Hypertriton and hyperspherical harmonics

Thesis/Dissertation · Sat Jan 01 04:00:00 EST 1983

OSTI ID:6466427

Clare, Jr, R B

The hypertriton /sub ..lambda../H/sup 3/ is studied using the formalism of hyperspherical harmonics (H.H.). The Schrodinger equation takes the form of an infinite set of one-dimensional coupled differential equations (c.d.e.). The set of equations are solved for the bound state eigenvalue using the renormalized Numerov method. The eigenvalue convergence rate is monitored using three approximation techniques: extreme adiabatic, uncoupled adiabatic and the variational adiabatic approximation. The NN and ..lambda..N potentials used in this work are spin-independent, central Gaussian shapes with the same parameters as VS (Verma and Sural). By truncating the wavefunction expansion at 9 H.H., agreement with VS is attained to within 24 keV. However, contrary to the claim of VS, the inclusion of 7 more H.H. adds 209 keV to the calculated binding energy and it is felt that at least 100 keV remain before convergence will be achieved. Unlike VS, this work finds the partial waves in the H.H. formalism and uses them to calculate various expectation values for interparticle separations within /sub ..lambda../H/sup 3/. The results are: = 13.3 fm/sup 2/ and = = 14.7 fm/sup 2/. An interesting result is = 11.4 fm/sup 2/ where d denotes the np (deuteron) center of mass. This seems contrary to the belief of many that /sub ..lambda../H/sup 3/ can be pictured as a ..lambda.. particle spending much of its time very far from the deuteron core.

• Research Organization: Rensselaer Polytechnic Inst., Troy, NY (USA)
• OSTI ID: 6466427
• Country of Publication: United States
• Language: English

Related Subjects

645201* -- High Energy Physics-- Particle Interactions & Properties-Theoretical-- General & Scattering Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ADIABATIC APPROXIMATION
BARYONS
BETA DECAY RADIOISOTOPES
BETA-MINUS DECAY RADIOISOTOPES
BINDING ENERGY
BOUND STATE
DATA
DIFFERENTIAL EQUATIONS
EIGENVALUES
ELEMENTARY PARTICLES
ENERGY
EQUATIONS
FERMIONS
FUNCTIONS
HADRONS
HYDROGEN ISOTOPES
HYPERGEOMETRIC FUNCTIONS
HYPERNUCLEI
HYPERONS
INFORMATION
ISOTOPES
LAMBDA PARTICLES
LIGHT NUCLEI
NUCLEAR FRAGMENTS
NUCLEAR PROPERTIES
NUCLEAR RADII
NUCLEI
NUMERICAL DATA
ODD-EVEN NUCLEI
ONE-DIMENSIONAL CALCULATIONS
PARTIAL DIFFERENTIAL EQUATIONS
PARTIAL WAVES
POTENTIALS
RADIOISOTOPES
SCHROEDINGER EQUATION
STRANGE PARTICLES
THEORETICAL DATA
TRITIUM
WAVE EQUATIONS
WAVE FUNCTIONS
YEARS LIVING RADIOISOTOPES