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Register a new userA Realistic Approach to the $Xi NN$ Bound-State Problem based on Faddeev Equation
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The Faddeev equations for the $Xi NN$ bound-state problem are solved where the three $S$=$-2$ baryon-baryon interactions of Julich-Bonn-Munchen chiral EFT, HAL QCD and Nijmegen ESC08c are used. The $T$-matrix $T_{Xi N, Xi N}$ obtained within the original $LambdaLambda$-$Xi N$-$SigmaSigma$ $/$ $Xi N$-$Lambda Sigma$-$SigmaSigma$ coupled-channel framework is employed as an input to the equations. We found no bound state for Julich-Bonn-Munchen chiral EFT and HAL QCD but ESC08c generates a bound state with the total isospin and spin-parity $(T,J^{pi})=(1/2, 3/2^+)$ where the decays into $LambdaLambda N$ are suppressed.
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We study the coupled $LambdaLambda nn-Xi^- pnn$ system to check whether the inclusion of channel coupling is able to bind the $LambdaLambda nn$ system. We use a separable potential three-body model of the coupled $LambdaLambda nn - Xi^- pnn$ system as well as a variational four-body calculation with realistic interactions. Our results exclude the possibility of a $LambdaLambda nn$ bound state by a large margin. However, we have found a $Xi^- t$ quasibound state above the $LambdaLambda nn$ threshold.
Solution of the scattering problem turns to be very difficult task both from the formal as well as from the computational point of view. If the last two decades have witnessed decisive progress in ab initio bound state calculations, rigorous solution of the scattering problem remains limited to A$leq$4 case. Therefore there is a rising interest to apply bound-state-like methods to handle non-relativistic scattering problems. In this article the latest theoretical developments in this field are reviewed. Five fully rigorous methods will be discussed, which address the problem of nuclear collisions in full extent (including the break-up problem) at the same time avoiding treatment of the complicate boundary conditions or integral kernel singularities. These new developments allows to use modern bound-state techniques to advance significantly rigorous solution of the scattering problem.
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We propose a method that allows for the efficient solution of the three-body Faddeev equations in the presence of infinitely rising confinement interactions. Such a method is useful in calculations of nonrelativistic and especially semirelativistic constituent quark models. The convergence of the partial wave series is accelerated and possible spurious contributions in the Faddeev components are avoided. We demonstrate how the method works with the example of the Goldstone-boson-exchange chiral quark model for baryons.
In this paper, we study the relativistic effects in a three-body bound state. For this purpose, the relativistic form of the Faddeev equations is solved in momentum space as a function of the Jacobi momentum vectors without using a partial wave decomposition. The inputs for the three-dimensional Faddeev integral equation are the off-shell boost two-body $t-$matrices, which are calculated directly from the boost two-body interactions by solving the Lippmann-Schwinger equation. The matrix elements of the boost interactions are obtained from the nonrelativistic interactions by solving a nonlinear integral equation using an iterative scheme. The relativistic effects on three-body binding energy are calculated for the Malfliet-Tjon potential. Our calculations show that the relativistic effects lead to a roughly 2% reduction in the three-body binding energy. The contribution of different Faddeev components in the normalization of the relativistic three-body wave function is studied in detail. The accuracy of our numerical solutions is tested by calculation of the expectation value of the three-body mass operator, which shows an excellent agreement with the relativistic energy eigenvalue.
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