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Background: The repulsive Coulomb force poses severe challenges when solving the three-body problem for (d,p) reactions on intermediate mass and heavy nuclei. Recently, a new approach based on the Coulomb-distorted basis in momentum space was proposed. Purpose: In this work, we demonstrate the feasibility of using the Coulomb-distorted basis in momentum space for calculating matrix elements expected in a wide range of nuclear reactions. Method: We discuss the analytic forms of the Coulomb wave function in momentum space. We analyze the singularities in the Coulomb-distorted form factors and the required regularization techniques. Employing a separable interaction derived from a realistic nucleon-nucleus optical potential, we compute and study the Coulomb-distorted form factors for a wide range of cases, including charge, angular momentum, and energy dependence. We also investigate in detail the precision of our calculations. Results: The Coulomb-distorted form factors differ significantly from the nuclear form factors except for the very highest momenta. Typically, the structure of the form factor is shifted away from zero momentum due to the Coulomb interaction. Unlike the Yamaguchi forms typically used in three-body methods, our realistic form factors have a short high-momentum tail, which allows for a safe and efficient truncation of the momentum grid. Conclusions: Our results show that the Coulomb-distorted basis can be effectively implemented. [ABSTRACT FROM AUTHOR]

Back in the mid-1980s, a new branch of investigation related to the interaction of eta mesons with nuclei came into existence. It started with the theoretical prediction of possible exotic states of eta mesons and nuclei bound by the strong interaction and later developed into an extensive experimental program to search for such unstable states as well as understand the underlying interaction via eta-meson producing reactions. The vast literature of experimental as well as theoretical works that studied various aspects of eta-producing reactions such as the &03co+n → ηp, pd → ³He η, p 6Li → 7Be → and γ ³He → η X, to name a few, had but one objective in mind: to understand the eta-nucleon (ηN) and hence the η-nucleus interaction which could explain the production data and confirm the existence of some η-mesic nuclei. In spite of these efforts, there remain uncertainties in the knowledge of the ηN and hence the η-nucleus interaction. Therefore, this review is an attempt to bind together the findings in these works and draw some global and specific conclusions which can be useful for future explorations. The ηN scattering length (which represents the strength of the η-nucleon interaction) using different theoretical models and analyzing the data on η production in pion, photon and proton induced reactions was found to be spread out in a wide range, namely, 0.18 ≤ ... aηN ≤ 1.03 fm and 0.16 ≤ ... aηN ≤ 0.49 fm. Theoretical searches of heavy η-mesic nuclei based on η-nucleus optical potentials and lighter ones based on Faddeev type few-body approaches predict the existence of several quasibound and resonant states. Although some hints of η-mesic states such as ³ηHe and 25ηMg do exist from previous experiments, the promise of clearer signals for the existence of η-mesic nuclei lies in the experiments to be performed at the J-PARC, MAMI and COSY facilities in the near future. This review is aimed at giving an overall status of these efforts. [ABSTRACT FROM AUTHOR]

The continuum-discretized coupled channels (CDCC) method is a well established theory for direct nuclear reactions which includes breakup to all orders. Alternatively, the three-body problem can be solved exactly within the Faddeev formalism which explicitly includes breakup and transfer channels to all orders. With the aim to understand how CDCC compares with the exact three-body Faddeev formulation, we study deuteroninduced reactions on (i) 10Be at Ed = 21 A, 40.9 and 71 MeV; (ii) 12C at Ed = 12 and 56 MeV; and (iii) 48Ca at £d = 56 MeV. We calculate elastic, transfer, and breakup cross sections. Overall, the discrepancies found for elastic scattering are small with the exception of very backward angles. For transfer cross sections at low energy, ∼ 10 MeV/u, CDCC is in good agreement with the Faddeev-type results and the discrepancy increases with beam energy. In contrast, breakup observables obtained with CDCC are in good agreement with Faddeev-type results for all but the lower energies considered here. [ABSTRACT FROM AUTHOR]

