Resumen de Structure and reactions of weakly-bound nuclei within a one-dimensional model
The line of research developed within the present work is the description of the structure and the dynamics of weakly-bound systems with one or more valence particles. Even considering inert cores, the problem is relatively easy only with one valence particle (one-particle halo), and starts to be more complex with two particles two-particle halo), becoming extremely complicated for systems with more active particles. For these reasons one typically resorts to approximated schemes (coupled-channels, first order approximation, space truncation, effective optical potentials and form factors, continuum discretization, etc) that need to be tested, not only against experimental data. So the main purpose of this work is the comparison between approximate models and exact ones. However, mathematical complexities and the high computational power required constitute a huge difficulty. Therefore, to make feasible the solution of the problem, particles are assumed to move just in one dimension and nuclei move according to a classical trajectory. In spite of the drastic assumptions, the problem retains the main features and properties of a full three-dimensional case. In addition, one could shed some light on the reaction mechanism, namely, on the description of the process in terms of single or repeated action of the external field in a perturbative expansion. A typical example is provided by the two-particle transfer process: is the pair transferred in a single step or in a correlated sequence of two single-particle transfer through a number of intermediate states? In the case of one-particle halo nuclei, the process involves one active neutron initially sitting on a single-particle level of a one-body Woods-Saxon potential (target) and feeling the action of a second moving potential (projectile). The target potential is assumed to be at rest in a fixed position, whereas the projectile moves following a fixed classical trajectory. The choice of the parameters entering the calculation will lead to various structural and kinematical conditions, corresponding to rather different physical situations and simulating different bombarding energy regimes, impact parameters, and Q-values for particle transfer. Essentially, one has to fix the parameters characterizing the potential wells (energies of single-particle states in both potentials), initial wavefunction (selecting one of the levels in target potential), distance of closest approach, and asymptotic energy of the collision. The ``exact'' results can be obtained by directly solving the time-dependent Schroedinger equation. The probability for populating the different channels after the collision is determined by projecting the asymptotic wavefunction (i.e. the solution for large values of t) onto the corresponding eigenstates of the wells. The same equation is solved within the first order approximation and standard coupled-channels formalism, thus testing the validity of the necessary truncations and continuum discretization (that is obtained through different methods). In particular, by this comparison, one might infer the importance of including the continuum to obtain the proper result expected from the ``exact'' calculation, even if the system is not very weakly-bound.
In the case of two-particle halo nuclei, as in previous case, the initial two-particle state is generated by the fixed well and the time evolution of the two-particle wave function is due to the action of two moving one-body potentials along a classical trajectory. In addition, one can include a residual short-range pairing interaction between the two valence particles. For simplicity the pairing interaction is taken to be a density-dependent zero-range potential, and hence it acts only when the two particles are both inside the same well. Again, the solution is obtained by solving the time-dependent two-particle Schroedinger equation. At the end of the process one can single out the population of the different final channels: elastic/inelastic (both particles still in the initial well), one-particle transfer (one particle in the initial well and one in the moving one), one-particle breakup (one particle in the continuum outside the wells and one in the initial or final well), two-particle transfer (both particles in the moving well), and breakup (one or both particles outside the wells). For the two-body process one can study the reaction mechanism by switching on or off the pairing interaction. Due to the absence of correlations the transfer process is induced by the one-body mean-field generated by the moving wells and, in terms of reaction mechanism, the two-particle transfer can only be interpreted as produced by the successive transfer of single particles. In the correlated case the probability of finding both particles on the same side is clearly favored, and the effect of this initial correlation will propagate during the scattering process. In fact one finds a final probability larger than that for the uncorrelated estimate. This rapresents therefore the enhancement factor due to the pairing correlation.
In conclusion, despite its simplicity, the model provides a framework for the understanding of direct reactions mechanisms involving one- and two-particle halo nuclei. In particular, it permits to test in a simple way the role of continuum and usual approximate approaches. It also allows to prove the role of pairing interaction between the two valence particles.
