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Nuclear transmutation by negative stopped muons and the activity induced by the cosmic-ray muons
NKcfear Pl?ysics A155 (137 1) 145-l Sf ; @ ~~~~~~~~l~~n~ ~~~~~s~i~~ Co., Amsierdam Not to be reproduced by photoprint
or microfilm without written permission
NUCLEAR TRANS~TATION
from the publisher
BY NEGATIVE STOPPED MUONS
AND THE ACTIVITY INDUCED BY THE COSMIC-RAY MUONS
Received 16 November
1970
Abstract: Nuclear transmutation and the involved factors when negative muons are stopped in matter are discussed. Some uncertainties about the atomic capture of muons in compounds and about the neutron emission probability following muon capture still exist. The stopping rate of negative cosmic-ray muons in the atmosphere and in the lithosphere up to large depths is reviewed. The activities of some radioisotopes induced by stopped negative muons in the atmosphere and in the lithosphere are calculated and compared with measurements and other calculations.
Negative muons slowing down in matter are finally captured by the Coulomb field of a nucleus into a Bohr orbit forming a pmesic atom. The muon cascades rapidly, z X0- ’ 1 set, down to the 1s level from which, through the weak interaction, it either decays (1) P- + e-+ii,+v, or is captured by a proton of the nucleus (2, A) p-+(2,
A) -+ (Z-1,
A)‘+v,,
(2)
where a proton changes into a neutron. The major part of 107 MeV liberated by the reaction (2) is carried off by the neutrino. The energy left to the neutron varies from w 5.7 MeV for the proton at rest, to some tens of MeV; this is deter~ned by the momentum balance in the capture process and is sensitive to the momentum of the capturing proton [for the mechanism of reaction (2), see sect. 41. The nucleus (Z- 1, A)* is de-excited mostly by the emission of one or more neutrons. The resultant nuclei are of the type: (Z-l,
A-X),
where
X=
0, 1, 2.. . neutrons.
(3)
Reaction (2) induces nuclear ~ansformations~ which can be followed with presentday technique in the case where resultant nuclei are radioactive. Secondary cosmicray muons bombarding the earth’s atmosphere and the first layer of the earth’s sur+ Present address: Physics Department,
University 145
of Thessaloniki,
Thessaloniki,
Greece.
146
S. CHARALAMBUS
face can induce such types of nuclear transmutations. The problem has been discussed to some extent ‘*“) and measurements were made on 3gC1, 5gFe, lg8Au and 26A1 [refs. “-“)I that were explained by the p- capture process. Calculations of isotope production by pL- should be based on the data given by Kaplan et al. 7, “) which concern the neutron emission probability distribution. However, these data should be carefully used “) (see below, sect. 6). A recent work lo) on the neutron emission distribution should also be considered. The production of isotopes by slow negative muons with emphasis on the isotopic transformations in the earth’s surface induced by stopped cosmic-ray muons is reviewed in the present work. The interaction of high-energy muons with nuclei (photonuclear effect) is not considered here. Production of nucleides (Z - 1, A -X) by cosmic-ray muons depends on many factors, such as negative muon stopping-rate, neutron emission probability, partial Coulomb capture of muons when the target is a compound, etc. While some of these parameters are accurately known, others have uncertainties of up to 50 %. These factors are listed in sect. 2, where the production formula is given, and discussed in the subsequent sections. In the last section an estimation is given of the production of some radioisotopes in the atmosphere and in the lithosphere. 2. Production formula The production or the decay rate, P (atomslsec), of the isotope (Z - 1, A -X), stable or radioactive in equilibrium, in one gram of matter is given by P = I,-(h)f,f,f,
atoms *g-l . set-I,
(4)
where I,,-(h) is the number of negative muons stopped per gram and per second at a depth h,f, is the fraction of stopping muons reaching the 1s muonic level of the target element in the case where the target element is one of the constituents of the compound (see sect. 4),fd is the fraction of muons captured by the nucleus from the 1s muonic level; the rest are decayed, and f, is the probability of production of the nucleide (Z-1,&X) f rom the nucleus (Z- 1, A)* by the emission of n neutrons. In the following we shall discuss the parameters of this formula. 3. Stopping rate of negative cosmic-ray muons The negative muon stopping rate versus depth relation, Ip- (h), can be derived from an experimental vertical intensity-depth curve for muons by taking into account the dependence of the intensity on the zenith angle and the p- to pc++p- charge ratio. We discuss briefly the parameters involved and present a stopping rate versus depth curve. Finally, since some of the induced radioisotopes may have short half-lives and are therefore affected by the variation of the cosmic-ray muons, we list the factors which should be taken into account.
NUCLEAR 3.1. MUON
INTENSITY-DEPTH
147
TRANSMUTATION
RELATION
The average intensity of muons is well known in the earth’s atmosphere up to a depth of 1200 m of rock and 1000 m of water. Takagi and Tanaka “) have derived a stopped muon-depth curve up to 100 metre water equivalent (mwe). Their calculations for depths between 10 and 100 mwe are made by the differentiation of the depthCosmic-ray
TABLE 1 muon vertical intensity 1, and n values for the angular Is = I, cos” B dependence in the calculation of the stopping rate of negative muons Depths @we) 500 816 850 1000 1574 1812 2000 3000 4000 4100
1, muons/cm2 +sec. sr 1.2 x 10-S
1.5 x10-6
1.4 x to-7 2.6 x 1O-8 6.2x 1O-9
used
n
1.85 1.93 *0.22 2.3 f0.3 2.25 3.06f0.10 3.03+0.16 3.2 4.2 4.8 5.12+0.82
1-q I*) 19) I’)
I’)
The IV values are taken from a curve given by Ramana Murthy et al. M* 16).
depth in rock
Fig. 1. Stopping rate of negative muons as a function of depth. d are due to Bardon and Slade ‘a) and -/- is due to Short 13).
148
S. CHARALAMBUS
intensity curve for cosmic-ray muons given by Hayakawa et al. “). At these depths their results are in fair agreement with the experimental findings given by Bardon and Slade 12) for 60 mwe depth and those given by Short 13) for a depth of 58 mwe and with the calculations of the latter based on the momentum spectrum of muons at sea level and the variation of this spectrum with the zenith angle. For depths less than 10 mwe, Takagi and Tanaka adopted the range spectrum of muons given by Rossi 14), applying a correction factor for the difference between the stopping power of the atmosphere and the rock. The two parts of the curve by Takagi and Tanaka are normalized for a depth of 10 mwe to 6.2 x 10s6 g-l * set-‘. For depths > lo2 mwe, we calculate the stopping rate using the vertical intensity-depths values I, given by Miyake et al. 15*16) and for the angular distribution, we assume the & = I, COS”0 dependence. Experimental values of n are given in table 1 [refs. “-“)]. A weighed curve of n versus depth was drawn through the experimental points and from this the n-values used in the calculation are taken; these are also shown in table 1. The overall depth of the muon stopping-rate curve so obtained is given in fig. 1 +. The experimental findings of Bardon and Slade and of Short for the 60 mwe depth are also given for comparison. The values of stopping rate are found from this curve to be higher by a factor of about two than those given by the emulsion technique 20-22) for depths up to 60 mwe. Short gives the following explanation: “The glass of the glass-backed emulsions restricts the search for a meson to the emulsion layer in which it stops, so that mesons are easily missed”. Discrepancies up to an or&r of magnitude exist between the present curve and the one given by La1 2V23). Recently, Calland and Glashow 24), on the basis of measurements at large depths performed by the Utah neutrino group of Bergeson et al. 2’) who found deviations from the set 8 law of Barrett et al. I’), proposed that “all cosmic-ray muons are not really muons”. This reasoning is not proved as yet. Therefore the U-particles of Calland-Glashow are not taken into account here. But if it were true, it would affect the stopping muon rate, particularly at large depths. 3.2. NEGATIVE-POSITIVE
MUON
RATIO
Since the primary cosmic-ray radiation consists about 90 % of protons, the excess of positive charge is transmitted to the first secondary x and K mesons and through these ultimately to the muons. The charge ratio of cosmic-ray muons has been measured by many authors. The charge ratio is measured precisely as a function of the momentum of muons, since this can give information on the nature of very highenergy interactions not yet attainable with accelerators. For the present work, the momentum dependence is also interesting to investigate, because, if it exists, it will change the charge ratio with depth. The Nagoya cosmic-ray group has recently published 26) results on the charge ratio obtained with a large magnet spectrometer and they included also data obtained from other laboratories. The authors conclude that t The curve of fig. 1 is for the negative muons. To obtain the muon curve, p+ +p-, multiplied by a factor 2.27.
