Ab initio approaches to nuclear structure and scattering

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2024-05
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Sharaf, Mamoon Ahmed
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Vary, James P.
Tuchin, Kirill
Evans, James W.
Lajoie, John
Luecke, Glenn
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Physics and Astronomy
Abstract
The use of the ab initio (from first principles) no core shell model (NCSM) has proven to be highly successful, especially in systematically solving low-energy bound state problems. While there are many advantages in using the NCSM, there are also major technical difficulties in applying it to describe non-relativistic scattering states and reactions in the continuum despite recent progress. To address those difficulties, a simplification of the harmonic oscillator representation of scattering equations (HORSE) technique developed earlier, the single-state HORSE (SS-HORSE) method has been developed to describe various observables for light nuclei. The cost of this simplification however, is the loss of information on the continuum wave function, which limits the applicability of the SS-HORSE–NCSM approach. Moreover, extending the approach to multi-channel problems is nontrivial. With this in mind, the modified Hulth´en–Kohn method extending the NCSM to the continuum spectrum was suggested by Efros to address those shortcomings by allowing one to accurately compute the continuum wave function in a computationally feasible manner. In view of this, we combine the ideas of the Efros method with some achievements of the HORSE formalism to further refine the Efros method. We provide an illustration of the technique by calculating the two-body scattering problem, with a view to extending the method to few-body problems. We show that generalization to multi-channel problems is straightforward. We demonstrate other two-body applications of the method, including calculation of the p(n, γ)d reaction and the use of the S-matrix pole technique to compute resonance energies (Er), widths (Γ), and bound states. We show that given low-lying eigenfunctions of a Hamiltonian H with a truncated nucleon-nucleon (NN) interaction, we get accurate results. This suggests great promise for applicability to few-body problems, of which we provide results for n + α → 5He scattering in the resonance region. In addition to the non-relativistic continuum, the NCSM can also be extended to the relativistic regime. In particular, one can use light-front (LF) quantum-chromodynamics (QCD) by applying fermion and boson degrees of freedom and LF coordinates. We demonstrate the simplest possible Lagrangian describing bosons interacting via the λϕ^4 interaction. We find surprisingly complex structures with regards to critical coupling phenomena and conduct extensive error analysis. The results help us to better understand phase transitions for not only the ϕ^4 problem, but also to other more realistic problems involving quarks and gluons.
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