A study of the pion–nucleon coupling constant based on scattering length and effective range for both pseudovector and pseudoscalar

Abstract

In this study, we critically evaluate the Yukawa potential using the meson field theory in 
order to establish a relationship between the energy (MeV) for both neutron–proton and 
proton–proton which is pseudoscalar and pseudovector in the case of scattering field, 
similar in the effect range from experimental values of pion atoms. We also deduce the 
charged pion–nucleon coupling constant systematically and with statistical uncertainties. 
The result shows that both models display good agreement with the experimental values 
with a trend as the energy increases for both interactions’ effective range on pseudovec
tor (proton–proton) and pseudoscalar (neutron–proton) is at a smaller length. Similarly, 
low energy is recorded for the scattering length interaction. The charge pion–nucleon cou
pling constant is at values of 
2
14.54 4
gπ
π
±
and 
2
14.52 4
gπ
π
±
for both pseudovector 
and pseudoscalar, respectively. This shows that the electromagnetic interaction associ
ated with the correction will likely be added or removed from the experimental values of 
the nuclear-Coulomb low-energy parameters of pp and np scattering
PACS numbers: 13.75.Cs, 13.75.G×, 14.20.Dh, 14.40.Be, 25.40.Cm, 25.40.Dn.