Energy-dependent Phase-shift Analysis Research Articles

Erratum: Pion-pion scattering amplitude. II. Improved analysis aboveK¯Kthreshold [Phys. Rev. D74, 014001 (2006)

We improve, in the energy region between $\bar{K}K$ threshold and $\sim~1.4$ GeV, the energy-dependent phase shift analysis of $\pi\pi$ scattering presented in a previous paper. For the S0 wave we have included more data above $\bar{K}K$ threshold and we have taken into account systematically the elasticity data on the reaction $\pi\pi\to\bar{K}K$. We here made a coupled channel fit. For the D0 wave we have considered information on low energy parameters, and imposed a better fit to the $f_2$ resonance. For both waves the expressions we now find are substantially more precise than the previous ones. We also provide slightly improved D2 and P waves, including the estimated inelasticity for the first, and a more flexible parametrization between 1 and 1.42 GeV for the second. The accuracy of our amplitudes is now such that it requires a refinement of the Regge analysis, for $s^{1/2}\geq1.42$ GeV, which we also carry out. We show that this more realistic input produces $\pi\pi$ scattering amplitudes that satisfy better forward dispersion relations, particularly for $\pi^0\pi^0$ scattering.

Pion-pion scattering amplitude. II. Improved analysis aboveK¯Kthreshold

We improve, in the energy region between the KK threshold and ~ 1.4 GeV, the energy-dependent phase shift analysis of π π scattering presented in a previous paper. For the S0 wave, we have included more data above the KK threshold and we have taken into account systematically the elasticity data on the reaction π π →KK. We here made a coupled channel fit. For the D0 wave, we have considered information on low energy parameters, and imposed a better fit to the f_2 resonance. For both waves the expressions we now find are substantially more precise than the previous ones. We also provide slightly improved D2 and P waves, including the estimated inelasticity for the first, and a more flexible parametrization between 1 and 1.42 GeV for the second. The accuracy of our amplitudes is now such that it requires a refinement of the Regge analysis, for^(1/2) ≥ 1.42 GeV, which we also carry out. We show that this more realistic input produces π π scattering amplitudes that satisfy better forward dispersion relations, particularly for π^0 π^0 scattering.

Determination of proton-deuteron scattering lengths

An energy dependent phase-shift analysis of p+d elastic scattering below the deuteron breakup threshold has been conducted. The analysis indicates the existence of a singularity in the doublet S-wave effective range function, resulting in a very small value for the scattering length 2 a pd. The inferred value of the quartet S-wave scattering length 4 a pd is in good agreement with theoretical predictions.

An energy-dependent phase shift analysis of low-energy proton-deuteron elastic scattering

An energy dependent phase shift analysis of p+d elastic scattering below the deuteron breakup threshold has been conducted. The phases are fit directly to the data with a Monte Carlo Markov Chain algorithm after being sampled from a parameter space which is constrained to satisfy the Coulomb-modified effective range expansion. The mixing parameters are required to obey analyticity constraints. The overall fit in the preliminary analysis reported here was satisfactory, giving a χ 2/datum of about 2.5. The analysis indicates the existence of a singularity in the spin-doublet S-wave effective range function. The inferred value of the quartet S-wave scattering length is in excellent quantitative agreement with theoretical predictions. Small changes to the theoretical P-wave phase shifts and somewhat larger changes to the theoretical J = 1 2 mixing parameters are required to reproduce the p+d data.

Differential cross section and analyzing power for elastic scattering of protons on 6Li below 2.2 MeV

Differential cross section dσdΩ and analyzing power Ay of elastic 6Li(p,p)6Li scattering have been measured in the energy range 0.4 MeV ⩽ Ep ⩽ 2.2 MeV. The angular distributions were obtained at thirteen different angles between θlab = 40° and 160° with statistical uncertainties of less than 2 × 10−3. The data show a resonance-like behaviour in the excitation functions for dσdΩ and Ay near Ep = 1.8 MeV (i.e. Ec.m. = 1.56 MeV). An energy-dependent phase-shift analysis has been performed from which resonance parameters have been deduced. The analysed data are well described in the whole energy range and support the predictions of recent refined resonating-group calculations.

Phase shift analysis of pi +/--4He elastic scattering.

An energy-dependent phase shift analysis of ${\mathrm{\ensuremath{\pi}}}^{\ifmmode\pm\else\textpm\fi{}\mathrm{\ensuremath{-}}4}$He elastic scattering data up to an energy ${\mathit{T}}_{\mathrm{\ensuremath{\pi}}}$=260 MeV was carried out. Using a careful treatment of Coulomb effects to describe the Coulomb nuclear interference we reexamined the constraints to the \ensuremath{\pi}${\mathrm{\ensuremath{-}}}^{4}$He forward scattering amplitude ${\mathit{f}}_{0}$ by dispersion relations. This allows a stringent consistency check of the data. A satisfactory description of the data could only be achieved assuming large error bars of the total cross section measurements and allowing normalization factors for the differential cross section data.

