R. Id Betan

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

A formalism to evaluate the resonant states produced by two particles moving outside a closed shell core is presented. It is found that long lived two-body states (including bound states) are mostly determined by either bound single-particle states or by narrow single-particle resonances. However, they can be significantly affected by the continuum part of the spectrum.

Gamow functionals on operator algebras

We obtain the precise form of two Gamow functionals representing the exponentially decaying part of a quantum resonance and its mirror image that grows exponentially, as a linear, positive and continuous functional on an algebra containing observables. These functionals do not admit normalization and, with an appropriate choice of the algebra, are time reversal of each other.

Quantum decay processes and Gamov states

By extending the notion of states to functionals acting on the space of observables we obtain a well-defined complex spectral decomposition for the time evolution of quantum-decaying systems, where Gamov states play a fundamental role. It is shown that Gamov vectors are well-defined state functionals and, therefore, they stand on the same footing as plane waves.

Shell model in the complex energy plane and two-particle resonances

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.

On the mean value of the energy for resonant states

Abstract In this work we discuss possible definitions of the mean value of the energy for a resonant (Gamow) state. The mathematical and physical aspects of the formalism are reviewed. The concept of rigged Hilbert space is used as a supportive tool in dealing with Gamow-resonances.

Description of the proton and neutron radiative capture reactions in the Gamow shell model

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 7Be(p,gamma)8B and 7Li(n,gamma)8Li. The GSM-CC formalism is applied to a translationally-invariant Hamiltonian with an effective finite-range 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 7Be/7Li and the proton/neutron wave function expanded in different partial waves.

Using continuum level density in the pairing Hamiltonian: BCS and exact solutions

Abstract Pairing plays a central role in nuclear systems. The simplest model for the pairing is the constant-pairing Hamiltonian. The aim of the present paper is to include the continuum single particle level density in the constant-pairing Hamiltonian and to make a comparison between the approximate BCS and the exact Richardson solutions. The continuum is introduced by using the continuum single particle level density. It is shown that the continuum makes an important contribution to the pairing parameter even in those case when the continuum is weakly populated. It is shown that while the approximate BCS solution depends on the model space the exact Richardson solution does not.

Complex energy approaches for calculating isobaric analogue states

Parameters of isobaric analog resonance (IAR) are calculated in the framework of the Lane model using different methods. In the standard method, the direct numerical solution of the coupled channel (CC) Lane equations served as a reference for checking two complex energy methods, namely the complex energy shell model (CXSM) and the complex scaling (CS) approaches. The IAR parameters calculated by the CXSM and the CS methods agree with that of the CC results within 1 keV for all partial waves considered. Although the CXSM and the CS methods have similarities, an important difference is that only the CXSM method offers a direct way for studying the configurations of the IAR wave function.

Quantified Gamow shell model interaction for psd -shell nuclei

Background: The structure of weakly bound and unbound nuclei close to particle drip lines is one of the major science drivers of nuclear physics. A comprehensive understanding of these systems goes beyond the traditional configuration interaction approach formulated in the Hilbert space of localized states (nuclear shell model) and requires an open quantum system description. The complex-energy Gamow shell model (GSM) provides such a framework as it is capable of describing resonant and nonresonant many-body states on equal footing. Purpose: To make reliable predictions, quality input is needed that allows for the full uncertainty quantification of theoretical results. In this study, we carry out the optimization of an effective GSM (one-body and two-body) interaction in the psdf-shell-model space. The resulting interaction is expected to describe nuclei with 5≤A≲12 at the p-sd-shell interface. Method: The one-body potential of the He4 core is modeled by a Woods-Saxon + spin-orbit + Coulomb potential, and the finite-range nucleon-nucleon interaction between the valence nucleons consists of central, spin-orbit, tensor, and Coulomb terms. The GSM is used to compute key fit observables. The χ2 optimization is performed using the Gauss-Newton algorithm augmented by the singular value decomposition technique. The resulting covariance matrix enables quantification of statistical errors within the linear regression approach. Results: The optimized one-body potential reproduces nucleon-He4 scattering phase shifts up to an excitation energy of 20 MeV. The two-body interaction built on top of the optimized one-body field is adjusted to the bound and unbound ground-state binding energies and selected excited states of the helium, lithium, and beryllium isotopes up to A=9. A very good agreement with experimental results was obtained for binding energies. First applications of the optimized interaction include predictions for two-nucleon correlation densities and excitation spectra of light nuclei with quantified uncertainties. Conclusion: The new interaction will enable comprehensive and fully quantified studies of structure and reactions aspects of nuclei from the psd region of the nuclear chart.

Quasiparticle resonances in the BCS approach

Abstract We present a simple method for calculating the energies and the widths of quasiparticle resonant states in nuclei close to the driplines. The method is based on BCS equations written in the Berggren representation. In this representation the quasiparticle resonances are associated to the Gamow states of the mean field. The method is illustrated for the case of neutron-rich nuclei 20–22O and 84Ni.