Three-neutron Resonance Research Articles

Three-neutron resonance study using transition operators

Existing bound-state type calculations of three-neutron resonances yield contradicting results. A direct study of the three-neutron continuum using rigorous scattering equations with realistic potentials and search for possible resonances is aimed. 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. Calculated three-neutron transition operators exhibit resonant behavior for sufficiently large enhancement factors; pole trajectories in the complex-energy energy plane are extracted from their energy dependence. However, the resonant behavior completely disappears for the physical interaction strength. There are no physically observable three-neutron resonant states consistent with presently accepted interaction models.

Is a Trineutron Resonance Lower in Energy than a Tetraneutron Resonance?

We present quantum MonteCarlo calculations of few-neutron systems confined in external potentials based on local chiral interactions at next-to-next-to-leading order in chiral effective field theory. The energy and radial densities for these systems are calculated in different external Woods-Saxon potentials. We assume that their extrapolation to zero external-potential depth provides a quantitative estimate of three- and four-neutron resonances. The validity of this assumption is demonstrated by benchmarking with an exact diagonalization in the two-body case. We find that the extrapolated trineutron resonance, as well as the energy for shallow well depths, is lower than the tetraneutron resonance energy. This suggests that a three-neutron resonance exists below a four-neutron resonance in nature and is potentially measurable. To confirm that the relative ordering of three- and four-neutron resonances is not an artifact of the external confinement, we test that the odd-even staggering in the helium isotopic chain is reproduced within this approach. Finally, we discuss similarities between our results and ultracold Fermi gases.

Three-neutron resonance trajectories for realistic interaction models

Three-neutron resonances are investigated using realistic nucleon-nucleon interaction models. The resonance pole trajectories are explored by first adding an additional interaction to artificially bind the three-neutron system and then gradually removing it. The pole positions for the three-neutron states up to $J=5/2$ are localized in the third energy quadrant---$\mathrm{Im}\phantom{\rule{0.2em}{0ex}}(E)\ensuremath{\leqslant}0,\phantom{\rule{0.3em}{0ex}}\mathrm{Re}\phantom{\rule{0.2em}{0ex}}(E)\ensuremath{\leqslant}0$---well before the additional interaction is removed. Our study shows that realistic nucleon-nucleon interaction models exclude any possible experimental signature of three-neutron resonances.

Indications for the nonexistence of three-neutron resonances near the physical region

The pending question of the existence of three-neutron resonances near the physical energy region is reconsidered. Finite rank neutron-neutron forces are used in Faddeev equations, which are analytically continued into the unphysical energy sheet below the positive real energy axis. The trajectories of the three-neutron S-matrix poles in the states of total angular momenta and parity J^\pi=1/2 +- and J^\pi= 3/2 +- are traced out as a function of artificial enhancement factors of the neutron-neutron forces. The final positions of the S-matrix poles removing the artificial factors are found in all cases to be far away from the positive real energy axis, which provides a strong indication for the nonexistence of nearby three-neutron resonances. The pole trajectories close to the threshold E=0 are also predicted out of auxiliary generated three-neutron bound state energies using the Pad\'e method and agree very well with the directly calculated ones.

Resonances in the three-neutron system

A study of three-body resonances has been performed in the framework of configuration-space Faddeev equations. The importance of keeping a sufficient number of terms in the asymptotic expansion of the resonance wave function is pointed out. We investigated three neutrons interacting in selected force components taken from realistic $\mathrm{nn}$ forces. Three-neutron resonance pole trajectories connected to artificially enhanced $\mathrm{nn}$ forces could be found. The final pole positions corresponding to the actual force strengths could not be found due to the onset of numerical instabilities. The numerically reliable results achieved, however, make it likely, that three-neutron resonance energies will have large imaginary parts and are therefore physically not interesting. A straightforward application of complex scaling to three-nucleon systems with realistic forces could not be controlled numerically.

Searching for three-nucleon resonances.

We search for three-neutron resonances which were predicted from pion double charge exchange experiments on {sup 3}He. All partial waves up to {ital J}=5/2 are nonresonant except the {ital J}{sup {pi}}=3/2{sup +} one, where we find a state at {ital E}=14 MeV energy with 13 MeV width. The parameters of the mirror state in the three-proton system are {ital E}=15 MeV and {Gamma}=14 MeV. The possible existence of an excited state in the triton, which was predicted from a H({sup 6}He,{alpha}) experiment, is also discussed. {copyright} {ital 1996 The American Physical Society.}

Semianalytical method for treatment of the N-body problem with complex total energy within the hyperharmonics approach

We develop the variable phase approach to analyze all the solutions of the N-body hyperradial equations. As a first result of this analysis, we display here how the usual cutoff of the long-range potential matrix generates unphysical solutions. As an example of such solutions we present a set of unphysical three-neutron resonances. To overcome this peculiarity of the standard hyperharmonics approach we introduce a well-defined solution of the Jost-type and construct it at large hyperradius analytically.

Is there a three-neutron resonance?

The three-neutron system is studied using the Reid potential. We determine the enhancement factors for the 1S 0 and the attractive p-wave forces in order to bind three neutrons near zero energy. The state with J P = 3/2 − turns out to be energetically most favourable and is dominated by the 3P 2- 3F 2 force. Since that force has to be enhanced by about a factor κ ≈ 4 and the variation of the three-neutron binding energy with K is large a low energy resonance is extremely unlikely.

Three-neutron resonance in the reaction [formula omitted

We have estimated the cross section for the reaction 3 He(π −, π +)3 n leading to a possible low-energy resonance in the three-neutron system.

On the investigation of a possible broad three-neutron state by means of the reaction 3H(n,p) 3n

The proton spectrum is calculated for the reaction 3H(n,p)3n in forward direction for 30 and 50 MeV neutron energy. It is found that the broad three-neutron resonance discussed in a previous paper should give a significant deviation from the phase space background.

Non-resonant attraction between neutrons in the [formula omitted] reaction

It is shown that the tendency for a low energy three-neutron system to be emitted in the π − + 3 He →π + + 3 n reaction does not imply the existence of a three-neutron resonance.