it must be
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the ratio of positive-to-negative muons in the range between 20 to 500 GeV/c is almost constant, with a mean value of 1.293+0.019. The charge ratio between 40 and 80 GeV/c seems to be slightly smaller than elsewhere. The above results refer to large zenith angles. Although Mackeown et al. “) have studied a large number of published data for different zenith angles, they have not found so far any marked dependence on the zenith angle. They have shown, for instant e, that the ratio of charge ratio for 80” and 0” decreases with increasing momentum. But the deviation from unity at high momenta is of the order of 10 % and can be neglected. This phenomenon is explained by the K/n ratio. Contrary to the results of the Nagoya group, early studies of momenta above 100 GeV/c have shown that the charge ratio increases with the momentum. Haymann and Wolfendale ‘“) and Rastin et al. “) give ratios 1.61 at 240 GeV/c and 1.45 at 290 GeV/c, respectively. The variation of charge ratio with momentum could be explained by the K/Z ratio as well as by K+/K- [ref. 3 O)]. But since the statistical errors of charge ratio at such high energies are very large, we allow for the omission of the variation of charge ratio with momentum, which is consistent with the conclusions of the Nagoya group. We have used the value pL+/p- = 1.27 + 0.05 for the p- stopped curve. Using the total muons stopping rate and the p-/(p’ +p-) ratio, we obtained the curve in fig. 1 for the negative muons stopping rate in rocks as a function of depth. 3.3. MUONS
STOPPED IN THE ATMOSPHERE
The negative muons stopping rate in air, at sea level and at geomagnetic latitudes of about 40” is calculated to be (0.56+0.06) * lo- 5 g-l . set-I. This value is obtained by using the experimental findings of stopped muons given by Bardon and Slade I’) and a charge ratio of 1.27. This stopping rate agrees fairly well with the calculated one by Takagi and Tanaka 4), but it is 20 Y0higher than that given by Rama and Hoda ‘). 3.4. VARIATION
OF COSMIC-RAY
MUONS
Muons in cosmic rays are secondaries that are produced in the earth’s atmosphere by the decay of free 7t and K mesons, which are also secondary products of primary cosmic radation interacting with the N and 0 nuclei on top of the earth’s atmosphere. Muons are produced at the average altitude of about 15 km. Their mean life at rest is about 2.2 ps and they reach sea level (still penetrate deep into the earths crust) by time dilation (“mesons paradox” of the special theory of relativity). From the production mechanism, the intensity of muons at a given point must follow the time variation of the galactic component of cosmic radiation. As already shown from studies of the meteorites, the galactic radiation might be considered constant within 10 % for the last 10’ years and constant within a factor of two for the past 10’ years, see for example the review article “Cosmic rays in the galaxy” by Meyer 31). However, small periodic variations exist for the muons that reach the earth’s surface which
150
S. CHARALAMBUS
may influence the production in air of radioisotopes with short half-life, such as 39C1 from 4oAr. Because the muons lose their energy by processes depending on the mass of the atmosphere’s layer, the intensity of ,u-particles at a given point, say at sea level, also depends on the atmospheric conditions (temperature, pressure, etc.) through the Duperier relation 32) . Variation of the stopping rate of muons up to 10 % could be attributed to the pressure variation. 10 % fluctuations are, however, not very important as compared with the overall uncertainties and can be neglected for a first approximation. However, when the other difficulties have been overcome, correction due to pressure variation should be carefully applied, as there exists a kind of hysteresis between /J intensity variation and rapid pressure variation 33*34). The negative correlation between the muon stopping rate and the magnetic storms (Forbush effect) should be look at. This variation depends on the altitude and latitude and its duration is from about 2 hours to 2 days [see review articles 3 5#36)]; deviation from the average stopping rate of muons, at sea level, up to 5 % can be observed 37). Further cycling variations of the stopping rate of muons exist, as diurnal, 27 days and 11 years, but these are much smaller than 5 % and therefore neglected. The “latitude effect” on the flux of slow muons stopping in the atmosphere and in the first layer of the earth’s crust must beincluded. Subramanian et al. 38) compared the ratio of the stopping rate of slow muons at atmospheric depths of 800 g/cm2 and 60 g/cm2 and at a geomagnetic latitude of 2”N with those under similar conditions at 50”N and found that they differ by a factor of three [see also Conversi “‘)I. 4. The chemical compound effect factor When the target is a chemical compound it implies the problem of the partial atomic capture probability of negative muons by the constituent atoms of the compound. Fermi and Teller 40) predicted, “ . . . by crude estimates . . .“, that the relative atomic capture probability should be proportional to the Z-ratio, weighed by the atomic concentration. They arrived at the so-called “Fermi-Teller Z-law”, assuming that the probability of atomic capture is proportional to the energy loss of very slow muons near the various atomic species. This was computed by Fermi and Teller and found to be proportional to Z. Following Fermi and Teller, the chemical compound effect factor for the constituent n will be:
(fc). =
6% alZ,+a2Z2+.
..
+a,z, ’
where the a are the atomic concentrations in the molecule. Many experimental studies made in the past on the atomic capture of negative muons in compounds, revealed strong “solid-state or chemical” effects. The atomic capture of muons takes place at very high quantum numbers corresponding to stationary levels, which are common to the entire molecule, and solid-state effects cannot be neglected. Measurements made on the intensity ratio between the same ,u-mesonic
NUCLEAR
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151
transition of the same element but in targets of different chemical composition or different physical states showed that there exist differences 41 -44). Quantitative data of the relative number of muons reaching the Is level in the constituentsof a compound were obtained by Zinov et al. 41, 4s) by the method of X-mesonic-rays. The results of Zinov et al. showed some regularities. They found, for instance, that the ratio of probabilities of atomic capture in oxides varies periodically with increasing nuclear charge according to the periods of the table of elements. They also found that the ratio of probabilities of atomic capture in compounds of metals with halogens and in alloys of metals is described satisfactorily by Z o.66. However, the results of Zinov et al. do not agree with those obtained by other experimental methods (seeappendix 1). Sens et al. 46) deduced the relative number of muons reaching the 1s level in the constituents of a compound by measuring the time distribution of decay electrons emerging from a chemical compound in which muons are brought to rest. In analysing the decay curves and knowing the characteristic lifetime of pL- in the individual constituents of the compound, they found the relative population at 1s level. In their results on insulators the prediction of Fermi and Teller does not hold and they suggest that the atomic capture of muons occurs in proportion to the atomic concentration only. Their results might be expected to be different from the Z-law because the Brillouin gap in the insulators (discussed by Fermi and Teller but finally omitted in their computation) does not allow arbitrary small amounts of energy to be transferred from the stopping muons to the electron of the insulator. Later on, the same group, Lathrop et al. 47), studied ILi (insulator) and found that the ratio for the atomic capture is: I/Li = 15312.0. This ratio is in flat contradiction with the behaviour observed earlier in the insulators, and rather supports the Fermi-Teller law, where I/Li = 17. Using a similar experimental method, Astbury et al. 48) agreed with the Z-law for the case of PbF2. Eckhause et al. 49) found, however, discrepancies for both insulators and alloys. But their results for those insulators studied differ also in the stoichiometric proportion finding of Sens et al. Knight et al. 50) found, from bubble chamber studies, that muon capture is equal to stoichiometric proportion. The chamber was filled with a mixture of CF 3Br and propane. They found that the ratio of capture by light (C, F) and heavy (Br) atoms was almost equal to the ratio of atomic concentration. Another experimental study using the time analysis, but measuring neutrons resulting from p- capture, was performed by Baijal et al. 51). Their results do not present any regularity. Assuming that the ratio of atomic capture probabilities in a binary compound can be described by a relation of the form Cl/C2 = (a,/az)(Zl/Zz )“, they found for their results that n covers the range between 0.5 and 1.5. From the above short description and from appendix 1, where we present most of the up-to-date published data, we see that there does not exist experimentally established regularities on the atomic capture. Further, for the same compounds in some cases there are large differences between the experimental data depending on the method used. The theoretical Fermi-Teller predictions do not, in general, hold with
152
S. CHARALAMBUS
the experimental findings. However, a recent theoretical work by Au-Yang and Cohen [ref. “‘)I seems promising. Their results are in good agreement with some experimental values and can, at least qualitatively, explain the periodicity observed by Zinov et al. The parameter of their model producing the periodicity is the effective charge transfer Z,, a notion obtained from Pauling s3), and this Z, is periodic in atomic number. 5. Nuclear capture probability We need to calculate from the stopped muons what fraction& is captured by the nucleus. Since the muons have a mean life of 2.2 ps, the decays during cascade are fd
1
IP
Fig. 2. Fraction of negative muons captured by the nucleus from the 1s muonic atom level as a function of the atomic number, left scale. Right scale gives the induced activity or the production rate, in atoms per kg and per day.
neglected and the stopped muons are all in the 1s level. Let us call & and 1, the probabilities for decay and for nuclear capture, respectively. Obviously we have:
2, being the probability that the muons stay in the 1s level and r. the mean life of ,uin this level. Well-known experimental values of the Lo exist throughout the periodic system and they have been recently reviewed by Weissenberg 54). The 1, is calculated from eq. (5) using zd = I/&, the mean life of free muons, about 2.2 /E.. Thef, value will then be:f, = &/lo. Using the values of L, and Izofrom Weissenberg’s compilation we trace the smooth curve of fig. 2 (left scale). There is a fine structure of the curve. The nuclear capture of p- is not only a function of Z (especially of Zc”,,) but also of A, “isotopic effect” 5‘15“). It seems moreover that the particular nuclear structure of the target plays a role 57*58). However, comparing the fd with the accuracy of the other factors of formula (4) we find that it is better known by at least an order of magnitude.
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6. Neutron multiplicity distribution After the nuclear capture of muons the compound nucleus (Z - 1, A)* de-excites by the emission of a number of neutrons. The neutron multiplicity distribution, f,, depends on the target nucleus (Z, A) through the momentum of the proton capturing the muon. We will give below a short theoretical consideration and some experimental data on the f,function. 6.1. THEORETICAL
CALCULATION
OF f.
The muon capture is a two-body process (~1~,p). If the proton and muon are at rest, the neutron recoils with about 5.7 MeV of energy and the neutrino carries off the rest, about 100 MeV. But since the capturing proton is in a nucleus, it has a momentum distribution. Hence a large momentum transfer is possible and the formed neutron can recoil with an energy E = f (Z, A) larger than 5.7 MeV. Two possibilities can be assumed here: first, that the neutron escapes directly from the nucleus (direct neutron emission), and second, that this energy E = f(Z, A) is shared between the other nucleons and a compound nucleus (Z- 1, A)* is formed, whose excitation depends on the momentum distribution of the capturing proton. The compound nucleus de-excites mostly by neutron emission. In fact, measurements of the neutron multiplicity give about 1.5 neutrons per muon capture, which indicates that excitation energies are moderate, about 15 MeV. At these excitation energies the nuclei de-excite mostly by neutron emission. It is highly probable that y-rays accompany the neutron emission, about 80 % of the time a muon is captured lo). The emission of protons and charged particles in general occurs very infrequently, 2 y0 of the time for protons and 0.5 % for a-particles 5g); these are not taken into consideration in the present work. The behaviour of excitation distribution of (Z - 1, A)* was given by assuming for the nuclear matter either a Fermi gas momentum distribution, as Kaplan et al. ‘* ‘), or a Gaussian distribution (Brueckner model) as Singer 60). The nuclear excitation was then related to the neutron multiplicity distribution by using the compoundnucleus theory. As pointed out by Singer 61), the direct neutron emission following the muon capture is not negligible. The direct emission must be high for low A, a exp( -bA”), according to the calculations of Singer, where a and b are constant. This emission probability is about 0.22 per muon capture for the silver target. In appendix 2, we give the neutron emission distribution for some elements following Singer’s conception. 6.2. EXPERIMENTAL
DATA
ON f.
