Hyperspherical study of Coulombic three-body problem

Miscellaneous · Tue Jan 01 00:00:00 EST 1991

OSTI ID:5315901

Zheng, Chen

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. The author examines the evolution of the approximate quantum numbers that are used for classifying bound and resonance states of the system as the mass ratio {lambda} = m{sub A}/m{sub B} changes from the atomic limit ({lambda} {yields} 0 as in H{sup {minus}}) to the diatomic molecular limit ({lambda} {much gt} 1 as in H{sub 2}{sup +}). It is shown that for states which exhibit rovibrational behaviors in the atomic limit ({lambda} {yields} 0), a single set of approximate quantum numbers can be used to describe three-body systems of any {lambda}'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-{lambda} 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 a Ps{sup {minus}}, d{mu}d and some fictitious systems as the immediate steps for the evolution of the approximate quantum numbers from H{sup {minus}} and H{sub 2}{sup +}. 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.

• Research Organization: Kansas State Univ., Manhattan, KS (United States)
• OSTI ID: 5315901
• Resource Relation: Other Information: Thesis (Ph.D.)
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
HYDROGEN IONS
QUANTUM NUMBERS
HYDROGEN IONS 1 MINUS
MOLECULAR IONS
ATOMIC MODELS
ATOMS
COORDINATES
COULOMB FIELD
ENERGY LEVELS
IONS
MASS
RESONANCE
THREE-BODY PROBLEM
ANIONS
CHARGED PARTICLES
ELECTRIC FIELDS
MANY-BODY PROBLEM
MATHEMATICAL MODELS
664100* - Theory of Electronic Structure of Atoms & Molecules- (1992-)