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

• URL: http://arxiv.org/abs/2312.05085v2
• Date: Fri, 24 May 2024 14:35:57 GMT
• Title: Feasibility of perturbative generation of bound-states from resonances or virtual states
• Abstract summary: I investigate whether it is possible to generate bound-states from resonances or virtual states through first-order perturbation theory. I show that it is possible to obtain negative-energy states by sandwiching a next-to-leading order interaction with the leading-order (LO) wavefunctions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 Schr\"odinger equation and Hermitian Hamiltonian, there is an inability to create bound-states with structure similar to those formed by the non-perturbative treatments.

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