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Fission of Cu, Br, Ag, Sn, and Ba Nuclei
Fission reactions of nuclei had, until recently, been described only for heavy elements with \(Z > 73\) (i.e., down to tantalum inclusive). Recently, however, it has been possible to observe*) reactions in which, apparently, fission also occurs for nuclei of lighter elements: copper, bromine, silver, tin, and barium.
The splitting of the nuclei of these elements was produced by high-energy protons from the 184-inch cyclotron. Cu, Ag, and Sn were used in the form of foils \(0.13\) to \(0.25\) mm thick. Bromine and barium were irradiated in the form of specially prepared, exceptionally pure powders of ammonium bromide and barium carbonate. The determination of the final nuclei—the reaction products—was carried out from their radioactivity.
1. Copper
When copper is bombarded with high-energy protons, first of all two reactions with the formation of radioactive \(\mathrm{Cl}^{38}\) are possible: \(\mathrm{Cu}^{63}(p,pn6\alpha)\mathrm{Cl}^{38}\) and \(\mathrm{Cu}^{63} + p \to \mathrm{Cl}^{38} + \mathrm{Al}^{25} + n\). The first of these is the usual reaction of nuclear spallation under the action of high-energy particles, while the second is a fission reaction. Further, two reactions are possible with the formation of radioactive \(\mathrm{Na}^{24}\): \(\mathrm{Cu}^{63}(p,p3n9\alpha)\mathrm{Na}^{24}\) and \(\mathrm{Cu}^{63} + p \to \mathrm{Na}^{24} + \mathrm{K}^{39} + n\). The second of these is also a fission reaction. The authors calculated the lower limits for the energies of the bombarding protons at which the enumerated reactions can still occur, and compared them with experimental curves of the dependence of the reaction cross sections on the proton energy. In this way it was possible to establish which reactions are observed and at what energies. In calculating the lower energy limit, first, the difference between the masses of the initial and final reaction products was taken into account and, second, the energy required by the emitted particles to overcome the potential barrier of the nucleus. In this way the following threshold values of the proton energy were calculated:
\[ \begin{aligned} &\mathrm{Cu}^{63}(p,pn6\alpha)\mathrm{Cl}^{38}\ .\ .\ .\ 110\ \text{MeV} \\ &\mathrm{Cu}^{63}(p,p3n9\alpha)\mathrm{Na}^{24}\ .\ .\ .\ 170\ \text{MeV} \\ &\mathrm{Cu}^{63} + p \to \mathrm{Cl}^{38} + \mathrm{Al}^{25} + n\ .\ .\ .\ \text{about }50\ \text{MeV} \\ &\mathrm{Cu}^{63} + p \to \mathrm{Na}^{24} + \mathrm{K}^{39} + n\ .\ .\ .\ 50\ \text{MeV} \end{aligned} \]
Fig. 1.
Figure 1 shows the experimental curves of the dependence of the reaction cross sections with formation of \(\mathrm{Cl}^{38}\) and \(\mathrm{Na}^{24}\) on the proton energy. As can be seen from these curves, \(\mathrm{Cl}^{38}\) is obtained already at proton energies of about \(70\ \text{MeV}\), i.e., considerably lower than is required by the reaction \(\mathrm{Cu}^{63}(p,pn6\alpha)\mathrm{Cl}^{38}\), and, conversely, close to the minimum proton energy in the fission reaction of \(\mathrm{Cu}^{63}\) into \(\mathrm{Cl}^{38}\) and \(\mathrm{Al}^{25}\). The same picture was observed—
*) R. E. Batzel and G. T. Seaborg, Phys. Rev. 82, 607 (1951).
is also produced in the formation of \( \mathrm{Na}^{24} \). From this the authors conclude that in these experiments, especially at relatively low proton energies, fission reactions of copper nuclei are in fact observed.
A similar theoretical calculation of reaction thresholds and comparison with experiment were also carried out for all the remaining targets (\(\mathrm{Br}\), \(\mathrm{Ag}\), \(\mathrm{Sn}\), and \(\mathrm{Ba}\)). The following results were obtained.
- Bromine. The theoretical value of the threshold for the reaction
\(\mathrm{Br}^{79}(p, p7n7\alpha)\mathrm{Sc}^{44}\) is about \(190\ \mathrm{Mev}\), for the fission reaction
\[ \mathrm{Br}^{79} + p \to \mathrm{P}^{34} + \mathrm{Sc}^{44} + 2n \]
about \(80\ \mathrm{Mev}\). Experiment gives for the threshold of the reaction a value somewhat greater than \(100\ \mathrm{Mev}\), i.e., the fission reaction does indeed take place. At \(125\ \mathrm{Mev}\) the cross section for the formation of radioactive scandium \(\mathrm{Sc}^{44}\) can already be measured; it is of the order of \(10^{-32}\ \mathrm{cm}^2\).
