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EXPERIMENTS ON THE NUCLEAR PHOTOELECTRIC EFFECT
Works on the nuclear photoelectric effect published before November 1948 (in Russian see \(^{1,2,5}\)) and later (reviewed here) led to the establishment of the following basic ideas:
a) the effective cross section of the \((\gamma,n)\) reaction has a maximum (resonance) located in the region of energies of the incident \(\gamma\)-quantum (for \(A \leq 12\)) around \(30\) MeV and shifting to the left with increasing atomic number;
b) the width of the maximum is about \(10\) MeV (for example, \(Cu^{63}\));
c) the fall of the effective cross section after the maximum is such that \(\gamma\)-quanta with energies greater than \(50\) MeV do not exert a noticeable influence on the yield of the reaction;
d) so far there are no facts that would testify to the inapplicability of these propositions to the reactions \((\gamma,p)\), \((\gamma,pn)\), \((\gamma,pp)\), and \((\gamma,nn)\);
e) Bohr’s mechanism of nuclear reactions, as applied to \(\gamma\)-reactions, leads to a smaller predominance of the \((\gamma,n)\)-reaction over \((\gamma p)\)-reactions than is observed.
Mouson and Perlman^4 measured the yield of the C\(^{12}\) \((\gamma,n)\)-reaction by the \(\beta\)-activity of C\(^{11}\). The \(\gamma\)-radiation (from a betatron) was detected by an ionization chamber calibrated, with the aid of a \(\gamma\)-spectrometer, for the number of quanta in the energy interval \(30 \pm 7.5\) MeV.
The measured quantities have the following meaning:
\(N_1\)—the number of \(\gamma\)-quanta in the energy interval near the assumed (in a number of cases, known) position of the resonance (energy interval \(\times\) irradiation time);
\(N_2\)—the number of events of the given reaction (number of target nuclei \(\times\) irradiation time).
The quotient
\[ \Sigma=\frac{N_2}{N_1}=\int_0^E \sigma(\varepsilon)n(\varepsilon)\,d\varepsilon, \]
where \(\varepsilon\) is the \(\gamma\)-quantum energy, \(E\) is the upper limit of the betatron \(\gamma\)-ray spectrum, and \(n_\varepsilon\) is the \(\gamma\)-ray spectrum, normalized so that \(n(\varepsilon)=1\) at \(\varepsilon=\varepsilon_{\text{resonance}}\). The authors consider the resonance in the region of 30 MeV to be sufficiently sharp and therefore interpret their result (see Table I) as the area of the effective cross section
\[ \Sigma \simeq \int \sigma(\varepsilon)\,d\varepsilon. \]
The accuracy of the measurements was \(\pm 20\%\). The weak dependence on \(E\) merely confirms the resonant character of the effective cross section.
Table I
| \(E\) (MeV) | 98 | 98 | 50 |
|---|---|---|---|
| \(\Sigma\) \((10^{-2}\ \text{cm}^2\cdot\text{MeV})\) | 0.148 | 0.148 | 0.146 |
A recalculation for Cu\(^{63}\), using the data of works 5, 6, gives for the reaction Cu\(^{63}(\gamma,n)\) the value
\[ \Sigma \simeq 1.5\cdot 10^{-24}\ \text{cm}^2\cdot\text{MeV}. \]
Gerttner and Jitter^7 observed, in a Wilson chamber, the splitting of N\(^{14}\) nuclei caused by \(100\) MeV \(\gamma\)-radiation from a betatron. The Wilson chamber operated synchronously with the betatron at a rate of one expansion in five seconds. A copper detector (the reaction Cu\(^{63}(\gamma,n)\)) monitored (through an ionization chamber) the intensity of the \(\gamma\)-radiation near \(\varepsilon=22\) MeV (the resonance position for Cu\(^{63}\)). Photodisintegrations with one and two tracks are interpreted by the authors as \((\gamma,n)\)- and \((\gamma,pn)\)-reactions, respectively. A larger number of tracks corresponds to stars. At \(E=100\) MeV the number of single and double tracks is 16% and 64% of the total number of disintegrations. When the betatron regime is changed from 50 MeV to 100 MeV, the number of paired tracks referred to the activity of copper changes from 1.00 to 0.89. Approximate normalization of the results obtained at \(E=20\) MeV gives a yield of about 0.05. Thus, the main yield of paired tracks falls in the interval \(\varepsilon=20\)—50 MeV. Table II gives the ratio of the number of stars to the number of paired tracks at various \(E\). There is an increase in the fraction of stars near 60 MeV.
