Abstract
We investigate the sensitivity of the three-nucleon system to changes in the neutron–neutron scattering length to next-to-leading order in the pionless effective field theory, focusing on the triton–3He binding energy difference and neutron–deuteron elastic scattering. Due to the appearance of a proton–deuteron three-body counterterm at this order, the triton–3He binding energy difference remains consistent with the experimental value even for large positive neutron–neutron scattering lengths while the elastic neutron–deuteron scattering phase shifts are insensitive. We conclude that a bound dineutron cannot be excluded to next-to-leading order in pionless EFT.
Highlights
The search for dineutron bound states has a long history in physics
From Eq (5) and its analog for the neutron–deuteron case one can extract both scattering information—for example the n–d doublet scattering length which we use as physical input to fix the three-nucleon force H(Λ)—and bound state properties
To extract the binding energies of the triton and 3He, we look for poles in the corresponding scattering amplitudes at negative energies
Summary
The search for dineutron bound states has a long history in physics. early experimental searches were negative [1,2], there has been some evidence for the presence of dineutron configurations in the decay of weakly bound nuclei recently. In the context of the nuclear few-body problem, Witała and Glöckle raised the possibility that a slightly bound dineutron might solve some open problems in three-body breakup reactions [12] They changed the neutron–neutron scattering length by multiplying the CD Bonn potential with an overall strength factor ranging from 0.9 to 1.4. Kirscher and Phillips [19] used pionless EFT to compute a model-independent correlation between the difference of the neutron–neutron and (Coulomb-modified) proton–proton scattering lengths and the triton–3He binding energy difference Their calculation was carried out at leading order (LO) in the pionless EFT but included isospin breaking effects from the physical scattering lengths in different charge channels. We present our analysis of three-nucleon observables as well as the naturalness of the counterterm and conclude
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