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We discuss various methods for determining the level shifts induced by short-range interactions in exotic atoms which are formed by a hadron and a nucleus of opposite charge. The energy shifts can be related to the effective range parameters through Deser or Trueman formulas. In order to assess the accuracy and the reliability of this indirect approach, its predictions are compared with direct bound-state calculations. Notably, the importance of including the Coulomb potential in scattering calculations is highlighted. Finally, the impact of multipole terms in the asymptotic electromagnetic interaction is examined. It is demonstrated that an indirect approach remains relevant by accounting for these effects perturbatively.

We explore the description of the bound $^{19}$B isotope in terms of a $^{17}$B+n+n three-body system where the two-body subsystems $^{17}$B+n and neutron-neutron (nn) have virtual states close to the continuum. Dimensionless scaling functions for the root-mean-square (rms) radii are defined and studied for different parameters of the neutron-core potential and considering three different models for neutron-neutron interaction. The scaling functions for the radii are rooted on the universal behavior of three-body systems close to the Efimov limit and depend only on dimensionless quantities formed by the two-neutron separation energies and scattering lengths. Our results show in practice the model independence of these scaling functions close to unitarity. We provide an estimation of the different rms relative separation distances between the constituents, as well as of the proton and matter radii., Comment: 9 pages, 7 figures

We present a reaction model to describe the fast removal of the $\alpha$-particle core in $^8$He nucleus with eventual emission of four neutrons. The obtained four neutron energy distributions allows to explain the sharp low energy peak observed by studying the missing mass spectra of four neutrons in [Nature Vol. 606, p. 678], as a consequence of dineutron-dineutron correlations., Comment: Accepted to PRL

We have investigated the possible existence of a $^7$H resonant state, considered as a five-body system consisting of a $^3$H core with four valence neutrons. To this aim, an effective n-$^3$H potential is constructed in order to reproduce the low energy elastic neutron scattering on $^3$H phase shifts and the $^5$H resonant ground state in terms of $^3$H-n-n system. The variational Gaussian Expansion Method is used to solve the 5-body Schr\"{o}dinger equation, while the resonant state parameters were estimated by means of the stabilization method. We have not found any sign of a narrow low energy resonance in the vicinity of $^3$H+4n threshold. However, we have identified a very broad structure at $E_R\approx 9$ MeV above this threshold, which corresponds to the $^7$H J$^{\pi}$=1/2$^+$ ground state. In the vicinity of this state, we have also identified a broad structure corresponding to the ground state of $^6$H isotope with quantum numbers $J^{\pi}=2^-$., Comment: 15 pages, 9 figures

We obtain the $s$- and $p$-wave low-energy scattering parameters for n$^3$H elastic scattering and the position of the $^4$H $J^\pi=1^-$ resonance using the pionless effective field theory at leading order. Results are extracted with three numerical techniques: confining the system in a harmonic oscillator trap, solving the Faddeev-Yakubovsky equations in configuration space, and using an effective two-body cluster approach. The renormalization of the theory for the relevant amplitudes is assessed in a cutoff-regulator range between $1\,\text{fm}^{-1}$ and $10\,\text{fm}^{-1}$. Most remarkably, we find a cutoff-stable/RG-invariant resonance in the $^4$H $J^\pi=1^-$ system. This $p$-wave resonance is a universal consequence of a shallow two-body state and the introduction of a three-body $s$-wave scale set by the triton binding energy. The stabilization of a resonant state in a few-fermion system through pure contact interactions has a significant consequence for the powercounting of the pionless theory. Specifically, it suggests the appearance of similar resonant states also in larger nuclei, like 16-oxygen, in which the theory's leading order does not predict stable states. Those resonances would provide a starting state to be moved to the correct physical position by the perturbative insertion of sub-leading orders, possibly resolving the discrepancy between data and contact EFT., Comment: 11 pages, 6 figures

By solving the Faddeev equations for the \={p}pn system, we compute the antiproton-deuteron level shifts and widths for the lowest hydrogenic states as well as the corresponding \={p}d scattering lengths and volumes. The \={p}d annihilation densities are obtained and compared to the nuclear density of deuterium. The validity of the Trueman relation for composite particles is studied. The strong part of \={N}N interaction is described by two different optical models, including the \={p}p-\={n}n coupling and n-p mass difference, while for NN several realistic interactions are used., Comment: To appear in Physics Letters B (2021)

The Faddeev Yakubovsky equations constitute a rigorous formulation of the quantum mechanical N body problem in the framework of non relativistic dynamics. They allow the exact solutions of the Schrodinger equation for bound and scattering states to be obtained. In this review, we will present the general formalism as well as the numerical tools we use to solve Faddeev Yakubovsky equations in configuration space. We will consider in detail the description of the four and five nucleon systems based on modern realistic nuclear Hamiltonians. Recent achievements in this domain will be summarized. Some of the still controversial issues related with the nuclear Hamiltonians as well as the numerical methods traditionally employed to solve few nucleon problems will be highlighted., Comment: Published in Frontiers in Physics 7:251 (2020)

