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Register a new userTriton binding energy with realistic precision
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We compute the binding energy of triton with realistic statistical errors stemming from NN scattering data uncertainties and the deuteron and obtain $E_t=-7.638(15) , {rm MeV}$. Setting the numerical precision as $Delta E_t^{rm num} lesssim 1 , {rm keV}$ we obtain the statistical error $Delta E_t^{rm stat}= 15(1) , {rm keV}$ which is mainly determined by the channels involving relative S-waves. This figure reflects the uncertainty of the input NN data, more than two orders of magnitude larger than the experimental precision $Delta E_t^{rm exp}= 0.1 , {rm keV}$ and provides a bottleneck in the realistic precision that can be reached. This suggests an important reduction in the numerical precision and hence in the computational effort.
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The process $gamma + t to n + d$ is treated by means of three-body integral equations employing in their kernel the W-Matrix representation of the subsystem amplitudes. As compared to the plane wave (Born) approximation the full solution of the integral equations, which takes into account the final state interaction, shows at low energies a 24% enhancement. The calculations are based on the semirealistic Malfliet-Tjon and the realistic Paris and Bonn B potentials. For comparison with earlier calculations we also present results for the Yamaguchi potential. In the low-energy region a remarkable potential dependence is observed, which vanishes at higher energies.
Properties of the three-nucleon bound state are examined in the Faddeev formalism, in which the quark-model nucleon-nucleon interaction is explicitly incorporated to calculate the off-shell T-matrix. The most recent version, fss2, of the Kyoto-Niigata quark-model potential yields the ground-state energy ^3H=-8.514 MeV in the 34 channel calculation, when the np interaction is used for the nucleon-nucleon interaction. The charge root mean square radii of the ^3H and ^3He are 1.72 fm and 1.90 fm, respectively, including the finite size correction of the nucleons. These values are the closest to the experiments among many results obtained by detailed Faddeev calculations employing modern realistic nucleon-nucleon interaction models.
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.
Chemical constants extracted from $^{124}$Xe+ $^{124}$Sn collisions at 32 AMeV are compared to the predictions of an extended Nuclear Statistical Equilibrium model including mean-field interactions and in-medium binding energy shifts for the light ($Zleq 2$) clusters. The ion species and density dependence of the in-medium modification is directly extracted from the experimental data. We show that the shift increases with the mass of the cluster and the density of the medium, and we provide a simple linear fit for future use in astrophysical simulations in the framework of the CompOSE data base. The resulting mass fractions are computed in representative thermodynamic conditions relevant for supernova and neutron star mergers. A comparison to the results of a similar analysis of the same data performed in the framework of a relativistic mean-field model shows a good agreement at low density, but significant discrepancies close to the Mott dissolution of clusters in the dense medium.
The quality of two different separable expansion methods ({sl W} matrix and Ernst-Shakin-Thaler) is investigated. We compare the triton binding energies and components of the triton wave functions obtained in this way with the results of a direct two-dimensional treatment. The Paris, Bonn {sl A} and Bonn {sl B} potentials are employed as underlying two-body interactions, their total angular momenta being incorporated up to $j leq 2$. It is found that the most accurate results based on the Ernst-Shakin-Thaler method agree within 1.5% or better with the two-dimensional calculations, whereas the results for the {sl W}-matrix representation are less accurate.
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