. Elaborate gamma-ray and meson shielding was employed as described elsewhere,4 giving a background of about 14 counts/ min. Under these conditions the enriched samples gave about 160 counts/min and the unenriched about 25 counts/min over background for 8 cm of hydrogen. The data which are summarized in Table I show that with this technique the tritium content of unenriched atmospheric hydrogen is readily measurable.

TABLE I. Summary of pertinent tritium data.

A. Atmospheric Hz from Buffalo, New York, Spring, 1952

Cm H2 Sample counted

1

2 2

3

4 4

8.0 8.2

4.0 8.0

3.8

4.0 8.0

Counts min -1 Enrichment (cm H2)-1 factor (T/H)X10is

18.1 ±1.1 6.84±0.34 14 700±900 19.4 ±1.2 15 800± 950

18.0 ±1.4 6.84 ±0.34 14 700 ± 900 18.5 ±1.3 15 200± 900

3.4 ±0.5 none 18 900 ±2800

2.75 ±0.50 none 15 300 ±2800 2.61 ±0.26 14 500±1450

Weighted average 15 400 ± 900 Corrected for decay 16 600 ± 970

B. Water from Buffalo latitude*

Sample (T/HXIO1*) (a) Chicago rains and snows (presumably uncontaminated

by atomic explosions): ~15 (b) Michigan Lake water: ~ 2

a See reference 5.

The atmospheric hydrogen sample was in storage for a period of 12 to 18 months at the time of measurement (September 15 to October 15, 1953). Data of the table indicate the ratio of the activities of the enriched and unenriched samples are in agreement within the experimental error, thus further attesting that the measured activity was due to tritium.

Libby5 has recently measured the tritium content of water from Lake Michigan and Chicago rain (Table I). These values can be assumed to hold for the Buffalo area. It can then be observed that the tritium content of the molecular hydrogen is about a thousand times greater than the water which is in direct contact with it. I t is believed that this is the only case where the isotopic ratios vary in nature by such a large extent. This is emphasized still more by the fact that the equilibrium constant of the reaction H O H + H T ^ H O T + H H at room temperature is about 6 in favor of enrichment of the tritium in the water molecule.

Libby6 originally assumed that the tritium is produced by fast neutrons from cosmic radiation on N14. Recently, Fireman7

reviewed all available data and came to the conclusion that a large fraction of tritons may be due to cosmic-ray stars. He calculated that the total rate of triton formation is between 0.4 to 0.9 triton per cm2 of earth surface per second. The maximum neutron pro­duction occurs at 15 km, which is below the ozone layer which absorbs an essential part of the ultraviolet radiation. Also, the altitude range of the main star production is 7 to 30 km.

In view of these facts the following explanation for the high concentration of tritium in atmospheric hydrogen may be pro­

posed, which is based on the fact that the rate of tritium exchange between molecular hydrogen and water is slow in the troposphere and even slower in the stratosphere. The "cold trap" of about — 60°C at the tropopause level prevents most of the water mass in the atmosphere from reaching higher altitudes. Above the troposphere some of the water vapor containing tritium atoms will diffuse upward to altitudes of high ultraviolet radiation intensity (—70 kilometers) where molecular hydrogen will be formed ac­cording to Harteck's2 mechanism. Since vertical mixing of the permanent gases (02, N2, A, Ne) insures practically constant composition of the whole atmosphere up to about 100 kilometers and is comparatively rapid, we would expect atmospheric molecular hydrogen to be more or less uniformly mixed. The tritium content of this molecular hydrogen will be mostly preserved in the lower atmosphere due to the slow exchange rate of H2 and H 20.

The rest of the water vapor, which did not diffuse upward, will condense in the form of snow, ice, or rain and be rapidly diluted by the vast water reservoir of the troposphere.

* Parts of this research were supported by the National Science Founda­tion and the U. S. Air Force, Cambridge Research Center.

1 Grosse, Johnston, Wolfgang, and Libby, Science 113, 1 (1951). 2 V. Feltings and P. Harteck, Z. Naturforsch. 5a, 438 (1950). 3 Tonawanda Laboratory of the Linde Air Products Company. 4 J. L. Kulp and L. E. Tryon, Rev. Sci. Instr. 23, 296 (1952). 5 W. F. Libby, Progress Report for U. S. Air Force contract, University

of Chicago (unpublished). e W. F. Libby, Phys. Rev. 69, 671 (1946). 7 E. L. Fireman, Phys. Rev. 91, 922 (1953).

Three-Body Scattering Problems* SIDNEY BOROWITZ, Department of Physics, College of Engineering,

New York University, New York, New York

BERNARD FRIEDMAN, Institute of Mathematical Sciences, Division of Electromagnetic Research, New York University,

New York, New York (Received August 7, 1953; revised manuscript received November 9, 1953)

IN a recent letter under this title,1 Dalgarno criticized a portion of our recent paper,2 which deals with exchange scattering.

We feel that these criticisms arise from a misunderstanding of our work.

The criticized section of our paper discusses whether the treat­ment of exchange scattering given by Mott and Massey3 was mathematically rigorous. Although it is not explicitly stated, their treatment requires that the solution be expressed as an infinite series with coefficients containing 5-function singularities. Such a procedure is mathematically unacceptable without rigorous justification. The solution which we present completely avoids this difficulty.

Dalgarno states that the Coulomb case is "not comparable,'' the implication being that the coefficients in the Coulomb case do not have the singularities possessed by the simple example in the appendix of our paper. The coefficients which occur in the Cou­lomb case are of the form Jl™ exp(ikor) sm(kr-}-k~1 log2kr+r})dr, with ko = k. These functions are even more singular than delta functions; thus, the Coulomb case is not only comparable to our example, but it is even more serious from the point of view of the mathematical objections stated in the preceding paragraph.

When no ionization occurs, then, as we indicated, our final result for the exchange scattered amplitudes is identical with that obtained by Mott and Massey. If the atom is ionized, our result is formally convergent, while Mott and Massey's is formally divergent. Dalgarno shows that, upon the introduction of wave packets, Mott and Massey's result in the ionized case becomes equivalent to ours. We believe that it is preferable to reserve the use of wave packets for those cases where the amplitudes them­selves and not their representations diverge. However, this is not such a case since our solution gives a definite value for the exchange scattered amplitudes.

While the method proposed by Mott and Massey gives results equivalent to those obtained by the method of our paper, the