# On mass polarization effect in three-body systems

## TL;DR

This paper investigates the mass polarization effect in three-body nuclear systems using Faddeev equations, revealing different behaviors in bosonic and isospin-involved systems, with implications for kaonic clusters.

## Contribution

It provides a detailed evaluation of the mass polarization term in various three-body systems, highlighting differences between simple bosonic and complex isospin systems, and introduces a model to account for these effects.

## Key findings

- Mass polarization effect varies between bosonic and isospin systems.
- For bosonic systems, the three-body energy exceeds twice the two-body energy.
- In isospin systems, the three-body energy is less than twice the two-body energy, but a spin-averaged potential can transform this behavior.

## Abstract

We evaluate the mass polarization term of the kinetic-energy operator for different three-body nuclear $AAB$ systems by employing the method of Faddeev equations in configuration space. For a three-boson system this term is determined by the difference of the doubled binding energy of the $AB$ subsystem $2E_{2}$ and the three-body binding energy $E_{3}(V_{AA}=0)$ when the interaction between the identical particles is omitted. In this case: $\left\vert E_{3}(V_{AA}=0)\right\vert >2\left\vert E_{2}\right\vert$. In the case of a system complicated by isospins(spins), such as the kaonic clusters $ K^{-}K^{-}p$ and $ppK^{-}$, the similar evaluation impossible. For these systems it is found that $\left\vert E_{3}(V_{AA}=0)\right\vert <2\left\vert E_{2}\right\vert$. A model with an $AB$ potential averaged over spin(isospin) variables transforms the later case to the first one. The mass polarization effect calculated within this model is essential for the kaonic clusters. Besides we have obtained the relation $|E_3|\le |2E_2|$ for the binding energy of the kaonic clusters.