Fig. 2.
- Silver. For the reaction \(\mathrm{Ag}^{107}(p, p6n10\alpha)\mathrm{Co}^{61}\) the threshold is about \(210\ \mathrm{Mev}\), and for the fission of silver nuclei into cobalt and scandium,
\[ \mathrm{Ag}^{107} + p \to \mathrm{Co}^{61} + \mathrm{Sc}^{45} + 2n, \]
respectively, \(60\ \mathrm{Mev}\). However, the experiments with Ag are less reliable than with the other elements. The point is that in silver an impurity of copper is usually encountered; spectral analysis of the target substance indicated an impurity of \(0.001\%\) copper. The cross section for the formation of radioactive \(\mathrm{Co}^{61}\) from \(\mathrm{Ag}^{107}\) is very small; for protons of \(180\ \mathrm{Mev}\) it is only \(10^{-32}\ \mathrm{cm}^2\). For the formation of \(\mathrm{Co}^{61}\) from copper the cross section is considerably larger, and therefore the negligible impurity of \(0.001\%\) copper gives, at \(180\ \mathrm{Mev}\), the same amount of \(\mathrm{Co}^{61}\) as does all the rest of the target substance.
- Tin. For the reaction of the breakup of tin nuclei with emission of \(\alpha\)-particles and formation of \(\mathrm{Na}^{24}\), the theoretical threshold is about \(425\ \mathrm{Mev}\); for the reaction
\[ \mathrm{Sn}^{118} + p \to \mathrm{Na}^{24} + \mathrm{Zr}^{94} + n \]
it is \(50\ \mathrm{Mev}\). The experimental results are given in Fig. 2; the experimental curve shown in Fig. 2 characterizes precisely the fission reaction.
Tin can also split according to another scheme—with the formation of radioactive isotopes \(\mathrm{Ga}^{66}\) and \(\mathrm{Ga}^{72}\). Natural tin is a mixture of several nonradioactive isotopes with mass numbers from 115 to 125. Below are the results of calculating the reaction threshold for \(\mathrm{Sn}^{118}\); for the other isotopes of tin the difference is only a few \(\mathrm{Mev}\) and does not affect the experimental conclusions. The proton-energy thresholds for the formation of gallium from tin are:
\[ \begin{aligned} \mathrm{Sn}^{118}(p, 7n10\alpha)\mathrm{Ga}^{72} &\ldots 230\ \mathrm{Mev} \\ \mathrm{Sn}^{118}(p, 13n10\alpha)\mathrm{Ga}^{66} &\ldots 280\ \mathrm{Mev} \\ \mathrm{Sn}^{118} + p \to \mathrm{Ga}^{72} + \mathrm{Ca}^{45} + 2n &\ldots 70\ \mathrm{Mev} \\ \mathrm{Sn}^{118} + p \to \mathrm{Ga}^{66} + \mathrm{Ca}^{49} + 4n &\ldots 90\ \mathrm{Mev} \end{aligned} \]
Results of the experiment: at a proton energy of 80 MeV, gallium was not detected at all; at 100 MeV, traces of radioactive gallium were found; at 150 and 180 MeV, there was already enough gallium for its quantitative determination; the reaction cross section at these energies is about \(10^{-32}\,\text{cm}^2\).
- Barium. The theoretical threshold for \(\mathrm{Ba}^{137}(p,20n\,13\alpha)\mathrm{Ga}^{66}\) is 370 MeV, and for \(\mathrm{Ba}^{137}+p\to \mathrm{Ga}^{66}+\mathrm{Fe}^{60}+12n\), respectively, 150 MeV. Experiment shows that both radioactive isotopes \(\mathrm{Ga}^{66}\) and \(\mathrm{Ga}^{72}\) are formed already when \(\mathrm{Ba}^{137}\) is bombarded with protons of energy 335 MeV (reaction cross section \(10^{-31}\,\text{cm}^2\)).
The lowering of the threshold energy of the bombarding particles as compared with its theoretical value could be caused not only by the fission reaction but also by the disintegration, under bombardment, of nuclei of various impurities. Therefore, in all cases a careful analysis was made of the impurity content and of their possible role, and on the basis of this analysis the authors conclude that the very low reaction thresholds they observed cannot be explained by foreign impurities and indicate, with complete certainty, the existence of fission reactions.
As the conclusion from their work, the authors express the opinion that, at the corresponding excitation energies, fission reactions occur in the nuclei of all elements.
M. Ginzburg