From Current Literature

Photonuclear Reactions with Proton Production

As is known, the first investigations of photonuclear reactions with proton production,1 carried out for a number of elements, revealed a considerable increase, in comparison with the expected one, in the yield of photoprotons. Recently several works have been carried out devoted to the further study of \(\gamma p\)-reactions, with the main attention in them given to the study of the energy spectrum and angular distribution of the protons.

Fig. 1. Diagram of the setup for investigating \(\gamma p\)-reactions by the photographic-plate method. \(E\)—chamber, \(C\)—collimator, \(T\)—betatron target, \(W\)—lead wall, \(F\)—foil, \(P\)—photographic plates, \(A\) and \(B\)—magnet poles; the dotted circle shows the size of the \(\gamma\)-beam.

The source of \(\gamma\)-rays in all these works was betatrons with a maximum photon energy \(E_{\gamma m}\) equal to \(20\)–\(25\) MeV, and the registration of protons was carried out by means of photographic plates placed near the sample irradiated by the beam. The most detailed is the work carried out with silver and aluminum.[^2] A well-collimated beam of \(\gamma\)-quanta (the total thickness of lead is \(37\) cm), produced in the target of a \(22\)-MeV betatron (Fig. 1), passes through a window of aluminum

foil (thickness \(t=0.075\ \mathrm{mm}\)) into the chamber. Silver (\(t=12.58\ \mathrm{mg/cm^2}\)) or aluminum (\(t=4.74\ \mathrm{mg/cm^2}\)) foil was placed in it at a small angle to the beam. The protons produced in the foil during irradiation (the exposure was from 2000 to 2500 roentgens) were recorded by two Ilford C-2 photographic plates placed in the lower part of the chamber in such a way that the plane of the emulsion was perpendicular to the plane of the foil. After evacuation, the chamber was filled with water vapor at \(p=18\ \mathrm{mm}\) Hg in order to prevent the emulsion from drying out. The background from electrons scattered in the foil was greatly reduced by applying a magnetic field of strength 2000 oersteds. The intensity of the beam was measured with a thimble ionization chamber (surrounded by a layer of aluminum, \(t=4\ \mathrm{cm}\)), which was placed in the beam emerging from the chamber. Additional monitoring of the intensity was carried out by measuring the activity (\(\tau=8.2\) hours) produced in tantalum foil as a result of the \(\gamma n\) reaction. In addition, the beam intensity in various regions of the foil was measured from the \(\beta\)-activity induced in strips of silver (\(\tau=24.5\) min.). This measurement also made it possible to determine the number of neutrons \(N_n\) produced in the foil. For each proton track emerging from the surface of the emulsion, the projection of the track onto the plane of the emulsion and the angles it made with the plane of the emulsion and with the direction of the beam were measured. Angles from 20 to 120° with respect to the beam direction were studied. The proton energy \(\varepsilon_p\) was determined from the ranges on the basis of the calibration given in the work of Lattes et al.\(^3\). The uncertainty in \(\varepsilon_p\) due to energy loss in the foil was from 0.1 to 0.6 MeV (protons with energy not less than 4 MeV were considered). The background was measured without the foil. The additional background from the \(np\) reaction, according to the authors’ calculations, was \(0.01\%\) for Ag and \(1\%\) for Al. The angular distribution of photoprotons from silver, obtained as a result of the measurements, is shown in Fig. 2. Along the ordinate is plotted the number of protons in a given energy interval per unit solid angle (relative scale). For the interval \(\varepsilon_p=10\div 14\ \mathrm{MeV}\), a clear predominance is observed of protons emitted at an angle of 90° with respect to the beam. The total yield was \(N_p=1.29\) protons per roentgen per \(1\ \mathrm{mm}\) of foil. The ratio \(N_p/N_n=0.023\pm0.008\). To facilitate comparison of the results with theory, the dependences of the yield \(A\) of the \((\gamma n)\) reaction on \(E_{\gamma M}\) were obtained in Ag, Al, and Cu samples:

Fig. 2. Angular distribution of photoprotons from silver. The maximum energy of the \(\gamma\)-rays is 20.8 MeV; \(\varphi\) is the angle of the proton with the beam direction.

\[ A=k\int_{B_n}^{E_{\gamma M}}\sigma_{(\gamma n)}N(E,E_M)\,dE\ \Bigg/\ \int_0^{E_M}N(E,E_M)i(E)\,dE . \]

Here \(k\) is the counter efficiency, \(\sigma(\gamma n)\) is the effective cross section of the \(\gamma n\) reaction, \(B_n\) is the threshold of the \(\gamma n\) reaction, \(i(E)\) is the sensitivity of the control ionization chamber in roentgens per 1 quantum of energy \(E\) per unit beam area.

