Hyperspherical study of Coulombic three-body systems.

摘要

Hyperspherical coordinates are used to study properties of Coulombic three-body systems of arbitrary masses. Consider a system ABA, which consists of two identical particles A and a third particle B, each with one unit of charge. We examine the evolution of the approximate quantum numbers that are used for classifying bound and resonance states of the system as the mass ratio {dollar}lambda{dollar} = {dollar}msb{lcub}sc A{rcub}{dollar}/{dollar}msb{lcub}sc B{rcub}{dollar} changes from the atomic limit ({dollar}lambda longrightarrow{dollar} 0 as in H{dollar}sp-{dollar}) to the diatomic molecular limit ({dollar}lambda gg{dollar} 1 as in H{dollar}sb2sp+{dollar}). It is shown that for states which exhibit rovibrational behaviors in the atomic limit ({dollar}lambda longrightarrow{dollar} 0), a single set of approximate quantum numbers can be used to describe three-body systems of any {dollar}lambda{dollar}'s. For states that display independent-particle behavior in the atomic limit, such as singly excited states, it is shown that these states display rovibrational behavior only in the large-{dollar}lambda{dollar} limit. The evolution of the spectroscopy of the three-body systems from the shell model of atoms to the rovibrational model of molecule is thus analyzed. Calculations of potential curves in hyperspherical coordinates were carried out for Ps{dollar}sp-{dollar}, {dollar}dmu d{dollar} and some fictitious systems as the immediate steps for the study of the evolution of the approximate quantum numbers from H{dollar}sp-{dollar} and H{dollar}sb2sp+{dollar}. The density distribution at each fixed hyperradius R was plotted to visualize the radial and angular correlation. Analysis of the T quantum number was also done in the atomic limit.