π+−pElastic Scattering at 310 Mev: Phase-Shift Analysis

We present isospin-zero phase-shift analyses of the world $\mathrm{np}$ data near 325 MeV. Inclusion of new ${D}_{t}$ (and $P$) measurements produces a unique $I=0$ phase-parameter solution; however, $\ensuremath{\delta}(^{3}G_{4})$ is almost 5 standard deviations below theoretical predictions. Fixing this phase shift and the other $G$-wave phase shifts at theoretical values results in a set of lower partial-wave phase parameters which interpolate well with phase shifts at adjacent energies. Theoretical consequences of this phase shift set are discussed.NUCLEAR REACTIONS $E=325$ MeV; nucleon-nucleon isospin-0 phase-shift analysis.

Previously determined experimental drift velocities Vdr and ratios of lateral diffusion coefficient to mobility DT/µ have been refitted directly with a three parameter modified effective range theory (MER T) representation of the S wave phase shift, a one parameter fit to the P wave phase shift and fixed higher partial wave phase shifts. The MERT representation now extends to 1·0 eV, a threefold extension of the energy range of the MERT fit reported by Milloy et al. (1977). The total cross section derived from the phase shifts is also reported, together with the differential cross section at 1·0 eV which is compared with a previous experimental determination.

Measurements have been made of the $p$+$^{4}\mathrm{He}$ elastic scattering angular distributions at $T=21.85, 23.90, 25.75, 28.10, 30.35, 32.15, 34.25, 36.90, 39.75, 42.45, 44.05, 44.95, \mathrm{and} 47.65$ MeV in the angular range $10\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\lesssim}{\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}\ensuremath{\lesssim}170\ifmmode^\circ\else\textdegree\fi{}$. The data obtained have in general relative errors smaller than 2%, while the absolute scale of the measurements has an uncertainty of less than 2.5%. These data together with differential cross sections and analyzing power angular distributions selected from the literature, as well as total reaction cross section information have been subjected to a phase shift analysis. Up to 45 MeV a single, continuous solution could be determined using phase shifts up through $G$-waves. As in an earlier phase shift analysis the phase shifts exhibit a smooth variation with energy except for the well-known resonance region around 23.4 MeV. Above 45 MeV some improvement was obtained with the inclusion of a small $H$-wave contribution. New total reaction cross section data were employed as a constraint on the imaginary parts of the phase shifts. The new analysis corroborates an early finding that the inelasticity is mainly associated with the even partial waves.NUCLEAR REACTIONS Measured $\frac{d\ensuremath{\sigma}}{d\ensuremath{\Omega}}$ for $^{4}\mathrm{He}(p, p)^{4}\mathrm{He}$ at $T=21.85, 23.90, 25.75, 28.10, 30.35, 32.15, 34.25, 36.90, 39.75, 42.45, 44.05, 44.95, \mathrm{and} 47.65$ MeV for $10\ifmmode^\circ\else\textdegree\fi{}\ensuremath{\lesssim}{\ensuremath{\theta}}_{\mathrm{c}.\mathrm{m}.}\ensuremath{\lesssim}170\ifmmode^\circ\else\textdegree\fi{}$; phase shift analysis using $\frac{d\ensuremath{\sigma}}{d\ensuremath{\Omega}}$ and other selected $\frac{d\ensuremath{\sigma}}{d\ensuremath{\Omega}}$, $A$, and ${\ensuremath{\sigma}}_{R}$ from the literature, $20 \mathrm{MeV}<T<~55 \mathrm{MeV}$.

Using the $\frac{N}{D}$ technique, $T=\frac{1}{2}, \frac{3}{2}$ $P$- and $S$-wave phase shifts are calculated. The $T=\frac{1}{2}$ $P$- and $S$-wave phase shifts are also calculated in the Khuri-Regge representation. For the purpose of comparison with experiments, we use our phase shifts to calculate the angular distributions in the reaction ${K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\overline{K}}^{0}p{\ensuremath{\pi}}^{\ensuremath{-}}$.

The effect of vacuum polarization upon $p\ensuremath{-}p$ scattering is considered by first solving the problem in the Coulomb plus vacuum polarization potentials (called "electric" potential) without the nuclear potential. The nuclear phase shifts are then defined with respect to the electric wave functions, and the scattering cross section is written in terms of these phase shifts. The connection with other nuclear phase shifts (in the presence of vacuum polarization) which appear in the literature is established.The effective-range expansion for the nuclear $s$-wave phase shift is derived. An analysis of three low-energy $p\ensuremath{-}p$ scattering experiments indicates that the omission of vacuum polarization from the analysis results in a value for the shape-dependent parameter which is 0.02 smaller than the value obtained when vacuum polarization is included in the analysis. A discussion of the accuracy required to usefully delimit this parameter is included.

The nonlinear phase shift and nonlinear damping of spin-electromagnetic waves were theoretically studied for the first time in sub-terahertz frequency range in infinite homogeneous longitudinal magnetized multiferroics. The research was based on the solution of the Ginzburg-Landau equation. It is shown that the saturation of the phase shift occurs due to the nonlinear damping if the nonlinear damping coefficients exceed v1=108 s-1 and v2=109 s-1.

In optics, a light beam experiences a spatial shift in the beam plane upon total internal reflection. This shift is usually referred to as the Goos-Hänchen shift. When dealing with plane waves, it manifests itself as a phase shift between an incoming and reflected wave that depends on the wave vector component along the interface. In the experiments presented here, plane spin waves are excited in a 60-nm-thick Permalloy film and propagate towards the edge of the film. By means of time-resolved scanning Kerr microscopy, we are able to directly detect a phase shift between the incoming and reflected wave. With the help of a numerical model, we show that this phase shift naturally occurs for spin waves in the dipolar regime.

