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Register a new userConstraining the neutron-neutron scattering length with eftnopi
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We compute a model-independent correlation between the difference of neutron-neutron and proton-proton scattering lengths |a(nn)-a^C(pp)| and the splitting in binding energies between Helium-3 and tritium nuclei. We use the effective field theory without explicit pions to show that this correlation relies only on the existence of large scattering lengths in the NN system. Our leading-order calculation, taken together with experimental values for binding energies and a^C(pp), yields a(nn)=-22.9 pm 4.1 fm.
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Model-independent constraints for the neutron-triton and proton-Helium-3 scattering lengths are calculated with a leading-order interaction derived from an effective field theory without explicit pions. Using the singlet neutron-proton scattering length, the deuteron, and the triton binding energy as input, the predictions $ants=9.2pm2.6 $fm, $antt=7.6pm1.6 $fm, $aphes=3.6pm0.32 $fm, and $aphet=3.1pm 0.23 $fm are obtained. The calculations employ the resonating group method and include the Coulomb interaction when appropriate. The theoretical uncertainty is assessed via a variation of the regulator parameter of the short-distance interaction from $400 $MeV to $1.6 $GeV. The phase-shift and scattering-length results for the proton-Helium-3 system are consistent with a recent phase shift analysis and with model calculations. For neutron-triton, the results for the scattering lengths in both singlet and triplet channels are significantly smaller than suggested by R-matrix and partial-wave-analysis extractions from data. For a better understanding of this discrepancy, the sensitivity of the low-energy four-body scattering system to variations in the neutron-neutron and proton-proton two-nucleon scattering lengths is calculated. Induced by strong charge-symmetry-breaking contact interactions, this dependence is found insignificant. In contrast, a strong correlation between the neutron-triton scattering length and the triton binding energy analogous to the Phillips line is found.
Recent experimental results for neutron-neutron scattering length are reanalyzed from the point of view of three-nucleon force contribution. We found that the limiting value of $a_{nn}=- 15.8pm 0.5$~fm must be free of any implicit three-body force contribution. We have also shown that the difference between the above experimental value of $a_{nn}$ and the well established value of neutron-proton scattering length $a_{np}$ can be explained by differences in the one-pion exchange potentials.
The reaction pi- d -> n n gamma is calculated in chiral perturbation theory so as to facilitate an extraction of the neutron-neutron scattering length (a_nn). We include all diagrams up to O(Q^3). This includes loop effects in the elementary pi- p -> gamma n amplitude and two-body diagrams, both of which were ignored in previous calculations. We find that the chiral expansion for the ratio of the quasi-free (QF) to final-state-interaction (FSI) peaks in the final-state neutron spectrum converges well. Our third-order calculation of the full spectrum is already accurate to better than 5%. Extracting a_nn from the shape of the entire pi- d -> n n gamma spectrum using our calculation in its present stage would thus be possible at the +-0.8 fm level. A fit to the FSI peak only would allow an extraction of a_nn with a theoretical uncertainty of +-0.2 fm. The effects that contribute to these error bars are investigated. The uncertainty in the $nn$ rescattering wave function dominates. This suggests that the quoted theoretical error of +-0.3 fm for the most recent pi- d -> n n gamma measurement may be optimistic. The possibility of constraining the nn rescattering wave function used in our calculation more tightly--and thus reducing the error--is briefly discussed.
We discuss the possibility of extracting the neutron-neutron scattering length $a_{nn}$ and effective range $r_{nn}$ from cross section data ($d^2sigma/dM_{nn}/dOmega_pi$), as a function of the $nn$ invariant mass $M_{nn}$, for $pi^+$ photoproduction on the deuteron ($gamma dto pi^+nn$). The analysis is based on a $gamma dto pi^+nn$ reaction model in which realistic elementary amplitudes for $gamma pto pi^+n$, $NNto NN$, and $pi Nto pi N$ are built in. We show that $M_{nn}$ dependence (lineshape) of a ratio $R_{rm th}$, $d^2sigma/dM_{nn}/dOmega_pi$ normalized by $dsigma/dOmega_pi$ for $gamma ptopi^+ n$ and the nucleon momentum distribution inside the deuteron, at the kinematics with $theta_pi=0^circ$ and $E_gammasim 250$ MeV is particularly useful for extracting $a_{nn}$ and $r_{nn}$ from the corresponding data $R_{rm exp}$. It is found that $R_{rm exp}$ with 2% error, resolved into the $M_{nn}$ bin width of 0.04 MeV (corresponding to the $p_pi$ bin width of 0.05 MeV$/c$), can determine $a_{nn}$ and $r_{nn}$ with uncertainties of $pm 0.21$ fm and $pm 0.06$ fm, respectively, for the case of $a_{nn}=-18.9$ fm and $r_{nn}=2.75$ fm. The requirement of such narrow bin widths indicates that the momenta of the incident photon and the emitted $pi^+$ have to be measured with high resolutions. This can be achieved by utilizing virtual photons of very small $Q^2$ from electron scattering at Mainz MAMI facility. The proposed method for determining $a_{nn}$ and $r_{nn}$ from $gamma dto pi^+ nn$ has a great experimental advantage over the previous one utilizing $pi^- dtogamma nn$ for being free from the formidable task of controlling the neutron detection efficiency and its uncertainty.
The present paper reports high-accuracy cross-section data for the 2H(n,nnp) reaction in the neutron-proton (np) and neutron-neutron (nn) final-state-interaction (FSI) regions at an incident mean neutron energy of 13.0 MeV. These data were analyzed with rigorous three-nucleon calculations to determine the 1S0 np and nn scattering lengths, a_np and a_nn. Our results are a_nn = -18.7 +/- 0.6 fm and a_np = -23.5 +/- 0.8 fm. Since our value for a_np obtained from neutron-deuteron (nd) breakup agrees with that from free np scattering, we conclude that our investigation of the nn FSI done simultaneously and under identical conditions gives the correct value for a_nn. Our value for a_nn is in agreement with that obtained in pion-deuteron capture measurements but disagrees with values obtained from earlier nd breakup studies.
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