40
ANALYTICAL CHEMISTRY, VOL. 50, NO. 1, JANUARY 1978
Use of Muonic X Rays for Nondestructive Analysis of Bulk Samples for Low Z Constituents James J. Reidy" University of Mississippi, University. Mississippi 38677
Richard L. Hutson Los Alamos Scientific Laboratory, Los Alamos, New Mexico 87545 Herbert Daniel' and Klaus Springer' Los Alamos Scientific Laboratory, Los Alamos, New Mexico 87545, and Technical University of Munich, 0-8046 Garching, West Germany
Muonic x rays have been used in quantitative analysis on bulk samples of "tissue equivalent" material whose primary constituents are low Zelements ( 2I20). The muonic x-ray spectrum resulting from negative muons stopping in "tissue equivalent" materials has been obtained. Relative muonic x-ray intensltles were determlned and correlated with atomic abundances in these materials. A comparison of the results for the various samples is presented. This work establishes the usefulness of this technique for analyses of gross specimens (1few grams) for elements with 6 5 Z 5 20 and atomic abundances greater than 0.15 YO.
Before the development of meson "factories", the possibility of using muonic x rays for elemental analyses had been suggested ( I , 2). Although some investigators have obtained muonic x-ray spectra from biological materials (3-7) there had been no programmatic effort devoted to studying the feasibility of using the muonic x-ray intensities for nondestructive analyses of materials. However, a program of this type has been initiated at the Clinton P. Anderson Meson Physics Facility (LAMPF) and some of the initial results from the elemental analyses of gross samples are reported here. In addition, it should be noted that the technique reported here is not applicable just a t LAMPF since other accelerators have sufficient muon beam intensity for such studies. Since this is a little known technique, but one with numerous potential applications, a detailed discussion of the physical basis for i t is presented here. Negative muons can be considered as heavy electrons (mass of muon = 207 X mass of the electron) and are produced in the decay of negative pions (mass of pion = 280 x mass of the electron). In the experiments reported here, the negative pions were reaction products obtained when the 800-MeV proton beam from the LAMPF accelerator struck a carbon target. A fraction of the negative pions emanating from this target are guided into the muon beam channel with a series of magnets. The negative pions travel down this 18-m long channel and many of them decay into negative muons during this time. T h e mean life of a negative pion a t rest is 2.55 X s. Near the end of the muon channel, a series of magnets is used to separate the negative muons from the rest of the beam and the resulting beam of negative muons is focused onto a sample of the material being analyzed. Since the mean life of the negative muons is relatively long (2.23 X s), few of them decay before they impinge on this sample. Once Permanent address; Technical University of Munich, D-8046 Garching, West Germany 0003-2700/78/0350-0040$01 OO/O
the muons enter the sample, they slow down by losing energy via ionization and, at the very end of the path, by collisions with the electron "Fermi gas". In this way the negative muon acts just like a heavy electron. One consequence of this is the straggle in the range of the muon is less than for an electron of the same range. At the end of its range, the negative muon is captured by an atom. Although the details of this capture process are not well understood, it is reasonable to picture the muon being captured into an orbit near the outer valence electrons. It then cascades down through the electron cloud via transitions between muonic atom Bohr orbits. The meson loses energy during this process, mainly by transferring energy to orbital electrons which are ejected from the atom (Auger electrons). The resulting vacancies tend to fill fairly rapidly, a t least in solids and liquids, so the electron cloud does not change appreciably during this process. However, once the muon occupies a level within the first electronic Bohr orbit (corresponding to a principal quantum number for the muonic Bohr orbit of -&= 14), the Auger process becomes less likely and, instead, the muon loses energy via electromagnetic transitions. These transitions are called muonic x rays. From an elemental sample in which muons have stopped, one observes series of muonic x-ray lines which are characteristic of the element and are analogous to the series of electronic x-ray lines observed in x-ray fluorescence on the same sample. Thus, one obtains the muonic Lyman series, Balmer series, etc. However, the energy of a member of the muonic x-ray series is over 200 times greater than the corresponding electronic x ray! This arises primarily from the muon being over 200 times as massive as the electron. For example, the energy of the 2p-1s transition (Kcu) in muonic oxygen is 133.5 keV whereas the Kcu electronic x ray in oxygen is 0.525 keV; in carbon, the muonic KO transition is 75.3 keV compared to the Kcu electronic value of 0.277 keV. Essentially all the negative muons eventually reach the muonic atom Is state where they remain until they are either captured by the nucleus or decay into an energetic electron and two neutrinos. The exception to this is muonic hydrogen. For a gaseous mixture containing hydrogen it has been shown (8,9) that the muons are not retained by the hydrogen but instead are transferred to the higher 2 constituents before they decay. It follows that the total intensity of the muonic Lyman series from an element is equal to the number of muons ultimately captured by that element. Thus, we find that characteristic muonic x rays are emitted from a sample in which negative muons have stopped, these x rays have an energy over 200 times the analogous electronic x rays and the total muonic Lyman intensity is equal to the number of muons captured
