scholarly journals The Nucleon Ground State

1979 ◽  
Vol 32 (5) ◽  
pp. 525
Author(s):  
EK Rose ◽  
JL Cook ◽  
E Clayton
Keyword(s):  
Probability Density ◽  
Ground State ◽  
State Potential ◽  
Pion Nucleon ◽  
Overlap Matrix ◽  
Nucleon State ◽  
Infinite Set ◽  
Nonlocal Potentials

From the parameters obtained in a previous paper for the Pll pion-nucleon state, the ground state potential is determined and the meson probability density is calculated. The results hold for the simplest form of the overlap matrix and are phase-equivalent to an infinite set of nonlocal potentials.

scholarly journals Local and Nonlocal Potentials for Low Energy Pion-Nucleon Scattering

1977 ◽  
Vol 30 (4) ◽  
pp. 369
Author(s):  
E Clayton ◽  
JL Cook ◽  
EK Rose
Keyword(s):  
Ground State ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Low Energy ◽  
Nonlocal Potential ◽  
Nucleon Scattering ◽  
Incident Pion ◽  
Reaction Matrix ◽  
Pion Nucleon ◽  
Nonlocal Potentials

Local and nonlocal potentials have been evaluated using the reaction matrix approach to the inverse scattering problem for low energy pion-nucleon scattering. The nonlocal potential gave the oorrect position for the Pll ground state nucleon mass, but the local potential did not. Incident pion energies up to 700 MeV were considered.

scholarly journals Counting monster potentials

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Riccardo Conti ◽  
Davide Masoero
Keyword(s):  
Excited States ◽  
Ground State ◽  
Hermite Polynomials ◽  
Large Momentum ◽  
Integer Partitions ◽  
Complex Equilibria ◽  
State Potential

Abstract We study the large momentum limit of the monster potentials of Bazhanov-Lukyanov-Zamolodchikov, which — according to the ODE/IM correspondence — should correspond to excited states of the Quantum KdV model.We prove that the poles of these potentials asymptotically condensate about the complex equilibria of the ground state potential, and we express the leading correction to such asymptotics in terms of the roots of Wronskians of Hermite polynomials.This allows us to associate to each partition of N a unique monster potential with N roots, of which we compute the spectrum. As a consequence, we prove — up to a few mathematical technicalities — that, fixed an integer N , the number of monster potentials with N roots coincides with the number of integer partitions of N , which is the dimension of the level N subspace of the quantum KdV model. In striking accordance with the ODE/IM correspondence.

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