(i) The neutron multiplicity distribution can be estimated by radiochemical methods if the products (Z- 1, A-X) are radioactive. The technique requires an intense CL-beam, a single isotope target and a maximum number of radioactive isotopes (Z - 1, A -X). Copper isotopes were identified from the interaction of p- with zinc
S. CHARALAMBUS
154
by Turkevich and Fung 62). They have measured the activity induced in ZnC1, and found a low yield for 6oCu and a high production of 67Cu. Winsberg 63) has measured tellurium isotopes as being the product of the interaction of negative muons with iodine. This quantitative measurement is based on the induced activity of two tellurium isotopes: “‘Te(f,) and lzsTe(fi), from which the production of 126Te(f,) and 124Te(f3) was obtained by ingenious extrapolation. The measurements are limited by the techniques and muon fluxes of 1954. However, except for the zero neutron production, which is the double of Kaplan’s value, as explained below, and in our opinion overestimated, the otherf,, are reasonably induced within &20 %. Neutron emission probabilities Element
PO
PI
Al Si Ca Fe Ag I AlI Pb
7.6 36.0 35.4 18.9 6.2 4.2 11.0 0.6
82.0 46.0 57.2 59.8 48.7 70.5 37.7 59.1
TABLE 2 resulting from the data by MacDonald PI -
6.2 21.0 9.2 9.1 28.3 9.2 40.0 23.6
p3
-
20.0 7.4 3.7 16.2 12.6 8.0 3.6 5.1
p4 38.0 4.4 4.4 - 9.3 10.3 7.0 5.3 12.4
PS -33.0 0.0 0.0 4.1 -6.3 0.4 3.1 0.0
et al. s) p.S 10.8 0.0 0.0 0.0 3.9 0.0 1.2 0.0
(ii) Kaplan et al. ‘* * ) have measured directly the neutron multiplicity distribution with a high-efficiency neutron detector. In principle, these results should be unambiguous. They nevertheless appear to have been misinterpreted owing to the manner the data were presented. Kaplan commented subsequently on this “). To obtain the neutron emission probability P, from Kaplan’s results, the following expression should be applied: bnax
P,
=
c
~“&-~(-llr-“(l-&E)n-“~),
which can be found by solving for P,, eq. (8) of the paper + by MacDonald et al. “). The F,, is the probability for the observed n neutrons and E is the neutron detection efficiency which is equal to 0.545. Using this expression and Kaplan’s data for F,, the neutron emission probabilities in table 2 were found. We see that the one-neutron emission probability is high, of the order of 60 ‘A, while the P, is low, except for Si, Co and Fe targets. (iii) Backenstoss et al. lo ) have measured the nuclear y-ray after muon capture in several targets. These y-rays occur when the neutron, after the muon capture, leaves the nuclei in an excited state. It was pointed out that the frequency with which the nuclei are left in an excited state after the neutron emission is high: almost 80 % of the + We have used in this paragraph the notation given by MacDonald corresponds to the f. of the present paper.
et al. 8). It is obvious that P,
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nuclei in which a muon was captured emitted y-lays. Compared with the neutron measurement, the investigation of y-rays has the advantage that the probability of zero neutron emission can be measured directly, and the disadvantage that neutron emission leading to the ground states of the final nucleus cannot be observed. The y-ray measurements must be considered as complementary to the neutrons: but owing to the fact that for almost every neutron emitted we have a y-ray, the identification of this allows one to deduce neutron emission probabilities. It is concluded from the results by Backenstoss et al. that the zero neutron emission probability is negligible and that the single-neutron emission is larger than 50 %. For the zero neutron emission, Backe et al. 64) also find no excited states for a europium target and Cohen et al. 65) found only 1.6 y0 formation of 16N following the p-capture in 160. TABLE 3 Proposed neutron emission probabilities Neutrons emitted
0
fil
0.10 <
6.3. CONCLUSIONS
1
0.60-0.70
for practical applications 2
0.15-0.20
3
0.05
4
0.02
ABOUT fn
From subsects. 6.1 and 6.2 it can be concluded that both the theoretical calculations and experimental data on neutron emission probabilities f, are still ambiguous. Leaving aside the notion that the form off, must depend on (2, A) and bearing in mind the results by Kaplan et al. as presented in table 2, as well as the results by Backenstoss et al., and the high direct neutron emission following the calculation by Singer, we propose forf,, for the purpose of general approximation, the values given in table 3. 7. Applications The above findings can be applied to the nuclear transmutation induced by cosmicray muons in both the atmosphere and the earth’s crust. As a guide for estimating the induced activity by negative cosmic-ray muons at depths underground corresponding to a few metres of water equivalent, we present the curve in fig. 2 (right scale). This gives the induced activity versus Z. We have selected this depth because the muons (and neutrinos) are the only survivors of the cosmic-ray particles and also because the muons reach their maximum stopping rate there (see fig. 1). This curve shows the activity at saturation (as well as the production rate) - atoms decayed (or produced) per kg and per day - for the product isotope resulting from the emission of a single neutron. To calculate the curve we assumed that fnE1 = 0.60, that the target has a single isotope, and that it is in a pure uncompound chemical state. As an estimation
156
S. CHARALAMBUS
of the overall production error for the optimum cases (uncompound target, experimental values off,, activation at a greater depth, etc.) gives a value of the order of 25 %. The only radioisotope produced by pFL-stopped in the earth’s atmosphere in quantities measurable with present-day techniques is 3gC1. This is produced by p- from 40Ar(p, n)” gC1+. The 40Ar nucleus is a suitable target because it represents about 1 % of the atmosphere and also because, for it, the factorfd is about 0.80. On the other hand, 3gC1 is a one-neutron emission product. By analysing rain water, Winsberg “) found 3 gC1 and proposed that it was mainly produced by cosmic-ray negative muons from 40Ar in the atmosphere. He found for the activity of 3gC1 at saturation about 500 dpm over a rain collection of 300 m2. This value is about an order of magnitude lower than that calculated by him. Since several meteorolo,gical factors determine the fate of 3gC1 after its formation, it is difficult to define a production rate from these results. Rama and Honda “) have measured 3‘Cl induced by muons and neutrons in laboratory 40Ar at sea level. They found that the activity at saturation was 0.2f0.02 atoms * kg-l * min -I. From our calculations we find that the activity at saturation due to only the p- component is 0.18 &0.04 atoms - kg-l - min- l which is about 50 % higher than that calculated by Takagi and Tanaka “). Rama and Honda “) have measured and calculated the activity of l’sAu+ “‘Au induced by cosmic-ray muons and neutrons at sea level or else at a mountain altitude of 685 g/cm2 in laboratory mercury. In comparing the induced activities at the two depths, using a neutron flux at 685 g/cm2, eleven times higher than that at sea level and using a factor of four for the stopping muons, they found for “*A + “‘Au a production rate of 0.06+_0.01 atoms - kg-l - min -I. They used for the calculation 4.35 x 10e6 ,u- stopped g-l - set-‘. They calculated for l’sAu+’ “Au an activity induced by p- at sea level of 0.087 atoms - kg-’ - min-‘. Our calculation gives 0.11 kO.03 atoms * kg-l * mine1 using thef, distribution given in table 4, the natural isotopic composition of mercury and 5.6 x lo- 6 ,u- stoppzd/g * sec. With our model of small probability product for zero neutron emission we do not agree with Takagi and Tanaka “) for the calculated activities of 32P and 5gFe induced by cosmic-ray muons in 32S and 5‘Co respectively. They have found 0.15 + 0.08 and 0.1610.08 atoms * kg-’ - min-’ for “P and 5‘Fe, respectively; our calculation gives activities of the order of 0.03 and 0.04 atoms - kg- l - min- 1 for 32P and “Fe, respectively. A search for 2 6A1 (T = 7.4 x lo5 y) induced by cosmic-ray muons in terrestrial silicate rocks was made by Tanaka et al. “) using a low-level yy coincidence spectrometer. They found from the measurements 0.02fO. 12 dpm/lO kg Si02 for the actual surface rock and 0.00+0.08 dpm/lO kg Si02 for the rock at 24 mwe depth. No clear evidence for muon-induced 26A1 could be demonstrated. Tanaka et al. have treated t 39CI can also be produced in the atmosphere from 40Ar by cosmic-ray neutrons, (n, np) reaction. The cross section of the reaction (n, np)- (n, np) 3 (n, np)+ (n, np)+ (n, d) - is in general high x 200 mb at 14.7 MeV [ref. 66)]. In a few cases u is small. The o in the case of 40Ar was measured at 14.7 MeV [ref. 67)] and found to be 2.9kO.5 mb.
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TRANSMUTATION
157
about 80 kg of rock from the surface sample, extracting A1203. They suggest that an important improvement for determining ’ 6A1 in silicate rocks can be achieved in two different ways: either by producing chemically pure Al counting samples instead of Al, O3 or by using large counting devices, NaI crystal larger than 7.6 cm x 7.6 cm. Our calculation of “Al production in ‘ ‘surface” rocks gives a rate of 0.13 f 0.04 dpm/ 10 kg Si02. We used the following values:_&=, = 0.20 andf, = 0.33, assuming that Si02 remained all the time in the past under some few mwe’s underground. La1 “) proposed to carry out neutrino and antineutrino measurements from the activity these particles induce in terrestrial materials. The particular physics interest, as well as the advantages and disadvantages of v and ? measurements using this method, are thoroughly discussed in Lal’s paper. The interest is focused on the measurements of 37Ar (35 d) - initially proposed by Pontecorvo) - and of 39Ar (270 y) induced in KC1 by neutrino and antineutrino: v+~~C~ --t 37Ar+e-,
Y+39K + 39Ar+e’.
Argon must be separated from large amounts of sylvite deposits in saline mines, in Stassfurt, Germany, for example. However, 37Ar and 39Ar could also be produced in sylvite by stopped negative muons (muon capture by 39!K and emission of two neutrons and the zero neutron, respectively). To avoid interference from stopped muons the sylvite must come from layers deep underground and the noble gas separation be made at more or less the same depth. In the following, we calculate the 37Ar activities due to neutrinos and stopped muons in sylvite: Davis et al. 68) found with their famous neutrino experiment that the upper limit of the product of the neutrino flux over the cross section for all known sources of solar neutrinos is: x(&0)
= 3 x 1O-36 set-l
per 37C1 atom.
This experimental value is an order of magnitude smaller than the theoretical one calculated by Bahcall 69, 7O), based on the current ideas concerning the way of fusion reactions producing the luminosity of the sun. Using the upper limit given by Davis, we find a production by the neutrinos of about 7 x 10e4 of 37Ar atoms per ton of sylvite per day. The 37Ar and 39Ar induced activity at saturation due to muons is calculated using the muon stopping rate versus depth (fig. 1) and f.= o = 0.1, fnZ2 = 0.15 andf, = 0.5. It is obvious that these productions follow the behaviour shown in fig. 1, multiplying only the scale of stopped muons by a factor of 0.046 for 39Ar and by 0.07 for 37Ar. The production rate per ton of sylvite per day at 1000 mwe is: 0.15 3‘Ar and 0.10 39Ar, while at 4000 mwe these rates are lower by a factor of more than 10e3. At a depth of about 2300 mwe the production rate of 37Ar due to stopped muons is equal to that due to neutrinos. The present work aims at showing some limits only; it does not intend to plan a neutrino and antineutrino spectroscopy by the radiochemistry method. If one day a bold and “adventurous” searcher undertakes this job, he will have to calculate carefully the factors involved, many of which are discussed in Lal’s paper.
