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The structure of the molecule-like state of $NK\pi$ with spin-parity$J^{\pi}={3/2}^-$ and isospin I=1 is studied within the chiral SU(3) quarkmodel. First we calculate the $NK$, $N\pi$, and $K\pi$ phase shifts in theframework of the resonating group method (RGM), and a qualitative agreementwith the experimental data is obtained. Then we perform a rough estimation forthe energy of $(NK\pi)_{J^{\pi}={3/2}^-,I=1}$, and the effect of the mixing tothe configuration $(\Delta K)_{J^{\pi}={3/2}^-,I=1}$ is also considered. Thecalculated energy is very close to the threshold of the $NK\pi$ system. Adetailed investigation is worth doing in the further study.Comment: 11 pages, 3 figures; accepted for publication in Phys. Rev.

physical review. c. nuclear physics/physical review. c, nuclear physics

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="italic">NK</mml:mi><mml:mi>π</mml:mi></mml:mrow></mml:math>molecular state with<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mi>J</mml:mi><mml:mrow><mml:mi>π</mml:mi></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mfrac><mml:mrow><mml:mn>3</mml:mn></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:mfrac><mml:mrow><mml:mo>−</mml…

NKπmolecular state withJπ=32−