Alpha-proton elastic scattering analyses up to 4 MeV

The elastic scattering cross section of 4He particles from protons is analysed at low energies up to E He = 4 MeV. Energy-dependent phase shift analyses are performed by means of the effective range parameterization. Starting from reported elastic cross section data which have been measured over the last seven years we obtain an energy-dependent solution, with two parameters (scattering length and effective range) retained in each phase shift expansion for the S 1 2 , P 1 2 and P 3 2 partial waves. The phase shifts obtained from the alpha-proton scattering analyses are presented in tabular form. The theoretical cross section values are calculated from the best-fit solutions for phase shifts. Finally a polynomial fit is proposed for a simple evaluation of differential cross sections.

The analyzing power for elastic 12C( [formula omitted], p) 12C scattering below 2.1 MeV

The analyzing power for elastic 12C( p , p) 12C scattering has been measured in the energy range 1.0⩽ E p⩽2.1MeV with statistical uncertainties of less than 0.004. The angular distributions were obtained at ten different angles between θ lab=40° and 160°. The targets were made by cracking isotopically pure (99.9%) 12C-acetylene in order to avoid impurities from the natural 13C-contamination. An energy-dependent phase-shift analysis has been performed using a Breit-Wigner parametrization. The results are presented in form of contour plots. Four regions were found where the analyzing power approaches extreme values.

Recent energy dependent phaseshift analysis and deuteron interaction models

The unusual low energy behaviour of the experimental mixing parameter epsilon 1 of the recent energy dependent phaseshift analysis has been reproduced by five simple local deuteron potential models. For a fixed very low energy, the relation between the quadrupole moment Q and epsilon 1 of standard potential models is a typical straight line which does not pass through the experimental point ( epsilon 1exp, Qexp) reported in this very low energy region. Correlations between Q and epsilon 1 are not found in the range of energies for which epsilon 1 has a pathological behaviour. The disagreement between the shape of the low energy behaviour of epsilon 1 of the data published in 1969, 1977 and 1983 disappears when the data are expressed in the RS-K-AR experimental mixing parameter Delta 12, of Ross and Shaw (1960), Kermode (1967) and Arndt and Roper (1970).

Energy-dependent phase-shift analysis of 2H+4He scattering in the energy range 0.87

An efficient method for construction of an analytic S matrix from experimental data based on the use of the statistical Pad\'e approximation is proposed. The method is applied to the energy-dependent phase-shift analysis of the elastic scattering of deuterons by alpha particles in the energy range 0.87${\mathit{E}}_{\mathit{d}}$5.24 MeV, and partial-wave phase shifts for l=0,1,2 are obtained. In addition, the energies and widths of the three known $^{6}\mathrm{Li}$ resonances are obtained, together with the energy of the $^{6}\mathrm{Li}$ bound state and the vertex constant of the virtual decay $^{6}\ensuremath{\rightarrow}^{2}$H${+}^{4}$He.

Padé-approximant techniques for processing scattering data II. Energy-dependent phase-shift analysis of low-energy4He +2H scattering

The general method for Pade-parametrization of experimental scattering data proposed by the authors recently has been applied to analytic parametrizations of theS-matrix and of partialwave amplitudes with the aim of carrying out an energy-dependent phase-shift analysis. It has been shown that the high universality and flexibility of the Pade-approximants make it possible to describe the partial-wave amplitudes by a very small number of parameters (say 2–3 in each partial wave) and to create a universal scheme for parametrization of the full reaction amplitude based on the following hybrid approach: the energy dependence of the inner partial amplitudes is represented by Pade approximants whereas the peripheral part of the full amplitude is taken from the low-order iterations of the exact many-particle Faddeev —Yakubovsky equations. As an example of the technique an energy-dependent phase-shift analysis of low-energy2H +4He scattering has been carried out and the parameters of the 3+ 0,2+ 0 and 1+ 0 resonant states of6Li have been obtained together with the value of the vertex constant of the virtual decay6Lig.s. → →4He +2H. The values of the energy and width obtained from experimental data of the 2+ 0 and particularly of the 1+ 0 level differ significantly from the values published in the literature.

Padé approximant technique for processing scattering data I. Theory, models and parametrization of the scattering data

The parametrization of experimental data (i.e. data known with errors) by the type-III Pade approximant (PA-III) technique is treated. Iterative linearized procedures for finding the PA parameters are proposed and their convergence verified. The methods proposed are shown to exhibit very rapid convergence compared with alternative methods. The methods are demonstrated to be effective when applied to describing the angular dependence of differential cross sections and analyzing powers of the elastic scattering of two nuclei and to parametrizing the low-energy electron-Krypton elastic scattering if explicit allowance is made for the long range polarization force. A subsequent paper in this series will be devoted to the energy-dependent phase shift analysis of low-energy2H-4He scattering.

Determination of the residue at the deuteron pole in an np phase-shift analysis.

