10 research outputs found

    Description of the two-nucleon system on the basis of the Bargmann representation of the S matrix

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    For the effective-range function kcotδk\cot \delta , a pole approximation that involves a small number of parameters is derived on the basis of the Bargmann representation of the SS matrix. The parameters of this representation, which have a clear physical meaning, are related to the parameters of the Bargmann SS matrix by simple equations. By using a polynomial least-squares fit to the function kcotδk\cot \delta at low energies, the triplet low-energy parameters of neutron-proton scattering are obtained for the latest experimental data of Arndt et al. on phase shifts. The results are at=5.4030a_{t}=5.4030 fm, rt=1.7494r_{t}=1.7494 fm, and v2=0.163v_{2}=0.163 fm3^{3}. With allowance for the values found for the low-energy scattering parameters and for the pole parameter, the pole approximation of the function kcotδk\cot \delta provides an excellent description of the triplet phase shift for neutron-proton scattering over a wide energy range (Tlab1000T_{\text{lab}}\lesssim 1000 MeV), substantially improving the description at low energies as well. For the experimental phase shifts of Arndt et al., the triplet shape parameters vnv_{n} of the effective-range expansion are obtained by using the pole approximation. The description of the phase shift by means of the effective-range expansion featuring values found for the low-energy scattering parameters proves to be fairly accurate over a broad energy region extending to energy values approximately equal to the energy at which this phase shift changes sign, this being indicative of a high accuracy and a considerable value of the effective-range expansion in describing experimental data on nucleon-nucleon scattering. The properties of the deuteron that were calculated by using various approximations of the effective-range function comply well with their experimental values.Comment: 39 pages, 3 figure

    Review of Organic Microchemistry

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