In the second work^8 the same authors observed disintegrations in nitrogen, oxygen, and air. The meaning of the observed results is the same as in work^4, apart from the difference in the experimental means. The quantity \(N_1\) was determined from the number of pairs formed in the gas of the Wilson chamber by \(\gamma\)-quanta with energies in the interval \(30 \pm 10\) MeV. The value of \(\Sigma\) thus obtained for paired tracks in air is equal to
\[ 0.3\cdot 10^{-24}\ \text{cm}^2\cdot\text{MeV} \pm 20\%. \]
The number of paired tracks in oxygen and nitrogen separately is, at equal \(\gamma\)-radiation intensities, 166 and 185, respectively, i.e. the value of \(\Sigma\) is the same for these nuclei. For nitrogen, \(\Sigma\) was obtained by an independent method (the \(\gamma\)-radiation was detected in the same way as in work^4, and is equal to \(0.36\cdot 10^{-24}\ \text{cm}^2\cdot\text{MeV} \pm 40\%\)). The measured number of sin-
nocturnal tracks is 25% and 52% of the number of paired ones, while the ratio of the number of stars to the number of paired tracks is 3 and 4.4 for nitrogen and oxygen, respectively. The authors consider that the effective photodisintegration cross sections have sufficiently sharp maxima, located at 30 MeV (formation of single and paired tracks) and at 40 MeV (stars). Then, for the effective absorption cross section of a γ quantum
Table II
| $E$ (MeV) | Number of tracks in each splitting: 2 | Number of tracks in each splitting: 3 | Number of tracks in each splitting: 4 | Number of tracks in each splitting: 5 | Ratio of the number of stars to the number of paired tracks |
|---|---|---|---|---|---|
| 20 | 6 | 0 | 0 | 0 | 0 |
| 25 | 40 | 0 | 1 | 0 | 0.02 |
| 30 | 125 | 4 | 1 | 0 | 0.04 |
| 40 | 493 | 57 | 20 | 0 | 0.16 |
| 50 | 517 | 79 | 40 | 0 | 0.23 |
| 60 | 197 | 29 | 24 | 0 | 0.36 |
| 70 | 197 | 44 | 22 | 0 | 0.34 |
| 100 | 2346 | 469 | 296 | 17 | 0.33 |
one obtains the estimate $\int \sigma_{\text{absorp}}\, d\varepsilon \simeq 0.6 \cdot 10^{-14}\ \text{cm}^2 \cdot \text{MeV}$. The authors’ results agree well with the work of the authors of refs. 4 and 5.
Another paper^9 by the same authors was devoted to the detection of γ quanta elastically scattered by nuclei (carbon and copper) at γ-quantum energies close to the resonance energy of γ reactions. The γ quanta from the 100-MeV betatron scattered in the target formed pairs in a Wilson chamber, which could be positioned at various angles of observation. The absolute intensity of the betatron radiation was determined from the number of pairs at an observation angle of 11°. It was assumed that the main mass of scattered γ quanta arises as a result of scattering by the electrons of the target and as a result of bremsstrahlung from secondary electrons. The separation of the sought nuclear resonance scattering was carried out on the basis of a theoretical angular distribution. The results give an upper limit for elastic resonance scattering of 1 and 3% of the effective γ-quantum absorption cross section by the nuclei C^12 and Cu^63, respectively. This is much less than was predicted by Goldhaber and Teller^10 on the basis of the model of dipole oscillations of nuclei proposed by them.
