Relativistic effects in three-body bound states

Abstract

%e formulate relativistic and nonrelativistic two-particle dynamics in such a manner that the two-body binding energies are the same for both. %e then formulate and solve the relativistic Faddeev equations for a simple s-wave potential (Malfliet-Tjon V). The relativistic effects are small {about 3%}and reduce the three-body binding energy. The expectation value of the relativistic energy operator with the nonrelativistic wave function is a fairly good approximation, but approximate expressions involving expansions in powers of the momentum are shown to be quite unreliable.

Calculations of the Triton Binding Energy with a Lorentz Boosted Nucleon-Nucleon Potential

“…However, the scale transformation is a very useful and simple parameterization of a relativistic NN potential, which preserves the NN phase shifts exactly. Using a s-wave approximation we solved the relativistic Faddeev equation with Lorentz boost of the scale transformed potential [17,18] and it agreed with the previous result [16].…”

“…The first attempt in solving the relativistic Faddeev equation for the three-nucleon bound state based on the second approach has been carried out in [16], resulting in a decrease of the binding energy compared to the nonrelativistic result. On the other hand, similar calculations based on the field theory approach [15] increase it.…”

Bakamjian-Thomas mass operator for few-nucleon systems from chiral dynamics

“…The superscript (1) refers to the sector of the Fock space with baryon number 1. The mass operator commutes with the baryon number, and there is the freedom to choose a different structure function f for each sector of the Fock space.…”

“…For what concerns the covariance properties, the structure function f (2) for the 2-nucleon sector can be chosen different from f (1) . However, as we will see in subsection II C, in order to have a consistent renormalization we have to choose f (1) = f (2) .…”

A theorem on light-front quantum models

“…The Poincaré group has two independent invariant polynomials in the infinitesimal generators, 6) where the spectrum of M 2 has a positive lower bound and the spin j 2 is defined by…”