Photonuclear tritium yields at 90 MeV

Nuclear Physics AI57 (1970) 49-60;

@

North-zodiac

Polishing

Co., Antsierdam

Not to be reproduced by photoprint or microfilm without written permission from the publisher

PHOTONUCLEAR

TRITIUM YIELDS AT 90 MeV

L. A. CURRIE and R. H. RODRfGUEZ-PASQUBS National Bureau of Standards, Washington, D.G. 20234 Received 17 July 1970 Abstract: Photonuclear (r, t> yields have been determined for Al, Zn, Sn and Bi using 90 MeV bremsstrahlung from the NBS electron synchrotron. The National Bureau of Standards P2 ionization chamber was used for primary monitoring of the bremsstrahhmg beam; supplementary C and Cu activation foils, whose absolute yields are reported, were employed for relative intensity measurements. Tritium yields were determined by quantitative extraction from the molten samples with hydrogen carrier followed by activity measurement by means of low-level gas counters. The observed yields were generahy consistent with those of other workers at lower energies. Comparison of the tritium yields with the results of statistical model calculations suggests the predominance of non-evaporative processes in the higher mass region (A 2 100). E

27A1, Zn, Sn, zOsBi(y, t), E = 90 MeV; NUCLEAR REACTIONS measured absolute 3H yield; deduced o-,(90 MeV), a&90 MeV). Statistical model comparison.

1. Introduction + Non-evaporative contributions to the photoproduction of nucleons and small nuclei have been observed by a number of workers, particularly for targets consisting of medium or heavy nuclei for which the statistical ~sumption (high level density) should be quite valid. The aim of the present work has been to explore the importance of such contributions to high-energy phototriton yields. Previous data have been reported for elements having atomic numbers up to 51 and for bremsstrahlung energies up to about 60 MeV [refs. ‘-“)I. The results to be discussed below were obtained with 90 MeV bremsstrahlung from the National Bureau of Standards electron synchrotron and with samples of Al, Zn, Sn and Bi. The samples were selected in order to span the mass range, and because their relatively low melting points would readily permit the chemical extraction of tritium. The experiments were possible only through the combination of quantitative extraction techniques and low-level gas counting which permitted the detection of as few as lo6 tritons, but the precision of the results was nevertheless limited because of the relatively low intensity of the bremsstrahlung and the very small effective cross sections. A slightly modified version of the programs SMLF and YSI supplied by the Darmstadt group 1, ‘), was employed to assess the relative contributions of nuclear t A more detailed report describing this work is availabIe from the authors on request. 49

50

L. A.

CURRlE

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R. H.

RODRkUEZ-PASQU~S

evaporation to our observed yields. As will be shown below, within the uncertainty limits of the experiments and the calculations, the yields for the two lower-2 targets were consistent with the evaporation model, but those for the higher-Z targets implied significant non-evaporative contributions.

2.1. IRRADZATION

samples were irradiated with 90 MeV bremsstra~lu~g produced by the NBS 180 MeV synchrotron. The bremsstrahl~n~ was produced at a tungsten wire target (OS1 mm diameter) and was intercepted by the samples at a distance of 1.84 m behind a collimator having an opening 2.2 cm in diameter. (The sample diameter was about 2.9 cm.) Monitoring of the bremsstrahlung beam was accomplished by means of an NBS P2 ionization chamber “) and by means of copper foils whi& were placed j~ediate~y ahead of and behind the sample. ~o~to~ng precision (using the P2) was estimated to be about 5 y0 under the conditions of the experiment. As will be seen later, overall un~rtainties in the determination of the 3W contents of the irradiated samples were at least as great. Due to the extremely low production rate of tritium it was necessary to irradiate each sample for long periods of time, frequently on an ~nte~ttent schedule. (Fresh carbon and copper foils were supplied for each sample exposure.) The average single irradiation time was about 3 h, and the number of such periods varied from one to six for the various sample. ,The corresponding total time intervals ~from ~n~t~a~to final irra~ation for a given sample) ranged from 1 to 47 d. The beam intensity proved relatively stable during each irradiation period, but the intensities differed s~g~~~nt~y among the various periods (maximum di~ere~~ was a factor of 2.6), although the ~~rnurn feasible intensity was used for each irradiation. A typical bremsstra~~g power density into the sample was about 1.3 mW/cm2. Because of the intermittent schedule and the changing intensity, induced activity had to be corrected by a saturation factor having the form T

s(n)