Resonance scattering was also observed by Dressel^11 et al. on a 22-MeV betatron, using the reaction Pr^141$(\gamma,n)$ as a detector of scattered photons. For lead they obtained $(1.1 \pm 0.6)$ and $(2.0 \pm 1)\times 10^{-27}\ \text{cm}^2/\text{steradian}$ at $\theta = 90^\circ$ and $145^\circ$, respectively. This agrees with the theory of Goldhaber and Teller^10; for lighter nuclei the authors obtained much smaller results. For Cu^64 their result is 10 times smaller than that in the preceding paper^9.
McElhinney et al.^12 continued the work begun by Baldwin and Koch^13 (see also^3) on the determination of thresholds of $(\gamma,n)$ reactions for various elements. They measured the β activity of the reaction products as
function of the limiting energy of the $\gamma$-radiation of a 22-MeV betatron. The radiation intensity was determined with an ionization chamber. For $\mathrm{Ta}^{180}$ and $\mathrm{Cu}^{62}$ the authors give the cross section of the $(\gamma,n)$ reaction as a function of energy, up to 21 MeV (see Fig.). The solid part of the curves was obtained from processing the data by means of the theoretical bremsstrahlung spectrum; the dotted part—with allowance for the target thickness. It is seen that the effective cross section rises sharply to an appreciable value immediately at the threshold point. This result agrees with the two points on the curve for $\mathrm{Cu}^{62}$ previously known from work 14 (see also 3). The observed thresholds are given in Table III.
[Figure: cross sections $\sigma_{\mathrm{Ta}}$ and $\sigma_{\mathrm{Cu}}$ as functions of the energy of $\gamma$-quanta in MeV, for $\mathrm{Ta}^{180}$ and $\mathrm{Cu}^{62}$.]
Table III
Observed thresholds of $(\gamma,n)$ and $(\gamma,p)$ reactions
| Reaction | Observed thresholds | Thresholds calculated from nuclear mass values |
|---|---|---|
| $\mathrm{H}^{2}\ (\gamma,n)$ | $2.20 \pm 0.05$ | $2.19 \pm 0.03$ |
| $\mathrm{Be}^{9}\ (\gamma,n)$ | $1.63 \pm 0.03$* | |
| $\mathrm{Li}^{7}\ (\gamma,p)$ | $9.8 \pm 0.5$ *** | $10.1 \pm 0.5$ |
| $\mathrm{C}^{13}\ (\gamma,n)$ | $18.7 \pm 0.1$ * | |
| $\mathrm{N}^{14}\ (\gamma,n)$ | $10.65 \pm 0.2$ | $10.51 \pm 0.1$ |
| $\mathrm{Mg}^{24}\ (\gamma,n)$ | $16.2 \pm 0.3$ | $15.5 \pm 1.0$ |
| $\mathrm{Mg}^{25}\ (\gamma,p)$ | $11.5 \pm 1.0$ | $10.9 \pm 1.0$ |
| $\mathrm{Mg}^{26}\ (\gamma,p)$ | $14.0 \pm 1.0$ *** | $15.0 \pm 1.6$ |
| $\mathrm{Al}^{27}\ (\gamma,n)$ | $14.0 \pm 0.4$ | $11.1 \pm 1.0$ |
| $\mathrm{Si}^{28}\ (\gamma,n)$ | $16.8 \pm 0.4$ | $16.0 \pm 1.0$ |
| $\mathrm{P}^{31}\ (\gamma,n)$ | $12.35 \pm 0.2$ | $11.1 \pm 1.0$ |
| $\mathrm{S}^{32}\ (\gamma,n)$ | $14.8 \pm 0.4$ | $16.7 \pm 0.5$ |
| $\mathrm{K}^{39}\ (\gamma,n)$ | $13.2 \pm 0.2$ | $12.7 \pm 1.5$ |
| $\mathrm{Ca}^{40}\ (\gamma,n)$ | $15.9 \pm 0.4$ | $13.7 \pm 1.5$ |
| $\mathrm{Fe}^{54}\ (\gamma,n)$ | $13.8 \pm 0.2$ | — |
| $\mathrm{Cu}^{63}\ (\gamma,n)$ | $10.2 \pm 0.2$ | — |
Continuation
| Reaction | Observed thresholds | Thresholds calculated from nuclear mass values |
|---|---|---|
| $\mathrm{Cu}^{63}(\gamma,n)$ | $10.9 \pm 0.2$ | — |
| $\mathrm{Br}^{79}(\gamma,n)$ | $10.7 \pm 0.2$ | — |
| $\mathrm{Br}^{81}(\gamma,n)$ | $10.2 \pm 0.2$ | — |
| $\mathrm{Sb}^{121}(\gamma,n)$ | $9.25 \pm 0.2$ | — |
| $\mathrm{I}^{127}(\gamma,n)$ | $9.3 \pm 0.2$ | — |
| $\mathrm{Ta}^{181}(\gamma,n)$ | $7.7 \pm 0.2$ | — |
| $\mathrm{Bi}^{209}(\gamma,n)$ | $7.45 \pm 0.2$ | — |
Thresholds by which the mass scale was calibrated are marked with an asterisk.
