Three-neutron resonance study using transition operators

Background: Existing bound-state-type calculations of three-neutron resonances yield contradicting results.

Purpose: A direct study of the three-neutron continuum using rigorous scattering equations with realistic potentials and search for possible resonances is aimed.

Methods: Faddeev-type integral equations for three-neutron transition operators are solved in the momentum-space partial-wave framework. The evolution of resonances is studied by enhancing the strength of the two-neutron interaction in partial waves with nonzero orbital momentum.

Results: Calculated three-neutron transition operators exhibit resonant behavior for sufficiently large enhancement factors; pole trajectories in the complex energy plain are extracted from their energy dependence. However, the resonant behavior completely disappears for the physical interaction strength.

Conclusions: There are no physically observable three-neutron resonant states consistent with presently accepted interaction models.

Figure 1

Energy dependence of real and imaginary parts of selected $J^{\mathrm{\Pi }}={\frac{3}{2}}^{-}$ three-neutron transition matrix elements calculated using SRG potential with higher wave enhancement factors $f=1.0$, 5.6, and 6.2. For the off-shell state ${\epsilon }_{\mathrm{off}}=9$ MeV was chosen. Matrix elements are given in arbitrary units but preserving the relative scale.

Figure 2

Energy dependence of transition strengths $|\langle {}^3\mathrm{P}_2^p|T_{3/2^{-}}{|{}^1\mathrm{S}_0^q\rangle |}^2$ obtained using the SRG potential with higher-wave enhancement factors $f=6.2$, 6.0, 5.6, 5.0, 4.0, 2.0, and 1.0. Transition strengths are given in arbitrary units but preserving the relative scale.

Figure 3

Three-neutron $J^{\mathrm{\Pi }}={\frac{3}{2}}^{-}$ resonance trajectories for SRG, CD Bonn, NLO, and Reid93 potentials obtained varying the higher-wave (only ${}^3\mathrm{P}_2-{}^3\mathrm{F}_2$ for Reid93) enhancement factor $f$ in the given interval with the step of 0.1 (CD Bonn and Reid93) or 0.2 (SRG and NLO). Lines are for guiding the eye only.

Figure 4

Energy dependence of transition strengths $|\langle {}^{2s+1}\mathrm{L}_j^p|T_{J^{\mathrm{\Pi }}}{|{}^1\mathrm{S}_0^q\rangle |}^2$ for $J\le \frac{5}{2}$ states obtained using physical SRG, CD Bonn, and NLO potentials. Transition strengths are given in arbitrary units but preserving the relative scale. ${\frac{3}{2}}^{+}$ and ${\frac{5}{2}}^{+}$ results are indistinguishable in the plot.

Figure 5

Three-neutron $J^{\mathrm{\Pi }}={\frac{3}{2}}^{+},{\frac{5}{2}}^{-}$, and ${\frac{5}{2}}^{+}$ resonance trajectories for the SRG potential obtained varying the higher-wave enhancement factor $f$ in the given interval with the step of 0.3. Lines are for guiding the eye only.

Figure 6

Three-neutron $J^{\mathrm{\Pi }}={\frac{1}{2}}^{+},{\frac{1}{2}}^{-}$, and ${\frac{3}{2}}^{-}$ resonance trajectories obtained with the attractive ${}^3\mathrm{P}_1$ potential as described in the text. Results are based on the SRG model while the enhancement factor $f$ is varied in the given interval with the step of 0.1 (0.2) for positive (negative) parity states.