=

a

f

dt r(t)e’“(T”), 0

where 7’ represents the total elapsed time, and r(b), the relative beam intensity, referred ta the initial intensity. The integral was represented by a sum of just a few terms for 3H, but it required finer subdivisions for the shorter-lived radioisotopes of carbon and copper, The relative beam intensity r(t) was therefore determined by frequent sampling of the charge accumulated by the P2 chamber. Activation monitors were included with the samples for two purposes; (i) to give an estimate of bremss~rahlung absorption by the respective samples (sample thickness varied from 1.2 x 10z3 at~rns~~rnz for Al to 5.60 x 10z2 atoms/cm2 for Bi); (ii) to provide insurance against significant changes in the experimental area which might

PHOTONUCLEAR TRITIUMYIELDS

51

affect the P2 monitoring. This Iatter hazard had to be recognized because of onr lengthy, intermittent irradiation schedule and the concomitant use of the synchrotron for various other experiments, Both of the foregoing applications of the activation monitors depended only upon their relative accuracy, which was found to be quite satisfactory (2-5 7$). Absolute (7, t) yield measurements were based upon the P2 ion chamber. Following Ehhalt ‘), we d&e the absolute yield as,

Y(&)

J5.5 dE N(E,, ~)~(~)

=rf~~.~~__~~~ f

[WMeVf,

(1)

dE N(E,, E)E 0

where: EM equals the maximum value of the bremsstrahlung energy E, NfE,,, E) represents the bremsstrahlung spectrum and a(E) represents the cross section for the reaction of interest. The numerator of eq. (1) may be derived from the observed counting rate once energy independent corrections have been made for the detection efficiency, decay (and intensity variations) and target thickness. Likewise, the denominator derives from the response and sensitivity of the energy detector (P2). Corrections were made for the effects of brcmsstrahlung absorption by the samples, using tabutated values for photon absorption coe~cients IO); the results were observed to be consistent with the observed activity ratios of initial and final monitor foils. TABLE1 Activation monitors “) Reaction 6Q(y,

n)“4Cu

6JCu(y, 2nj6’Cu 12C(y, n)“C

‘tr

Observed yield (90 MeV)

Total uncertainty

12.9 h

0.58 mb/MeV

z!zll%

3.3 h 20.3 min

Y,,/Ys,

= 0.094 b,

39 yb/MeV

xk 3% “12%

“> Yields are based upon the measurement of positon annihilation radiation with a Nal detector, least-squares analysis of the resulting decay curves, and beam power monitoring with the PZ-chamber. b, Relative yield: 6’Cu/6~Cu.

Although the monitor reactions were originally intended for relative measurements, it is of interest to examine their derived absolute yields. The relevant information is summarized in table 1. The estimated uncertainties for the absolute yields (64Cu, “C) are comprised of components arising from counting statistics (decay curve analysis), positon detection efficiency, and brcmsstrahlung monitoring. The uncertainty in the yield ratio, Y6i/Y64, however, contains only the contribution from counting statistics. There are relatively few absolute yield data in the literature for comparison

52

L. A. CURRIE

AND

R. Ii.

RODRfOURZ-PASQUI!.??

in this energy region, but data for the first two yields have been obtained independently by Steinberg using the NBS synchrotron ‘l). His results at 88 MeV were: Yb4 = 0.50 mb/MeV and Ysl/Y64 = 0.094. The uncertainties were probably comparable or somewhat smaller than those shown in table 1. An absolute yield at 90 MeV for llC is given by Bonazzola 12) as 32 pb/MeV. The uncertainty is hard to assess as the result was derived from normalization of Bonazzola’s relative yield curve to Barber’s 13) absolute yield curve at lower energies. Further, Barber’s observations were based upon llC produced in thin (8 mg/cm’) foils of polystyrene, and it is known that l’C may be lost by recoil chemical reactions from thin foils of polymers14). Our ‘IC yield was based upon a relatively thick (163 mg/cm”) polystyrene monitor; we obtained yields with thin (10 mg/cm2) polyethylene monitors which were approximately 5 y0 smaller, The ideal activation monitor is one having the same halt-life and excitation function shape as the reaction product of interest (3H). As this is generally not practicable, we decided to include a set of monitor reactions having different product half-lives and sensitive to different mean bremsstrahlung energies. The general consistency of the results indicates that there were no gross errors arising from bremsstrahlung distortion nor from intensity variations. 2.2. TRITIUM

