Yield of \((\gamma,n)\)-Reactions for Light Isotopes of Elements with \(Z = 6—68\)

N. A. Tikhonov

(Presented by the scientific seminar of the Physico-Technical Faculty)

Several works by foreign authors have been devoted to the present question. The obtained values of the relative yield of photoneutrons under the action of bremsstrahlung from accelerators with different maximum energies are approximated by a power function of the atomic number \(Z\) of the irradiated element.

In work [1] it is shown that the relative yield of neutrons under the action of high-energy radiation—above 50 MeV—does not depend on the energy of the \(\gamma\)-radiation. On the contrary, at energies not very far from threshold values for \((\gamma,n)\)-reactions (18.7 MeV for carbon), the form of the function depends substantially on the maximum energy of the radiation. Price and Kerst [2] obtained, for the relative yield of photoneutrons under the action of betatron radiation with maximum energy 22 MeV, the function:

\[ N = 2270 \cdot Z^{2.1}, \]

where \(N\) is the yield of photoneutrons, referred to one mole of the irradiated element and to a dose of one roentgen.

At other maximum energies of the incident radiation, the form of the function turns out somewhat different [3].

We carried out measurements of the relative yield of \((\gamma,n)\)-reactions under the action of betatron bremsstrahlung with maximum calculated energy 25 MeV on the elements: C, N, O, Mg, Cl, K, Fe, Cu, Zn, Br, Ag, Sb, Pr, Nd, and Er.

In almost all cases the yield was determined for the reaction occurring on the lightest isotope of the irradiated element.

The samples were placed at a distance of 70 cm from the betatron target and were irradiated with constant intensity. To simplify the calculations, the irradiation time was taken equal to the half-life of the expected activity. When obtaining isotopes with a short half-life (\(\mathrm{O}^{15}\), \(\mathrm{Mg}^{23}\), \(\mathrm{Ag}^{108}\), \(\mathrm{Pr}^{140}\), and \(\mathrm{Er}^{165}\)), the time was taken equal to \(4\tau\), and the activity was considered saturated.

The induced activity was counted with an end-window \(\beta\)-counter. The activity, reduced to the beginning of decay and to saturation, was referred to unit irradiation dose and to one mole of the isotope giving the observed reaction. As a standard, the yield of the reaction \(\mathrm{Cu}^{63}(\gamma,n)\mathrm{Cu}^{62}\) was adopted, which has been well studied and gives a ten-minute activity convenient for measurement.

The data for all \((\gamma,n)\) reactions were referred to the yield of this reaction, taken as 10000. To avoid measurement errors, measurements on each sample were carried out several times. The maximum scatter of the data for copper, for which statistics of more than 20 measurements were accumulated, was about 4%. The half-life values found and the relative yields are collected in Table 1.

Table 1

Special measurements were carried out to exclude counting due to the neutron flux generated by the betatron. A change in activity as a result of neutron capture may occur for Cl, Ag, and Er, which have a considerable neutron-capture cross section. The \((n,\gamma)\) reaction on \(Cl^{35}\) gives a 38.5-minute activity that is difficult to separate from the analyzed 33-minute activity of \(Cl^{34}\). In the case of Ag and Er, the analyzed 2.5-min and 70-sec activities may be due in part, respectively, to the reactions \(Ag^{107}(n,\gamma)Ag^{108}\) and \(Er^{164}(n,\gamma)Er^{165}\).

Samples of these materials were placed in a paraffin block and shielded with a thin layer of cadmium. The difference in counts for the shielded and cadmium-unshielded samples, due to neutron capture, was in all cases small and lay within the error of measuring the activity induced in the direct beam of \(\gamma\)-radiation.

On irradiation of antimony, a 17-minute activity was clearly observed, the yield of which proved to be much lower than expected. This is explained by the existence of two energy states of the isotope \( \mathrm{Sb}^{120} \). Taking the yield value from the curve in Fig. 1, one can determine the percentage of the state with 17-minute activity. It is approximately equal to 18%.

Fig. 1

The yield of \((\gamma,n)\) reactions on rare-earth elements has not yet been sufficiently studied and may be of interest for rapid activation analysis of difficult-to-separate mixtures of rare earths (for example Pr—Nd, Ho—Er, etc.). In the experiments, pure preparations obtained chromatographically on ion-exchange columns were used (purity above 99.5%). In one of the measurements a sample of only 40 mg of Er was used; moreover, the activity obtained at a radiation intensity of 4 r/min at one meter from the target exceeded the background by a factor of 7. At the intensities attainable on our betatrons, of the order of 40–60 r/min, it is possible to activate 3–4 mg of an element, and impurities—in tens of mg—and analyze them quantitatively.

The dependence of the photoneutron yield—\(N\)—on the atomic number of the element—\(Z\)—is shown in Fig. 1.

The values of \(\sqrt{N}\) for all elements, beginning with \(Z=19\), fall well on a straight line, from which it follows that the yield is a quadratic function of \(Z\). If the yield of photoneutrons for copper is taken to be \(2.7 \cdot 10^6\) particles per mole per roentgen [2], then the yields of \((\gamma,n)\)-reactions on other elements for \(Z>19\) are determined by the formula:

\[ N = 8.3 \cdot 10^5 + 2260\, Z^2. \]

The yield of photoneutrons due to \((\gamma,2n)\)-reactions, at the radiation energy used, can apparently be neglected. In none of the measurements was any appreciable activity due to the \((\gamma,2n)\) reaction detected.

The dependence obtained makes it possible to carry out preliminary calculations in further studies of \((\gamma,n)\)-processes.

REFERENCES

1. M. Perlman. Phys. Rev. v. 72, No. 12, p. 1272 (1947)
2. B. McDaniel. Phys. Rev. v. 77, No. 1, p. 806 (1950)
3. G. Baldwin. Phys. Rev. 78, 1, p. 76 (1950); I. Zawson. Phys. Rev. 75, 3, p. 433 (1949).