We consider the evolution of the neutron-nucleus scattering length for the lightest nuclei. We show that, when increasing the number of neutrons in the target nucleus, the strong Pauli repulsion is weakened and the balance with the attractive nucleon-nucleon interaction results into a resonant virtual state in $^{18}$B. We describe $^{19}$B in terms of a $^{17}$B-$n$-$n$ three-body system where the two-body subsystems $^{17}$B-$n$ and $n$-$n$ are unbound (virtual) states close to the unitary limit. The energy of $^{19}$B ground state is well reproduced and two low-lying resonances are predicted. Their eventual link with the Efimov physics is discussed. This model can be extended to describe the recently discovered resonant states in $^{20,21}$B., Comment: Proceedings for the 24th edition of European Few Body Conference, Surrey, UK, 2-4 September 2019

We briefly summarize the main steps leading to the Faddeev-Yakubovsky equations in configuration space for N=3, 4 and 5 interacting particles.

We present a model description of the bound $^{17}$B isotope in terms of a $^{17}$B-n-n three-body system where the two-body subsystems $^{17}$B-n and n-n are unbound (virtual) states close to the unitary limit. The $^{17}$B ground state is well described in terms of two-body potentials only, and two low-lying resonances are predicted. Their eventual link with the Efimov physics is discussed. This model can be naturally used to describe the recently discovered resonant states in $^{20,21}$B., Comment: Accepted as a Rapid Communication in Physical Review C

This manuscript, presented to receive habilitated doctor degree, contains an overview of my recent works in developing complex scaling method and its applications in the few-body physics., Comment: Habilitation thesis

The first ever numerical solution of five-body Faddeev-Yakubovsky equations is presented in this work. Modern realistic Nucleon-Nucleon Hamiltonians have been tested when describing low energy elastic neutron scattering on $^4$He nucleus. Obtained results have been compared with those available in the literature and based on solution of the Schr\"odinger equation.

This work is an attempt to model the $4n$ response function of a recent RIKEN experimental study of the double charge exchange $^4$He($^8$He,$^8$Be)$^4$n reaction in order to put in evidence an eventual enhancement mechanism of the zero energy cross section, including a near-threshold resonance. This resonance can indeed be reproduced only by adding to the standard nuclear Hamiltonian an unphysically large T=3/2 attractive 3n-force which destroys the neighboring nuclear chart. No other mechanisms like cusps or related structures were found.

Determination of the proper power-counting scheme is an important issue for the systematic application of Chiral Effective Field Theory in nuclear physics. We analyze the cutoff dependence of three-nucleon observables (the neutron-deuteron scattering lengths and the triton binding energy) at the leading and next-to-leading orders of a power counting that ensures order-by-order renormalization in the two-nucleon system. Our results imply that three-body forces are not needed for renormalization of the three-nucleon system up to next-to-leading order, as usually assumed in the literature. (Erratum to the original article is included), Comment: 40 pages, 24 figures, (Erratum: 5 pages, 4 figures)

Time reversal invariance violating parity conserving (TVPC) effects are calculated for elastic proton deuteron scattering with proton energies up to $2~$MeV. Distorted Wave Born Approximation is employed to estimate TVPC matrix elements, based on hadronic wave functions, obtained by solving three-body Faddeev-Merkuriev equations in configuration space with realistic potentials.

A formalism based on the complex-scaling method is presented to solve the few particle scattering problem in configuration space using bound state techniques with trivial boundary conditions. Several applications to A=3,4 systems are presented to demonstrate the efficiency of the method in computing elastic as well as break-up reactions with Hamiltonians including both short and long-range interaction., Comment: FB20 conference proceedings

Nuclear electric dipole moments of $^{3}He$ and $^{3}H$ are calculated using Time Reversal Invariance Violating (TRIV) potentials based on the meson exchange theory, as well as the ones derived by using pionless and pionful effective field theories, with nuclear wave functions obtained by solving Faddeev equations in configuration space for the complete Hamiltonians comprising both TRIV and realistic strong interactions. The obtained results are compared with the previous calculations of $^{3}He$ EDM and with time reversal invariance violating effects in neutron-deuteron scattering.

Parity violating (PV) effects in neutron-deuteron radiative capture are studied using Desplanques, Donoghue, and Holstein (DDH) and effective field theory weak potentials. The values of PV effects are calculated using wave functions, obtained by solving three-body Faddeev equations in configuration space for phenomenological strong potentials. The relations between physical observables and low-energy constants are presented, and dependencies of the calculated PV effects on strong and weak potentials are discussed. The presented analysis shows the possible reason for the existing discrepancy in PV nuclear data analysis using the DDH approach and reveals a new opportunity to study short range interactions in nuclei.

