The spin-orbit splitting of resonant states in the ${}^4\mathrm{He}+n$ system is investigated by using the complex scaling method (CSM). The calculated energy difference between the $p_{3/2}$ and $p_{1/2}$ states is very small, which is inferred by the R-matrix analyses, though the spin-orbit potential employed for the ${}^4\mathrm{He}-n$ system is strong for the bound states. Furthermore, we show that the calculated energy difference between the $p_{3/2}$ and $p_{1/2}$ states is not the same as the energy difference of the expectation value of the spin-orbit potential; those of the kinetic energy and the central potential are also needed for explanation of the energy difference between the $p_{3/2}$ and $p_{1/2}$ states. To clarify this, we calculate the complex expectation values of the operators in the ${}^4\mathrm{He}-n$ Hamiltonian for the $p_{3/2}$ and $p_{1/2}$ resonant states with a new method recently developed in the framework of the CSM.

• Received 6 July 1998

DOI:https://doi.org/10.1103/PhysRevC.59.531