Influence of energetics on the thresholds of heavy ion transfer reactions
2014 The possibility of sub-barrier transfers is discussed from the point of view of the energetics of the reaction. The position of the entrance channel potential energy curve Vi(R) relative to that of the exit channel corrected for the mass balance Vf(R) Qgg appears to be crucial. When the former curve is situated above the latter one, the transfer is energetically probable and will occur as soon as the colliding nuclei are sufficiently close to each other, i.e. for sub-barrier incident energies. Experimental examples are given. Considerable experimental and theoretical attention has recently been centered on questions that relate to thresholds of nuclear reactions and to the interaction barrier [1-5]. However, the notion of interaction barrier is still not quite clear. Generally, the interaction barrier is defined as the value Bi at which the interaction potential (nucleon + Coulomb) for the s-wave passes through a maximum; but this must be regarded as a strong interaction barrier, or a fusion barrier and some nuclear reactions, namely transfer reactions can take place at incident energies somewhat lower than Bi. The above definition, however, will be adopted here, and in considering the possibility of sub-barrier reactions, we shall ask the following question : for a given projectile target system, can one predict whether or not a given transfer reaction will occur with significant cross section for incident energies lower than Bi ? This question will be studied here from the point of view of the energetics involved in the reaction, which have been shown, in previous studies [6-13], to play a fundamental role. Many authors have underlined the influence of the Q value on reaction probabilities, (*) Laboratoire de Chimie Nucleaire, Centre d’Etudes Nucleaires de Bordeaux, 33170 Gradignan, France. and the enhancements of transitions for which Q = Qopt, where , e~ = E. Z3 Z4 1 1 Qopt 1 2 1 (1) Ei being the c.m. incident energy, Zl Z2 the atomic numbers of the colliding nuclei and Z3 Z4 those of the transfer products [6-9]. Others [10-11] have discussed the dramatic influence on the transfer cross sections of Qgg AP~, Qgg being the Q’value for a ground state transition, and d Y~ the difference between the Coulomb energies in the final and initial states A~ = Ve ~,. Similar ideas are involved in the present paper, but firstly we shall focus on the feasibility of subbarrier reactions, and secondly we shall include a ’ nuclear part in addition to Pc in the expression for the interaction potential. This nuclear contribution may have a non negligible influence for incident energies slightly lower than the interaction barrier. 1. Experimental evidence. Let us consider the two systems 14N + 209Bi and 160 + 209Bi. In figures 1 and 2 are shown the experimental excitation functions obtained by activation techniques [14, 15] for 21 opo and 211 At which correspond respectively to transfers of 1 and 2 protons from the projectile Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyslet:0197500360305900
Simple formulae for heavy ion subcoulomb transfer probabilities. Application to one and two-proton transfers in bismuth
A simple analytical formula is given to express the transition probability in a quasi-elastic transfer reaction. This formula is derived from the DWBA amplitude, using assumptions based on the fact that the main contribution to the DWBA integral comes from a narrow domain of distances of approach. Recoil effects are taken into account. This method is applied to calculate the excitation functions for one and two-proton transfer reactions induced in209Bi by heavy ions, below and near the barrier. The curves obtained are compared to the excitation functions measured for the production of residual210Po and211At. The corresponding transfer reactions involve excitation energiesE* of the residue lying in the range 0–8 MeV. This excitation energy is taken as a free parameter in the calculation, and the valuesEopt* which lead to the best agreement between the calculated and experimental curves are consistent with the classical values for the optimum reactionQ-values.Nuclear Reactions. Simplified transition probability for quasi-elastic transfer. Calculatedσ(E)209Bi(X, Y)210Po,211At,X=14N,16O,19F,40Ar,40Ca,56Fe,63Cu near threshold. Compared experimental data. Deduced optimum excitation energy.
Nucleon and nucleon-group transfer reactions induced in the bombardment of 197Au and 232Th by 12C, 14N and 15N projectiles
Abstract Targets of 197 Au and 232 Th were bombarded by 12 C, 14 N and 15 N projectiles at 82, 110 and 98.5 MeV, respectively. Differential cross sections and energy spectra were measured for the transfer of one proton, one neutron, a deuteron, 3 He and 4 He. The angular distributions of all transfer reactions have a peak at the angle corresponding to the Rutherford scattering of two nuclei by grazing collision. The cross section of the few-nucleon transfer differs only slightly from that of the single-nucleon transfer. The energy spectra of the 3 He transfer were narrower than those of the proton transfer. These results indicate the possibility of cluster level excitation by the few-nucleon transfer. The 4 He pick-up cross section was smaller than a few μb; it is possible that the alpha particle enters the unbound levels of the projectiles.