Time reversal invariance violating parity conserving effects for low energy elastic neutron deuteron scattering are calculated for meson exchange and EFT-type of potentials in a Distorted Wave Born Approximation, using realistic hadronic wave functions, obtained by solving three-body Faddeev equations in configuration space., Comment: There was a technical mistake in calculations due to singular behavior of Yukawa functions at short range. We corrected the integration algorithm. There were some typos which are corrected. arXiv admin note: text overlap with arXiv:1104.3051

Time reversal invariance violating (TRIV) effects for low energy elastic neutron deuteron scattering are calculated for meson exchange and EFT-type of TRIV potentials in a Distorted Wave Born Approximation, using realistic hadronic strong interaction wave functions, obtained by solving three-body Faddeev equations in configuration space. The relation between TRIV and parity violating observables are discussed.

Formalism based on complex-scaling method is developed for solving the few particle scattering problem by employing only trivial boundary conditions. Several applications are presented proving efficiency of the method in describing elastic and three-body break-up reactions for Hamiltonians which may include both short and long-range interaction.

Parity violating effects for low energy elastic neutron deuteron scattering are calculated for DDH and EFT-type of weak potentials in a Distorted Wave Born Approximation, using realistic hadronic strong interaction wave functions, obtained by solving three-body Faddeev equations in configuration space. The results of relation between physical observables and low energy constants can be used to fix low energy constants from experiments. Potential model dependencies of parity violating effects are discussed., Comment: version accepted for publication in Phys. Rev. C

The cross section for radiative thermal neutron capture on ${}^{3}He$ ($\He3 +n \to \He4 +\gamma$; known as the $hen$ reaction) is calculated based on heavy-baryon chiral perturbation theory. The relevant M1 operators are derived up to next-to-next-to-next-to-leading order (N${}^3$LO). The initial and final nuclear wave functions are obtained from the rigorous Faddeev-Yakubovski equations for five sets of realistic nuclear interactions. Up to N${}^3$LO, the M1 operators contain two low-energy constants, which appear as the coefficients of non-derivative two-nucleon contact terms. After determining these two constants using the experimental values of the magnetic moments of the triton and ${}^3 He$, we carry out a parameter-free calculation of the $hen$ cross section. The results are in good agreement with the data., Comment: 26 pages, 2 figures

Elastic proton scattering on ${}^{3}{H}$ nucleus is studied inbetween p-% ${}^{3}{H}$ and n-${}^{3}{He}$ thresholds, in the energy region where $\alpha$-particles first excited state is inbeded in the continuum. For this aim Faddeev-Yakubovski equations are solved in configuration space, fully considering effects due to the isospin breaking as well as rigorously treating Coulomb interaction. Different realistic nuclear Hamiltonians are tested, elucidating open problems in nuclear interaction description., Comment: 13 pages,3 figures

M1 properties, comprising magnetic moments and radiative capture of thermal neutron observables, are studied in two- and three-nucleon systems. We utilize meson exchange current derived up to N$^3$LO using heavy baryon chiral perturbation theory a la Weinberg. Calculations have been performed for several qualitatively different realistic nuclear Hamiltonians, which permits us to analyze model dependence of our results. Our results are found to be strongly correlated with the effective range parameters such as binding energies and the scattering lengths. Taking into account such correlation, the results are in good agreement with the experimental data with small model-dependence., Comment: 24 pages, 3 figures

In this article an efficient method to calculate the matrix elements of three-nucleon force is presented. The new method is improved version of partial-wave decomposition presented in Few-Body Syst. 22 (1997) 107, which simplifies expression to be evaluated and permits to reduce computational effort as much as six times. Proposed method naturally applies to Faddeev-type calculations but also can be used by any method relaying on partial-wave decomposition.

The magnetic moments of ${}^2{H}$, ${}^3{He}$ and ${}^3{H}$ as well as the thermal neutron capture rate on the proton are calculated using heavy baryon chiral perturbation theory {\it \`{a} la} Weinberg. The M1 operators have been derived up to {N$^3$LO}. The nuclear matrix elements are evaluated with the use of wave functions obtained by carrying out variational Monte Carlo calculations for a realistic nuclear Hamiltonian involving high-precision phenomenological potentials like Argonne Av18 and Urbana IX tri-nucleon interactions. We discuss the potential- and cutoff-dependence of the results., Comment: 14 pages, 2figures

The Faddeev-Yakubovski equations are solved in configuration space for the $% \alpha$-particle and n-$^3$H continuum states. We test the ability of nonlocal nucleon-nucleon interaction models to describe 3N and 4N systems., Comment: 16 pages, 6 figures