c 1977 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 50, NO. 1 , JANUARY
by a given element. T h e relatively high energy of the characteristic x rays from low 2 elements raises the possibility of using negative muon atomic capture especially t o obtain, with nondestructive analysis, low 2 elemental abundances in gross samples. For example, it takes nearly 4 cm of water to attenuate the muonic Kcu carbon line by a factor of two. Consequently, carbon imbedded in a bulk sample may be readily detected. Furthermore, this technique is nondestructive and no special source preparation is necessary. One merely places the bulk sample in the negative muon beam and, using suitable detector systems, records the muonic x-ray spectra. With suitable collimation or tracing ( l ) ,it should be possible to interrogate the sample for elemental distribution as well. In order to exploit this technique for quantitative analysis, one must have some way of correlating the number of muonic x rays from a single element in a multielement sample with the relative abundance of t h a t element in the sample. This requires a means of determining the relative probability for a muon t o be captured by a given type of atom. Attempts have been made t o calculate this probability (9-12) but, as the exact nature of the capture mechanism is not completely understood, these attempts have met with limited success. Certainly the total capture probability by a n element is affected strongly by the atomic number 2 and the abundance of the element in the sample. A simple theory which enables one t o calclulate this capture probability was proposed by Fermi and Teller (10) and their results are often referred t o as the “2-law”. This “2-law” states that the capture probability is proportional t o 2 times the concentration of the atoms of that element present in the sample. Different relative capture probabilities have been obtained by Haff e t al. (11) and Daniel (12) but for mixtures of low 2 elements (2 5 lo), the results are similar. It is well known that the 2-law, although serving as a guide, does not exactly predict capture ratios ( 1 1 , 12). Furthermore, the observed muonic x-ray intensities are not expected to be directly correlated with the capture probabilities, especially in compounds containing hydrogen. This is due t o the apparently unique behavior of muonic hydrogen. Instead of the muon decaying after reaching the 1s orbit in hydrogen it is transferred to a nearby heavier atom. This results in additional characteristic muonic x rays from this heavier atom although the original capture was in hydrogen. Consequently, it may be difficult in the general case to correlate the observed muonic x-ray intensities with atomic abundances in a sample. However, for mixtures of low 2 elements, especially in nonordered bulk systems, the deviations from an exact correlation may be smaller than the uncertainties due to absorption corrections and statistical analysis. In samples containing hydrogen, a simple correction for the hydrogen transfer may suffice t o provide adequate correlatim of muonic x-ray intensities with elemental abundance. In order to explore the feasibility of using muonic x-ray analysis (MXA), samples of reasonably well known elemental content were studied. T h e results from negative muons stopping in samples of tissue equivalent liquid and Shonka plastic are presented here. The plastic is often used as “muscle tissue equivalent material” in dosimetry studies and has a fairly well defined composition. Tissue equivalence means that, for a given y-ray flux, the same energy per unit volume will be deposited in the material as in the corresponding type of tissue. The tissue equivalent liquid also has a well defined composition which should closely resemble the elemental composition of muscle (13).
EXPERIMENTAL An arrangement shown schematically in Figure 1 was placed in the beam at the stopped muon channel at LAMPF. The energy
1978
41
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Figure 1. Schematic of experimental arrangement
of the incident muon beam was 110 MeV and the average flux about 90 X lo3 negative muons per second for a 6 - 4 proton beam. With the 5% duty cycle of the machine, this gave an instantaneous flux of about 18 X lo5 8. A t times the proton beam was increased which resulted in a 5070 increase in these flux values. The contamination in the beam was less than 0.17’0 negative pions and about 2% electrons. The samples each had a thickness of 2.0 g/cm2 and were 10 cm wide by 7.5 cm high. They were oriented vertically and 45’ to the beam. This gave a sample area perpendicular t o the beam of 7.1 cm by 7.5 cm and a thickness of 2.8 g/cm2 parallel to the beam. The muon stop rate in the sample was characterized by a 1233 coincidence requirement. By 1233 one means that signals from each of the first three counters must occur within the resolving time of the fast coincidence circuit while no signal must come from counter 4. If one also gets a signal from counter 4 this indicates, in general, that a muon has passed through the sample. The fast coincidence system was of conventional design with a resolving time of lo--@ s. The 1233 rate was maximized by inserting a total of 11.5 cm of polyethylene in the beam. This gave an average stopping rate in the