N. M. Petrov

Determination of low-energy parameters of neutron-proton scattering in the the shape-parameter approximation from present-day experimental data

On the basis of the total cross sections for neutron-proton scattering in the region of laboratory energies below 150 keV, the value of σ0 = 20.4288(146) b was obtained for the total cross sections for neutron-proton scattering at zero energy. This value is in very good agreement with the experimental cross sections obtained by Houke and Hurst, but it is at odds with Dilg’s experimental cross section. By using the value that we found for σ0 and the experimental values of the neutron-proton coherent scattering length f, the deuteron binding energy ɛt, the deuteron effective radius ρt(−ɛt, −ɛt), and the total cross section in the region of energies below 5 MeV, the following values were found in the shape-parameter approximation for the low-energy parameters of neutron-proton scattering in the spin-triplet and spin-singlet states: at = 5.4114(27) fm, r0t = 1.7606(35) fm, v2t = 0.157 fm3, as = −23.7154(80) fm, r0s = 2.706(67) fm, and v2s = 0.491 fm3.

Determination of low-energy parameters of neutron-proton scattering on the basis of modern experimental data from partial-wave analyses

The triplet and singlet low-energy parameters in the effective-range expansion for neutron-proton scattering are determined by using the latest experimental data on respective phase shifts from the SAID nucleon-nucleon database. The results differ markedly from the analogous parameters obtained on the basis of the phase shifts of the Nijmegen group and contradict the parameter values that are presently used as experimental ones. The values found with the aid of the phase shifts from the SAID nucleon-nucleon database for the total cross section for the scattering of zero-energy neutrons by protons, σ0 = 20.426 b, and the neutron-proton coherent scattering length, f = −3.755 fm, agree perfectly with experimental cross-section values obtained by Houk, σ0 = 20.436 ± 0.023 b, and experimental scattering-length values obtained by Houk and Wilson, f = −3.756 ± 0.009 fm, but they contradict cross-section values of σ0 = 20.491 ± 0.014 b according to Dilg and coherent-scattering-length values of f = −3.7409 ± 0.0011 fm according to Koester and Nistler.

Low-energy parameters of neutron-neutron interaction in the effective-range approximation

The effect of the mass difference between the charged and neutral pions on the low-energy parameters of nucleon-nucleon interaction in the 1S0 state is studied in the effective-range approximation. On the basis of experimental values of the singlet parameters of neutron-proton scattering and the experimental value of the virtual-state energy for the neutron-neutron systemin the 1S0 state, the following values were obtained for the neutron-neutron scattering length and effective range: ann = −16.59(117) fm and rnn = 2.83(11) fm. The calculated values agree well with present-day experimental results.

Study of the charge dependence of the pion–nucleon coupling constant on the basis of data on low-energy nucleon–nucleon interactions

The relation between quantities that characterize the pion–nucleon and nucleon–nucleon interactions is studied with allowance for the fact that, at low energies, nuclear forces in nucleon–nucleon systems are mediated predominantly by one-pion exchange. On the basis of the values currently recommended for the low-energy parameters of the proton–proton interaction, the charged pion–nucleon coupling constant is evaluated at gπ2±/4π = 14.55(13). This value is in perfect agreement with the experimental value of gπ2±/4π = 14.52(26) found by the Uppsala Neutron Research Group. At the same time, the value obtained for the charged pion–nucleon coupling constant differs sizably from the value of the pion–nucleon coupling constant for neutral pions, which is gπ2 0/4π = 13.55(13). This is indicative of a substantial charge dependence of the coupling constant.

Determination of the root-mean-square radius of the deuteron from present-day experimental data on neutron-proton scattering

The correlation between the root-mean-square matter radius of the deuteron, rm, and its effective radius, ρ, is investigated. A parabolic relationship between these two quantities makes it possible to determine the root-mean-square radius rm to within 0.01% if the effective radius ρ is known. The matter (rm), structural (rd), and charge (rch) radii of the deuteron are found with the aid of modern experimental results for phase shifts from the SAID nucleon-nucleon database, and their values are fully consistent with their counterparts deduced by using the experimental value of the effective deuteron radius due to Borbély and his coauthors. The charge-radius value of 2.124(6) fm, which was obtained with the aid of the SAID nucleon-nucleon database, and the charge-radius value of 2.126(12) fm, which was obtained with the aid of the experimental value of the effective radius ρ, are in very good agreement with the present-day chargeradius value of 2.128(11) fm, which was deduced by Sick and Trautmann by processing world-average experimental data on elastic electron scattering by deuterons with allowance for Coulomb distortions.

Description of Scattering and of a Bound State in the Two-Nucleon System on the Basis of the Bargmann Representation of the S Matrix

For the effective-range function kcotδ, a pole approximation that involves a small number of parameters is derived on the basis of the Bargmann representation of the S matrix. The parameters of this representation, which have a clear physical meaning, are related to the parameters of the Bargmann S matrix by simple equations. By using a polynomial least squares fit to the function kcotδ at low energies, the triplet low-energy parameters of neutron-proton scattering are obtained for the latest experimental data of Arndt’s group on phase shifts. The results are at = 5.4030 fm, rt = 1.7494 fm, and v2 = 0.163 fm3. With allowance for the values found for the low-energy parameters and for the pole parameter, the pole approximation of the function kcotδ provides an excellent description of the triplet phase shift for neutron-proton scattering over a wide energy range (Tlab ≲ 1000 MeV), substantially improving the description at low energies as well. For the experimental phase shifts of Arndt’s group, the triplet shape parameters vn of the effective-range expansion are obtained by using the pole approximation. It turns out that they are positive and decrease with increasing n. The description of the phase shift by means of the effective-range expansion featuring values found for the low-energy parameters of scattering 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.

Determination of low-energy parameters of neutron-neutron scattering from an analysis of the binding-energy difference between the 3 H and 3 He mirror nuclei

A relation between quantities that characterize the breaking of the charge symmetry of nuclear forces in systems of two and three nucleons is found on the basis of an analysis of the binding-energy difference between the 3H and 3He mirror nuclei. For the neutron-neutron scattering length and effective range, the values of ann = −18.38(55) fm and rnn = 2.84(4) fm, respectively, were obtained by using purely nuclear parameters of proton-proton scattering in the 1S0 state. The calculated values agree with present-day experimental results.

Correlation between the properties of the deuteron and the low-energy triplet parameters of neutron-proton scattering

The correlation relationship between the deuteron asymptotic normalization constant,

P -Matrix Approach and Parameters of Low-Energy Scattering in the Presence of a Coulomb Potential

A_{S}

On the correlation between the deuteron quadrupole moment, the deuteron asymptotic D/S ratio, and the S-wave normalization constant

, and the triplet np scattering length,