Indications for the Nonexistence of Three-Neutron Resonances Near the Physical Region

Abstract

This work presents the calculations of three-neutron(3n) resonance trajectories by solving Faddeev equations in momentum space for the states 3/2^± and 1/2^±. The neutron-neutron (nn) forces for the states ¹S₀, ³P₀, ³P₂ and ¹D₂ are of rank 2 [1]. This implies Faddeev calculations including up to 10 channels. To calculate the resonance positions the kernel of the Faddeev equations has to be analytically continued into the second energy sheet below the positive real energy axis by contour deformation. There one hits singularities arising from the form factors of the potential and the free propagator. We follow ref.[2] to avoid the singularities. The resonance trajectories are generated by changing an artificial enhancement factor of the nn forces from values larger than 1 towards 1, the physical case. The final resonance positions for three-neutrons are in the four studied states far away from the real energy axis as shown in Fig. 1. If the resonance positions are located near the real energy axis, the Padé method can be used to predict their energies using the knowledge of the 3n bound state energies for different enhancement factors [3]. This requires, however, a high precision of the ”artificial” bound state energies. One example is displayed in Table 1 for the state 3/2^2212;. For that state it was sufficient to enhance only the nn force component in the state ³ P ₂ and we could keep all other force components at their physical values. The resonance positions calculated directly by contour deformation are compared to those predicted by the Padé approximation in Table 2. We see that the agreement among the two approaches is quite good.