This paper investigates the possible use of the Hyperspherical Adiabatic basis in the description of scattering states of a three-body system. In particular, we analyze a 1+2 collision process below the three-body breakup. The convergence patterns for the observables of interest are analyzed by comparison to a unitary equivalent Hyperspherical Harmonic expansion. Furthermore, we compare and discuss two different possible choices for describing the asymptotic configurations of the system, related to the use of Jacobi or hyperspherical coordinates. In order to illustrate the difficulties and advantages of the approach two simple numerical applications are shown in the case of neutron-deuteron scattering at low energies using s-wave interactions. We found that the optimization driven by the Hyperspherical Adiabatic basis is not as efficient for scattering states as in bound state applications.
We formulate a hyperspherical approach within standard configuration interaction calculations aiming at a description of large-scale dynamics of $N$-particle system. The channel wave function and the adiabatic channel energy are determined by solving a hyperradius-constrained eigenvalue problem of the adiabatic Hamiltonian. The needed matrix elements are analytically evaluated using correlated Gaussians with good orbital angular momentum and parity. The feasibility of the approach is tested in three-$α$ system. A spectrum of the adiabatic channel energies is determined depending on the degree …
We have studied the solution of the six-nucleon bound state problem using the hyperspherical harmonic (HH) approach. For this study we have considered only two-body nuclear forces. In particular we have used a chiral nuclear potential evolved with the similarity renormalization group unitary transformation. A restricted basis has been selected by performing a careful analysis of the convergence of different HH classes. Finally, the binding energy and other properties of ${}^6$Li ground state are calculated and compared with the results obtained by other techniques. Then, we present a calculati…
With the goal of using chiral interactions at various orders to explore properties of the few-body nuclear systems, we write the recently developed local chiral interactions as spherical irreducible tensors and implement them in the hyperspherical harmonics expansion method. We devote particular attention to three-body forces at next-to-next-to leading order, which play an important role in reproducing experimental data. We check our implementation by benchmarking the ground-state properties of $^3$H, $^3$He and $^4$He against the available Monte Carlo calculations. We then confirm their order…
Convergence of the $ppp$ correlation function within the hyperspherical adiabatic basis
Instituto de Estructura de la Materia, CSIC（材料结构研究所，西班牙科学研究中心）；Istituto Nazionale di Fisica Nucleare（意大利国家核物理研究所）；Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague（捷克布拉格理工大学核科学与物理工程学院）；Experimental Physics Department, CERN（欧洲核子研究组织实验物理部）；University of Pisa（比萨大学）
This work presents further analysis of the three- and four-neutron systems in the low energy regime using adiabatic hyperspherical methods. In our previous Phys. Rev. Lett. article (Phys. Rev. Lett. 125, 052501 (2020)), the low-energy behavior of these neutron systems was treated in the adiabatic approximation, neglecting the off-diagonal non-adiabatic couplings. A thorough analysis of the density of states through a multi-channel treatment of the three-and four-neutron scattering near the scattering continuum threshold is performed, showing no evidence of a 4n resonance at low energy. A detai…
A method to identify and characterize three-body resonances in a discrete basis is discussed in the context of two-nucleon emitters. For this purpose, a resonance operator is introduced and diagonalized in a basis of energy pseudostates within the hyperspherical formalism. Then, the energy and width of the resonance are obtained from its time dependence. The approach is illustrated for $^{16}$Be ($^{14}\text{Be}+n+n$).
The Hyperspherical Harmonics (HH) method is one of the most accurate techniques to solve the quantum mechanical problem for nuclear systems with $A\le 4$. In particular, by applying the Rayleigh-Ritz or Kohn variational principle, both bound and scattering states can be addressed, using either local or non-local interactions. Thanks to this versatility, the method can be used to test the two- and three-nucleon components of the nuclear interaction. In the present review we introduce the formalism of the HH method, both for bound and scattering states. In particular, we describe the implementat…
Active-learning construction of hyperspherical-harmonics spaces for A = 3
European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*), Fondazione Bruno Kessler（欧洲核物理及相关领域理论研究中心 (ECT*)，布鲁诺·克勒斯勒基金会）；Data Science for Industry and Physics (DSIP), Fondazione Bruno Kessler（工业与物理学数据科学 (DSIP)，布鲁诺·克勒斯勒基金会）；Dipartimento di Fisica “E. Fermi”, Università di Pisa（比萨大学“E. 费米”物理系）；INFN-Sezione di Pisa（意大利国家核物理研究所比萨分部）
Weakly bound and unbound three-body nuclei are studied by using the pseudostate method within the hyperspherical formalism. After introducing the theoretical framework, the method is applied first to the $\boldsymbol{^9}$Be nucleus, showing a good agreement with the available data for its low-lying dipole response. Then, recent results on the structure and decay of the two-neutron emitters $\boldsymbol{^{26}}$O and $\boldsymbol{^{16}}$Be are presented. In particular, the role of the $\boldsymbol{n}$-$\boldsymbol{n}$ correlation in shaping their properties is discussed.
The electromagnetic potential consisting in the Coulomb plus the magnetic moment interactions between two nucleons is studied in nucleon-deuteron scattering. For states in which the relative N-d angular momentum L has low values the three--nucleon problem has been solved using the correlated hyperspherical harmonic expansion basis. For states in which the angular momentum L has large values, explicit formulae for the nucleon-deuteron magnetic moment interaction are derived and used to calculate the corresponding T-matrices in Born approximation. Then, the transition matrices describing N-d ela…
The low energy systems of three or four neutrons are treated within the adiabatic hyperspherical framework, yielding an understanding of the low energy quantum states in terms of an adiabatic potential energy curve. The dominant low energy potential curve for each system, computed here using widely accepted nucleon-nucleon interactions with and without the inclusion of a three-nucleon force, shows no sign of a low energy resonance. However, both systems exhibit a low energy enhancement of the density of states, or of the Wigner-Smith time-delay, which derives from long-range universal physics …
The $n+{}^3$H, $p+{}^3$He, $p+{}^3$H, and $n+{}^3$He elastic and charge exchange reactions at low energies are studied by means of the hyperspherical harmonic method. The considered nuclear Hamiltonians include modern two- and three-nucleon interactions, in particular results are reported in case of chiral two-nucleon potentials, with and without the inclusion of chiral three-nucleon (3N) interactions. A detailed study of the convergence and numerical stability of the method is presented. We have found that the effect the 3N force is in general tiny except for $p+{}^3$H scattering below the op…
The contribution of a three-nucleon (3N) force, acting between the neutron and proton in the incoming deuteron with a target nucleon, to the deuteron-target potential in the entrance channel of the $A(d,p)B$ reaction has been calculated within the adiabatic distorted wave approximation (ADWA). Four different 3N interaction sets from local chiral effective field theory ($χ$EFT) at next-to-next-to-leading order (N2LO) were used. Strong sensitivity of the adiabatic deuteron-target potential to the choice of the 3N force format has been found, which originates from the enhanced sensitivity to the …
We generalize the hidden-fermion family of neural network quantum states to encompass both continuous and discrete degrees of freedom and solve the nuclear many-body Schrödinger equation in a systematically improvable fashion. We demonstrate that adding hidden nucleons to the original Hilbert space considerably augments the expressivity of the neural-network architecture compared to the Slater-Jastrow ansatz. The benefits of explicitly encoding in the wave function point symmetries such as parity and time-reversal are also discussed. Leveraging on improved optimization methods and sampling tec…
