No Arabic abstract
In nuclear reactions induced by hadrons and ions of high energies, nuclei can disintegrate into many fragments during a short time (~100 fm/c). This phenomenon known as nuclear multifragmentation was under intensive investigation last 20 years. It was established that multifragmentation is an universal process taking place in all reactions when the excitation energy transferred to nuclei is high enough, more than 3 MeV per nucleon, independently on the initial dynamical stage of the reactions. Very known compound nucleus decay processes (sequential evaporation and fission), which are usual for low energies, disappear and multifragmentation dominates at high excitation energy. For this reason, calculation of multifragmentation must be carried on in all cases when production of highly excited nuclei is expected, including spallation reactions. From the other hand, one can consider multifragmentation as manifestation of the liquid-gas phase transition in finite nuclei. This gives way for studying nuclear matter at subnuclear densities and for applications of properties of nuclear matter extracted from multifragmentation reactions in astrophysics. In this contribution, the Statistical Multifragmentation Model (SMM), which combines the compound nucleus processes at low energies and multifragmentation at high energies, is described. The most important ingredients of the model are discussed.
The ratio of pairing-energy coefficient to temperature ($a_{p}/T$) of neutron-rich fragments produced in spallation reactions has been investigated by adopting an isobaric yield ratio method deduced in the framework of a modified Fisher model. A series of spallation reactions, 0.5$A$ and 1$A$ GeV $^{208}$Pb + $p$, 1$A$ GeV $^{238}$U + $p$, 0.5$A$ GeV $^{136}$Xe + $d$, 0.2$A$, 0.5$A$ and 1$A$ GeV $^{136}$Xe + $p$, and $^{56}$Fe + $p$ with incident energy ranging from 0.3$A$ to 1.5$A$ GeV, has been analysed. An obvious odd-even staggering is shown in the fragments with small neutron excess ($Iequiv N - Z$), and in the relatively small-$A$ fragments which have large $I$. The values of $a_{p}/T$ for the fragments, with $I$ from 0 to 36, have been found to be in a range from -4 to 4, and most values of $a_{p}/T$ fall in the range from -1 to 1. It is suggested that a small pairing-energy coefficient should be considered in predicting the cross sections of fragments in spallation reactions. It is also concluded that the method proposed in this article is not good for fragments with $A/A_{s} >$ 85% (where $A_{s}$ is the mass number of the spallation system).
The Bayesian neural network (BNN) method is used to construct a predictive model for fragment prediction of proton induced spallation reactions with the guidance of a simplified EPAX formula. Compared to the experimental data, it is found that the BNN + sEPAX model can reasonably extrapolate with less information compared with BNN method. The BNN + sEPAX method provides a new approach to predict the energy-dependent residual cross sections produced in proton-induced spallation reactions from tens of MeV/u up to several GeV/u.
We demonstrate, within symmetry unrestricted time-dependent density functional theory, the existence of new effects in low-energy nuclear reactions which originate from superfluidity. The dynamics of the pairing field induces solitonic excitations in the colliding nuclear systems, leading to qualitative changes in the reaction dynamics. The solitonic excitation prevents collective energy dissipation and effectively suppresses fusion cross section. We demonstrate how the variations of the total kinetic energy of the fragments can be traced back to the energy stored in the superfluid junction of colliding nuclei. Both contact time and scattering angle in non-central collisions are significantly affected. The modification of the fusion cross section and possibilities for its experimental detection are discussed.
We studied the complete dynamics of the proton-induced spallation process with the microscopic framework of the Constrained Molecular Dynamics (CoMD) Model. We performed calculations of proton-induced spallation reactions on 181Ta, 208Pb, and 238U targets with the CoMD model and compared the results with a standard two-step approach based on an intranuclear cascade model (INC) followed by a statistical deexcitation model. The calculations were also compared with recent experimental data from the literature. Our calculations showed an overall satisfactory agreement with the experimental data and suggest further improvements in the models. We point out that this CoMD study represents the first complete dynamical description of spallation reactions with a microscopic N-body approach and may lead to advancements in the physics-based modelling of the spallation process.
The $^9$C nucleus and related capture reaction, ${^8mathrm{B}}(p,gamma){^9mathrm{C}}$, have been intensively studied with an astrophysical interest. Due to the weakly-bound nature of $^9$C, its structure is likely to be described as the three-body (${^7mathrm{Be}}+p+p$). Its continuum structure is also important to describe reaction processes of $^9$C, with which the reaction rate of the ${^8mathrm{B}}(p,gamma){^9mathrm{C}}$ process have been extracted indirectly. We perform three-body calculations on $^9$C and discuss properties of its ground and low-lying states via breakup reactions. We employ the three-body model of $^9$C using the Gaussian-expansion method combined with the complex-scaling method. This model is implemented in the four-body version of the continuum-discretized coupled-channels method, by which breakup reactions of $^9$C are studied. The intrinsic spin of $^7$Be is disregarded. By tuning a three-body interaction in the Hamiltonian of $^9$C, we obtain the low-lying $2^+$ state with the resonant energy 0.781 MeV and the decay width 0.137 MeV, which is consistent with the available experimental information and a relatively high-lying second $2^+$ wider resonant state. Our calculation predicts also sole $0^+$ and three $1^-$ resonant states. We discuss the role of these resonances in the elastic breakup cross section of $^9$C on $^{208}$Pb at 65 and 160 MeV/A. The low-lying 2$^+$ state is probed as a sharp peak of the breakup cross section, while the 1$^-$ states enhance the cross section around 3 MeV. Our calculations will further support the future and ongoing experimental campaigns for extracting astrophysical information and evaluating the two-proton removal cross-sections.