Multiparticle Partial-Wave Amplitudes and Inelastic Unitarity. III. Solution of the Three-Body Unitarity Equations Using Characteristic Operator Functions

1973 ◽  
Vol 7 (10) ◽  
pp. 2989-2997 ◽  
Author(s):  
William H. Klink
Keyword(s):  
Partial Wave ◽  
Characteristic Operator ◽  
Operator Functions ◽  
Three Body

Singularities of the partial-wave amplitudes in the three-body problem

1978 ◽  
Vol 36 (1) ◽  
pp. 600-606 ◽  
Author(s):  
L. D. Blokhintsev ◽  
Yu. A. Simonov
Keyword(s):  
Partial Wave ◽  
Body Problem ◽  
Three Body Problem ◽  
Three Body

About the general solution of a linear homogeneous differential equation in a Banach space in the case of complex characteristic operators

2019 ◽  
pp. 211-217 ◽  
Author(s):  
Vasiliy. I Fomin
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
General Solution ◽  
Operator Equation ◽  
Bounded Operator ◽  
Characteristic Operator ◽  
Homogeneous Differential Equation ◽  
Operator Functions ◽  
Linear Homogeneous Differential Equation ◽  
Real Argument

A linear inhomogeneous differential equation (LIDE) of the n th order with constant bounded operator coefficients is studied in Banach space. Finding a general solution of LIDE is reduced to the construction of a general solution to the corresponding linear homogeneous differential equation (LHDE). Characteristic operator equation for LHDE is considered in the Banach algebra of complex operators. In the general case, when both real and complex operator roots are among the roots of the characteristic operator equation, the n -parametric family of solutions to LHDE is indicated. Operator functions eAt ; sinBt ; cosBt of real argument t ∈ [0;∞) are used when building this family. The conditions under which this family of solutions form a general solution to LHDE are clarified. In the case when the characteristic operator equation has simple real operator roots and simple pure imaginary operator roots, a specific form of such conditions is indicated. In particular, these roots must commute with LHDE operator coefficients. In addition, they must commute with each other. In proving the corresponding assertion, the Cramer operator-vector rule for solving systems of linear vector equations in a Banach space is applied

RESONANCE DYNAMICS IN COUPLED CHANNELS

2014 ◽  
Vol 26 ◽  
pp. 1460054 ◽  
Author(s):  
MICHAEL DÖRING
Keyword(s):  
Partial Wave ◽  
Gauge Invariance ◽  
Pion Photoproduction ◽  
General Properties ◽  
Coupled Channels ◽  
Resonance Properties ◽  
S Matrix ◽  
Three Body ◽  
Coupled Channel

General properties of the S-matrix, such as constraints from two- and three-body unitarity as well as gauge invariance, are discussed and illustrated for the example of a dynamical coupled channel approach. The Jülich model has been updated to analyze πN, ηN, and KY production as well as pion photoproduction. Partial wave amplitudes and resonance properties are determined.

scholarly journals Partial Wave Expansion of Three-particle Continuum. States in Hyperspherical Coordinates: Application to Ionisation Problems

1994 ◽  
Vol 47 (6) ◽  
pp. 743 ◽  
Author(s):  
JN Das
Keyword(s):  
Hydrogen Atom ◽  
Partial Wave ◽  
Hyperspherical Coordinates ◽  
Continuum State ◽  
Partial Wave Expansion ◽  
Continuum States ◽  
Wave Expansion ◽  
Three Body

A partial wave expansion of three-particle continuum states has been developed using hyperspherical coordinates. An approximate three-particle continuum state appears which may be useful in electron-hydrogen atom ionisation studies. Further improvement in the result is also possible. The analysis may be easily extended for application to other three-body ionisation problems.

Sign in / Sign up

Export Citation Format

Share Document