Role Of Continuum Research Articles

Role of continuum in nuclear direct reactions with one-neutron halo nuclei: A one-dimensional model

We study the evolution of a single-particle wave function during the collision of a one dimensional potential well by another well, which can be regarded as a simple model for the problem of the scattering of a one-neutron halo nucleus by another nucleus. This constitutes an effective three-body problem, whose solution in three dimensions can be extremely complicated, particularly when breakup and rearrangement channels are to be considered. Our one-dimensional model provides the essential three-body nature of this problem, and allows for a much simpler application and assessment of different methods of solution. To simplify further the problem, we assume that the potential well representing the projectile moves according to a predetermined classical trajectory, although the internal motion of the "valence" particle is treated fully quantum-mechanically. This corresponds to a semiclassical approach of the scattering problem. Different approaches are investigated to understand the dynamics involving one-body halo-like systems: the "exact" time-dependent solution of the Schr\"odinger equation is compared to a numerical continuum-discretized coupled-channels (CC) calculation presenting various model cases including different reaction channels. This framework allows us to discuss the reaction mechanism and the role of continuum, whose inclusion in the CC calculation results to be crucial to reproduce the "exact" solution, even when the initial and final states are well bound. We also link each dynamical situation with analogous problem solved in a three dimensional (3D) CC framework, discussing the main challenges experienced in the usual 3D models.

The thermodynamic properties of diatomic molecules at elevated temperatures: Role of continuum and metastable states

A complete quantum formulation of diatomic partition functions uses the energy variation of the elastic scattering phase shift to represent the phase space associated with the molecular continuum states. The resonance structure in the phase shift, due to tunneling through rotational barriers, gives a rigorous interpretation of the metastable states which lie behind the barrier, and we can justify the need to include such states in the evaluation of thermodynamic properties. However, we also find that it is inconsistent merely to include the metastable phase space without considering the remaining contributions from the continuum. If either component is ignored in treating the dimer, then, of necessity, their presence will appear as the virial coefficients which cause nonideal behavior for the atomic fragments of the molecule. Both approaches are consistent and yield a proper equation of state for the vapor. We will show quantitative agreement between the exact quantal results and the approximate classical expressions for the partition function at high temperatures. Since the classical theory automatically includes all the effects of the molecular continuum, we suggest that this is both the simplest and most unambiguous procedure for extending thermodynamic tables to elevated temperatures. Explicit calculations are presented for Li2 and Na2.