Two asterisks indicate that the given value is equal to the difference between the experimentally observed threshold and approximately one-half of the maximum height of the Coulomb potential barrier for the proton.
It should be mentioned that Perlman’s work$^{15}$ is a supplement to the work of Perlman and Friedlander. The new data (see Table IV), obtained by the author, testify (in conjunction with the old—
Table IV
| Reaction | $\mathrm{N}^{14}(\gamma,n)$ | $\mathrm{G}^{30}(\gamma,n)$ | $\mathrm{Fe}^{54}(\gamma,n)$ | $\mathrm{Ni}^{58}(\gamma,n)$ | $\mathrm{Cu}^{65}(\gamma,n)$ | $\mathrm{Zn}^{64}(\gamma,n)$ | |
|---|---|---|---|---|---|---|---|
| Relative yield | 100 MeV | 1 | 13 | 15 | $>6.3$ | 41 | 26 |
| Relative yield | 50 MeV | 1 | 12 | 15 | $>6.0$ | 32 | 26 |
| $\mathrm{Ge}^{76}(\gamma,n)$ | $\mathrm{I}^{127}(\gamma,n)$ | $\mathrm{Pr}^{141}(\gamma,n)$ | $\mathrm{Ge}^{74}(\gamma,p)$ | $\mathrm{Ge}^{70}(\gamma,pn)$ |
|---|---|---|---|---|
| 54 | $>29$ | 73 | 2.5 | 3.4 |
| $>30$ | 76 |
...reported in Uspekhi Fizicheskikh Nauk on the existence of an increase in the yield of the \((\gamma,n)\)-reaction in the region \(A=60\) (\(A\) is the atomic number) by several times over a range of approximately 15 atomic numbers, and the probability of a similar jump in the region \(A=130\).
Levinger and Bethe, in a paper whose content lies outside the scope of the present abstract, using minimal and simplest assumptions about the wave functions of the nucleus and nuclear forces*), obtain the value \(\int \sigma_{\text{absorbed}}\,d\varepsilon\) and the mean energy of the absorbed quanta
\[ \bar{\varepsilon}= \frac{\int \sigma_{\text{absorbed}}\,\varepsilon\,d\varepsilon} {\int \sigma_{\text{absorbed}}\,d\varepsilon}. \]
The elastic resonance scattering of \(\gamma\)-quanta is, according to their theory, somewhat smaller than in Goldhaber and Teller\({}^{10}\). The article contains an indication that the \(\alpha\)-particle model gives a qualitative explanation of the regularity noted in point a of the present abstract, as well as of the fact, known from the works of Hirzel and Wäffler\({}^{17}\) and Perlman and Friedlander\({}^{5}\), of an anomalously large ratio of the yield of the \((\gamma,p)\)-reaction to the yield of the \((\gamma,n)\)-reaction, in comparison with that required by the Bohr mechanism of nuclear reactions. In discussing the experimental data, the authors do not come into contradiction with their theory.
Yu. Kholnov
References Cited
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*) The principal features of the method and some results are already contained in the work of A. B. Migdal, Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki 15, 81 (1945).