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, σ ₀ = 20.426 b, and the neutron-proton coherent scattering length, f = ?3.755 fm, agree perfectly with experimental cross-section values obtained by Houk, σ ₀ = 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 σ ₀ = 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.     

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, r _m , and its effective radius, ρ, is investigated. A parabolic relationship between these two quantities makes it possible to determine the root-mean-square radius r _m to within 0.01% if the effective radius ρ is known. The matter (r _m ), structural (r _d ), and charge (r _ch) 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.     

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

The correlation between the asymptotic normalization constant for the deuteron, A_S, and the neutron-proton scattering length for the triplet case, a_t, is investigated. It is found that 99.7% of the asymptotic constant A_S is determined by the scattering length a_t. It is shown that the linear correlation between the quantities A _S ^?2 and 1/a_t provides a good test of correctness of various models of nucleon-nucleon interaction. It is revealed that, for the normalization constant A_S and for the root-mean-square deuteron radius r_d, the results obtained with the experimental value recommended at present for the triplet scattering length a_t are exaggerated with respect to their experimental counterparts. By using the latest experimental data obtained for phase shifts by the group headed by Arndt, it proved to be possible to derive, for the low-energy parameters of scattering (a_t, r_t, P_t) and for the properties of the deuteron (A_S, r_d) results that comply well with experimental data.     

Quark-Model Nucleon–Nucleon Interaction Applied to Nucleon-Deuteron Scattering

We have examined the neutron-deuteron low-energy effective-range parameters, differential cross sections and spin polarization observables of the elastic nucleon-deuteron scattering up to the incident nucleon energy E _N  = 65 MeV, using the quark-model nucleon–nucleon interaction fss2. These observables are consistently described without introducing three nucleon forces except for the nucleon analyzing power A _y (θ) and the deuteron vector analyzing power iT ₁₁(θ) in the low-energy region E _N  ≤ 25 MeV. The long-standing A _y puzzle is slightly improved, but still remains. We have incorporated the screened Coulomb force to the proton-deuteron scattering, modifying the Vincent–Phatak approach for the sharp cutoff Coulomb force. The Coulomb effect on the elastic scattering observables is discussed.     

Analysis of experimental data on neutron-proton scattering in the energy range between 0 and 150 keV

Experimental data on neutron-proton scattering in the energy range between 0 and 150 keV are analyzed by using various sets of effective-range parameters. It is shown that, in contrast to the parameters corresponding to the phase shifts of a Nijmegen group, the parameters corresponding to the experimental phase shifts reported by a group from George Washington University (GWU group) lead to very good agreement between the calculated cross sections and their experimental counterparts in the energy region under consideration. On the basis of the experimental value of the cross section for neutron—proton scattering at an energy of 2 keV, the total cross section for neutron-proton scattering at zero energy was found to be σ ₀ = 20.428(16) b, which is in very good agreement with a value of σ ₀ = 20.423(9) b, which was obtained as the weighted mean of the cross sections presented by Houke and Hurst. It is shown that, in the energy region around several tens of keV units, the effective-range parameters matched with Dilg’s cross-section value of σ ₀ = 20.491(14) b lead to calculated cross sections whose values are in excess of their experimental counterparts.     

Simple local NN potentials involving forbidden states and polarization in ed scattering

A simple NN potential is proposed in an analytic form. The parameters of this potential are fixed by fitting the effective range, the scattering length, and the deuteron binding energy. The phase shifts for np scattering at energies ranging up to 500 MeV and the properties of the deuteron are calculated with the resulting parameters. The effect of the πNN coupling constant on the potential parameters and on the accuracy in describing various properties of NN interaction is explored. The results of the present calculations are found to be in good agreement with experimental data, with available results from NN partial-wave analyses, and with the results of calculations with Nijmegen potentials. The tensor polarization t ₂₀ in elastic electron-deuteron scattering is analyzed by using some NN interactions.     

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 ¹ S ₀ 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 ¹ S ₀ state, the following values were obtained for the neutron-neutron scattering length and effective range: a _nn = ?16.59(117) fm and r _nn = 2.83(11) fm. The calculated values agree well with present-day experimental results.     

Absolute normalization of (p,t), (p, 3He) and (d, α) reaction cross sections

Pick-up reactions in which A = 3 and A = 4 particles emerge are considered with the DWBA zero-range approximation theory. Exact calculations were carried out with nucleon-nucleon interactions which describe low-energy scattering data as well as the binding energy of the deuteron very well. The values of the absolute normalization constant obtained are all in very good agreement with experimental results.     

