Coalescence of Two Exceptional Points in the Anti-hermitian 3-level Pairing Model

An essential part of the motion of short-lived nucleonic matter is in classically forbidden regions and, hence, its properties are effected by both the continuum and many-body correlations 1,2. The effect of resonances and the non-resonant scattering states can be considered in the OQS extension of the shell model (SM), the so-called continuum shell model (CSM) 1. Two realizations of the CSM have been studied recently: the real-energy CSM 3 and the complex-energy CSM 4,5, the so-called Gamow Shell Model (GSM). For hermitian Hamilton operators, both real-energy CSM and complex-energy CSM (GSM) lead to the complex-symmetric, non-hermitian eigenvalue problem. As a result, OQSs exhibit unintuitive properties, qualitatively different from closed quantum systems (CQSs). One of them is the phenomenon of sharp crossing of resonances with same quantum numbers (same symmetries). Among degeneracies associated with avoided crossings in quantal spectra, one finds a diabolic point (DP) 9, and an exceptional point (EP) 7, which appears in complex extended hermitian Hamiltonians. In this Letter, we shall discuss some aspects of degeneracies in spectra of a prototypical