DETERMINATION

Extraction of the photo-produced tritium was carried out in essentially the same manner as for previous studies of proton-produced tritium ’ “). The irradiated samples were thus introduced into a glass extraction chamber, connected to a glass vacuum line (represented schematically in fig. 1). The chamber, which is surrounded by an PIRANI GAUGE

Fig. 1. Tritium extraction system.

53

PHOTONUCLEAR TRITIUMYIELDS

electric furnace, was evacuated and then filled with carrier hydrogen to a pressure of about 0.6 Torr, (1 Torr = 133.3 N/m’) and the sample was heated above its melting temperature for 3-5 h. The connecting stopcock was then opened in order to expand the gases into a chamber which contained a closed-end palladium tube surrounded by a resistance coil heater. Chemical separation of the tritium was accomplished by means of the selective permeability of the palladium to hydrogen isotopes. Following chemical purification, the tritium-containing hydrogen was quantitatively transferred into a low-level gas counter by means of the Toepler pump. The filling of the detector was then completed to 800 + 5 Torr with argon-helium-isobutane counting gas, fed from the upper part of the line. TABLE2 Tritium counter characteristics Counter

Capacity at 24.4 “C (ml)

Background (min-‘)

Efficiency (%)

A

9.17kO.09

0.32

55.4*2.8

B

4.8040.07

0.19

77.3f3.9

1.86

87.2h4.4

C

46.9 ho.4

Fig. 2. Low-level gas counters. The counters are in order A, B, C from top to bottom of the photograph.

54

L. A.

CURRIE

AND

R. H. RODRfGUEZ-PASQlJiS

Each extraction operation was repeated as necessary in order to ensure that the release of tritum from a given sample was complete. Since experience showed that the counter performance was impaired when the partial pressure of hydrogen in the detector was greater than 120 Torr, the initial carrier gas pressure in the extraction chamber was selected so as to not exceed that final value. Occasionally, experiments (with blanks) had to be repeated because too much dissolved hydrogen evolved from the metal sample upon heating; the initial addition of hydrogen had to be in such cases consequently reduced, since the carrier was provided by the sample itself. Measurements of the extracted tritium were performed in low-background, internal gas-source, cylindrical Geiger-Mueller counters. From fig. 2, one may deduce the dimensions and general construction of the counters. Note that the efficiency of the most sensitive detector (B) has been enhanced by means of a capillary entrance tube. The capacities, background count rates and efficiencies of the detectors are given in table 2; background values were obtained with fillings of pure counting gas at 800 Torr. (Checks were made to assure that the contribution to the blank from the hydrogen used as carrier was negligible.) Counting was carried out in a shield consisting of about 20 cm of iron, an anticoincidence counter umbrella, and about 2.5 cm of mercury. A control routine for counting performance was set up after a very careful study of the counting characteristics of each counter for different filling gas compositions; in actual practice these compositions ranged from pure counting gas mixture to 13 % hydrogen plus 87 % counting mixture. As the varying compositions reflect in the detector performance and also as there are second order sources of variation (i.e., small differences of gas pressure and ambient temperature) observed counting rates were normalized for efficiency using an external 6oCo reference source, which was measured just before and after each sample measurement. The counters were calibrated by means of the NBS tritiated water Standard Reference Material No. 4927 using a standard procedure for reduction 16). The results, which are given in table 2, are believed to have a maximum inaccuracy of + 5%, as deduced from a study of error propagation and differences between the paired calibration results. Every measurement result was corrected for blank rate, counter efficiency and tritium activity decay. 3. Results 3.1. ABSOLUTE

TRITIUM

YIELDS

Absolute yields, as defined by eq. (l), were derived from the observed counting rates of the extracted tritium and the observed rates of charge accumulation by the P2 ionization chamber bremsstrahlung monitor. The experimental yield is given by the ratio of the saturation tritium activity to the incident bremsstrahlung intensity. As the irradiations of several of the samples consisted of a number of discontinuous periods of time, it was necessary to refer both the saturation activity and the beam

PHOTONUCLEAR TRITIUMYIELDS

intensity

to the initial

period.

