Two-Particle Resonant States in a Many-Body Mean Field

Abstract

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...

Density matrix renormalization group approach to two-fluid open many-fermion systems

“…Calculations were carried out for the proton-neutron systems 7 Li (three-nucleon problem) and 8 Li (four-nucleon problem). As compared to our previous work [29], two significant improvements of the GSM+DMRG technique have been made.…”

“…This example nicely demonstrates the validity of the manybody completeness relation in the GSM. The GSM Hamiltonian for 8 Li is the same as for 7 Li, the only modification being the change of T = 0 couplings in Eq. (19) owing to the different number of neutrons (N v = 3).…”

“…The solution of the configuration-interaction problem in the presence of continuum states has been recently advanced in the real-energy continuum SM [4][5][6] and in the complex-energy SM, the so-called Gamow shell model (GSM) [7][8][9][10][11]. In the GSM, the s.p.…”

“…IV. Illustrative calculations are carried out for 7 Li (three-nucleon systems) and 8 Li (four-nucleon systems). We study the impact of different starting conditions on the DMRG result and introduce two different truncation schemes in the DMRG procedure and discuss their virtues.…”

Current Status of Nuclear Physics Research

“…Other models start from a molecular viewpoint that employs composite particles, such as the α-particles as the building blocks for nuclear structure. A major task is underway to connect the two seemingly disjoint points of view and how nuclear excitations can emerge from a unified picture of the nucleus [257][258][259][260][261][262][263][264][265][266][267][268][269][270][271][272].…”