EXCITATION FUNCTIONS OF (p, pn) AND (p, αn) REACTIONS

As has already been reported*) in studies of nuclear reactions accompanied by the emission of charged particles, significant deviations were found from the predictions of the statistical theory of nuclear reactions1–4. To explain these deviations, expressed in anomalously large values of the experimental cross sections, several assumptions were advanced, among them: 1) the limited applicability of the usually used formula for the density of nuclear levels at low excitation energies; 2) competition of direct interaction with the process of formation of the compound nucleus5; and 3) lowering of the Coulomb barrier due to surface oscillations of the compound nucleus6 (according to the model of collective oscillations of part of the nuclear surface, these oscillations spend a considerable time at distances greater than the mean distance from the center of the nucleus). Below a paper is reviewed7, whose authors undertook an experimental verification of the latter proposal. For this purpose, the excitation functions of the reactions (p, pn) and (p, αn) on various elements were studied. From statistical theory it follows that the cross section of a reaction of the type \((x, yn)\) not far from threshold can be related to the energetic

Fig. 1.

) See UFN 50*, 459 (1953).

distribution of the particles \(y\) emitted from the nucleus. This latter quantity, in the case where \(y\) denotes a proton or an \(\alpha\)-particle, depends essentially on the penetrability of the Coulomb barrier. Therefore, a study of the energy dependence of the cross sections of the reactions \((p, pn)\) and \((p, \alpha n)\) makes it possible to test whether the penetrability factor of the Coulomb barrier has been chosen correctly.

Fig. 2.

The source of protons with an energy of \(23.5\) MeV was an 86-inch cyclotron. By special measures the authors succeeded in obtaining a small spread in the energies of the proton beam incident on a stack of foils placed inside the chamber (less than \(0.5\) MeV). The protons were registered by measuring the 38-minute activity induced in copper in the \((p, pn)\) reaction. Excitation functions were measured for the reactions \((p, pn)\) on the nuclei \(\mathrm{Cu}^{65}\), \(\mathrm{Pd}^{110}\), \(\mathrm{Ag}^{109}\), and \(\mathrm{Ta}^{181}\), and for the reaction \(\mathrm{Zn}^{64}(p,\alpha n)\mathrm{Cu}^{60}\). As is seen from Figs. 1 and 2, where the results obtained for tantalum and zinc are presented, the experimental data agree comparatively well with the curves calculated on the basis of the statistical theory and normalized at an excitation energy \((E)\) equal to \(23\) MeV, under the assumption of a Coulomb-barrier penetrability factor for an undeformed spherical nucleus. If the Coulomb barrier were reduced by a factor of two, the excitation functions of the reactions presented would be shifted to the left by \(4\)–\(5\) MeV in comparison with the observed curves.

At the same time, the absolute values of the cross sections of the \((p, pn)\) reaction proved to be several times larger than those predicted by the statistical theory (Fig. 3). It should be noted that, since after the emission of a proton from the nucleus the latter remains strongly excited (enough for neutron emission), assumption 1) concerning the level density turns out to be inapplicable. In addition,

calculations in this case are only slightly sensitive to the choice of nuclear temperature and to the ratio of the neutron and proton binding energies.

Fig. 3.

Thus, the experiments described do not confirm the assumption of a reduction of the Coulomb barrier due to surface oscillations of the excited nucleus. This assumption cannot therefore serve to explain the observed large yield of charged particles in nuclear reactions.

B. R.

Cited Literature

1. H. Wäffler, Helv. Phys. Acta 23, 239 (1950).
2. B. L. Cohen, Phys. Rev. 81, 184 (1951).
3. E. B. Paul, R. L. Clarke, Can. J. Phys. 31, 267 (1953).
4. S. N. Ghoshal, Phys. Rev. 80, 939 (1950).
5. H. McManus and W. T. Sharp, Phys. Rev. 87, 188 (1952).
6. J. A. Wheeler, Phys. Rev. 92, 843 (1953).
7. B. L. Cohen, E. Newman, R. A. Charpie and T. H. Handley, Phys. Rev. 94, 620 (1954).