55

Thus, the effective saturation

activity

is given by,

A, = R/[rlf?%(nz)],

(2)

where R represents the observed tritium counting rate; n, the number of target nuclei per cm2; b, the overall efficiency factor, which is the product of detection efficiency, chemical yield, radioactive decay prior to counting, and bremsstrahlung absorption within the sample; and S(IT), the saturation factor, corrected far intensity variations, as discussed in subsect. 2.1. The bremsstrahlung intensity incident upon the sample was derivtd from the product of the calibration factor for the P2 chamber, 3.84 x lo5 J/C at 90 MeV [ref. “)I; the effective capacitance, 0.6092pF; the observed rate of voltage increase; a correction factor for temperature and pressure changes (taken here to be 1.02 on the average); and a correction factor for bremsstrahlung absorption by the sample. Excluding the last factor, the overall calibration constant was found to be 1.49 x lOr2 MeV/V. Taking sample Al-2, for example, beam transmission by the sample was 0.89, and 174.6 V were accumulated in the irradiation period of 161 min. Thus, the incident bremsstrahlung intensity was 1.814 x 1Ol2 MeV/min.

Irradiation Sample

Bremsstrahlung intensity (g

Sample mass (g)

TABLE3 data and tritium yields R(3H)&S.D. (cpm)

Overall “) efficiency

90 MeV 3H Yield (ztBSD)

WlMeV)

x10’“)

Al-l

0.881

34.57

7.11hO.26

0.794

0.86 (& 6.2 %)

Al-2

1.814

34.54

2.07f0.15

0.794

0.70 (&

Zn

1.177

90.88

0.53&0.09

0.675

0.082 (&22

Sn

1.106

93.34

0.676

0.72 (& 7.9 %)

Bi

0.937

0.491

0.080 (+39

124.7

10.450.5 0.13+0.05

(dpm)

“) Factor including corrections for detection efficiency, hydrogen counting, and sample (bremsstrahlung) absorption.

8.8 %) %)

%)

chemical yield, decay before

A summary of the experimental data for all samples is given in table 3, together with the resulting estimates for the absolute yields for the (y, t) reaction at 90 MeV. The final errors (relative standard deviations) quoted refer to random errors only namely, uncertainties arising from Poisson counting statistics, P2 monitor voltage measurements, and uncertainties associated with tritium recovery and blank contributions. No activity was detected in any of the blanks which were processed. Among the irradiated samples, only Sn required multiple chemical extractions to recover the photonuclear tritium. In the case of Al-l, for example, the net rate for the second

56

L. A. CURRIE

AND

R. H. RODRiGUEZ-PASQUfS

extraction was 0.04 + 0.07 cpm, corresponding to an upper limit (significance level = 0.05) of 2.7 % of the tritium found in the first extraction. Recovery uncertainties were not serious, because the chemical yield was high (w 96 %), but attempts to directly measure individual recoveries of added hydrogen were thwarted by hydrogen evolution from the samples upon fusion. The added hydrogen was about 0.05 mg, whereas the excess hydrogen evolved varied from about 0.02 to 0.3 mg, corresponding to hydrogen concentrations of 0.2 to 6 ppm in the various samples. (Note that this evolved hydrogen frequently prevented the use of the smaller detectors, and, hence, limited the sensitivity of the experiments.) In addition to the above random errors, the results contain systematic errors due to the calibration factor for the ionization chamber and the correction for beam absorption by the samples. The uncertainty in the P2 calibration may be taken as l-2 % [ref. “)I. As the absorption coefficients and the activation cross sections are both energy-dependent, the absorption corrections include some uncertainty which varies with the element irradiated. The estimated limits of systematic error due to these corrections are as follows: Al, kO.4 %; Zn, +3.6 %; Sn, +4.5 %; Bi, f8.5 %. The second aluminum sample (Al-2) was run in order to provide a test of the precision of the overall measurement process. Both the total iradiation time and the total elapsed time were very different than in the case of Al-l, as was the net counting rate. Therefore, important errors depending upon these particular variables might be expected to be seen. The two results are consistent (significance test level = 0.05), however, and the resulting weighted mean is 0.80 (& 5.6 %) pb/MeV. 3.2. STATISTICAL