In an energy-dependent phase-shift analysis of all low-energy $\mathrm{np}$ scattering data below ${T}_{\mathrm{lab}}=30$ MeV we reach $\frac{{\ensuremath{\chi}}^{2}}{{N}_{\mathrm{DF}}}=1.1$, where ${N}_{\mathrm{DF}}$ is the number of degrees of freedom. In our fit we determine the $S$ matrix elements in the coupled $^{3}S_{1}+^{3}D_{1}$ channels, which allows us to compute the residue at the deuteron pole. Expressed in terms of the deuteron parameters, we find for the asymptotic normalization of the $^{3}S_{1}$ state ${A}_{S}=0.8838(4)$ ${\mathrm{fm}}^{\ensuremath{-}1/2}$ and for the asymptotic $\frac{D}{S}$ ratio $\ensuremath{\eta}=0.02712(22)$. Compared with other determinations, there seems to be some indication for the presence of closed isobar channels and/or energy-dependent potentials in the deuteron system.

An energy dependent phase shift analysis of proton-proton scattering between 700 and 1300 MeV

An energy dependent phase shift analysis of proton-proton scattering between 700 and 1300 MeV

Nucleon-nucleon phase shift analysis

An energy dependent phase-shift analysis is reported for pp, np and pn elastic scattering between 10 and 800 MeV. For the pp case a unique solution smoothly varying with energy is found. A resonant behaviour is observed only in the 1D2 phase shift near the mass 2.14 GeV. For np and pn scattering only a few complex polarization parameters are available ; therefore the solution is less precise, especially above 500 MeV. A fixed-energy analysis at 1 GeV is also reported providing a unique phase-shift set. The formalism, data base and compatibility with other analyses are discussed.

Amplitude description of elastic pp scattering at 800 MeV.

Recent polarization data on proton-proton elastic scattering at 800 MeV taken at LAMPF are used for an amplitude analysis using the optimal formalism. The direct analysis of data is done in the transversity frame, which is best suited to parity-conserving reactions. From the results, amplitudes are also obtained in the helicity frame and the ``magic'' frame. Agreement with previous amplitudes obtained from an energy-dependent phase-shift analysis is good. The comparison of the helicity amplitudes c and e strengthens previous suggestions for a possible triplet-state dibaryon resonance. The comparison of the amplitudes ${a}_{m}$ and ${c}_{m}$ in the magic frame indicates a possible domination of the process near 90\ifmmode^\circ\else\textdegree\fi{} scattering angle by one-particle-exchange mechanism involving exchanged particles with natural parity.

He3(p,p)He3scattering in the energy range 19 to 48 MeV

Differential cross sections for $^{3}\mathrm{He}$(p,p)$^{3}\mathrm{He}$ elastic scattering have been measured at 11 energies in the laboratory energy range 19.5 to 47.5 MeV. The most forward c.m. angle for the angular distributions varies from 10.1\ifmmode^\circ\else\textdegree\fi{} to 13.4\ifmmode^\circ\else\textdegree\fi{}, and the most backward angle varies from 163.2\ifmmode^\circ\else\textdegree\fi{} to 173.4\ifmmode^\circ\else\textdegree\fi{}. The relative errors in the data are usually less than 2%, and the scale error is 1.5%. The present data, together with analyzing power and total reaction cross section data of others, have been subjected to an energy-dependent phase shift analysis. The extracted phase shifts and the differential cross sections are compared with the results of a simple resonating-group calculation.

Pion-nucleon σ term calculation using results of the energy-dependent phase-shift analysis

A method of pion-nucleon σ term calculation is suggested using expansion of the πN amplitude near physical threshold and results of the energy-dependent phase-shift analysis. This gives σ πN = 42±8 MeV. Various estimates of σ πN are discussed.

Study ofπ−πscattering amplitudes in the reactionπ+p→Δ++π0π0at 8.0 GeV

An experiment studying the reaction ${\ensuremath{\pi}}^{+}p\ensuremath{\rightarrow}{\ensuremath{\Delta}}^{++}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ using the Argonne National Laboratory 1.5-m streamer chamber combined with a lead-glass hodoscope is described. The data were analyzed in terms of ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}{\ensuremath{\pi}}^{0}$ scattering, and the details of the extrapolation to the pole are discussed. An energy-independent amplitude analysis from threshold to 2.3 GeV is presented. In this analysis the ${f}^{0}(1270)$, the ${h}^{0}(2040)$, and a ${J}^{P}={2}^{+}$ state at 1.8 GeV with a width of 0.280 GeV are observed. The amplitude ambiguity arising from analyses of ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}$ data in the 1.6-GeV region is resolved. An energy-dependent phase-shift analysis from 1.0 to 1.5 GeV is presented.

Phase shift analysis ofππ scattering

A novel approach to energy dependent phase shift analysis ofππ scattering is proposed. Optimised polynomial expansions of Roskies’ amplitudes are given. The parameters of these expansions are searched out by making a fit to the differential cross-sections. Then the transformation matrix between Roskies’ amplitudes and the conventional partial waves is used to compute the phase shifts and inelasticities. Significant improvement is observed in so far as the number of free parameters for a fixed energy phase shift analysis is concerned. Value for the effective Chew-Mandelstam coupling constant, λCM, is also estimated.