158
S. CHARALAMBUS
8. Conclusions
The above analysis showed that the behaviour of muons stopped in matter and captured by the nucleus is at present well known. However, while some of the factors determining the phenomenon are accurately known, the large uncertainties for other factors still exist. The following remarks concern the uncertainties in question. (i) It is not yet clear what exactly happens during the atomic capture of negative muons when the target atom is the constituent of a compound. (ii) Thef, neutron emission probability function is ambiguous. We saw that the zero neutron emission is small, < 0.10, while the f,= 1 is predominant. It is certain thatf, is a function of (Z, A) of the target. We propose, however, to use in practice the values given in table 3. The changes induced in the lithosphere could be useful for studying geophysica1 processes, such as erosion of surface rocks. They could also be useful for estimating, by means of muon compound, the high-energy cosmic-ray fluxes in the past [see La1 and Peters ‘“)I. M ore measurements of 26A1in silicate rocks with improved techniques are necessary. In the case of neutrino and antineutrino spectroscopy by induced activity in sylvite, serious difficulties might arise from the production of 37Ar and 3gAr by stopped muons. It will be interesting from many physics points of view to undertake measurements of 3‘Ar and 3‘Ar in sylvite deposited at various depths. To eliminate uncertainties resulting from chemical effects and neutron emission distribution, a thorough study of the production of 37Ar and 3gAr in sylvite by muons from the accelerators should be undertaken. Appendix 1
In table Al most of the up-to-date published data (column 4) on the relative number of negative muons reaching the 1s level in the constituents of a compound are given. Appendix 2
We present in table A2 the neutron emission distribution for some elements following Singei’s conceptions 60). The following parameters were used: nuclear parameter a2/2M = 20 MeV, nuclear temperature = 0.75 MeV and effective nucleon mass M* = 0.5 M in Singer’s formulation for the evaporation contribution. In the calculation, his direct neutron emission was also included. The neutron binding energy and mass difference A, _ 1 -A, were taken from Mattauch et al. “). The direct neutron emission (and consequently the total neutron emission distribution) is sensitive to the nuclear radius. In the calculations we used R = R,A* with R. = 1.4 fm. If particular experimental radii will be used, deviations up to 10 % could be found. For example the second line for aluminium (:iAl*) is calculated using the electromagnetic
NUCLEAR
TRANSMUTATION
159
TABLB Al Compound 1
Ratio 2
Fermi-Teller prediction 3
Observed 4
Stoichiomet~~ ratio 5
Sens et al. 46)
p205 A1203
SiOz KOH KHFz Cs Hq Clz liq. Cs H4 Cl, sol. CCI‘$
p/o
Al/O SijO
K/O K/F Cl/C Cl/C Cl/C
0.15 1.08 0.87 2.38 1.05 0.94 0.94 11.3
0.371 fO.041 0.435~0.038 0.386&0.025 0.455+o.os3 O.S88&0.138 0.435 *0.03s 0.476 &to.045 4.1 10.8
0.4 0.66 0.55 1.0 0.5 0.33 0.33 4.0
15.8 zh2.0 2.2 kO.7
1.0 1.0
4.8
0.5
Lathrop et al. 47) I/Li
LiI AgZn
AglZn
17.7 1.57
PbF2
Pb/F
4.5
BiFB
Bi/F
UFI CuAIz
U/F CuiAl
3.1 2.6 1.1
NaF CaCls Cd12 AgI PbIz NaCI KI LiF NaI PbClz PbFa
F/Na Cl/Ca Cd/I
Astbury et nl. 48) &0.7
Eckhause et al. 4g) 1.58 so.15 1.52 10.15 1.75 10.18
0.33 0.25 0.5
0.82 1.7 0.45 0.89 0.77 1.55 2.79 3.0 4.82 2.4 4.5
0.64 1.28 0.5 1.5 0.61 1.22 2.0 3.6 3.4 1.6 2.3
hO.05 10.14 5o.t io.2 10.06 io.11 10.2 10.4 10.4 10.2 10.2
1.0 2.0 0.5 1.0 0.5 1.0 1.0 1.0 1.0 0.5 0.5
OS 0.42 1.5 0.75 1.1 0.88 2.5 1.37 7.2 3.6 3.7 2.5 7.0 5.1 10.2 6.9 3.8
0.12 0.15 0.83 0.29 0.57 0.39 1.36 1.35 7.6 3.6 2.66 I.2 2.27 2.1 5.8 2.9 4.0
10.04 10.03 10.07 +0.02 co.04 AO.03 &O.lO +0.10 11.8 10.4 *0.32 io.1 10.22 iO.2 +0.7 +0.4 *0.4
1.0 0.67 1.0 OS 0.67 0.66 1.0 0.5 2.0 1.0 1.0 OS 1.0 0.5 1.0 0.67 0.33
Zinov et al. 41)
Be0
Ii& PbjI Cl/Na I/K F/Li IjNa Pb/C1 Pb/F Be/O
SiOz CaO TiOz cuz 0 cue ZnO ZrOz BaO PbOz PbO Bi203
B/O Mgto Mgio Al/O SifO CajO Ti/O Cu/O CU/O Zn/O Zr/O Ba/O Pb/O PbjO Bi/O
UOII
UiO
ho3 M@ M&z AL
03
160
S. CHARALAMBUS TABLE
Element
PO
A2
PI
P2
P3
P4
%
14.1
55.9
17.1
12.6
0.3
:;A’*
13.1
59.0
15.9
11.7
6.2
:$Si
17.6
60.4
18.4
3.7
0.0
t:Si
21.4
48.1
24.8
5.4
0.2
;;A1
3oSi 14
16.4
53.0
18.6
11.4
0.5
40Ar 18 39K 19
14.0
48.7
17.7
16.4
3.0
14.7
55.8
19.2
10.1
0.2
:$a
17.6
58.4
19.9
3.9
0.0
s6Fe
17.5
51.7
20.7
9.6
0.5
16.4
45.6
19.6
15.1
3.0
11.0
39.7
23.6
18.7
5.9
26 1271 53
‘i:Bi
rms radius (R = 3.02540.023 fm) from mesonic atoms, as this is given by Backendoss et al. 72). References 1) G. Fowler and A. Wolfendale, Progr. Element. Particle Cosmic Ray Phys. 4 (1958) 107 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22)
13. Lal, Proc. Int. Conf. cosmic rays, Jaipur, 1963 (1964) vol. 6, p. 190 L. Winsberg, Geoch. Cosm. Acta 9 (1956) 183 J. Takagi and S. Tanaka, INSJ-110 (1968) Rama and M. Honda, J. Geoph. Res. 66 (1961) 3533 S. Tanaka, K. Sakamoto, J. Takagi and M. Tsuchimoto, J. Geophys. Res. 73 (1968) 3303 S. Kaplan, B. Moyer and R. Pyle, Phys. Rev. 112 (1958) 968 B. MacDonald, S. Diaz, S. Kaplan and R. Pyle, Phys. Rev. 139 (1965) B1253 S. Kaplan, in High-energy physics and nuclear capture (Plenum Press, New York, 1970) p. 143 G. Backenstoss, S. Charalambus, H. Daniel, W. Hamilton, H. Lynen, Ch. von der Malsburg, G. Poelz and P. Povel, Nucl. Phys. Al62 (1971) 541 S. Hayakawa, J. Nishimura and Y. Yamamoto, Suppl. Progr. Theor. Phys. 32 (1964) 104 J. Bardon and M. Slade, Proc. 9th Int. Conf. cosmic rays, London, 1965 A. Short, Proc. Phys. Sot. 81 (1963) 841 B. Rossi, Rev. Mod. Phys. 20 (1948) 537 S. Miyake, V. Narasimham and P. Ramana Mm-thy, Nuovo Cim. 32 (1964) 1505 M. Menon and P. Ramana Murthy, Progr. Element. Particle Cosmic Ray Phys. 9 (1967) 163 C. Achar, V. Narasimham, P. Ramana Murthy, D. Greed, J. Pattison and A. Wolfendale, PFoC. 9th Int. Conf. Cosmic Rays, London (1965) C. Randall and W. Hazen, Nuovo Cim. 8 (1958) 878 P. Barrett, L. Bollinger, G. Cocconi, Y. Eisenberg and K. Greisen, Rev. Mod. Phys. 24 (1952) 133 E. George and J. Evans, Proc. Phys. Sot. A68 (1955) 829 S. Kaneko, T. Kubozoe, M. Okazaki and M. Takahama, J. Phys. Sot. Jap. 10 (1955) 600 S. Kaneko, T. Kubozoe and M. Takahama, J. Phys. Sot. Jap. 9 (1954) 147
NUCLEAR 23) 24) 25) 26) 27) 28) 29) 30) 31) 32) 33) 34) 35) 36) 37) 38) 39) 40) 41) 42) 43) 44) 45) 46) 47) 48) 49) 50) 51) 52) 53) 54) 55) 56) 57) 58) 59) 60) 61) 62) 63) 64)
65) 66) 67) 68) 69) 70) 71) 72)
TRANSMUTATION
161
D. La1 and B. Peters, Handbuch fiir Physik XLXI/Z (1967) 551 C. Calan and S. Glashow, Phys. Rev. Lett. 20 (1968) 779 H. Bergeson, J. Kenffel, M. Larson, E. Martin and G. Mason, Phys. Rev. Lett. 19 (1967) 1487 Z. Fujii, S. lida, Y. Kamiya, S. Kawaguchi and A. Takenaka, Nuovo Cim. Lett. 1 (1969) 845 P. Mackeown, S. Said, J. Wdowczyk, and A. Wolfendale, Proc. 9th Int. Conf. cosmic rays, London, 1965 P. Hayman and A. Wolfendale, Nature 195 (1962) 166 B. Rastin, S. Baber, R. Bull and W. Nash, Proc. 9th Int. Conf. cosmic rays, London, 1965 L. Voldova and G. Zatsepin, Proc. 9th Conf. cosmic rays, London, 1965 P. Meyer, Arm. Rev. Astr. and Aph. 7 (1969) 1 A. Duperier, Proc. Phys. Sot. A62 (1949) 684 P. Tanskanen, Ann. Acad. Sci Fennicae A.VI (1965) 185 J. Kangas, H. Kananen and J. Kokkeniemi, Geophysics 9 (1967) 321 G. Fowler and A. Wolfendale, Handbuch der Physik XLVI/l (1961) 272 J. Quenby, Handbuch der Physik XLVI/Z (1967) 310 A. Fenton, K. MacCracken, D. Rose and B. Wilson, Can. J. Phys. 37 (1959) 970 A. Subramanian, S. Naranan, P. Ramana Murthy, A. Sahiar and S. Lal, Nuovo Cim.7 (1958) 110 M. Conversi, Phys. Rev. 79 (1950) 749 E. Fermi and E. Teller, Phys. Rev. 72 (1947) 399 V. Zinov, A. Konin and A. Mukhin, Sov. J. Nucl. Phys. 2 (1966) 613 H. Daniel, H. Koch, G. Poelz, H. Schmitt, L. Tauscher, G. Backenstoss and S. Charalambus, Phys. Lett. 26B (1968) 281 