MODEL COMPARISON

The observed (y, t) yields were compared with the predictions of the statistical model of nuclear reactions as formulated by Blatt and Weisskopf I*). With the exception of the level density formula used, the approach taken by von Buttlar and Huber ‘*‘) was followed precisely. Details will therefore not be repeated here. For the level density in the final nucleus, Q(U), we used the expression Q(U) = const exp [2&J*,

(3)

where U represents the excitation energy of the residual nucleus corrected for the effects of pairing, and a is the level density parameter. Eq. (3) is, perhaps, the most commonly used expression for the level density of an excited nucleus, and it is specifically justified for use at high excitation energies by Porile I’). The level density parameter, a, is frequently taken to be proportional to A (mass number), with the constant of proportionality typically varying from 0.05 to 0.10 [ref. ‘“)I. Following Albert et al. 21), we assumed a value of &A for this parameter, using the values cited in ref. 20) to establish limits for the calculation. The result of the calculation was the triton emission probability (P1) as a function of photon energy in the first stage of decay of the compound nucleus. If sufficient excitation energy remains following the first stage for further particle emission, one

PHOT0NUCLEAR

TFJTIUM

57

YIELDS

must include additional terms for the total probability of triton emission. Such calculations require large, multiple integrals, or a Monte Carlo approach “). In general, however, the emission of the larger, charged fragments is most likely in the first stage of de-excitation, because of the effects of binding energy and Coulomb barriers. For the target nucieides and photon energies of concern in this work, the relative tritium yield coming from the second stage of de-excitation was estimated to amount to about 10 % to 20 %. . In order to compare calculated results with our observations, it was necessary to transform the triton evaporation probabilities into photonuclear yields at 90 MeV. This is ~ompIished by inte~ation using the bremsstrahlung spectrum and the photon absorption cross section a,:

+%f)

= hi WA

=

EM I”dE A$%, , E)o,(E)P,(E) s O EM s0

.

(4)

dE N(E,, E)E

In eq. (4) we have multiplied the yield (pb/MeV) by the bremsstrahlung maximum energy, E,, in order to obtain the effective cross section, or yield per effective quantum, &b). Absorption cross section data (up to about 35 MeV) were taken from the work of Wyckoff, Ziegler, Koch and UhIig *‘), Gavrilov and Lazareva 23), and Jones and Terwilliger 24). Uncertainties or the complete absence of such data

SC 0 40

80

120 tvjA!%

160 200

240

NUMBER

Pig. 3. Experimental (0) and statistical model (x) absolute phototriton yields (90 MeV). Yields, expressed in terms of “effective cross sections” (rub), are plotted versus mass number. Limits for the experimental yields represent rfrone standard deviation; those for the calculated yields correspond to limiting values for the level density parameter (-) and for the photon absorption cross section (c).