samples of about 4 X lo4 s-’. Scintillator 3 (Figure 1)had an area 7.5 cm x 7.5 cm thereby insuring that a muon passing through this scintillator would hit the sample (except for the small fraction that may scatter). Scintillator 3 was set 5.5 cm from the center of the sample and parts of it could be “seen” by the Ge detector. This resulted in a significant muonic carbon x-ray contribution from muons stopping in this scintillator. By running a “dummy” sample of beryllium (having a thickness of 2 g/cm2) the amount of this background (nonsample) radiation was determined. The germanium detector located 6.5 cm from the center of the sample is an intrinsic device in the shape of a right circular cylinder with a diameter of 35 mm and a thickness of 12 mm. It is housed in a stainless steel cryostat with a 0.025-mm beryllium window. The resolution of the system was 800 eV at 122 keV. The efficiency of the system for a 133 keV x ray originating at the center of the sample was 0.6%. The signal from the germanium detector was amplified and put into a constant fraction discriminator. The output of this discriminator and of the fast coincidence system were used as inputs into a time-to-amplitude converter (TAC). Consequently, the output of the TAC is characterized by a (1233)-Ge coincidence requirement. A discriminator at the output of the TAC allowed one to select the slow coincidence timing range. A resolving time of 70 ns resulted in a uniform range of coincidence from 15 keV to about 2 MeV and a coincidence efficiency greater than 95%. The average count rate a t the output of this discriminator was about 200 s-’. This output was used to gate a Canberra Model 8100 multichannel analyzer. The input to this analyzer was the signal from the germanium detector suitahly amplified and shaped. Data acquisition was followed by subsequent storage on a magnetic tape. Some spectra were accumulated without the (1234)-Ge requirement and instead the analyzer was gated with a pulse obtained from the primary proton beam. The analyzer accumulation rate increased by about a factor of two in this case, primarily because of an increase in the background. The x-ray spectra were analyzed using the Los Alamos version of the y-ray analysis program, GAMANAL ( 2 4 ) . Background corrections were made using the data from the beryllium sample
42
ANALYTICAL CHEMISTRY, VOL. 50, NO. 1, JANUARY 1978
Table I. Relative Muonic X-ray Intensities Element Transition Intensity, %' Shonka plastic C 2p-1s 55 3p-1s 20 4p-1s 11 5p-1s 3.3 6p-1s 0.85 N 2p-1s 2.3 3p-1s 0.76 4p-1s 0.38 5p-1s 0.24 0 2p-1s 3.7 3p-1s 1.3 4p-1s 0.94 5p-1s 0.40 F 2p-1s 0.57 Ca 3d-2p 0.30 2p-lsb 0.38 TE-liquid C 2p-1s 8.5 3p-1s 3.5 4p-1s 1.8 5p-1s 0.87 N 2p-1s 2.2 3p-1s 1.1 4p-1s 0.34 0 2p-1s 48 3p-1s 14 4p-1s 12 5p-1s 5.4 6p-1s 1.8 a See text for a discussion of the uncertainties. Ca(2p-1s) intensity deduced from Ca( 3d-2p) intensity; the uncertainty in this value is approximately 20%. Table 11. Muonic X-ray Energies (keV) EleKCI Kp K7 K6 ment C 75.3 89.2 94.1 96.4 102.4 121.4 128.1 131.2 N 133.5 158.4 167.1 171.1 0 F 168.6 200.0 LP = 135.7 S La = 1 0 0 . 7 LP = 192.0 K La = 142.6 LO = 212.9 La = 158.2 Ca
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runs and source absorption and detector efficiency corrections were applied.
RESULTS AND DISCUSSION T h e intensity values for the muonic x rays from the Shonka
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plastic and a tissue equivalent liquid sample are presented in Table I. In contrast to electronic x-ray spectra, muonic x-ray spectra have many separated lines for the Lyman series. T h e first column lists the element of interest, the second column designates the x-ray transition, and t h e last column gives the measured relative x-ray intensity. Including systematic errors, the overall uncertainty in these values is estimated t o be about 15%. However, within each elemental grouping, the relative uncertainties are about 5 70,except for the carbon series where source absorption corrections lead to a relative uncertainty of about 10%. T h e intensities are normalized so the total corrected Lyman x-ray intensity for each target is 100%. T h e spectrum obtained with the Shonka plastic sample is shown in Figure 2. Besides the C, N, and 0 Lyman series lines the F K a and C a b are also evident. Figure 3 presents the spectrum obtained from the tissue equivalent liquid sample. The titanium lines result from muons stopping in the titanium container. Table I1 lists the energies of the muonic x-ray lines of interest. T h e results for the calculated and measured relative total Lyman series x-ray intensities for the Shonka plastic and tissue equivalent (TE) liquid samples are given in Table 111. Hydrogen cannot be detected by this method so the hydrogen content is not included. Consequently, these intensities are
Table 111. Comparison of Calculated and Measured Muonic X-ray Yields Percentage yield of muonic Lyman x rays Sample Element (Atomic % ) Atomic % Predicted 2-law Modified 2-law Shonka plastic ... ... ... H (58.28 f 0.58) C (37.38 f 0.13) 89.61 f 0.31 86.65 i 0.30 87.99 f 0.30 N ( 1.46 f 0.02) 3.50 i 0.06 3.95 f 0.07 3.76 i 0.06 0 ( 2.43 f 0.16) 5.81 i. 0.37 7.50 t 0.48 6.65 i 0.42 F ( 0.30 i 0.08) 0.72 f 0.18 1.04 f 0.26 0.85 * 0.21 0.36 2 0.09 1.14 f 0.29 0.94 f 0.24 Ca ( 0.15 f 0.04) TE liquid ... ... ... H (63.47 f 0.63) C ( 6.35 * 0.06) 17.56 f 0.18 13.75 t 0.14 14.70 t 0.15 N ( 1.56 * 0.02) 4.29 f 0.04 3.92 i 0.04 5.00 i 0.05 0 (28.38 * 0.31) 78.15 f 0.80 81.60 i 0.82 8 0 . 3 0 + -0.80 S ( 0 . 0 6 f 0.01) 0.16 i 0.03 0.33 f 0.06 ... K ( 0.06 0.01) 0.16 -f. 0.03 0.40 f 0.07 ...