The effective cross sections \(\sigma_{\gamma n}\) (Fig. 3) were calculated for a number of values of \(E_{\gamma M}\) and for Ag and Cu have maxima, respectively, at \(E_\gamma=16.5\) and \(17.5\) MeV. Table I presents the measurement results for \(\mathrm{Ag}^{109}\) and \(\mathrm{Cu}^{63}\).

Table I

For comparison of the energy spectrum of protons \(F(\varepsilon_p)\) of the \(\mathrm{Ag}(\gamma p)\mathrm{Pd}\) reaction, calculations of four variants with various expressions for the level density of the excited nucleus and the nuclear \(r_0\) were carried out. According to Weisskopf and Ewing \(^{5}\), the number of protons leaving the compound nucleus is

\[ I(\varepsilon_p)=c\cdot \varepsilon_p\sigma_p(E)\omega_k, \]

where \(\varepsilon_p\) is the proton energy, \(\sigma_p(E)\) is the cross section of the inverse process of proton absorption of energy \(\varepsilon_p\) by the nucleus, and \(\omega_k\) is the level density of the residual nucleus. If the known capture cross section \(\sigma_\gamma(E)\) and the photon spectrum \(N(E,E_M)\) in quanta per \(\mathrm{cm}^2\ \mathrm{MeV}\) are known, then

\[ F(\varepsilon_p)=\varepsilon_p\sigma_p \int_{B_p+\varepsilon_p}^{E_{\gamma M}} \frac{\sigma_\gamma(E)N(E,E_M)\omega_k(E-B_p-\varepsilon_p)} {\sum_{b'}\Gamma_{b'}}\,dE. \]

Using

\[ \frac{\sigma_\gamma}{\sigma_{\gamma n}} = \frac{\sum_{b'}\Gamma_{b'}}{\Gamma_n}, \]

we obtain:

\[ F(\varepsilon_p)=\varepsilon_p\sigma_p \int_{B_p+\varepsilon_p}^{E_{\gamma M}} \frac{\sigma_{\gamma n}(E)N(E,E_M)\omega_k(E-B_p-\varepsilon_p)} {\Gamma_n}\,dE. \]

Fig. 3. Effective cross sections of the \(\gamma n\) reaction for silver, aluminum, and copper.

Fig. 4. Ratio of the number of protons per energy interval of \(1\) MeV to the total number of neutrons emitted under the same irradiation. The histogram shows the observed distribution.

The following calculation variants were taken:

\[ \begin{aligned} \text{I.}\quad & \omega_1 = c \exp(aE)^{1/2}; \qquad a = A/5; \qquad r_0 = 1.42\cdot 10^{-13}\ \text{cm}.\\ \text{II.}\quad & \omega_2 = c \exp(aE)^{1/2}; \qquad a = 1.6(A-40)^{1/2}; \qquad r_0 = 1.3\cdot 10^{-13}\ \text{cm}.\\ \text{III.}\quad & \text{the same as II, except } r_0 = 1.5\cdot 10^{-13}\ \text{cm}.\\ \text{IV.}\quad & \omega_4 = c\ln(E+b)/b, \qquad b=20/A. \end{aligned} \]

The threshold \(B_p\) for \(\mathrm{Ag}^{107}\) was found by calculation from the threshold of the reaction \(\mathrm{Ag}^{107}(\gamma n)\mathrm{Ag}^{106}\), obtained earlier experimentally, and the energies of positrons emitted by \(\mathrm{Ag}^{106}\). The calculations were carried out for each of the silver isotopes, and its isotopic composition was taken into account in the final distribution. From consideration of the results (Fig. 4) it is seen that variants I and II in the region \(\varepsilon_p\) below \(8\text{--}9\) MeV give satisfactory agreement with experiment. However, protons of high energies (above 10 MeV) are obtained in substantially larger number than should be the case if one proceeds from the statistical model of the nucleus. The values of the areas under the curves, expressing \(N_p:N_n\), are presented in Table II.