58

L. A. CURRIE

AND R. H. RODRiGUEZ-PASQlltk

at high energies, however, required us to take limiting values for c, in the high energy region. Following Wiik ‘) we used a constant extrapolated value for the cross section as an upper limit. For a lower limit we set the absorption cross section to zero above 50 MeV. In fig. 3 the experimental results appear together with those arising from the calculation. The experimental yields quoted in table 3, expressed in terms of effective cross sections, are shown with uncertainty bounds corresponding to k one standard deviation (systematic error limits have not been included). Two sets of bounds have been given for the calculated values: one set corresponding to the uncertainty in the level density parameter, and the other, to the uncertainty in the photon absorption cross section. The central values correspond to the geometric means of the results obtained with the two limiting values for a,, using -&A for the level density parameter. Unlike the experimental uncertainties indicated, the uncertainties in the calculations probably are somewhat correlated from element to element, and therefore the trend of the calculated values with mass number should be considered more accurate than the absolute values. (It should be noted that no normalization has been applied in the figure. Both sets of yields represent independent, absolute values.) With the exception of Sn, it appears that the experimental results lie within the bounds of the model calculation. On the other hand, the general trends versus mass number, which should be less subject to certain systematic errors, appear somewhat discordant. That is, the experimental yields do not seem to decrease quite so rapidly with mass number as those based upon the statistical model. The experimental yield for Sn is clearly inconsistent with the theoretical estimate, however, for it lies about a factor of 30 above the calculated value. This discrepancy was at first surprising, but no grounds could be found for questioning the experimental result. 4. Discussion It may be seen that up to 90 MeV the (y, t) mode of reaction contributes only an extremely small fraction to the competing modes following photon absorption. This is demonstrated by comparing our 90 MeV yields with the dipole absorption sum rules for the bremsstrahlung weighted cross sections and the integrated cross sections. Using the definition for the yield (eq. (l), plus the l/E approximation for bremsstrahlung spectrum shape, one obtains the following relations for the bremsstrahlungweighted (g--1) and integrated (cJ,-,)cross sections.

(5) (6) fi in eq. (6) is defined by the ratio /:“dE

N(E, , E)o(E)E

//:“dE

N(E,

, E)c(E).

PHOTONUCLEAR TRITlUM YIELDS

59

Knowledge of the excitation function would be required to determine I?, but it may be fairly well estimated as the arithmetic mean of the threshold-plus-Coulomb barrier energy and the maximum energy (E,). For the four elements studied here, the former sum (threshold plus barrier) ranges from 22 MeV to 26 MeV, resulting in an arithmetic mean of 56 to 58 MeV. The maximum error in assuming the arithmetic mean for I? is about a factor of two (resulting from a delta-function excitation function at either energy extreme). Based upon reasonable (analytic) extreme shapes for the excitation functions, however, the assumed values for E are believed to be correct to within about + 15 %. TABLE 4 Bremsstrahlung-weighted 2’AI

u- (mb) 1

a,,(MeV

. mb)

and integrated

@/, t) cross sections

(90 MeV) ZOSBi

ZII

Sn

0.072

0.007.

0.065

0.0072

4.0

0.42

3.8

0.41

Given the foregoing definitions and approximations, estimates for 6-t and co have been calculated from the experimental results (table 4). Comparison of the (y, t) results for cr_ 1 with Levinger’s sum rule formula2’) shows that the phototriton contribution is a minimum for Bi (0.002 o/,) and a maximum for Al (0.3 %). Similarly, using Gell-Mann’s expression for rye [ref. 26)], one finds values ranging from 0.001% for Bi to 0.7 % for Al. A detailed comparison has been made of our results at 90 MeV with those of other workers at lower energies and with the statistical model calculations. The bulk of the existing data of acceptable precision comes from the Darmstadt group ‘- ‘), whose experiments included samples ranging from He to Ag and energies up to 56 MeV. Al, Co, Cu and Ag were studied by Heinrich and Waffler “) at 31 MeV, and rather imprecise results for a few medium-Z elements were obtained by Raymond and Medicus “‘) at 37 MeV. Our observations, which extend the range of results to higher energies and higher masses are reasonably consistent with those of other workers at lower energies. They appear to substantiate the previously-stated conclusion that phototriton yields are consistent with the expectations of evaporation theory for nuclei with masses up to about 70, but that beyond the region of mass number z 100 the observed yields are considerably greater than the predictions of the statistical theory. The relative contribution of nuclear evaporation for these medium weight nuclei appears to increase with increasing excitation energy, however. Wiik ‘) reported experimental yields for Ag which exceeded the theoretical estimates by a factor of 1000 at about 30 MeV and a factor of 100 at about 60 MeV, while our observed 90 MeV yield for Sn exceeds the calculated value by about a factor of 30. The gross behaviour of phototriton production is thus comparable with that of other small clusters and nucleons. For example, Osokina 2”) examined the role of

