THE PHYSICAL REVIEW A Jounal of Experimental and Theoretical Physics Established by E. L. Nichols in 1893 VoL. 59. No. 3 FEBRUARY 1, 1941 SECOND SERIES Variation of the Rate of Decay of Mesotrons with Momentum BRUNo ROSSI* AND DAVID B. HALL Universily of Chicago, Chicago, Illinois (Received December 13, 1940) In order to determine the dependence of the probability of decay on momentum, mesotron h range between 196 and 311 g/cm2 of lead and mesotron with than 311 g/cm of lead were investigated separately. The softer group of mesotron disintegrate at a rate about three times faster than the more penetrating group, retical predictions based on the relativity change in rate of a movin ew value of proper lifetime of mesotron of (2.4 0.3)X10-6 sec is determined measurement with particles with momentum of approximately 5X105 ev/c INTRODUCTIO traveling in the atmosphere No appreciable RECENT experiments on the variation of lumber of mesotron, however, will disintegrate ray intensity with altitude have within a condensed absorber, even equivalent in mass to the whole thickness of the atmosphere shown that the rate of decrease of the mesotron because the time required for the traversal of component with increasing atmospheric depth such an absorber is very short compared with the cannot be accounted for completely by ordinary lifetime of mesotron ionization losses. It has been established, namely, A simple relativistic consideration shows that that the number of mesotron is much more if the absorption anomaly of mesotron is due to strongly reduced by a layer of air than by a \me for meneous decay it must be more pronounced air layer with regard to ionization losse The anomalous absorption in air is interpreted high energy. In fact, let To be the "proper life- timeof mesotron: i.e., the lifetime measured of a few microseconds. According to this as- rest, and T the lifetime measured in a frame of sumption, a considerable fraction of the mesotron beam will disappear by disintegration while velocity B 6 Then Ithaca, New York oag,(a)Phys. Rev. and the" average range before decay'"L; i.e., the L=r=力T0/k 6 A. Ehmert, Zeits. f. Physik 115, 333(1940)
224 B. ROSSI AND D HALL buted to the decay, or an increasing fur the aly attributed to the polarizat S An attempt to determine the rates of decay of mesotron of different momenta has been re- ported by Nielsen, Ryerson, Nordheim and Mesotron groups of diffe 30 ected by taking the diffe between the intensities of the mesotron beam after filtration through various thicknesses of lead By this method, however, it is hardly possible to reach a sufficient accuracy, since the Y STEEL difference is small compared with the quantities directly measured. In our experiments the sta- E LEAD tistical precision was greatly improved by meas- uring the difference directly; i.e., by recording only mesotron which can traverse a given thick opped by a here u is the mass and p=uB/(1-B) is the ditional absorber lomentum of the mesotron. The probability of decay per centimeter path is obviously 1/L. It is EXPERIMENTAL METHOD seen that the average range is directly pro- The experimental arrangement is schematically portional, and the probability of decay inversely represented in Fig. 1. The Geiger-Muiller counter proportional, to the momentum ubes were of the self-quenching type. Their The experiments described in the present internal diameter was 4 cm and their effective paper were primarily designed to test the de- lengths were as follows: counters A, B, cand E disintegration probability on mo- 27 cm: counter D, 20 cm: counters f, 60 cm. The mentum expressed by Eg.(2). The to provide an additional check of the disintegra- connected in parallel. The counter battery F relativistic transformation formula for time inter- counters 4. B, C and D. In order to cut off the vals. Further experimental evidence on the sub- soft component, 5 cm of lead was permanently ject of the decay particularly desirable in placed above counter A and 10 cm of lead be- view of Fermis recent theory showing that the tween counters B and C. Including the material energy losses of fast particles in condensed of the frame, the permanent absorber above or materials are appreciably reduced by the dielectric between counters A, B, C and D was equivalent polarization of the medium. According to this in absorption power to 186 g/cm2 of lead, while theory even stable mesotron are absor bed by that between D and F was equivalent to 10 g/cm2 of lead. Counters A, B, C and D were pro materials of the same mass per cm. The differ- tected on the side by lead walls 11.5 cm thick ence in absorption due to polarization increases An additional lead absorber 2 of 115 g/cm2could with increasing mesotron momentum; i.e., varies oppositely from the difference due to decay. The be introduced between D and F and an absorber polarization effect, as calculated by Fermi, was Smade of iron plates could be arranged above the quantitatively inade equate to account for the apparatus so as to cover the whole solid angle experimental results already obtained. Yet it was subtended by counters A, B,Cand D.The interesting to investigate whether the observed apparatus was set up in a moving van which absorption anomaly was a decreasing function of could be taken to different altitudes on mountain the mesotron momentum, as the anomaly attri roads. The whole syste pt for the absorber S, was enclosed in a thermostatic box. E. Fermi, Phys. Rev. 57, 485 (1940 By means of an appropriate vacuum-tube