L. Tauscher, G. Backenstoss, S. Charalambus, H. Daniel, H. Koch, G. Poelz and H. Schmitt, Phys. Lett. 27A (1968) 581 G. Grin and R. Kunselman, Phys. Lett. 31B (1969) 116 V. Zinov, A. Konin, A. Mukhin and R. Polyakova, Sov. J. Nucl. Phys. 5 (1967) 420 J. Sens, R. Swanson, V. Telegdi and D. Yovanovitch, Nuovo Cim. 7 (1958) 536 J. Lathrop, R. Lundy, R. Swanson, V. Telegdi and D. Yovanovitch, Nuovo Cim. IS (1960) 83 1 P. Astbury, P. Hattersley, H. Mussain, M. Kemp and H. Muirhead, Nuovo Cim. I8 (1960) 1267 M. Eckhause, T. Filippas, R. Sutton, R. Welsh and T. A. Romanowski, Nuovo Cim. 24 (1962) 666 W. Knight, L. Stannart, F. Oppenheimer, F. Rickey and K. Wilson, Nuovo Cim. 32 (1964) 598 J. Baijal, J. Diaz, S. Kaplan and R. Pyle, Nuovo Cim. 30 (1963) 711 M. Y. Au-Yang and M. Cohen, Phys. Rev. 174 (1968) 468 L. Pauling, The nature of the chemical bond (Cornell Univ. Press, Ithaca, 1960) A. Weissenberg, Muons (North-Holland, Amsterdam, 1967) W. Bertram, R. Reiter, T. A. Romanowski and R. Sutton, Phys. Rev. Lett. 5 (1960) 61 W. Cramer, V. Telegdi, R. Winston and R. Lundy, Nuovo Cim. 24 (1962) 546 H. Tolhoek and J. Luyten, Nucl. Phys. 3 (1957) 679 G. Backenstoss, S. Charalambus, W. Hamilton, H. Koch and P. Povel, Phys. Lett. to be published H. Morinaga and W. Fry, Nuovo Cim. 10 (1953) 308 P. Singer, Nuovo Cim. 23 (1962) 669 P. Singer, Phys. Rev. 124 (1961) 1602 A. Turkevich and S. Fung, Phys. Rev. 92 (1953) 521 L. Winsberg, Phys. Rev. 95 (1954) 205 H. Backe, R. Engfer, U. Jahnke, E. Kankeleit, K. Lindenberger, C. Petijean, W. Schriider, H. Walter and K. Wien, in High-energy physics and nuclear capture (Plenum Press, New York, 1970) p. 169 R. Cohen, S. Devons and A. Kanaris, Nucl. Phys. 57 (1964) 255 E. Bramlitt and R. Fink, Phys. Rev. 131 (1963) 2649 P. Gray, A. Zander and T. Ebrey, Nucl. Phys. 62 (1965) 172 R. Davis, S. Haraner and K. Hoffman, Phys. Rev. Lett. 20 (1968) 1205 J. Bahcall, Phys. Rev. Lett. 17 (1966) 398 J. Bahcall, N. Bahcall and G. Shaviv, Phys. Rev. Lett. 20 (1968) 1209 J. Mattauch, W. Thiele and A. Wapstra, Nucl. Phys. 67 (1965) 1 G. Backenstoss, S. Charalambus, H. Daniel, H. Koch, G. Poelz, H. Schmitt and L. Tauscher Phys. Lett. 25B (1967) 547
or microfilm without written permission
NUCLEAR TRANS~TATION
from the publisher
BY NEGATIVE STOPPED MUONS
AND THE ACTIVITY INDUCED BY THE COSMIC-RAY MUONS
Received 16 November
1970
Abstract: Nuclear transmutation and the involved factors when negative muons are stopped in matter are discussed. Some uncertainties about the atomic capture of muons in compounds and about the neutron emission probability following muon capture still exist. The stopping rate of negative cosmic-ray muons in the atmosphere and in the lithosphere up to large depths is reviewed. The activities of some radioisotopes induced by stopped negative muons in the atmosphere and in the lithosphere are calculated and compared with measurements and other calculations.
Negative muons slowing down in matter are finally captured by the Coulomb field of a nucleus into a Bohr orbit forming a pmesic atom. The muon cascades rapidly, z X0- ’ 1 set, down to the 1s level from which, through the weak interaction, it either decays (1) P- + e-+ii,+v, or is captured by a proton of the nucleus (2, A) p-+(2,
A) -+ (Z-1,
A)‘+v,,
(2)
where a proton changes into a neutron. The major part of 107 MeV liberated by the reaction (2) is carried off by the neutrino. The energy left to the neutron varies from w 5.7 MeV for the proton at rest, to some tens of MeV; this is deter~ned by the momentum balance in the capture process and is sensitive to the momentum of the capturing proton [for the mechanism of reaction (2), see sect. 41. The nucleus (Z- 1, A)* is de-excited mostly by the emission of one or more neutrons. The resultant nuclei are of the type: (Z-l,
A-X),
where
X=
0, 1, 2.. . neutrons.
(3)
Reaction (2) induces nuclear ~ansformations~ which can be followed with presentday technique in the case where resultant nuclei are radioactive. Secondary cosmicray muons bombarding the earth’s atmosphere and the first layer of the earth’s sur+ Present address: Physics Department,
University 145
of Thessaloniki,
Thessaloniki,
Greece.
146
S. CHARALAMBUS
face can induce such types of nuclear transmutations. The problem has been discussed to some extent ‘*“) and measurements were made on 3gC1, 5gFe, lg8Au and 26A1 [refs. “-“)I that were explained by the p- capture process. Calculations of isotope production by pL- should be based on the data given by Kaplan et al. 7, “) which concern the neutron emission probability distribution. However, these data should be carefully used “) (see below, sect. 6). A recent work lo) on the neutron emission distribution should also be considered. The production of isotopes by slow negative muons with emphasis on the isotopic transformations in the earth’s surface induced by stopped cosmic-ray muons is reviewed in the present work. The interaction of high-energy muons with nuclei (photonuclear effect) is not considered here. Production of nucleides (Z - 1, A -X) by cosmic-ray muons depends on many factors, such as negative muon stopping-rate, neutron emission probability, partial Coulomb capture of muons when the target is a compound, etc. While some of these parameters are accurately known, others have uncertainties of up to 50 %. These factors are listed in sect. 2, where the production formula is given, and discussed in the subsequent sections. In the last section an estimation is given of the production of some radioisotopes in the atmosphere and in the lithosphere. 2. Production formula The production or the decay rate, P (atomslsec), of the isotope (Z - 1, A -X), stable or radioactive in equilibrium, in one gram of matter is given by P = I,-(h)f,f,f,
atoms *g-l . set-I,
(4)
where I,,-(h) is the number of negative muons stopped per gram and per second at a depth h,f, is the fraction of stopping muons reaching the 1s muonic level of the target element in the case where the target element is one of the constituents of the compound (see sect. 4),fd is the fraction of muons captured by the nucleus from the 1s muonic level; the rest are decayed, and f, is the probability of production of the nucleide (Z-1,&X) f rom the nucleus (Z- 1, A)* by the emission of n neutrons. In the following we shall discuss the parameters of this formula. 3. Stopping rate of negative cosmic-ray muons The negative muon stopping rate versus depth relation, Ip- (h), can be derived from an experimental vertical intensity-depth curve for muons by taking into account the dependence of the intensity on the zenith angle and the p- to pc++p- charge ratio. We discuss briefly the parameters involved and present a stopping rate versus depth curve. Finally, since some of the induced radioisotopes may have short half-lives and are therefore affected by the variation of the cosmic-ray muons, we list the factors which should be taken into account.
NUCLEAR 3.1. MUON
INTENSITY-DEPTH
147
TRANSMUTATION
RELATION
The average intensity of muons is well known in the earth’s atmosphere up to a depth of 1200 m of rock and 1000 m of water. Takagi and Tanaka “) have derived a stopped muon-depth curve up to 100 metre water equivalent (mwe). Their calculations for depths between 10 and 100 mwe are made by the differentiation of the depthCosmic-ray
TABLE 1 muon vertical intensity 1, and n values for the angular Is = I, cos” B dependence in the calculation of the stopping rate of negative muons Depths @we) 500 816 850 1000 1574 1812 2000 3000 4000 4100
1, muons/cm2 +sec. sr 1.2 x 10-S
1.5 x10-6
1.4 x to-7 2.6 x 1O-8 6.2x 1O-9
used
n
1.85 1.93 *0.22 2.3 f0.3 2.25 3.06f0.10 3.03+0.16 3.2 4.2 4.8 5.12+0.82
1-q I*) 19) I’)
I’)
The IV values are taken from a curve given by Ramana Murthy et al. M* 16).
depth in rock
Fig. 1. Stopping rate of negative muons as a function of depth. d are due to Bardon and Slade ‘a) and -/- is due to Short 13).