Measured
87.78 f 0.29 3.67 f 0.13 6.48 f 0.25 0.93 I 0.20 0.46 f 0.15
14.12 f 0.55 3.94 i 0.22 81.94 i 0.59 Unobserved Unobserved
ANALYTICAL CHEMISTRY, VOL. 50, NO. 1, JANUARY 1978
normalized so the total Lyman series intensities for all elements heavier than hydrogen equals 100%. Column 1 lists the element and its atomic abundance in percent. The elemental abundances in the Shonka plastic are an average of values obtained by conventional chemical techniques (16, 17) with the Ca and F (in the form of CaF2) percent abundances determined by subtracting the sum of the H , C, N , and 0 percent values from 100%. The elemental abundances in the TE liquid were calculated from the mass of the constituents which were used in preparing the solution. Column 2 gives the calculated total intensity for each Lyman series (except hydrogen) based only on the atomic abundance, column 3 gives the calculated intensity assuming a 2-law correction (lo), column 4 gives the calculated intensity assuming a “modified” 2-law correction, and column 5 lists the values obtained from the measurements. In calculating the values for the intensities, we assumed that those muons which were initially captured by hydrogen are ultimately transferred to the heavier atoms. For the values in column 2, we assumed the number of muons “distributed“ to each atom (heavier than hydrogen) was proportional to the number of heavier atoms present in the sample (Le., the atomic abundance). The values in column 3 were calculated assuming the number transferred was proportional to the atomic number of the atom (Le., capture predicted from the simple 2-law). For the values obtained in column 4, we assumed that the muons were initialy captured in proportion predicted with the 2-law-this includes capture in hydrogen. However, we further assumed that the muons would be transferred from hydrogen to the nearest heavy atom to which the hydrogen is bonded. For the tissue equivalent liquid, we assumed no dissociation. T h e values for C, N, nd 0 in column 5 were derived from the corresponding total intensity of the Lyman series. The value for F was obtained by determining the Ka transition intensity and multiplying this by the factor 1.64 which is the ratio of the total Lyman intensity to the KO intensity for fluorine (18)in C6FI4.We make the assumption that this ratio will be roughly the same for the fluorine (as CaF2) in the Shonka plastic. T h e value for the Ca was obtained by calculating the Ca(Kcu) transition from the measured Ca(La) transition (see Table I) using the factor Ca(La)/Ca(Ka) = 0.80 & 0.08. This ratio was determined in a subsequent measurement on Ca metal. This deduced Kcu intensity was multiplied by the factor 1.21 to obtain the total Lyman intensity. This latter factor had been determined by other investigators for calcium metal (19). T h e qualitative usefulness of this technique is well demonstrated by these results. In addition, the quantitative agreement between the measured values and the calculated values is striking. Most of the measured values are in reasonable agreement with the values calculated by the three different methods. T h e exception is calcium where the measured value is in agreement only with the value calculated solely from the atomic percent abundance. However, the other measured values are in slightly better agreement with the values calculated from the 2-law or modified 2-law. Thus, it is shown that for low 2 elements (6 I 2I 20) one can use the measured muonic Lyman intensities to deduce qualitative elemental composition with a threshold sensitivity of about 0.15%. Quantitatively, the elemental composition can be obtained with good accuracy for 6 5 2 5 9. The accuracy can be as good as a few percent although deviations of the order of 10-15% between the deduced and actual atomic percentages may occur in some cases. However, for many analyses, an accuracy of this order is quite sufficient, particularly for large samples. The precision is much better than this, of course, being of order of a few percent for atomic
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