Nuclear Reactions initiated by Recoil Nuclei

Abstract

When a proton of relativistic energy strikes a heavy nucleus, it is possible for the target nucleus, or a large amount of it, to recoil with a substantial fraction of the incident proton's energy. If this energy is sufficient to penetrate the Coulomb barrier between the recoiling particle and another heavy nucleus in the target, nuclear reactions can take place. Thus, if bombardment of a target of high atomic number (Z) by high energy protons yielded a sufficient flux of heavy recoil nuclei with energies exceeding, for example, 500 MeV, then one could study reactions between heavy nuclei without the need to accelerate the heavy ions. Marinov et al.¹ recently invoked this process to account for the possible production of a nuclide with Z=112 in a tungsten target when it was irradiated with 24 GeV protons. In this communication we estimate the rate of production of high energy recoil nuclei in such proton-tungsten collisions; the results are very similar for any other heavy nuclide target. We find that the frangibility of nuclear matter, expressed by the rapid decrease of nuclear form factors with increasing momentum transfer, makes it very difficult to transfer large amounts of energy to the nucleus or to a substantial nuclear subunit. Therefore, the cross-section to produce energetic heavy ions in interactions of protons with heavy nuclei is extremely small. We estimate that a conservative upper bound for the cross-section to produce heavy ions with A > 75 having an energy of 20 MeV or more is 10⁻³ µbarn for all incident proton energies above 20 GeV. The corresponding cross-section to produce ions with energy exceeding 500 MeV is expected to be many orders of magnitude smaller. Because the total cross-section for high energy protons approximately corresponds to the geometrical value, that is, of the order of 1 barn, the effective flux of heavy ions with energy E> 500 MeV produced by high energy proton bombardment would therefore be much less than 10⁻¹⁵ of the incident proton flux. Thus, using such recoil nuclei as secondary projectiles to initiate reactions between heavy nuclei is not a promising idea. In particular, we show that the phenomena reported by Marinov et al.¹ are unlikely to have arisen from such secondary reactions caused by recoil nuclei.