148
S. CHARALAMBUS
intensity curve for cosmic-ray muons given by Hayakawa et al. “). At these depths their results are in fair agreement with the experimental findings given by Bardon and Slade 12) for 60 mwe depth and those given by Short 13) for a depth of 58 mwe and with the calculations of the latter based on the momentum spectrum of muons at sea level and the variation of this spectrum with the zenith angle. For depths less than 10 mwe, Takagi and Tanaka adopted the range spectrum of muons given by Rossi 14), applying a correction factor for the difference between the stopping power of the atmosphere and the rock. The two parts of the curve by Takagi and Tanaka are normalized for a depth of 10 mwe to 6.2 x 10s6 g-l * set-‘. For depths > lo2 mwe, we calculate the stopping rate using the vertical intensity-depths values I, given by Miyake et al. 15*16) and for the angular distribution, we assume the & = I, COS”0 dependence. Experimental values of n are given in table 1 [refs. “-“)]. A weighed curve of n versus depth was drawn through the experimental points and from this the n-values used in the calculation are taken; these are also shown in table 1. The overall depth of the muon stopping-rate curve so obtained is given in fig. 1 +. The experimental findings of Bardon and Slade and of Short for the 60 mwe depth are also given for comparison. The values of stopping rate are found from this curve to be higher by a factor of about two than those given by the emulsion technique 20-22) for depths up to 60 mwe. Short gives the following explanation: “The glass of the glass-backed emulsions restricts the search for a meson to the emulsion layer in which it stops, so that mesons are easily missed”. Discrepancies up to an or&r of magnitude exist between the present curve and the one given by La1 2V23). Recently, Calland and Glashow 24), on the basis of measurements at large depths performed by the Utah neutrino group of Bergeson et al. 2’) who found deviations from the set 8 law of Barrett et al. I’), proposed that “all cosmic-ray muons are not really muons”. This reasoning is not proved as yet. Therefore the U-particles of Calland-Glashow are not taken into account here. But if it were true, it would affect the stopping muon rate, particularly at large depths. 3.2. NEGATIVE-POSITIVE
MUON
RATIO
Since the primary cosmic-ray radiation consists about 90 % of protons, the excess of positive charge is transmitted to the first secondary x and K mesons and through these ultimately to the muons. The charge ratio of cosmic-ray muons has been measured by many authors. The charge ratio is measured precisely as a function of the momentum of muons, since this can give information on the nature of very highenergy interactions not yet attainable with accelerators. For the present work, the momentum dependence is also interesting to investigate, because, if it exists, it will change the charge ratio with depth. The Nagoya cosmic-ray group has recently published 26) results on the charge ratio obtained with a large magnet spectrometer and they included also data obtained from other laboratories. The authors conclude that t The curve of fig. 1 is for the negative muons. To obtain the muon curve, p+ +p-, multiplied by a factor 2.27.
it must be
NUCLEAR
TRANSMUTATION
149
the ratio of positive-to-negative muons in the range between 20 to 500 GeV/c is almost constant, with a mean value of 1.293+0.019. The charge ratio between 40 and 80 GeV/c seems to be slightly smaller than elsewhere. The above results refer to large zenith angles. Although Mackeown et al. “) have studied a large number of published data for different zenith angles, they have not found so far any marked dependence on the zenith angle. They have shown, for instant e, that the ratio of charge ratio for 80” and 0” decreases with increasing momentum. But the deviation from unity at high momenta is of the order of 10 % and can be neglected. This phenomenon is explained by the K/n ratio. Contrary to the results of the Nagoya group, early studies of momenta above 100 GeV/c have shown that the charge ratio increases with the momentum. Haymann and Wolfendale ‘“) and Rastin et al. “) give ratios 1.61 at 240 GeV/c and 1.45 at 290 GeV/c, respectively. The variation of charge ratio with momentum could be explained by the K/Z ratio as well as by K+/K- [ref. 3 O)]. But since the statistical errors of charge ratio at such high energies are very large, we allow for the omission of the variation of charge ratio with momentum, which is consistent with the conclusions of the Nagoya group. We have used the value pL+/p- = 1.27 + 0.05 for the p- stopped curve. Using the total muons stopping rate and the p-/(p’ +p-) ratio, we obtained the curve in fig. 1 for the negative muons stopping rate in rocks as a function of depth. 3.3. MUONS
STOPPED IN THE ATMOSPHERE
The negative muons stopping rate in air, at sea level and at geomagnetic latitudes of about 40” is calculated to be (0.56+0.06) * lo- 5 g-l . set-I. This value is obtained by using the experimental findings of stopped muons given by Bardon and Slade I’) and a charge ratio of 1.27. This stopping rate agrees fairly well with the calculated one by Takagi and Tanaka 4), but it is 20 Y0higher than that given by Rama and Hoda ‘). 3.4. VARIATION
OF COSMIC-RAY
MUONS
Muons in cosmic rays are secondaries that are produced in the earth’s atmosphere by the decay of free 7t and K mesons, which are also secondary products of primary cosmic radation interacting with the N and 0 nuclei on top of the earth’s atmosphere. Muons are produced at the average altitude of about 15 km. Their mean life at rest is about 2.2 ps and they reach sea level (still penetrate deep into the earths crust) by time dilation (“mesons paradox” of the special theory of relativity). From the production mechanism, the intensity of muons at a given point must follow the time variation of the galactic component of cosmic radiation. As already shown from studies of the meteorites, the galactic radiation might be considered constant within 10 % for the last 10’ years and constant within a factor of two for the past 10’ years, see for example the review article “Cosmic rays in the galaxy” by Meyer 31). However, small periodic variations exist for the muons that reach the earth’s surface which
150
S. CHARALAMBUS
may influence the production in air of radioisotopes with short half-life, such as 39C1 from 4oAr. Because the muons lose their energy by processes depending on the mass of the atmosphere’s layer, the intensity of ,u-particles at a given point, say at sea level, also depends on the atmospheric conditions (temperature, pressure, etc.) through the Duperier relation 32) . Variation of the stopping rate of muons up to 10 % could be attributed to the pressure variation. 10 % fluctuations are, however, not very important as compared with the overall uncertainties and can be neglected for a first approximation. However, when the other difficulties have been overcome, correction due to pressure variation should be carefully applied, as there exists a kind of hysteresis between /J intensity variation and rapid pressure variation 33*34). The negative correlation between the muon stopping rate and the magnetic storms (Forbush effect) should be look at. This variation depends on the altitude and latitude and its duration is from about 2 hours to 2 days [see review articles 3 5#36)]; deviation from the average stopping rate of muons, at sea level, up to 5 % can be observed 37). Further cycling variations of the stopping rate of muons exist, as diurnal, 27 days and 11 years, but these are much smaller than 5 % and therefore neglected. The “latitude effect” on the flux of slow muons stopping in the atmosphere and in the first layer of the earth’s crust must beincluded. Subramanian et al. 38) compared the ratio of the stopping rate of slow muons at atmospheric depths of 800 g/cm2 and 60 g/cm2 and at a geomagnetic latitude of 2”N with those under similar conditions at 50”N and found that they differ by a factor of three [see also Conversi “‘)I. 4. The chemical compound effect factor When the target is a chemical compound it implies the problem of the partial atomic capture probability of negative muons by the constituent atoms of the compound. Fermi and Teller 40) predicted, “ . . . by crude estimates . . .“, that the relative atomic capture probability should be proportional to the Z-ratio, weighed by the atomic concentration. They arrived at the so-called “Fermi-Teller Z-law”, assuming that the probability of atomic capture is proportional to the energy loss of very slow muons near the various atomic species. This was computed by Fermi and Teller and found to be proportional to Z. Following Fermi and Teller, the chemical compound effect factor for the constituent n will be:
(fc). =
6% alZ,+a2Z2+.
..
+a,z, ’
where the a are the atomic concentrations in the molecule. Many experimental studies made in the past on the atomic capture of negative muons in compounds, revealed strong “solid-state or chemical” effects. The atomic capture of muons takes place at very high quantum numbers corresponding to stationary levels, which are common to the entire molecule, and solid-state effects cannot be neglected. Measurements made on the intensity ratio between the same ,u-mesonic
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transition of the same element but in targets of different chemical composition or different physical states showed that there exist differences 41 -44). Quantitative data of the relative number of muons reaching the Is level in the constituentsof a compound were obtained by Zinov et al. 41, 4s) by the method of X-mesonic-rays. The results of Zinov et al. showed some regularities. They found, for instance, that the ratio of probabilities of atomic capture in oxides varies periodically with increasing nuclear charge according to the periods of the table of elements. They also found that the ratio of probabilities of atomic capture in compounds of metals with halogens and in alloys of metals is described satisfactorily by Z o.66. However, the results of Zinov et al. do not agree with those obtained by other experimental methods (seeappendix 1). Sens et al. 46) deduced the relative number of muons reaching the 1s level in the constituents of a compound by measuring the time distribution of decay electrons emerging from a chemical compound in which muons are brought to rest. In analysing the decay curves and knowing the characteristic lifetime of pL- in the individual constituents of the compound, they found the relative population at 1s level. In their results on insulators the prediction of Fermi and Teller does not hold and they suggest that the atomic capture of muons occurs in proportion to the atomic concentration only. Their results might be expected to be different from the Z-law because the Brillouin gap in the insulators (discussed by Fermi and Teller but finally omitted in their computation) does not allow arbitrary small amounts of energy to be transferred from the stopping muons to the electron of the insulator. Later on, the same group, Lathrop et al. 47), studied ILi (insulator) and found that the ratio for the atomic capture is: I/Li = 15312.0. This ratio is in flat contradiction with the behaviour observed earlier in the insulators, and rather supports the Fermi-Teller law, where I/Li = 17. Using a similar experimental method, Astbury et al. 48) agreed with the Z-law for the case of PbF2. Eckhause et al. 49) found, however, discrepancies for both insulators and alloys. But their results for those insulators studied differ also in the stoichiometric proportion finding of Sens et al. Knight et al. 50) found, from bubble chamber studies, that muon capture is equal to stoichiometric proportion. The chamber was filled with a mixture of CF 3Br and propane. They found that the ratio of capture by light (C, F) and heavy (Br) atoms was almost equal to the ratio of atomic concentration. Another experimental study using the time analysis, but measuring neutrons resulting from p- capture, was performed by Baijal et al. 51). Their results do not present any regularity. Assuming that the ratio of atomic capture probabilities in a binary compound can be described by a relation of the form Cl/C2 = (a,/az)(Zl/Zz )“, they found for their results that n covers the range between 0.5 and 1.5. From the above short description and from appendix 1, where we present most of the up-to-date published data, we see that there does not exist experimentally established regularities on the atomic capture. Further, for the same compounds in some cases there are large differences between the experimental data depending on the method used. The theoretical Fermi-Teller predictions do not, in general, hold with
152
S. CHARALAMBUS
the experimental findings. However, a recent theoretical work by Au-Yang and Cohen [ref. “‘)I seems promising. Their results are in good agreement with some experimental values and can, at least qualitatively, explain the periodicity observed by Zinov et al. The parameter of their model producing the periodicity is the effective charge transfer Z,, a notion obtained from Pauling s3), and this Z, is periodic in atomic number. 5. Nuclear capture probability We need to calculate from the stopped muons what fraction& is captured by the nucleus. Since the muons have a mean life of 2.2 ps, the decays during cascade are fd
1
IP
Fig. 2. Fraction of negative muons captured by the nucleus from the 1s muonic atom level as a function of the atomic number, left scale. Right scale gives the induced activity or the production rate, in atoms per kg and per day.
neglected and the stopped muons are all in the 1s level. Let us call & and 1, the probabilities for decay and for nuclear capture, respectively. Obviously we have:
2, being the probability that the muons stay in the 1s level and r. the mean life of ,uin this level. Well-known experimental values of the Lo exist throughout the periodic system and they have been recently reviewed by Weissenberg 54). The 1, is calculated from eq. (5) using zd = I/&, the mean life of free muons, about 2.2 /E.. Thef, value will then be:f, = &/lo. Using the values of L, and Izofrom Weissenberg’s compilation we trace the smooth curve of fig. 2 (left scale). There is a fine structure of the curve. The nuclear capture of p- is not only a function of Z (especially of Zc”,,) but also of A, “isotopic effect” 5‘15“). It seems moreover that the particular nuclear structure of the target plays a role 57*58). However, comparing the fd with the accuracy of the other factors of formula (4) we find that it is better known by at least an order of magnitude.
