NUCLEAR PHOTOEFFECT WITH EMISSION OF ONE PROTON¹

In volume 20 of Helvetica Physica Acta for 1947 there is an interesting experimental paper by Chordely and Wäffler, devoted to the study of the nuclear photoeffect (the reaction \((\gamma, p)\)). The theory of this effect was given by Weisskopf and Ewing², who based it on the well-known Bohr theory of nuclear reactions. From their calculations one can obtain the ratio of the effective cross sections for emission of a proton and of a neutron,

\[ \frac{\sigma(\gamma,p)}{\sigma(\gamma,n)}, \]

as a function of the energy of the exciting \(\gamma\)-rays, the binding energy of the emitted particle in the initial nucleus, and the maximum energy of the \(\beta\)-rays of the product nucleus. The authors of the paper under review set themselves the goal of testing these theoretical predictions. They used \(\gamma\)-rays emitted in the resonance reaction of lithium with protons, \(\mathrm{Li}^7(p,\gamma)\mathrm{Be}^8\). As is known, these rays, having an energy of 17.2 MeV, produce a photoeffect with neutron emission in almost all elements. Since the binding energies of the proton and neutron in a nucleus are scarcely seriously different from one another, one might have expected that phenomena with proton emission would also occur (except, perhaps, in heavy nuclei, in which there exist ...

tively increases). The fact of the reaction was established from the radioactivity of the product nucleus. In order that this could be done with some degree of reliability, it was necessary that: a) the number of reactions possible after the photoeffect be very limited, and b) the activities arising under this irradiation not be masked by analogous activities caused by the \((\gamma,n)\)-processes of the same isotope.

The measurements were carried out with an apparatus described in previous works by one of the authors and collaborators. Protons for producing \(\gamma\)-rays were accelerated by a constant electric field (maximum voltage—90 kV), and a proton current of up to \(5\text{–}8\ \mathrm{mA}\) could be produced. The preparation was placed above a lithium target in a hollow cylinder, whose wall thickness always equaled, in limiting measure, the maximum range of the \(\beta\)-particles of the product nucleus. The intensity of the \(\gamma\)-rays was measured continuously by a counter placed \(1.4\ \mathrm{m}\) from the target behind a lead shield \(1\ \mathrm{cm}\) thick (under the usual experimental conditions the \(\gamma\)-ray intensity in the counter was approximately the same as if \(10\ \mathrm{mg}\) of radium had been placed at the target position). The activity of the product nuclei was measured with an aluminum counter with wall thickness \(0.1\ \mathrm{mm}\), internal diameter \(24\ \mathrm{mm}\), and length \(5\ \mathrm{cm}\). Since the activities arising in the \((\gamma,p)\)-process are usually very weak, it was very important to reduce the background as much as possible. For this purpose the main counter was surrounded by ten large counters (diameter \(4\ \mathrm{cm}\), length \(20\ \mathrm{cm}\), wall thickness \(1\ \mathrm{mm}\)) made of brass and connected with it according to an anticoincidence circuit. Such a device reduced the background by a factor of \(5\text{–}6\).

The authors determined the yield of the reaction (by which they mean the activity of the product nucleus under infinitely long irradiation by \(\gamma\)-rays of a given “normal intensity”—400 counts per minute on the intensity counter). Obviously, the reaction yield \(A\) is determined by the formula

\[ A=\frac{400}{I_{\gamma}}\, \frac{\displaystyle \int_{t_1}^{t_2}\frac{dN}{dt}\,dt} {e^{-\lambda t_1}-e^{-\lambda t_2}}\cdot \frac{\lambda}{1-e^{-\lambda t}}, \tag{1} \]

where \(t\) is the irradiation time, \(t_1\) is the time between the end of irradiation and the beginning of measurement, \(t_2\) is the time between the end of irradiation and the end of measurement, and \(I_{\gamma}\) is the \(\gamma\)-ray intensity (in counts per second).

The results obtained were compared with the known yield of the nuclear photoeffect on copper. For this purpose, in place of the preparation, an empty copper cylinder of exactly the same shape and dimensions as the counter was placed, and the 10-minute activity arising in the reaction \(\mathrm{Cu}^{63}(\gamma,n)\mathrm{Cu}^{62}\) was measured with the counter. Knowing the ratio of the yields, it is easy to calculate the ratio of the effective cross sections. Indeed, it is easy to see that, for an exponential form of the \(\beta\)-ray absorption curve (which is usually the case), the following relation is fulfilled:

\[ \sigma=\frac{A e^{\mu' d_z}}{c n \overline{R}}, \tag{2} \]

where \(\mu'\) is the absorption coefficient of \(\beta\)-rays in aluminum, \(d_z\) is the wall thickness of the counter, \(n\) is the number of atoms of the original isotope in \(1\ \mathrm{cm}^3\), \(\overline{R}\) is the mean range of the \(\beta\)-rays in the material of the preparation, and \(c\) is a constant depending on the intensity of the \(\gamma\)-rays and on the angle between the directions of irradiation and registration. Taking into account that

\[ n=\frac{L\rho \varepsilon}{M}, \tag{3} \]

where \(L=6\cdot 10^{23}\), \(\rho\) is the density, and \(M\) is the molecular weight of the given isotope,

$\varepsilon$ is its percentage content, and, expressing $K$ in g/cm$^2$, the authors obtain for the ratio of the effective cross sections:

$$ \frac{\sigma_1}{\sigma_2} = \frac{A_1 M_1 R_2 \varepsilon_2}{A_2 M_2 R_1 \varepsilon_1} e^{(\mu_1' - \mu_2')dz}. \tag{4} $$