A model for the p d→p dη reaction published earlier, including the final state interaction (FSI) of all particles, is revisited to investigate the low energy data on this reaction. The three-body problem of p–d–η scattering in the final state is approximated in terms of pairwise interactions between the three particles in the final state. Apart from a comparison with some preliminary data, two new findings relevant to the near threshold data analysis are reported. The first one points toward the limitations of an FSI factor used conventionally to extract the eta-deuteron scattering length and infer subsequently on the existence of eta-mesic states. The second result emphasizes the role of the p–d FSI and the strong Coulomb repulsion near threshold. Finally, a comparison of the above model calculation with low energy data, excludes very large eta-nucleon scattering lengths. [ABSTRACT FROM AUTHOR]

We present a study of the η production at low energies in pd collision with 3He and pd nuclear systems in the final state. The η production mechanism is described by a two-step model and the final state interactions are included fully. The η - d and η - 3He final state interactions are incorporated through the solution of the Lippmann Schwinger equation for a half off-shell η - AT-matrix. For η - d this t-matrix is written in a factorized form, with an off-shell form factor multiplying an on-shell part having the scattering length representation. The p - d final state interaction is included by multiplying the production matrix element by the inverse of the Jost function which includes the strong as well as the Coulomb interaction. The total cross sections are found to be strongly affected by both the η - d and the p - d final state interactions. The η - 3HeT-matrix is obtained in the Finite Rank Approximation (FRA) by solving few-body equations. The calculated total cross sections are in good accord with the available experimental data. Through the time delay method of Wigner, we also explore the possibility of the existence of quasi-bound η-3He mesic states in this η - 3HeT-matrix. We find that the T-matrix which reproduces the low energy pd → 3He η data implies a quasi-bound eta state near threshold. This is in accord with experimental indications. [ABSTRACT FROM AUTHOR]

We present a calculation for η production in the p-6Li fusion near threshold including the η-7Be final state interaction (FSI). We consider the 6Li and 7Be nuclei as α-d and α-3He clusters respectively. The calculations are done for the lowest states of 7Be with $J = (\frac{3}{2}^-, \frac{1}{2}^-)$ resulting from the L = 1 radial wave function. The η-7Be interaction is incorporated through the η-7BeT–matrix, constructed from the medium modified matrices for the η-3He and η-α systems. These medium modified matrices are obtained by solving few body equations, where the scattering in nuclear medium is taken into account. [ABSTRACT FROM AUTHOR]

Study of the scattering process in the nonlocal interaction framework leads to an integro-differential equation. The purpose of the present work is to develop an efficient approach to solve this integro-differential equation with high degree of precision. The method developed here employs a Taylor approximation for the radial wave function which converts the integro-differential equation into a readily solvable second-order homogeneous differential equation. This scheme is found to be computationally efficient by a factor of 10 when compared to the iterative scheme developed in Upadhyay et al. [J. Phys. G: Nucl. Part. Phys. 45, 015106 (2018)]. The calculated observables for neutron scattering off 24Mg, 40Ca, 100Mo, and 208Pb with energies up to 10 MeV are found to be within at most 8% of those obtained with the iterative scheme. Further, we propose an improvement over the Taylor scheme that brings the observables so close to the results obtained by iterative scheme that they are visually indistinguishable. This is achieved without any appreciable change in the run time. [ABSTRACT FROM AUTHOR]

Different models for the nonlocal description of the nuclear interaction are compared through a study of their effects on the half-lives of radioactive nuclei decaying by the emission of alpha particles. The half-lives are evaluated by considering a preformed a particle (4He nucleus), which tunnels through the Coulomb barrier generated by its interaction with the daughter nucleus. An effective potential obtained from a density-dependent double-folding strong potential between the a and the daughter nucleus within the nonlocal framework is found to decrease the half-lives as compared to those in the absence of nonlocalities. Whereas the percentage decrease within the older Perey-Buck and São Paulo models ranges between 20 to 40% for medium to heavy nuclei, a recently proposed effective potential leads to a decrease of only 2 to 4%. In view of these results, we provide a closer examination of the approximations used in deriving the local equivalent potentials and propose that, apart from the scattering data, the a decay half-lives can be used as a complementary tool for constraining the nonlocality models. [ABSTRACT FROM AUTHOR]