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6. Neutron multiplicity distribution After the nuclear capture of muons the compound nucleus (Z - 1, A)* de-excites by the emission of a number of neutrons. The neutron multiplicity distribution, f,, depends on the target nucleus (Z, A) through the momentum of the proton capturing the muon. We will give below a short theoretical consideration and some experimental data on the f,function. 6.1. THEORETICAL
CALCULATION
OF f.
The muon capture is a two-body process (~1~,p). If the proton and muon are at rest, the neutron recoils with about 5.7 MeV of energy and the neutrino carries off the rest, about 100 MeV. But since the capturing proton is in a nucleus, it has a momentum distribution. Hence a large momentum transfer is possible and the formed neutron can recoil with an energy E = f (Z, A) larger than 5.7 MeV. Two possibilities can be assumed here: first, that the neutron escapes directly from the nucleus (direct neutron emission), and second, that this energy E = f(Z, A) is shared between the other nucleons and a compound nucleus (Z- 1, A)* is formed, whose excitation depends on the momentum distribution of the capturing proton. The compound nucleus de-excites mostly by neutron emission. In fact, measurements of the neutron multiplicity give about 1.5 neutrons per muon capture, which indicates that excitation energies are moderate, about 15 MeV. At these excitation energies the nuclei de-excite mostly by neutron emission. It is highly probable that y-rays accompany the neutron emission, about 80 % of the time a muon is captured lo). The emission of protons and charged particles in general occurs very infrequently, 2 y0 of the time for protons and 0.5 % for a-particles 5g); these are not taken into consideration in the present work. The behaviour of excitation distribution of (Z - 1, A)* was given by assuming for the nuclear matter either a Fermi gas momentum distribution, as Kaplan et al. ‘* ‘), or a Gaussian distribution (Brueckner model) as Singer 60). The nuclear excitation was then related to the neutron multiplicity distribution by using the compoundnucleus theory. As pointed out by Singer 61), the direct neutron emission following the muon capture is not negligible. The direct emission must be high for low A, a exp( -bA”), according to the calculations of Singer, where a and b are constant. This emission probability is about 0.22 per muon capture for the silver target. In appendix 2, we give the neutron emission distribution for some elements following Singer’s conception. 6.2. EXPERIMENTAL
DATA
ON f.
(i) The neutron multiplicity distribution can be estimated by radiochemical methods if the products (Z- 1, A-X) are radioactive. The technique requires an intense CL-beam, a single isotope target and a maximum number of radioactive isotopes (Z - 1, A -X). Copper isotopes were identified from the interaction of p- with zinc
S. CHARALAMBUS
154
by Turkevich and Fung 62). They have measured the activity induced in ZnC1, and found a low yield for 6oCu and a high production of 67Cu. Winsberg 63) has measured tellurium isotopes as being the product of the interaction of negative muons with iodine. This quantitative measurement is based on the induced activity of two tellurium isotopes: “‘Te(f,) and lzsTe(fi), from which the production of 126Te(f,) and 124Te(f3) was obtained by ingenious extrapolation. The measurements are limited by the techniques and muon fluxes of 1954. However, except for the zero neutron production, which is the double of Kaplan’s value, as explained below, and in our opinion overestimated, the otherf,, are reasonably induced within &20 %. Neutron emission probabilities Element
PO
PI
Al Si Ca Fe Ag I AlI Pb
7.6 36.0 35.4 18.9 6.2 4.2 11.0 0.6
82.0 46.0 57.2 59.8 48.7 70.5 37.7 59.1
TABLE 2 resulting from the data by MacDonald PI -
6.2 21.0 9.2 9.1 28.3 9.2 40.0 23.6
p3
-
20.0 7.4 3.7 16.2 12.6 8.0 3.6 5.1
p4 38.0 4.4 4.4 - 9.3 10.3 7.0 5.3 12.4
PS -33.0 0.0 0.0 4.1 -6.3 0.4 3.1 0.0
et al. s) p.S 10.8 0.0 0.0 0.0 3.9 0.0 1.2 0.0
(ii) Kaplan et al. ‘* * ) have measured directly the neutron multiplicity distribution with a high-efficiency neutron detector. In principle, these results should be unambiguous. They nevertheless appear to have been misinterpreted owing to the manner the data were presented. Kaplan commented subsequently on this “). To obtain the neutron emission probability P, from Kaplan’s results, the following expression should be applied: bnax
P,
=
c
~“&-~(-llr-“(l-&E)n-“~),
which can be found by solving for P,, eq. (8) of the paper + by MacDonald et al. “). The F,, is the probability for the observed n neutrons and E is the neutron detection efficiency which is equal to 0.545. Using this expression and Kaplan’s data for F,, the neutron emission probabilities in table 2 were found. We see that the one-neutron emission probability is high, of the order of 60 ‘A, while the P, is low, except for Si, Co and Fe targets. (iii) Backenstoss et al. lo ) have measured the nuclear y-ray after muon capture in several targets. These y-rays occur when the neutron, after the muon capture, leaves the nuclei in an excited state. It was pointed out that the frequency with which the nuclei are left in an excited state after the neutron emission is high: almost 80 % of the + We have used in this paragraph the notation given by MacDonald corresponds to the f. of the present paper.
et al. 8). It is obvious that P,
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nuclei in which a muon was captured emitted y-lays. Compared with the neutron measurement, the investigation of y-rays has the advantage that the probability of zero neutron emission can be measured directly, and the disadvantage that neutron emission leading to the ground states of the final nucleus cannot be observed. The y-ray measurements must be considered as complementary to the neutrons: but owing to the fact that for almost every neutron emitted we have a y-ray, the identification of this allows one to deduce neutron emission probabilities. It is concluded from the results by Backenstoss et al. that the zero neutron emission probability is negligible and that the single-neutron emission is larger than 50 %. For the zero neutron emission, Backe et al. 64) also find no excited states for a europium target and Cohen et al. 65) found only 1.6 y0 formation of 16N following the p-capture in 160. TABLE 3 Proposed neutron emission probabilities Neutrons emitted
0
fil
0.10 <
6.3. CONCLUSIONS
1
0.60-0.70
for practical applications 2
0.15-0.20
3
0.05
4
0.02
ABOUT fn
From subsects. 6.1 and 6.2 it can be concluded that both the theoretical calculations and experimental data on neutron emission probabilities f, are still ambiguous. Leaving aside the notion that the form off, must depend on (2, A) and bearing in mind the results by Kaplan et al. as presented in table 2, as well as the results by Backenstoss et al., and the high direct neutron emission following the calculation by Singer, we propose forf,, for the purpose of general approximation, the values given in table 3. 7. Applications The above findings can be applied to the nuclear transmutation induced by cosmicray muons in both the atmosphere and the earth’s crust. As a guide for estimating the induced activity by negative cosmic-ray muons at depths underground corresponding to a few metres of water equivalent, we present the curve in fig. 2 (right scale). This gives the induced activity versus Z. We have selected this depth because the muons (and neutrinos) are the only survivors of the cosmic-ray particles and also because the muons reach their maximum stopping rate there (see fig. 1). This curve shows the activity at saturation (as well as the production rate) - atoms decayed (or produced) per kg and per day - for the product isotope resulting from the emission of a single neutron. To calculate the curve we assumed that fnE1 = 0.60, that the target has a single isotope, and that it is in a pure uncompound chemical state. As an estimation
156
S. CHARALAMBUS
of the overall production error for the optimum cases (uncompound target, experimental values off,, activation at a greater depth, etc.) gives a value of the order of 25 %. The only radioisotope produced by pFL-stopped in the earth’s atmosphere in quantities measurable with present-day techniques is 3gC1. This is produced by p- from 40Ar(p, n)” gC1+. The 40Ar nucleus is a suitable target because it represents about 1 % of the atmosphere and also because, for it, the factorfd is about 0.80. On the other hand, 3gC1 is a one-neutron emission product. By analysing rain water, Winsberg “) found 3 gC1 and proposed that it was mainly produced by cosmic-ray negative muons from 40Ar in the atmosphere. He found for the activity of 3gC1 at saturation about 500 dpm over a rain collection of 300 m2. This value is about an order of magnitude lower than that calculated by him. Since several meteorolo,gical factors determine the fate of 3gC1 after its formation, it is difficult to define a production rate from these results. Rama and Honda “) have measured 3‘Cl induced by muons and neutrons in laboratory 40Ar at sea level. They found that the activity at saturation was 0.2f0.02 atoms * kg-l * min -I. From our calculations we find that the activity at saturation due to only the p- component is 0.18 &0.04 atoms - kg-l - min- l which is about 50 % higher than that calculated by Takagi and Tanaka “). Rama and Honda “) have measured and calculated the activity of l’sAu+ “‘Au induced by cosmic-ray muons and neutrons at sea level or else at a mountain altitude of 685 g/cm2 in laboratory mercury. In comparing the induced activities at the two depths, using a neutron flux at 685 g/cm2, eleven times higher than that at sea level and using a factor of four for the stopping muons, they found for “*A + “‘Au a production rate of 0.06+_0.01 atoms - kg-l - min -I. They used for the calculation 4.35 x 10e6 ,u- stopped g-l - set-‘. They calculated for l’sAu+’ “Au an activity induced by p- at sea level of 0.087 atoms - kg-’ - min-‘. Our calculation gives 0.11 kO.03 atoms * kg-l * mine1 using thef, distribution given in table 4, the natural isotopic composition of mercury and 5.6 x lo- 6 ,u- stoppzd/g * sec. With our model of small probability product for zero neutron emission we do not agree with Takagi and Tanaka “) for the calculated activities of 32P and 5gFe induced by cosmic-ray muons in 32S and 5‘Co respectively. They have found 0.15 + 0.08 and 0.1610.08 atoms * kg-’ - min-’ for “P and 5‘Fe, respectively; our calculation gives activities of the order of 0.03 and 0.04 atoms - kg- l - min- 1 for 32P and “Fe, respectively. A search for 2 6A1 (T = 7.4 x lo5 y) induced by cosmic-ray muons in terrestrial silicate rocks was made by Tanaka et al. “) using a low-level yy coincidence spectrometer. They found from the measurements 0.02fO. 12 dpm/lO kg Si02 for the actual surface rock and 0.00+0.08 dpm/lO kg Si02 for the rock at 24 mwe depth. No clear evidence for muon-induced 26A1 could be demonstrated. Tanaka et al. have treated t 39CI can also be produced in the atmosphere from 40Ar by cosmic-ray neutrons, (n, np) reaction. The cross section of the reaction (n, np)- (n, np) 3 (n, np)+ (n, np)+ (n, d) - is in general high x 200 mb at 14.7 MeV [ref. 66)]. In a few cases u is small. The o in the case of 40Ar was measured at 14.7 MeV [ref. 67)] and found to be 2.9kO.5 mb.
