Fission of Nuclei with Mass Numbers 63–118

When various nuclei were bombarded with neutrons, protons, deuterons, and $\alpha$-particles with energies of the order of 100–400 MeV, fission was observed for nuclei of elements heavier than tantalum.

For lighter elements, processes of knocking out a large number of some relatively light particles $(n, p, d, \alpha)$ were observed, as a result of which nuclei were obtained that were very far removed in charge and mass from the original ones. Recently a report appeared*) that, in the case of nuclei with intermediate mass-number values, fission processes are also observed. The authors of this report examined the energy relations characterizing knockout processes (i.e., emission of light nuclei) and fission for several nuclei with mass numbers from 63 to 118, and came to the conclusion that the experimental data obtained in bombarding these nuclei with fast protons rule out the possibility of explanation by knockout processes and can be explained only by the presence of fission.

These experimental data include the formation of $\mathrm{Cl}_{17}^{38}$ from $\mathrm{Cu}_{29}^{63}$, $\mathrm{Sc}_{21}^{44}$ from $\mathrm{Br}_{35}^{79}$, $\mathrm{Co}_{27}^{61}$ from $\mathrm{Ag}_{47}^{107}$, and $\mathrm{Ga}_{31}^{72}$ from $\mathrm{Sn}_{50}^{118}$. The threshold for knockout processes was calculated for the energetically most favorable case of such processes, when the maximum possible number of $\alpha$-particles flies out from the initial nucleus. In this case, because of the considerable binding energy of the $\alpha$-particle (28.1 MeV), substantially less energy is required than when protons, neutrons, or deuterons are emitted by the initial nucleus.

In calculating the knockout thresholds it was necessary to take into account the mass difference of the initial and final products and the height of the Coulomb barrier that must be overcome by the $\alpha$-particles emitted from the nucleus. The authors obtained the following threshold values for the knockout process:

1. $\mathrm{Cu}^{63}(p, pn\,6\alpha)\mathrm{Cl}^{38}$; $E = 100$ MeV.
2. $\mathrm{Br}^{79}(p, p\,7n\,7\alpha)\mathrm{Sc}^{44}$; $E = 180$ MeV.
3. $\mathrm{Ag}^{107}(p, p\,6n\,10\alpha)\mathrm{Co}^{61}$; $E = 210$ MeV.
4. $\mathrm{Sn}^{118}(p, 7n\,10\alpha)\mathrm{Ga}^{72}$; $E = 230$ MeV.

Experimentally it was found that the formation of $\mathrm{Cl}^{38}$ is observed already at bombarding-proton energies of 60–70 MeV (the yield cross section in this case is of the order of $10^{-32}\ \mathrm{cm}^2$) and increases noticeably at 100 MeV ($\sigma \sim 10^{-31}\ \mathrm{cm}^2$). $\mathrm{Sc}^{44}$ is formed at energies of 125 and 140 MeV with a cross section of the order of $10^{-32}\ \mathrm{cm}^2$, and an increase of the energy within the indicated limits by 15 MeV is accompanied by an increase of the yield severalfold. At 70 MeV the formation of $\mathrm{Sc}^{44}$ could not yet be detected. When silver was bombarded with protons of energy 180 MeV, the yield of $\mathrm{Co}^{61}$ corresponded to a cross section of the order of $10^{-32}\ \mathrm{cm}^2$. Finally, the formation of $\mathrm{Ga}^{72}$ was observed at proton energies of 150 MeV ($\sigma \sim 10^{-32}\ \mathrm{cm}^2$) and was several times greater at 180 MeV. At 100 MeV it was already almost impossible to identify $\mathrm{Ga}^{72}$; at 80 MeV the yield was zero. In three of the cases mentioned, special checking by the method of fractional crystallization showed that the formation of $\mathrm{Cl}^{38}$, $\mathrm{Sc}^{44}$, and $\mathrm{Ga}^{72}$ cannot be attributed to the presence of any impurities in the initial elements. Only in the case of silver were impurities of copper noted, which could have been responsible for a substantial part of the observed formation of $\mathrm{Co}^{61}$.

*) R. E. Batzel and G. T. Seaborg, Phys. Rev. 79, 528 (1950).

Since the thresholds of recoil processes are appreciably higher than the energies at which the formation of the above-listed isotopes was observed, the authors calculated the thresholds of fission processes in which the corresponding nuclei can be formed. In doing so, for fission as well, the most energetically favorable cases were calculated. In calculating the fission thresholds it was assumed that the fragments have a spherical shape and that their radius is \(R=1.48\cdot 10^{-13} A^{1/3}\) cm. Then the thresholds of the fission processes are equal to:

\[ \begin{aligned} 1.\;& \mathrm{Cu}^{63}+p \to \mathrm{Cl}^{38}+\mathrm{Al}^{25}+n; \qquad &&E=50\ \text{MeV}.\\ 2.\;& \mathrm{Br}^{79}+p \to \mathrm{Sc}^{44}+\mathrm{P}^{34}+2n; \qquad &&E=80\ \text{MeV}.\\ 3.\;& \mathrm{Ag}^{107}+p \to \mathrm{Co}^{61}+\mathrm{Sc}^{45}+2n; \qquad &&E=60\ \text{MeV}.\\ 4.\;& \mathrm{Sn}^{118}+p \to \mathrm{Ga}^{72}+\mathrm{Ca}^{45}+2n; \qquad &&E=70\ \text{MeV}. \end{aligned} \]

Comparison of the experimental data with the calculated fission thresholds indicates the possibility of formation of the nuclei considered by this mechanism. True, in none of the four cases did the authors identify the second fission fragments, which might correspond to chlorine, scandium, cobalt, or gallium. Since the quoted cross-section values (\(10^{-32}\)—\(10^{-31}\ \mathrm{cm}^{2}\)) correspond only to the yield of some one fission product, the total fission cross sections must be considerably higher. The authors indicate that a continuous spectrum in the masses of the products of bombardment of nuclei by fast particles should be observed, since, in addition to the recoil of light particles and fission into two “heavy” fragments, intermediate cases of the formation of light nuclei, for example Li, Be, etc., should also be observed.

In conclusion, the authors note that the number of such cases in which one can observe fission of nuclei with intermediate mass numbers is comparatively small, since a high degree of purification of the initial elements from all impurities and high sensitivity of the method for determining the reaction products are required.

G. I.