Feasibility of perturbative generation of bound-states from resonances or virtual states

Abstract

I investigate whether it is possible to generate bound-states from resonances or virtual states through first-order perturbation theory. Using contact-type potentials as those appeared in pionless effective field theory, I show that it is possible to obtain negative-energy states by sandwiching a next-to-leading order (NLO) interaction with the leading-order (LO) wavefunctions, under the presence of LO resonances or virtual states. However, at least under the framework of time-independent Schrödinger equation and Hermitian Hamiltonian, there is an inability to create bound-states with structure similar to those formed by the non-perturbative treatments.

17 pages, 14 figures. Published version with an appendix added and the title changed

References in corpus (21)

• Universal Properties of the Four-Body System with Large Scattering Length
• No-core shell model in an effective-field-theory framework
• Universal properties of infrared oscillator basis extrapolations
• Short-range nuclear forces in singlet channels
• Renormalization of Singular Potentials and Power Counting
• Effective Theory for Trapped Few-Fermion Systems
• Radiative corrections in K --> 3 pi decays
• Subtractive renormalization of the NN scattering amplitude at leading order in chiral effective theory
• Deconstructing triplet nucleon-nucleon scattering
• Subtractive renormalization of the NN interaction in chiral effective theory up to next-to-next-to-leading order: S waves
• Ultraviolet extrapolations in finite oscillator bases
• Power counting in chiral effective field theory and nuclear binding
• Infinite-cutoff renormalization of the chiral nucleon-nucleon interaction at N3LO
• Chiral potential renormalized in harmonic-oscillator space
• Three-body resonances in pionless effective field theory
• Constructing chiral effective field theory around unnatural leading-order interactions
• What Can Possibly Go Wrong?
• Bayesian Analysis of $\chi$EFT at Leading Order in a Modified Weinberg Power Counting Approach
• Perturbative chiral nucleon-nucleon potential for the ${}^3{P}_0$ partial wave
• Effective field theory with resonant P-wave interaction
• Nucleon-nucleon scattering with perturbative pions: The uncoupled $P$-wave channels

Cited by in corpus (2)

• A further study on the renormalization group aspect of perturbative corrections
• Auxiliary counterterms and their role in effective field theory