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about 80 kg of rock from the surface sample, extracting A1203. They suggest that an important improvement for determining ’ 6A1 in silicate rocks can be achieved in two different ways: either by producing chemically pure Al counting samples instead of Al, O3 or by using large counting devices, NaI crystal larger than 7.6 cm x 7.6 cm. Our calculation of “Al production in ‘ ‘surface” rocks gives a rate of 0.13 f 0.04 dpm/ 10 kg Si02. We used the following values:_&=, = 0.20 andf, = 0.33, assuming that Si02 remained all the time in the past under some few mwe’s underground. La1 “) proposed to carry out neutrino and antineutrino measurements from the activity these particles induce in terrestrial materials. The particular physics interest, as well as the advantages and disadvantages of v and ? measurements using this method, are thoroughly discussed in Lal’s paper. The interest is focused on the measurements of 37Ar (35 d) - initially proposed by Pontecorvo) - and of 39Ar (270 y) induced in KC1 by neutrino and antineutrino: v+~~C~ --t 37Ar+e-,
Y+39K + 39Ar+e’.
Argon must be separated from large amounts of sylvite deposits in saline mines, in Stassfurt, Germany, for example. However, 37Ar and 39Ar could also be produced in sylvite by stopped negative muons (muon capture by 39!K and emission of two neutrons and the zero neutron, respectively). To avoid interference from stopped muons the sylvite must come from layers deep underground and the noble gas separation be made at more or less the same depth. In the following, we calculate the 37Ar activities due to neutrinos and stopped muons in sylvite: Davis et al. 68) found with their famous neutrino experiment that the upper limit of the product of the neutrino flux over the cross section for all known sources of solar neutrinos is: x(&0)
= 3 x 1O-36 set-l
per 37C1 atom.
This experimental value is an order of magnitude smaller than the theoretical one calculated by Bahcall 69, 7O), based on the current ideas concerning the way of fusion reactions producing the luminosity of the sun. Using the upper limit given by Davis, we find a production by the neutrinos of about 7 x 10e4 of 37Ar atoms per ton of sylvite per day. The 37Ar and 39Ar induced activity at saturation due to muons is calculated using the muon stopping rate versus depth (fig. 1) and f.= o = 0.1, fnZ2 = 0.15 andf, = 0.5. It is obvious that these productions follow the behaviour shown in fig. 1, multiplying only the scale of stopped muons by a factor of 0.046 for 39Ar and by 0.07 for 37Ar. The production rate per ton of sylvite per day at 1000 mwe is: 0.15 3‘Ar and 0.10 39Ar, while at 4000 mwe these rates are lower by a factor of more than 10e3. At a depth of about 2300 mwe the production rate of 37Ar due to stopped muons is equal to that due to neutrinos. The present work aims at showing some limits only; it does not intend to plan a neutrino and antineutrino spectroscopy by the radiochemistry method. If one day a bold and “adventurous” searcher undertakes this job, he will have to calculate carefully the factors involved, many of which are discussed in Lal’s paper.
158
S. CHARALAMBUS
8. Conclusions
The above analysis showed that the behaviour of muons stopped in matter and captured by the nucleus is at present well known. However, while some of the factors determining the phenomenon are accurately known, the large uncertainties for other factors still exist. The following remarks concern the uncertainties in question. (i) It is not yet clear what exactly happens during the atomic capture of negative muons when the target atom is the constituent of a compound. (ii) Thef, neutron emission probability function is ambiguous. We saw that the zero neutron emission is small, < 0.10, while the f,= 1 is predominant. It is certain thatf, is a function of (Z, A) of the target. We propose, however, to use in practice the values given in table 3. The changes induced in the lithosphere could be useful for studying geophysica1 processes, such as erosion of surface rocks. They could also be useful for estimating, by means of muon compound, the high-energy cosmic-ray fluxes in the past [see La1 and Peters ‘“)I. M ore measurements of 26A1in silicate rocks with improved techniques are necessary. In the case of neutrino and antineutrino spectroscopy by induced activity in sylvite, serious difficulties might arise from the production of 37Ar and 3gAr by stopped muons. It will be interesting from many physics points of view to undertake measurements of 3‘Ar and 3‘Ar in sylvite deposited at various depths. To eliminate uncertainties resulting from chemical effects and neutron emission distribution, a thorough study of the production of 37Ar and 3gAr in sylvite by muons from the accelerators should be undertaken. Appendix 1
In table Al most of the up-to-date published data (column 4) on the relative number of negative muons reaching the 1s level in the constituents of a compound are given. Appendix 2
We present in table A2 the neutron emission distribution for some elements following Singei’s conceptions 60). The following parameters were used: nuclear parameter a2/2M = 20 MeV, nuclear temperature = 0.75 MeV and effective nucleon mass M* = 0.5 M in Singer’s formulation for the evaporation contribution. In the calculation, his direct neutron emission was also included. The neutron binding energy and mass difference A, _ 1 -A, were taken from Mattauch et al. “). The direct neutron emission (and consequently the total neutron emission distribution) is sensitive to the nuclear radius. In the calculations we used R = R,A* with R. = 1.4 fm. If particular experimental radii will be used, deviations up to 10 % could be found. For example the second line for aluminium (:iAl*) is calculated using the electromagnetic
NUCLEAR
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TABLB Al Compound 1
Ratio 2
Fermi-Teller prediction 3
Observed 4
Stoichiomet~~ ratio 5
Sens et al. 46)
p205 A1203
SiOz KOH KHFz Cs Hq Clz liq. Cs H4 Cl, sol. CCI‘$
p/o
Al/O SijO
K/O K/F Cl/C Cl/C Cl/C
0.15 1.08 0.87 2.38 1.05 0.94 0.94 11.3
0.371 fO.041 0.435~0.038 0.386&0.025 0.455+o.os3 O.S88&0.138 0.435 *0.03s 0.476 &to.045 4.1 10.8
0.4 0.66 0.55 1.0 0.5 0.33 0.33 4.0
15.8 zh2.0 2.2 kO.7
1.0 1.0
4.8
0.5
Lathrop et al. 47) I/Li
LiI AgZn
AglZn
17.7 1.57
PbF2
Pb/F
4.5
BiFB
Bi/F
UFI CuAIz
U/F CuiAl
3.1 2.6 1.1
NaF CaCls Cd12 AgI PbIz NaCI KI LiF NaI PbClz PbFa
F/Na Cl/Ca Cd/I
Astbury et nl. 48) &0.7
Eckhause et al. 4g) 1.58 so.15 1.52 10.15 1.75 10.18
0.33 0.25 0.5
0.82 1.7 0.45 0.89 0.77 1.55 2.79 3.0 4.82 2.4 4.5
0.64 1.28 0.5 1.5 0.61 1.22 2.0 3.6 3.4 1.6 2.3
hO.05 10.14 5o.t io.2 10.06 io.11 10.2 10.4 10.4 10.2 10.2
1.0 2.0 0.5 1.0 0.5 1.0 1.0 1.0 1.0 0.5 0.5
OS 0.42 1.5 0.75 1.1 0.88 2.5 1.37 7.2 3.6 3.7 2.5 7.0 5.1 10.2 6.9 3.8
0.12 0.15 0.83 0.29 0.57 0.39 1.36 1.35 7.6 3.6 2.66 I.2 2.27 2.1 5.8 2.9 4.0
10.04 10.03 10.07 +0.02 co.04 AO.03 &O.lO +0.10 11.8 10.4 *0.32 io.1 10.22 iO.2 +0.7 +0.4 *0.4
1.0 0.67 1.0 OS 0.67 0.66 1.0 0.5 2.0 1.0 1.0 OS 1.0 0.5 1.0 0.67 0.33
Zinov et al. 41)
Be0
Ii& PbjI Cl/Na I/K F/Li IjNa Pb/C1 Pb/F Be/O
SiOz CaO TiOz cuz 0 cue ZnO ZrOz BaO PbOz PbO Bi203
B/O Mgto Mgio Al/O SifO CajO Ti/O Cu/O CU/O Zn/O Zr/O Ba/O Pb/O PbjO Bi/O
UOII
UiO
ho3 M@ M&z AL
03
160
S. CHARALAMBUS TABLE
Element
PO
A2
PI
P2
P3
P4
%
14.1
55.9
17.1
12.6
0.3
:;A’*
13.1
59.0
15.9
11.7
6.2
:$Si
17.6
60.4
18.4
3.7
0.0
t:Si
21.4
48.1
24.8
5.4
0.2
;;A1
3oSi 14
16.4
53.0
18.6
11.4
0.5
40Ar 18 39K 19
14.0
48.7
17.7
16.4
3.0
14.7
55.8
19.2
10.1
0.2
:$a
17.6
58.4
19.9
3.9
0.0
s6Fe
17.5
51.7
20.7
9.6
0.5
16.4
45.6
19.6
15.1
3.0
11.0
39.7
23.6
18.7
5.9
26 1271 53
‘i:Bi
rms radius (R = 3.02540.023 fm) from mesonic atoms, as this is given by Backendoss et al. 72). References 1) G. Fowler and A. Wolfendale, Progr. Element. Particle Cosmic Ray Phys. 4 (1958) 107 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22)
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