E. Gadioli Erba

Boltzmann master equation theory of angular distributions in heavy-ion reactions

Abstract A generalization of the Boltzmann master equation theory in order to evaluate the angular distributions of the ejectiles emitted during the nucleon-nucleon interaction cascade which brings about the thermalization of the composite nucleus formed in the fusion of two heavy ions is discussed. The spectra of light ejectiles, up to α-particles, produced in many projectile-target combinations and at many different relative energies of the two ions are very reasonably reproduced.

Monte Carlo calculations using the Boltzmann Master Equation theory of nuclear reactions

Abstract The Boltzmann Master Equation theory of nuclear reactions is used to predict average multiplicities of particles emitted during the thermalization of an excited nucleus by a nucleon-nucleon interaction cascade. It is shown how it may also be used, together with a Monte Carlo calculation, to predict possible sequences of events and hence the cross-sections and other measurable observables of individual reactions.

Nuclear surface, mean field and isospin effects in Boltzmann master equation theory of pre-equilibrium reactions

Pre-equilibrium emission of nucleons and light charged particles is investigated in central collisions leading to the complete fusion of two heavy ions, within the Boltzmann master equation approach. Realistic nucleon momentum density distributions for both projectile and target nuclei are used and mean field effects are schematically introduced in the early stage of the reaction process. The isospin dependence of the calculation parameters is also discussed. Theoretical predictions of the spectra of the particles emitted both in symmetric and asymmetric interactions at incident energies of a few ten MeV/nucleon are in satisfactory agreement with the experimental findings.

Alpha particle emission in the interaction of

Abstract The results of measured inclusive double differential cross section of α particles emitted in the interaction of 12 C ions with 59 Co and 93 Nb at incident energies of 300 and 400 MeV are presented. The analysis of these data allows us to isolate the contributions of the different reaction mechanisms, thereby confirming previous conclusions of a comprehensive analysis of a large number of excitation function, forward recoil ranges and angular distributions of residues produced in the interaction of 12 C with a target nucleus in the same mass range. In particular, the probabilities associated with α-particle reemission following incomplete fussion processes have been reaffirmed. Several refinements to the theoretical model proposed in earlier studies of the interaction of 12 C with nuclei are presented.

^{12}

The continuous energy spectrum of secondary α particles emitted in (α, α′) reactions is interpreted in terms of an incoherent sum of α emissions after single and multiple α-nucleon collisions. The absolute yield of each contribution is evaluated utilising a generalisation of the Exciton Model and a satisfactory reproduction of the data is achieved. Also the angular distribution of α particles after a single α-nucleon interaction is satisfactorily reproduced. The possible role of processes involving interactions of the incident α with preformed αs is discussed.

C with

Abstract In this letter we discuss how one may evaluate the ejectile angular distributions with the Boltzmann Master Equation theory of nuclear reactions. The comparison of the calculations with the experimental ejectile double differential spectra is satisfactory confirming the validity of the theory. The possibility, offered by present calculations, of estimating how the nucleon momentum correlation disappears with increasing time, allows one to predict more accurately than with previous calculations the absolute value of the cross-sections for complex particle emission.

^{59}

In a recent letter GINOCCHIO and BLANN (2) compared results of intranuclear cascade model (ICM) calculations obtained either with a nucleon mean-free-path (mfp) in nuclear matter corresponding to free 3~-2C scattering cross-sections, or with a four times longer mfp. The latter assumption was reported to give far poorer agreement with the experimental data; and this conclusion was reported as evidence in favour of the use of the shorter mfp values in pre-equilibrium decay models, whose alternate formulations have been lately discussed at some length (2.6). We maintain tha t ICI~[ calculations performed with the free ~ ~ scatter mfp in general do not afford an accurate reproduction of the excitation functions of reactions induced by protons of some tens of MeV, and of the energy integrated spectra of the emitted particles. In fact, published results of ICM calculations have shown a systematic tendency to underestimate the emission of high-energy particles, and to overestimate compound-nucleus production. We made this statement, which agrees with an opinion already expressed by MILLER (D, on the basis of the findings of several works cited in ref. (2). Our belief is further supported by other results of BERTINI et al. (S) (e l . Specifically fig. 4 thereof), and even by the figures reported by the authors of ref. (1). However, in spite of such inadequacies of the ICM calculations, the model seems to retain a good measure of appeal as an intui t ive tool much in use for practical purposes.

Co and

Three years ago it has been suggested that the exciton model could satisfactorily reproduce the energy dependence of the excitation functions of (p, a) reactions induced in odd light nuclei (L~). However the ignorance of the decay rates of the composite nucleus for cxeiton-exeiton interaction, forbade the evaluation of the absolute values of the cross-sections. Since that time several attempts have been reported to evaluate the decay rates, starting from free nucleon-nucleon cross-sections and the Fermi-gas model of the nucleus (3.7). In this letter we report the evaluation of the excitation functions of (p, ~) reactions on 11B, ~SN, I~F, for transitions to definite levels of the residual nucleus. The calculations make use of the decay rates for exeiton-exciton interaction evaluated with the semi-phenomenological approach of ref. (~,~), which proved to be successfull in reproducing the cross-sections of nucleon and a-particle induced reactions (~-s). The energy dependence of the excitation functions of these reactions suggests tha~ the most usual configuration of the composite system, just after the interaction of the projectile with the target nucleus, is of the 2p-Oh type Q). Without attempting in this letter to explain this finding, the initial configuration of the composite system does not appear to be of the 2p-lh type, as in the case of proton interactions with heavier nuclei, presumably as a consequence of the large amplitude, in the wave functions of the light nuclei here considered, of configurations in which several nucleons are closely correlated. The interaction of the incident proton with single nucleons of the Fermi sea could be hindered so that only interactions with a loosely bound nucleon with no excitation of hole states could be enhanced.

^{93}

The experimental information on reactions induced by stopped ..pi../sup -/ absorbed in nuclei is critically reviewed. Evidence for the presence of ..cap alpha..-cluster absorptions is presented and arguments are given to show that approx. =25% of ..pi../sup -/ absorptions are of this kind. In the case of two-nucleon absorption, the existing experimental information concerning the ratio of n-p to p-p absorbing pairs is discussed. Calculations of particle spectra and residue spallation yield distributions that, in addition to two-nucleon absorption, include ..cap alpha..-cluster absorption are presented, and it is shown that a satisfactory reproduction of the data is achieved.

Nb at incident energies of 300 and 400 MeV

SummaryThe angular and energy distributions of α-particles from the reactions142,144Nd(n, α)139,141Ce have been measured at incident neutron energies of ≈ 14.2 and 18.1 MeV. The comparison of the angle-integrated α spectra with those from the reaction143Nd(n, α)140Ce, shows that the 83th valence neutron of143Nd acts as a spectator in the (n, α) process, while the two paired neutrons outside theN= 82 shell of144Nd play an active role. This result, together with analogous data from (p, α) reactions, clearly indicates that the protons and the neutrons of the emitted α in a (nucleon, α) reaction must be already paired in the target nucleus.