DECAY OF MESOTRONS 225 circuit, the following events were simultaneously number of anticoincidence, which is not neces- recorded:(1) Fivefold coincidences between sarily the same with and without the absorber. counters A, B, C, D and one of counters F or E Since, however, only slow mesotron are ap- (coincidences [ABCD(E+F)];(2)coincidences preciably scattered as well as absorbed, the between counters A, B, C and d not accompanied difference in the number of anticoincidence due by a pulse either of counters F or of counters e to scattering is a small and constant fraction of anticoincidence [ABCD-(E+F)D. The co- the difference in the number of anticoincidence incidences [ABCD(E+F)] were mainly caused due to absorption. Thus, the difference between by mesotron going through counters A, B, C, d the number of anticoincidence recorded with and F, After entering the apparatus; i.e after and without lead in 2 is proportional, if not crossing the surface indicated by a in Fig. 1, accurately equal, to the number of mesotron these mesotron had to traverse 196g/cm?? of lead which traverse 10 g/cm of lead and are absorbed when there was no absorber in 2, or 311 g/cm of by 125 g/cm? of lead between D and F. These lead when 115 g/cm2 of lead were placed in 2. mesotrons are those which enter the apparatus Chance coincidences were negligible and coinci- with a residual range between Ra=196 and dences due to air showers were certainly rare on Ra=311 g/ cm of lead account of the heavy lead shield at the side of the punters. Coincidences caused by ionization THE MEASUREMENTS showers generated by me esotrons Measurements were taken alternately at absorbers could not introduce any error because they were a small and constant fraction of the Denver, Colorado, and at Echo Lake, approxi- mately 30 miles west of Denver. The geomagnetic coincidences caused directly by mesotron trav- latitude is practically the same(49 N) for both ersals 8 Thus, one is justified in taking the counting rate [ABCD(E+F)] as a measure of locations. The difference in altitude is 1624 m the number n of mesotron entering the appa The difference in atmospheric pressure, as meas ratus with a residual range larger than the total ured during the experiments, was 108 mm Hg quivalent to 147 g/ cm amount of matter present above or between the The measurements at Echo Lake were per- counters. Anticoincidences [ABCD-(E+F)] could be formed partly with an iron absorber of 200 g/cm2 counted for by one of the following events in S and partly without this absorber. No iron (a)A mesotron has traversed A, B, C and D and absorber was used at Denver. Three complete has been stopped between D and F.(b)A meso- sets of measurements were carried out at Denver counter battery F has failed to detect it for lack single readings from the averages were within the pulses of counters A, B, C and D has occurred. summarized in Table l. The errors given are the (d)A mesotron has traversed counters A,B, c standard statistical deviations and D, but has been scattered through a wide table SBcde + f ]e md tabcd-(e+hJare the angle so as to miss the counter battery F. The stopping of mesotron between D and F a is the diference between the nsem anticoincidence recorded with lead in 2, which The errors are the standard statistical deviation. lead in zs (case (a)) is certainly the main origin of the are, as we shall see, several times more equent than those recorded without lead. The events LOcATION S(Fe)2(Pb) scattering(case(d)) ttribute a small This was not always the case for the experimental f-7deskoo 1 13686492420.06 0.183#0.021 120.8 cussion on p. 464, reference 1(b)
