A formalism to evaluate the resonant states produced by two particles moving outside a closed shell core is presented. The two particle states are calculated by using a single particle representation consisting of bound states, Gamow resonances and scattering states in the complex energy plane (Berggren representation). Two representative cases are analysed corresponding to whether the Fermi level is below or above the continuum threshold. It is found that long lived two-body states (including bound states) are mostly determined by either bound single-particle states or by narrow Gamow resonances. However, they can be significantly affected by the continuum part of the spectrum. PACS number(s): 25.70. Ef,23.50.+z,25.60+v,21.60.Cs Typeset using REVT E X 1 The prospect of reaching and measuring very unstable nuclei, as is materializing now, opens the possibility of studying spectroscopic processes occuring in the continuum part of nuclear spectra. Much work has already been done in this subject, particularly regarding halo nuclei [1]. Still, the role played by single-particle resonances and of the continuum itself upon particles moving in the continuum of a heavy nucleus is not fully understood. For instance, one may wonder whether two particles outside a core where the Fermi level is immersed in the continuum may produce a quasibound state and, in this case, whether that state is built upon narrow single-particle resonances or by an interplay between the two-particle interaction and the continuum, or by a combination of these mechanisms, as it happens in typical halo nuclei. To answer such questions is a difficult undertaking, particularly because the resonances on the real energy axis do not correspond to a definite state. A way of approaching this problem is by solving the Schrödinger equation with outgoing boundary conditions. One thus obtains the resonances as poles of the S-matrix in the complex energy plane. These poles (Gamow resonances) can be considered discrete states on the same footing as bound states (see Ref.[2] and references therein). However, in this case one finds that physical quantities, like energies and probabilities, become complex. One may attempt to give meaning to these complex quantities. Thus, it is usually assumed that the imaginary part of the energy of a decaying resonance is (except a minus sign) half the width. Other examples are the interpretation of complex cross sections done by Berggren [3] or the widely used radioactive decay width evaluated by Thomas as the residues of the S-matrix [4]. All these interpretations are valid only if the resonances are isolated and, therefore, narrow. In this case the residues of the S-matrix becomes real. One may thus apply this theory and evaluate all resonances, giving physical meaning to the narrow ones only. To achieve this goal a representation consisting of bound states, Gamow resonances and the proper continuum was proposed some years ago [2] (Berggren representation). One chooses the proper continuum as a given contour in th...

We formulate the Gamow shell model (GSM) in coupled-channel (CC) representation for the description of proton/neutron radiative capture reactions and present the first application of this new formalism for the calculation of cross-sections in mirror reactions 7 Be(p, γ) 8 B and 7 Li(n, γ) 8 Li. The GSM-CC formalism is applied to a translationally-invariant Hamiltonian with an effective finiterange two-body interaction. Reactions channels are built by GSM wave functions for the ground state 3 2 − and the first excited state 1 2 − of 7 Be/ 7 Li and the proton/neutron wave function expanded in different partial waves.PACS numbers: 03.65. Nk, 33.15.Ry

An implementation of the shell-model to the complex energy plane is presented. The representation used in the method consists of bound single-particle states, Gamow resonances and scattering waves on the complex energy plane. Two-particle resonances are evaluated, and their structure in terms of the single-particle degrees of freedom is analyzed. It is found that two-particle resonances are mainly built upon bound states and Gamow resonances, but the contribution of the scattering states is also important.