Elastic and inelastic scattering of 11.8 MEV polarized deuterons from 34S

The elastic and inelastic scattering of 11.8 MeV vector polarized deuterons from ³⁴S has been studied. Angular distributions of the cross section σ(θ) and vector analyzing power iT₁₁(θ) have been measured for the ground state and the first three excited states in ³⁴S. Optical model parameters were first obtained by fitting the elastic deuteron scattering data alone. DWBA calculations with a collective model form factor were performed for the inelastic scattering to the excited states. Coupled-channels calculations were also done both for the one-phonon and the two-phonon excited states. The optical model parameters were suitably modified to obtain simultaneous fit to elastic and inelastic data when channel coupling was introduced. The values of the vibrational parameter β₂ for one- and two-phonon states are discussed and compared with those obtained from γ-decay width studies.     

Systematics of low-energy πN scattering

A simple current algebra model is shown to account for a wide range of low-energy πN experimental data including twenty-eight subthreshold expansion coefficients, six scattering lengths, and the scattering phase shifts below T_π = 300 MeV. A sigma term of σ_NN = 62 ± 10 MeV is obtained.     

Solving the differential Yakubovsky equations for p 3He scattering by the cluster-reduction method

The cluster-reduction method has been used to solve numerically the differential equations for the s-wave Yakubovsky components in the nppp system. Proton scattering on a ³He nucleus has been considered for energies below the three-body threshold in the singlet and triplet spin states of the system. Nucleon-nucleon interaction has been simulated by the MT I–III potential, and the Coulomb interaction between the protons has been taken into account. Effective equations that describe the relative motion of clusters have been derived. The low-energy behavior of phase shifts has been analyzed. The values of ¹ A=8.2 fm and ³ A=7.7 fm have been obtained for, respectively, the singlet and triplet scattering lengths. The calculated phase shifts agree well with experimental data.     

Differential cross section,analyzing power and phase shifts for p-3He elastic scattering below 1.0 MeV

Differential cross sections and analyzing powers for the elastic scattering of polarized protons by unpolarized ³He nuclei have been measured at eight energies between 0.3 MeV and 1.0 MeV for scattering angles θ_c.m. = 52.4°–173.3°. The cross-section values were normalized to the Rutherford cross section for proton-krypton scattering. The analyzing powers have been measured with a statistical accuracy of about 0.001. The phase-shift analysis based on these data included all phases for orbital angular momenta l ≦ 1 and the channel-spin mixing parameter for the P waves. An energy parametrization of the phase shifts by an effective-range approximation allowed a simultaneous utilization of all data.     

Neutron–Deuteron Scattering Observables at E lab = 14.1 MeV

Inelastic neutron–deuteron scattering is studied on the basis of configuration-space Faddeev equations. Calculated are neutron–deuteron breakup amplitudes using AV14 nucleon–nucleon potential at incident neutron energy of 14.1 MeV. The results of calculations are presented for the differential cross sections under quasi free scattering and space–star configurations, and compared with those of the previous calculations and experimental data. The choice of the cutoff radius R _cutoff for asymptotic conditions is discussed.     

A new approach to the problem of electron-atom collision cross section measurements in the low-energy range

Momentum-transfer cross sections for He and Ar have been determined in the energy ranges 5×10^-3?3 eV and 5×10^-3?0.6 eV, respectively using a modified effective-range analysis of the shape of experimental ECR-absorption lines, registered in the afterglows. The following values have been obtained for the scattering length: 1.17±0.01a³₀ for He and 1.53±0.01a³₀ for Ar.     

Doublet coulomb-nuclear scattering length and other parameters of the effective-range function for proton-deuteron scattering from an analysis of present-day data

Parameters of the effective-range function K(k ²) having a pole are found from the results that were obtained by calculating the S-wave phase shifts for doublet proton-deuteron scattering and the binding energies of three-nucleon nuclei on the basis of Faddeev equations and within the N/D method and which are known from the literature. The convergence of the expansion of K(k ²) in powers of the momentum is studied. The energy of the proton-deuteron resonance corresponding to the virtual triton state is calculated.     

Calculation of the binding energy and of the parameters of low-energy scattering in the Λnp system

The cluster-reduction method is used to solve the differential Faddeev equations for S=1/2, T=0 and S=3/2, T=0 spin-isospin states of the Λnp system in the s-wave approximation. The NN interaction is simulated on the basis of the MT I–III potential model, and the ΛN potential is set to V _ΛN =V _NN /2. This simple option makes it possible to reproduce faithfully the binding energy of the hypertriton _Λ ³ H. The doublet and quadruplet Λd scattering lengths and the low-energy phase shifts are calculated. It is shown that the effective-range approximation is applicable to the cases of doublet and quadruplet scattering.     

Effect of the deuteron anisotropy: Longitudinal and transverse components of the electric dipole polarizability

The anisotropy effect of the electric polarization (stretching) of the deuteron in the Coulomb field, caused by the tensor character of the nuclear force, is investigated. The values of the longitudinal (with the major axis, or the spin of the deuteron, directed along the electric field), and transverse components of the deuteron electric dipole polarizability that correspond to the low-energy n-p data, are predicted to be α₆ = 0.669 fm³ and α_⊥ = 0.555 fm³ (the potential YYm). The values of the major and minor semi-axes of the deuteron are calculated.