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This white paper reports on the discussions of the 2018 Facility for Rare Isotope Beams Theory Alliance (FRIB-TA) topical program From bound states to the continuum: Connecting bound state calculations with scattering and reaction theory. One of the biggest and most important frontiers in nuclear theory today is to construct better and stronger bridges between bound state calculations and calculations in the continuum, especially scattering and reaction theory, as well as teasing out the influence of the continuum on states near threshold. This is particularly challenging as many-body structure calculations typically use a bound state basis, while reaction calculations more commonly utilize few-body continuum approaches. The many-body bound state and few-body continuum methods use different language and emphasize different properties. To build better foundations for these bridges, we present an overview of several bound state and continuum methods and, where possible, point to current and possible future connections.
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We investigate the influence of couplings among continuum states in collisions of weakly bound nuclei. For this purpose, we compare cross sections for complete fusion, breakup and elastic scattering evaluated by continuum discretized coupled channel (CDCC) calculations, including and not including these couplings. In our study, we discuss this influence in terms of the polarization potentials that reproduce the elastic wave function of the coupled coupled channel method in single channel calculations. We find that the inclusion of couplings among the continuum states renders the real part of the polarization potential more repulsive, whereas it leads to weaker apsorption to the breakup channel. We show that the non-inclusion of continuum-continuum couplings in CDCC calculations may not lead to qualitative and quantitative wrong conclusions.
We study ground and radial excitations of flavor singlet and flavored pseudoscalar mesons within the framework of the rainbow-ladder truncation using an infrared massive and finite interaction in agreement with recent results for the gluon-dressing function from lattice QCD and Dyson-Schwinger equations. Whereas the ground-state masses and decay constants of the light mesons as well as charmonia are well described, we confirm previous observations that this truncation is inadequate to provide realistic predictions for the spectrum of excited and exotic states. Moreover, we find a complex conjugate pair of eigenvalues for the excited $D_{(s)}$ mesons, which indicates a non-Hermiticity of the interaction kernel in the case of heavy-light systems and the present truncation. Nevertheless, limiting ourselves to the leading contributions of the Bethe-Salpeter amplitudes, we find a reasonable description of the charmed ground states and their respective decay constants.
We have performed CDCC calculations for the $^{6}$Li + $^{59}$Co, $^{144}$Sm and $^{208}$Pb systems, to investigate the dependence of the relative importance of nuclear and Coulomb breakup on the target charge (mass) at near barrier energies. The calculations were in good agreement with the experimental elastic scattering angular distributions for these systems and then, their predictions to the nuclear, Coulomb and total breakup were investigated. Although the relative importance of the nuclear breakup is, as expected, larger for lighter targets, this effect is not very pronounced. We also investigate a scaling of the nuclear breakup with the target mass and we compare the predictions for the integrated total breakup cross sections with experimental fusion cross sections at similar energies.
Nucleon-knockout reactions on proton targets (p, pN ) have experienced a renewed interest due to the availability of inverse-kinematics experiment with exotic nuclei. Various theoretical descriptions have been used to describe these reactions, such as the Distorted-Wave Impulse Approximation (DWIA), the Faddeev-type formalism and the Transfer to the Continuum method. Our goal is to benchmark the observables computed with the Faddeev and Transfer to the Continuum formalisms in the intermediate energy regime relevant for the experimental (p, pn) and (p, 2p) studies. In this paper, we analyze the 11 Be(p,pn)10Be reaction for different beam energies, binding energies and orbital quantum numbers with both formalisms to assess their agreement for different observables. We obtain a good agreement in all cases considered, within 10%, when the input potentials are taken consistently and realistically.
In order to clarify the nature of hypernuclear low-lying states, we carry out a comprehensive study for the structure of $^{144-154}_{~~~~~~~~Lambda}$Sm-hypernuclei, which exhibit a transition from vibrational to rotational characters as the neutron number increases. To this end, we employ a microscopic particle-core coupling scheme based on a covariant density functional theory. We find that the positive-parity ground-state band in the hypernuclei shares a similar structure to that of the corresponding core nucleus. That is, regardless of whether the core nucleus is spherical or deformed, each hypernuclear state is dominated by the single configuration of the $Lambda$ particle in the $s_{1/2}$ state ($Lambda s_{1/2}$) coupled to one core state of the ground band. In contrast, the low-lying negative-parity states mainly consist of $Lambda p_{1/2}$ and $Lambda p_{3/2}$ configurations coupled to plural nuclear core states. We show that, while the mixing amplitude between these configurations is negligibly small in spherical and weakly-deformed nuclei, it strongly increases as the core nucleus undergoes a transition to a well-deformed shape, being consistent with the Nilsson wave functions. We demonstrate that the structure of these negative-parity states with spin $I$ can be well understood based on the $LS$ coupling scheme, with the total orbital angular momentum of $L=[Iotimes 1]$ and the spin angular momentum of $S=1/2$.
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