Table II

For aluminum, the work obtained an approximately isotropic angular distribution. The energy spectrum of the protons agrees satisfactorily with the theoretical one, under the assumption \(\omega_k=\mathrm{const}\) (Fig. 5). The threshold of the \(\gamma p\) reaction was determined from the maximum energy of the registered protons,

\[ B_p = E_{\gamma m} - E_{pm} = 17.1 - 8.5 = 8.6\ \text{MeV}, \]

which is in agreement with the value of \(B_p\) found from the threshold of the \(\gamma n\) reaction. The effective cross section of the \(\gamma p\) reaction at \(E_{\gamma m}=18\) MeV was found equal to

\[ 6\cdot 10^{-27}\ \text{cm}^2, \]

which is close to the value obtained earlier for \(\sigma(\gamma n)\) at \(E_\gamma=17.6\) MeV.

Fig. 5. Distribution by energies of photoprotons from aluminum at \(E_{\gamma m}=20.8\) MeV. The smooth curve is the theoretical distribution for \(\omega=\mathrm{const}\).

The authors of another work\(^6\), carried out with the aid of a similar method, investigated the \(\gamma p\) reaction on rhodium at \(E_{\gamma m}=17.5\) MeV. The angular distribution of protons from rhodium had a maximum at \(\theta=90^\circ\) to the beam direction, especially sharp in the region of high energies, as is seen from Table III.

Table III

The threshold of the reaction \(\mathrm{Rh}^{103}(\gamma p)\mathrm{Ru}^{103}\) is \(8 \pm 1\) MeV. The effective cross section of the reaction, found by comparison with \(\sigma\) for deuterium, at \(E_{\gamma m}=17.5 \pm 1.0\) MeV, proved to be \(3.6 \pm 0.5 \cdot 10^{-28}\ \mathrm{cm}\) per steradian.

The study of 423 tracks of protons obtained in the photodisintegration of magnesium nuclei\(^7\) does not provide grounds for assuming an asymmetric distribution of the emitted protons.

The results obtained with Rh confirm the conclusions of the authors’ first work that the resonant excitation of silver nuclei by \(\gamma\)-quanta is accompanied by the emission of: 1) a high-energy group of protons, predominantly in the direction \(90^\circ\) to the beam, in an amount that does not agree with the statistical nuclear model, and 2) an isotropic group of low-energy protons, the number of which agrees with the theory.

To explain the observed phenomena, the authors cite the suggestion, put forward by Levinger and Bethe\(^8\) and by Courant\(^9\), that the principal process in the absorption of a photon by a nucleus is the excitation of a separate proton. In some cases it may leave the nucleus without having had time to transfer its excitation energy to other particles of the nucleus. In this case the emission of an energetic proton at an angle close to \(90^\circ\) with respect to the beam will be probable.

B. R.

Cited Literature

1. O. Hirzel and H. Wäffler, Helv. Phys. Acta 20, 373 (1947).
2. Diven and Almy, Phys. Rev. 80, 407 (1950).
3. Lattes, Fowler and Cuer, Proc. Phys. Soc. 59, 883 (1947).
4. G. A. Price and D. W. Kerst, Phys. Rev. 77, 806 (1950).
5. Weisskopf and Ewing, Phys. Rev. 57, 472 (1940).
6. Curtis, Hornbostel, Lee and Galant, Phys. Rev. 77, 290 (1950).
7. Toms, Halpern and Stephens, Phys. Rev. 77, 753 (1950).
8. Levinger and Bethe, Phys. Rev. 78, 115 (1950).
9. Courant, Phys. Rev. 74, 1226 (1948).

1. See UFN, Vol. XXXV, 276 (1948). ↩