Shell Model States in the Continuum

Abstract

We suggest a method for calculating scattering phase shifts and energies and widths of resonances which utilizes only eigenenergies obtained in variational calculations with oscillator basis and their dependence on oscillator basis spacing $\hslash \Omega$. We make use of simple expressions for the $S$-matrix at eigenstates of a finite (truncated) Hamiltonian matrix in the oscillator basis obtained in the HORSE ($J$-matrix) formalism of quantum scattering theory. The validity of the suggested approach is verified in calculations with model Woods--Saxon potentials and applied to calculations of $n\alpha$ resonances and non-resonant scattering using the no-core shell model.

Revision due to journal referee recommendations; 26 pages, 52 figures

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Cited by in corpus (22)

• A Guided Tour of Ab Initio Nuclear Many-Body Theory
• From bound states to the continuum
• Effective interactions in the sd shell
• Nucleon-$\alpha$ Scattering and Resonances in ${}^5$He and ${}^5$Li with JISP16 and Daejeon16 $NN$ interactions
• Ab initio calculations of low-energy nuclear scattering using confining potential traps
• Ab initio descriptions of $A=16$ mirror nuclei with resonance and continuum coupling
• Nuclear scattering via quantum computing
• Five-body calculation of $s$-wave $n$-${}^4$He scattering at next-to-leading order pionless effective field theory
• Ground-state properties of light $4n$ self-conjugate nuclei in $ab$ $initio$ no-core Monte Carlo shell model calculations with nonlocal $NN$ interactions
• SS-HORSE Extension of the No-Core Shell Model: Application to Resonances in ${}^7\mathrm{H}e$
• Coulomb Excitation of Deuteron in Peripheral Collisions with a Heavy Ion
• Asymptotic characteristics of decay channels of light nuclei states in the ab initio approach
• Calculations of $p(n,\gamma )d$ reaction in chiral effective field theory
• S-shell $\Lambda \Lambda$ hypernuclei based on chiral interactions
• Trineutron resonances in the SS-HORSE-NCSM approach
• Calculating reactions with use of no-core shell-model states
• Nucleon-deuteron scattering with the JISP16 potential
• Harmonic Oscillator Representation of Scattering Theory in the Presence of Coulomb Potential
• Study on $\Lambda nn$ Bound State and Resonance
• Applications of the Modified Hulthén-Kohn Method for Bound and Scattering States
• Tracing the evolution of nuclear forces under the similarity renormalization group
• Tetraneutron resonance and its isospin analogues