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Register a new userPhotodisintegration of the triton with realistic potentials
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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.
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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.
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.
The Schroedinger equation is solved for an A-nucleon system using an expansion of the wave function in nonsymmetrized hyperspherical harmonics. Our approach is both an extension and a modification of the formalism developed by Gattobigio et al.. The extension consists in the inclusion of spin and isospin degrees of freedom such that a calculation with more realistic NN potential models becomes possible, whereas the modification allows a much simpler determination of the fermionic ground state. The approach is applied to four- and six-body nuclei (4He, 6Li) with various NN potential models. It is shown that the results for ground-state energy and radius agree well with those from the literature.
The potentials $V (v)$ in the nonrelativistic (relativistic) nucleon-nucleon (NN) Schroedingerequation are related by a quadratic equation. That equation is numerically solved, thus providing phase equivalent v- potentials related for instance to the high precision NN potentials, which are adjusted to NN phase shift and mixing parameters in a nonrelativistic Schroedinger equation. The relativistic NN potentials embedded in a three-nucleon (3N)system for total NN momenta different from zero are also constructed in a numerically precise manner. They enter into the relativistic interacting 3N mass operator, which is needed for relativistic 3N calculations for bound and scattering states.
Large angle photodisintegration of two nucleons from the 3He nucleus is studied within the framework of the hard rescattering model (HRM). In the HRM the incoming photon is absorbed by one nucleons valence quark that then undergoes a hard rescattering reaction with a valence quark from the second nucleon producing two nucleons emerging at large transverse momentum . Parameter free cross sections for pp and pn break up channels are calculated through the input of experimental cross sections on pp and pn elastic scattering. The calculated cross section for pp breakup and its predicted energy dependency are in good agreement with recent experimental data. Predictions on spectator momentum distributions and helicity transfer are also presented.
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