Efficient emulator for solving three-nucleon continuum Faddeev equations with chiral three-nucleon force comprising any number of contact terms

We demonstrate a computational scheme which drastically decreases the required time to get theoretical predictions based on chiral two- and three-nucleon forces for observables in three-nucleon continuum. For a three-nucleon force containing N short-range terms all workload is reduced to solving N+1 Faddeev-type integral equations. That done, computation of observables for any combination of strengths of the contact terms is done in a flash. We demonstrate on example of the elastic nucleon-deuteron scattering observables the high precision of the proposed emulator and its capability to reproduce exact results.

Perturbative Treatment of Three-Nucleon Force Contact Terms in Three-Nucleon Faddeev Equations

We present a perturbative approach to solving the three-nucleon continuum Faddeev equation. This approach is particularly well suited to dealing with variable strengths of contact terms in a chiral three-nucleon force. We use examples of observables in the elastic nucleon-deuteron scattering as well as in the deuteron breakup reaction to demonstrate high precision of the proposed procedure and its capability to reproduce exact results. A significant reduction of computer time achieved by the perturbative approach in comparison to exact treatment makes this approach valuable for fine-tuning of the three-nucleon Hamiltonian parameters.

Effect of isospin averaging for $ppK^-$ kaonic cluster

The kaonic cluster ppK^-ppK− is described by isospin-dependent N{\bar K}NK‾ potentials with significant difference between singlet and triplet components. The quasi-bound state energy of the system is calculated based on the configuration space Faddeev equations within isospin and averaged potential models. The isospin averaging of N{\bar K}NK‾ potentials is used to simplify the isospin model to isospinless one. We show that three-body bound state energy E_{3}E3 has a lower bound within the isospin formalism due to relation \left\vert E_{3}(V_{NN}=0)\right\vert<2\left\vert E_{2}\right\vert|E3(VNN=0)|<2|E2|, where E_{2}E2 is the binding energy of isospin singlet state of the N{\bar K}NK‾ subsystem. The averaged potential model demonstrates opposite relation between |E_{2}||E2| and |E_{3}(V_{NN}=0)||E3(VNN=0)|.

Particle representation for $NN{\bar K}$ system

In the framework of the Faddeev equations in configuration space we perform an analysis of quasi-bound state of the NN{\bar K}NNK‾ system within a particle model. In our approach, the system NN{\bar K}(s_{NN}=0)NNK‾(sNN=0) (NN{\bar K}(s_{NN}=1))NNK‾(sNN=1)) is described as a superposition of ppK^{-}ppK− and pn{\bar K}^0pnK‾0 (nn{\bar K}^{0}nnK‾0 and pn{ K}^-pnK−) states, which is possible due to a particle transition. The relation of the particle model to the theory of a two-state quantum system is addressed and discussed taking into account the possibilities of deep and shallow NN{\bar K}(s_{NN}=0)NNK‾(sNN=0) quasi-bound states.

Exploring the unknown Lambda-neutron interaction

No published \LambdaΛn scattering data exist. A relativistic heavy-ion experiment has suggested that a \LambdaΛnn bound state was seen. However, several theoretical analyses have cast serious doubt on the bound-state assertion. Nevertheless, there could exist a three-body \LambdaΛnn resonance. Such a resonance could be used to constrain the \LambdaΛn interaction. We discuss \LambdaΛnn calculations using nn and \LambdaΛn pairwise interactions of rank-one, separable form that fit effective range parameters of the nn system and those hypothesized for the as yet unobserved \LambdaΛn system based upon four different \LambdaΛN potentials. The use of rank-one separable potentials allows one to analytically continue the \LambdaΛnn Faddeev equations onto the second complex energy plane in search of resonance poles, by examining the eigenvalue spectrum of the kernel of the Faddeev equations. Although each of the potential models predicts a \LambdaΛnn sub-threshold resonance pole, scaling of the \LambdaΛn interaction by as little as \sim∼5% does produce a physical resonance. This suggests that one may use photo-(electro-)production of the \LambdaΛnn system from tritium as a tool to examine the strength of the \LambdaΛn interaction.

INVESTIGATION OF THREE-ATOMIC CLUSTERS WITHIN FADDEEV EQUATIONS

The binding energies of 4He3 and 4He26Li three-atomic clusters were calculated within the differential Faddeev equations. Obtained results show that different methods provide similar results for different potential models. It is shown that the excited state energy of each system is close to it’s respective two-body threshold, which could indicate on the Efimov nature of the excited state of 4He26Li.