#### Date of Award

1986

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Abstract

In an effort to unravel the dependence of the dynamics of three-bound-particle systems on the relative masses of the particles, an adiabatic treatment in hyperspherical coordinates is used to study the ground state and some doubly excited states of Ps('-) (positronium negative ion) and other three-particle systems, including H('-) and M('-) (muonium negative ion). Two different methods for the solution of the adiabatic eigenvalue equation are presented; one uses a "prediagonalized" basis of hyperspherical harmonics, and the other uses an asymptotic basis which consists of hydrogenic functions for the positronium. Potential curves for Ps('-) and M('-) in the ('1)S('e), ('1)P('o), ('3)P('e), ('3)P('o) and ('1)D('e) states and for H('-) in the ('1)P('o) states are presented. A method for calculating the probability density as a function of the hyperspherical coordinates (R,(alpha),(theta)(,12)) is introduced and used for the P states of Ps('-). This helps to understand the different symmetries and to distinguish among them. A remarkable linear dependence of the binding energy of the ground state and of the doubly excited states on the reduced mass of the atom, discovered in this study, is presented and discussed.

#### Recommended Citation

Botero, Javier, "An Adiabatic Study of the Positronium Negative Ion and Other Three-Particle Systems." (1986). *LSU Historical Dissertations and Theses*. 4221.

https://digitalcommons.lsu.edu/gradschool_disstheses/4221

#### Pages

124

#### DOI

10.31390/gradschool_disstheses.4221