Taking the absorption of $\beta$ rays to be known (the corresponding data are taken from work 4), the authors were thus able to determine the ratio $\sigma(\gamma,p)$ for the given isotope to $\sigma(\gamma,p)$ on Cu$^{63}$. However, as the authors note, the interpretation of the results was complicated by one essential circumstance. Namely, the $(\gamma,p)$ reactions of interest to us are always accompanied by $(n,p)$ processes on the neighboring isotope (which has one neutron fewer than the isotope under study), owing to the same activity with which the $(\gamma,p)$ reactions also are associated. The causes of the appearance of neutrons are quite clear: first, in the reaction of protons with lithium (the same one in which the $\gamma$ rays used by the authors are emitted), beryllium nuclei arise which prove to be unstable and each decay into two $\alpha$ particles. The latter, reacting with lithium (Li$^7(\alpha,n)$B$^{10}$), produce neutrons with energy 4.3 MeV. Second, in the proton source bombarding the target, ordinary hydrogen, which always contains an admixture of deuterium, falls in, and consequently deuterons will be present in the proton beam. In the reaction D + Li$^7$ neutrons with energy 14.4 MeV appear. The intensity of the neutrons under the experimental conditions reached 75 millicuries of radium-beryllium equivalent. By feeding into the proton source hydrogen subjected to electrolysis (i.e., with a reduced deuterium content), the authors could change the number of deuterons bombarding the target. In this way it was possible to determine what part of the intensity was due to the (Li + D)-neutrons. It turned out that they play the principal role (of the 7 millicuries of total intensity only 9 are due to the $(\alpha,n)$ reaction). This circumstance allowed the authors to exclude the activity produced by neutrons. Repeatedly electrolyzing the hydrogen fed into the proton source, they reduced more and more the amount of deuterium in it and, by linear extrapolation, determined the activity in the complete absence of deuterons in the proton beam. Since the reaction Li$^7(\alpha,n)$B$^{10}$, as was shown, plays no role, this activity must be ascribed to the protons arising in the $(\gamma,p)$ process of interest to us.

For control, a method based on the resonance character of the reaction Li$^7(p,\gamma)$Be$^8$ was used: the preparation was irradiated with protons of energy slightly different from the resonance energy. In this case the intensity of the $\gamma$ rays (and, consequently, the activity produced by them) decreased by a factor of about 20, whereas the intensity of the neutrons changed by only a factor of two or three. The neutron activity could be determined by the first method, after which, subtracting it from the total activity, the authors found the neutron effect. In this case all neutrons are taken into account, and not only those arising in the reaction of lithium with deuterons. As the authors note, the fact that in all cases the activity values found, due to the $(\gamma,p)$ process, agree within the limits of error is good evidence that $(\alpha,n)$ neutrons play no role here.

The nuclear photoeffect with emission of a proton was found on the following isotopes: Mg$^{25}$, Mg$^{26}$, Si$^{29}$, Si$^{30}$, Ti$^{50}$, Cr$^{53}$, Se$^{77}$, Mo$^{98}$, Pd$^{115}$, Cd$^{112}$, Cd$^{113}$, Sn$^{117}$ and Sn$^{118}$. For $Z>50$ the effect could not be detected, which is fully attributable to the significance of the Coulomb barrier. The results of the measurements are given in Table 1.

For comparison with theory it is also necessary to know the ratio

$$ \frac{\sigma(\gamma,n)\ \text{on copper}} {\sigma(\gamma,n)\ \text{on the isotope under investigation}}. \tag{5} $$

Nuclear Photoeffect with Emission of One Proton

Table I

Table II

*) The binding energy was calculated from Pollard’s data on the masses of the corresponding stable isotopes.

It is known that for different isotopes of one and the same element (in the case of medium and heavy nuclei) the effective cross sections \(\sigma(\gamma,n)\) are, within the limits of error, approximately the same (see \(^{3}\)). The authors therefore believe that no substantial error will be made if, for copper and for the element adjacent to the isotope of interest, the ratio (5) is taken. In this way the authors obtain the experimental value

\[ \frac{\sigma(\gamma,p)}{\sigma(\gamma,n)}, \]

which is to be compared with the results of the theory. For this, however, it is also necessary to know the binding energy of the proton (neutron) in the nucleus. The authors carried out calculations with two values of the latter (10 MeV and 7.5 MeV). The results are collected in Table II on p. 279. As can be seen, the theoretical values prove to be considerably smaller than the experimental ones. The results for light elements are given in Table III. In the case of light nuclei, the probabilities of \((\gamma,n)\)- and \((\gamma,p)\)-processes turn out to be approximately the same, although the potential barrier here is still quite appreciable and, theoretically, this should not be so. The authors believe that so sharp a discrepancy between theory and experiment (both for medium and for light nuclei!) requires a modification of the Bohr ideas concerning the course of this nuclear reaction.

Table III

V. Averbakh

CITED LITERATURE

1. O. Hurzel and H. Wäffler, Helvetica Physica Acta, 20, 373 (1947).
2. V. F. Weisskopf and D. H. Ewing, Phys. Rev. 57, 472 (1940).
3. O. Huber, O. Lienhard, P. Scherrer and H. Wäffler, Helvetica Physica Acta, 16, 33 (1943).
   O. Huber, O. Lienhard and H. Wäffler, Helvetica Physica Acta, 17, 195 (1943).
4. O. Huber, O. Lienhard, P. Scherrer and H. Wäffler, Helvetica Physica Acta, 18, 221 (1945).
5. E. Pollard. Phys. Rev., 57, 1186 (1940).