60

L. A. CURRIE

AND

R. H. RODRfGUEZ-PASQd

evaporation in photoproton and photoneutron reactions as a function of target nucleus, and he found that, while evaporation played a dominant part in (y, p) reactions on nuclei having 2 w 30, its contribution became quite small for Z w 50. Similarly, Carver 2g), and Meneghetti and Vitale 30) have demonstrated that while (y, a) yields are consistent with evaporation theory for lower-2 elements, for Z > 50 experimental yields suggest the importance of non-evaporative processes. Appreciation is extended to Evans Hayward, W. B. Mann, and H. v. Buttlar and his students for beneficial discussions; to H. v. Buttlar and B. Huber for listings of YSI and SMLF; to V. Dantzler, G. Hill, and H. L. Steinberg for programming assistance; to J. E. Harding for target preparation; and to the NBS synchrotron crew for able assistance with the bremsstrahlung irradiations. References 1) B. Wiik, Z. Phys. 189 (1966) 423 2) H. v. Buttlar, F. Freund and G. Gammel, Z. Phys. 200 (1967) 1 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) 14) 15) 16) 17) 18) 19) 20) 21) 22) 23) 24) 25) 26) 27) 28) 29) 30)

K. Kramer, H. v. Buttlar, A. Goldmann and B. Huber, Z. Phys. 207 (1967) 1 A. Goldmann, P. Kneisel and H. v. Buttlar, Z. Phys. 192 (1966) 282 P. Kneisel, A. Goldmann and H. v. Buttlar, Z. Phys. 199 (1967) 440 F. Heinrich, H. Wtiler and M. Walter, Helv. Phys. Acta 29 (1956) 3 H. v. Buttlar and B. Huber, Laborbericht Nr. 22, Inst. Tech. Kemphysik, Tech. Hochsch. Darmstadt, 1965 J. S. Pruitt and S. R. Domen, NBS Monograph 48 (1952) D. Ehhalt, R. Kosiek and R. Pfeiffer, Z. Phys. 187 (1965) 210 J. H. Hubbell, Photon cross sections, attenuation coefficients, and energy absorption coefficients from 10 keV to 100 GeV, NSRDS-NBS 29 (1969) H. L. Steinberg, Thesis, University of Maryland (1966), unpublished G. Bonazzola, 0. Borrello, S. Costa and S. Ferroni, Nucl. Phys. 34 (1962) 637 W. C. Barger, W. D. George and D. D. Reagan, Phys. Rev. 98 (1955) 73 H. Fuchs and K. H. Lindenberger, Nucl. Instr. 7 (1960) 219 L. A. Currie, W. F. Libby and R. L. Wolfgang, Phys. Rev. 101 (1956) 1557 W. B. Mann, R. W. Medlock and 0. Yura, Int. J. Applied Rad. and Isotopes 15 (1964) 351 J. S. Pruitt and S. R. Domen, J. Res. NBS 68A 703 (1964) J. M. Blatt and V. F. Weisskopf, Theoretical nuclear physics (Wiley, New York, 1952) N. T. Porile, in Nuclear chemistry, ed. L. Yatfe (Academic Press, New York, 1968) vol. 1, pp. 62 ff, p. 110 J. Hudis, in Nuclear chemistry, ed. L. Yatfe (Academic Press, New York, 1968) vol. 1, p. 217 R. D. Albert, J. D. Anderson and C. Wang, Phys. Rev. 120 (1960) 2149 J. M. Wyckoff, B. Ziegler, H. W. Koch and R. Uhlig, Phys. Rev. 137 (1965) B576 B. I. Gavrilov and L. E. Lazareva (Sov. Phys.) JETP 3 (1957) 871 L. W. Jones and K. M. Terwilliger, Phys. Rev. 91 (1953) 699 J. S. Levinger, Nuclear photodisintegration (Oxford Univ. Press, 1960) M. Gell-Mann, M. L. Goldberger and W. E. Thirring, Phys. Rev. 95 (1954) 1612 D. J. Raymond and H. A. Medicus, Bull. Am. Phys. Sot. 10 (1965) 542 R. M. Osokina, Proc. Conf. direct interactions and nuclear reaction mechanisms, Padua (1962) p. 297 J. H. Carver, Proc. Phys. Sot. 77 (1960) 417 L. Meneghetti and S. Vitale, Nucl. Phys. 61 (1965) 316