Contents
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8 No-Core Gamow Shell Model. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 365
8.1 Formulation of the No-Core Gamow Shell Model .. . . . . . . . . . . . . . . . . . 370
8.2 Benchmarking of No-Core Gamow Shell Model Against
Other Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 373
8.2.1 Binding Energies and Center-of-Mass Excitations .. . . . . . . . 373
8.2.2 5 He Unbound Nucleus .. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 378
8.2.3 Radial Overlap Integral and Asymptotic
Normalization Coefficient . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 381
8.3 Multi-Neutron Resonances .. . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 385
8.3.1 Tetraneutron Energy from the Extrapolation
of Overbinding Interactions . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 386
8.3.2 Trineutron and Tetraneutron in the Auxiliary
Potential Method .. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 389
8.4 Renormalization of Realistic Interactions in a Finite Model
Space Using ˆ ¯
Q-Box Method .. . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 391
8.4.1 Application of the ˆ ¯
Q-Box Method in Oxygen
and Fluorine Chains of Isotopes .. . . . . . . .. . . . . . . . . . . . . . . . . . . . 393
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 395
9 The Unification of Structure and Reaction Frameworks .. . . . . . . . . . . . . . . 401
9.1 Nucleon–Nucleus Reactions . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 405
9.1.1 Coupled-Channel Hamiltonian for Structure
and Reaction Observables . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 407
9.1.2 Electromagnetic Transitions in a Gamow
Coupled-Channel Formalism .. . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 411
9.1.3 Cross Sections .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 414
9.2 Generalization to Many-Nucleon Projectiles . . . . .. . . . . . . . . . . . . . . . . . . . 422
9.2.1 Clusters in the Berggren Basis Formalism .. . . . . . . . . . . . . . . . . 423
9.2.2 Numerical Treatment of Well-Bound Projectiles .. . . . . . . . . . 423
9.2.3 Inclusion of Break-up Reactions . . . . . . . .. . . . . . . . . . . . . . . . . . . . 425
9.2.4 Berggren Basis Expansion of Center-of-Mass States . . . . . . 427
9.2.5 Orthogonalization of Composites with Respect
to the Core .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 429
9.2.6 Asymptotic Cancellation of Correlations at High
Projectile Energy .. . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 430
9.2.7 Coupled-Channel Equations and Wave Functions
for Structure and Reactions with Multi-Nucleon
Projectiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 435
9.2.8 Treatment of Faddeev Equations with the Berggren
Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 440
9.2.9 Elastic and Inelastic Scattering Cross Sections .. . . . . . . . . . . . 442
9.2.10 Radiative Capture Cross Sections . . . . . . .. . . . . . . . . . . . . . . . . . . . 443