226 B. ROSSI AND D. B. HALL According to the discussion in the foregoing transferable energy, and I=13.5 ev (this ex- section, the counting rates [aBCD(E+F)] with pression differs by a factor 1/B from the expres 115 g/cm2 of lead in 2 can be taken as a measure sion for the energy loss). a correction has to be of the number N of mesotron entering the applied to account for the polarization effect apparatus with a residual range larger than pointed out by Fermi. The correction, however Rb=311 g/cm of lead, while the figures listed is very small for the mesotron momenta in which under A can be taken as a measure of the number we are interested According to some recent n of mesotron entering the apparatus with a calculations of Halpern and Hall, it is of the residual range between Ro=196 and R=311 order of 2 percent for iron and of 3 percent for g/cm2 of lead lead. Numerical integration of the equation for Let Nl, NI and Ne be the values of N at echo the momentum loss yields the range as a function Lake under 200 g/cm of iron, at Echo Lake of the momentum. The ranges Ra=196 g/cm2 of without the iron absorber and at denver without lead and R,=311 g/cm of lead, which define the the iron absorber, respectively. Let ni, n and n2 mesotron groups considered in the present ex- be the corresponding values of n. Considering periments, are thus found to correspond to the first the measurements taken without the iron momenta Pa=3.1x108 and Pb=4.5X10 ev/c, respectively. Mesotrons reaching Denver with n1/N1=0.082+0.005, n3/N2=0.058+0.002. momenta equal to pa and Po had momenta equal It appears that the fractional number of slow altitude of Echo Lake. For mesotron with mesotron increases rapidly with altitude, in momentum between 3. 1x10 and 7. 3 X108 ev/c agreement with the results of the absorption the ratio between momentum losses per g/cm of measurement nts in carbon by Rossi, Hilberry and air and of iron is very nearly a constant and Hoag. Because of a possible effect of scattering equal to 1. 23. Thus, as far as collision losses are on the determination of n, the above figures concerned, 200 g/cm2 of iron is approximately cannot be trusted to represent accurately the equivalent to 147 g/cm of air. 10 Consequently, if n2/N,. However, the ratios between values of the same mesotron intensity at Echo Lake under LABCD(E+F)] or A at different depths should 709 g/cm of air plus 200 g/cm? of iron as at ot be appreciably affected by scattering or by Denver under 856 g/cm2 of air alone. This other disturbing effects. Thus we have applies to the mesotron band between 3. 1 x105 M2/N1=0.883±0.00772/71=0.698±0.031 and45×10°ev/ cas well as to the whole mesotron N2/N=0.738±0.009n/m=0.520+0.035 pectrum above45×10°e/c Our experimental results show that both N and here the actual errors should not exceed the n are larger at Echo Lake under the iron absorber statistical errors indicated than at Denver without this absorber The difference is accounted for by the decay of mesotron on their way down from 3240 m to In order to discuss our experimental results, we 1616 m. Let us define the probability of survival and momenta for mesotron. The momentum loss due to collision is See O Halpern and H Hall, Phys. Rev. 57, 459(1940) given by the Bethe-Bloch formula 2roNZuelo gmy如H31hw where ro is the classical radius of the electron, N bad. iHewevergebofthr tht cofncideisces ect becepreterere he number of atoms per cm, Z the atomic and the an number,He the rest energy of the electron, B the slowly with the thickness of the velocity of the mesotron, Wm the maximum mental resu
DECAY OF MESOTRONS TabLe II. Co 吧心吧 p=(p2+ah2) for p2>3.0X108 ev/c have been ob 1+l2力2+a(h2-h /u h .(5) with range >186 g/cma of lead. Here h and ha are the atmospheric depths at the ERs BV/C-CAr \CaSR A ING elevations a1 and 2, P: is the momentum of A,3135 mesotron at s and a is the momentum loss per 94士0.9 323333133en g/cm2 of air. 1 The momentum p is intermediate 2594士 between the initial momentum pi=P2+a(h2-hi) and the final momentum pe. We shall refer to it 翡辈罐 he counters as the efective momentum Let us first consider the experimental result concerning mesotron which have residual mo- Rossi and ha +4-5.8/4.5340./counters the menta between 3. 1 and 4.5x108 ev/c at the lower elevation. The corresponding effective momenta are44×10sand5.8×108ev/ c and we may take 5.0X10 ev/ c as an average. For this probability that a mesotron present at th mesotron group the experimental value of the higher level s1 does not disintegrate before reaching the lower level 22. Then w1=n,/n, is 012=0.698+0.031, and therefore L=(4.5+0.6) 105 allows from (2): To/ 0.698 is the experimental value for the average =(9.07=1.3)X10-4 cm c/ev and accordingly, probability of survival between 1=3240 m and taking=8X107ev/c,, T0=(7. 2+0.9)x104cm/c, 32=1616 m of the mesotron which reach 32 with or so=(2.4+0.3)X10-6 sec. We shall next con momenta between Pa and Po, and Wi=Na/Ni sider the continuous mesotron spectrum which 0.883 is the corresponding value for the meso- reaches 1616 m with a residual momentum larger trons which reach ss with momenta larger than than 4.5x108 ev/c. The probability of survival Po. One sees that w1 is much smaller than Wi2, for this mesotron group is W12=0.883, and if hich shows that slow mesotron disintegrate at we take Eq. (4)as an experimental definition of a much faster rate than the more energetic ones. L we get L=(13.3_+0.9)X105 cm.Assuming his result is in agreement with the predictions To=2.4X10-6 sec., we then calculate formally based upon the disintegration hypothesis(see from Eq (2), p=1.5x10% ev/c. This momentum Eq.