Renormalized three-body equations with short-range forces

2011 ◽  
Vol 89 (10) ◽  
pp. 1009-1013
Author(s):  
Ahmed Osman
Keyword(s):  
Effective Field Theory ◽  
Short Range ◽  
Body Problem ◽  
Phase Shifts ◽  
Effective Field ◽  
Three Body Problem ◽  
Deuteron Breakup ◽  
Deuteron Scattering ◽  
Group Invariant ◽  
Three Body

A three-body problem for a system of three nucleons interacting with short-range forces is discussed following effective field theory. Considering the case of a system of neutron–deuteron scattering, three-body equations are demonstrated such that the eigenvalues greater than unity are removed from the kernel leading to an equation that is renormalization-group invariant. The phase shifts are developed from a unique solution of the case of the doubled channel in neutron–deuteron scattering. The calculated neutron–deuteron phase shifts are well described below the deuteron breakup threshold.

scholarly journals The three-body problem in dimension one: From short-range to contact interactions

2018 ◽  
Vol 59 (7) ◽  
pp. 072104 ◽  
Author(s):  
Giulia Basti ◽  
Claudio Cacciapuoti ◽  
Domenico Finco ◽  
Alessandro Teta
Keyword(s):  
Short Range ◽  
Body Problem ◽  
Contact Interactions ◽  
Three Body Problem ◽  
Three Body ◽  
Dimension One

Three-body problem of two electron atoms. II

1980 ◽  
Vol 58 (6) ◽  
pp. 760-762 ◽  
Author(s):  
S. G. Lie ◽  
Y. Nogami
Keyword(s):  
Wave Function ◽  
Correlation Function ◽  
Electron Correlation ◽  
Ground State ◽  
Short Range ◽  
Body Problem ◽  
Ground State Wave Function ◽  
Three Body Problem ◽  
State Wave ◽  
Three Body

With the ansatz that the ground state wave function for a helium-like atom is of the form of [Formula: see text], the optimal correlation function [Formula: see text] is determined. Here x and y are the distances of the electrons from the nucleus, while z is that between the electrons. The parameters α and β are determined by minimizing the energy of the system. The method is particularly useful for calculating quantities which are sensitive to the short-range electron–electron correlation.

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