(2))and affords strong support to the should represent a sort of average effective hypothesis itself. For a mono-energetic group of momentum for the mesotron group considered mesotron, the probability of decay has a very The value p=1.5X10 ev/ c is quite compatible ple theoretical expression, provided the with our present knowledge of the momentum momentum loss in the air layer between 21 and 2? spectrum of mesotron 12 Thus, while a quanti can be neglected. In this case, Eg.(2)gives tative proof of Eg.(2)is still wanting, its ap (4) proximative validity may be considered as established It is convenient to use Eq (4)as a definition of L In evaluating the experimental results we have also when the momentum loss cannot be neg- only considered mesotron coming in the vertical lected. It can easily be proved that L is still direction. As a matter of fact, our experimental related to the lifetime To by an expression of the arrangement was strongly selective for vertical type of Eg.(2) l1 This follows immediatel L=p0/μ (2)r。 llowing (1937);D
228 B, ROSSI AND D. B, HALL mesotron, but detected also mesotron coming removed from the beam by scattering, and this in directions inclined up to an angle of almost may have reduced the magnitude of the ab- 45. The inclined mesotrons travel a longer sorption anomaly due to decay. We may add distance and have on that account a smaller that the results recently obtained by neher and probability of survival than the vertical ones. Stever with an ionization chamber, concerning The increase in the path length, however, is mesotron coming in all directic partially compensated by an increase in the with our present results and with those of effective momentum. Thus the correction is not Hilberry and Hoag and of Nielsen, Ry large and can be disregarded at the present state Nordheim and Morgan than with the results of of the experimental accuracy. Ageno, Bernardini, Cacciapuoti, Ferretti and Wick COMPARISON WITH PREVIOUS RESULTS CONCLUSION Table II summarizes the data on the mesotron The experiments described have shown, in decay which can be deduced from the measure- agreement with previous results, that the number for vertical mesotron. L is calculated, according by a layer of air than by a dense absorber 4), from the probability of survival. The results of Nielsen, ionization losses.The indication from earlier groups with pa from 1.8X10 to 3.5X10 ev/cand experiments that the difference in stopping from35×105to59×10sev/ c are not ower between air and condensed materials enough for a quantitative comparison with our decreased has been definitely established. This to 4.5X108 ev/c. No other measurements on se. result verifies a theoretical prediction based upon lected groups of mesotrons are available. all the the disintegration hypothesis, thus confirming remaining data in Table Ii refer to mesotron for which only the lower limit of the momentum is by spontaneous decay of mesotron in the defined. A comparison between these data is not atmosphere. A value of the proper lifetime straightforward because L depends not only on To=2.4X10-6 sec is deduced from measurements the minimum effective momentum Pmin of the a fairly monokinetic group of mesotron. mesotron recorded, but also on the shape of the We are greatly indebted to Professor A. H Compton for discussions of the problem and for momentum spectrum, which is probably different the encouragement given to this work. We also at different altitudes. One may expect, however an approximate correlation to exist between the express our appreciation to Professor J. C values of pmin and l in the various experiments. collaboration, and to Professor N. Hilberry and Table II shows that this is actually the case if we Mrs. Jane E. Hamilton for their valuable assist- exclude the measurements of Ageno, bernardini Cacciapuoti, Ferretti and Wick, who found a Company for making available for two months a value of L much larger than that determined by suitable truck, to the Denver City Parks for other authors for nearly the same value of Pmin. their helpful cooperation and to the Carnegie The reason for the disagreement is not com- Institution of Washington for financial support, pletely clear. It may be noted that Ageno and we wish to express our sincere gratitude. One of collaborators used a lead absorber placed bet veen us(B R. acknowledges with thanks the fi the counters to compensate for the difference in support granted to him by the Committee in aid atmospheric depth between the higher and the of Displaced Foreign Scholar lower station. With this arrang preciable number of mesotron may have been 57, 3(1940) ference 2. Also M. A. Pomerantz, Phys. Rev