Phase parameters for nucleon-deuteron scattering

Using the existing high-accuracy data for proton-deuteron and deuteron-proton elastic scattering, a phase-shift analysis has been performed in the laboratory proton energy range from E p = 4 to 10 MeV. The AV18-based proton-deuteron phase shifts were used as starting values in the phase-shift search procedure. The low-partial wave phase shifts, especially the 4 P J phase shifts have been determined very precisely, thus providing valuable guidance for theoretical approaches to tackle the quest for a successful description of three-nucleon bound-state and continuum observables in a more efficient and consistent way. Furthermore, it was found that the phase shift and the mixing parameter determined in the present analysis cannot be generated by nucleon-nucleon interactions which are consistent with two-nucleon analyzing power data. Therefore, three-nucleon forces must play an essential role in resolving the long-standing three-nucleon analyzing-power puzzle.

A study has been made of the proton and $\ensuremath{\alpha}$-particle yields from the 28-MeV (lab) bombardment of $^{4}\mathrm{He}$ by $^{3}\mathrm{He}$. From these measurements a total reaction cross section ${\ensuremath{\sigma}}_{R}$ of $433\ifmmode\pm\else\textpm\fi{}10$ mb was deduced. A reaction-model analysis of the $\ensuremath{\alpha}$-particle continuum revealed a significant contribution from the sequential reaction $^{3}\mathrm{He}+^{4}\mathrm{He}\ensuremath{\rightarrow}^{6}\mathrm{Li}(2.18)+p\ensuremath{\rightarrow}\ensuremath{\alpha}+d+p$ in which the breakup of the excited $^{6}\mathrm{Li}$ nucleus is nearly isotropic in its rest system. A phase-shift study was performed for $^{3}\mathrm{He}$ + $^{4}\mathrm{He}$ elastic scattering at this energy using our ${\ensuremath{\sigma}}_{R}$ value as a constraint. A pronounced odd-even dependence of the real parts of the phase shifts on the orbital angular momentum was found. The results of this work are compared with other experiments, optical-model and phase-shift analyses, and resonating-group calculations.[NUCLEAR REACTIONS $^{4}\mathrm{He}(^{3}\mathrm{He},p)$, ($^{3}\mathrm{He},\ensuremath{\alpha}$), $E=28.00$ MeV; measured $\ensuremath{\sigma}({E}_{p},\ensuremath{\theta})$, $\ensuremath{\sigma}({E}_{\ensuremath{\alpha}},\ensuremath{\theta})$; deduced ${\ensuremath{\sigma}}_{R}$. $\ensuremath{\alpha}$-continuum analysis. Phase-shift analysis. Resonating-group comparison.]

Recently, Green has shown explicitly that different potentials which fit the same $S$-wave phase shifts from 0 to 250 MeV (lab system) can give quite different binding energies of nuclear matter. In this paper we show, for two particular potentials, a velocity-dependent one vs one with a hard core, how this different behavior is related to the form of the two-particle wave function at small interparticle distances. The equality of the phase shift vs energy for two potentials requires that the two-particle wave function must have not only the same asymptotic form but also the same value of an effective-range integral, which places some constraint on the form of the interior wave function as well. It is shown that the potentials give also nearly the same results to first order in the "separation method," an approximation to the treatment of nuclear matter in which the wave function is assumed to equal the interior wave function at short distances joining on smoothly with the unperturbed wave function at a distance of about 1 F. However, the change in the particle propagator due to the velocity dependence of the nucleon-nucleus potential gives a positive contribution to the energy, which depends on the wave function at short distances. This contribution is much bigger for the hard-core potential than for the velocity-dependent one, since there is more of a short-range correlation effect in the former case.

We simulate $K\ensuremath{\pi}$ scattering in $s$ wave and $p$ wave for both isospins $I=1/2$, $3/2$ using quark-antiquark and meson-meson interpolating fields. We extract the elastic phase shifts $\ensuremath{\delta}$ at several values of the $K\ensuremath{\pi}$ relative momenta. The resulting phases exhibit qualitative agreement with the experimental phases in all four channels. We express the $s$-wave phase shifts near threshold in terms of the scattering length and the effective range. Our $K\ensuremath{\pi}$ system has zero total momentum and is simulated on a single ensemble with two dynamical quarks, so results apply for ${m}_{\ensuremath{\pi}}\ensuremath{\simeq}266\text{ }\text{ }\mathrm{MeV}$ and ${m}_{K}\ensuremath{\simeq}552\text{ }\text{ }\mathrm{MeV}$ in our simulation. The backtracking contractions in both $I=1/2$ channels are handled by the use of Laplacian-Heavyside smeared quarks within the distillation method. Elastic phases are extracted from the energy levels using L\"uscher's relations. In all four channels, we observe the expected $K(n)\ensuremath{\pi}(\ensuremath{-}n)$ scattering states, which are shifted due to the interaction. In both attractive $I=1/2$ channels, we observe additional states which are related to resonances; we attribute them to ${K}_{0}^{*}(1430)$ in $s$ wave and ${K}^{*}(892)$, ${K}^{*}(1410)$ and ${K}^{*}(1680)$ in $p$ wave.

Recently, a new measurement of the $^{6}\mathrm{Li}$ (150 A MeV)dissociation in the field of $^{208}\mathrm{Pb}$ has been reported [Hammache et al., Phys. Rev. C 82, 065803 (2010)] to study the radiative capture $\ensuremath{\alpha}+d\ensuremath{\rightarrow}{}^{6}\mathrm{Li}+\ensuremath{\gamma}$ process. However, the dominance of the nuclear breakup over the Coulomb one prevented the information about the $\ensuremath{\alpha}+d\ensuremath{\rightarrow}{}^{6}\mathrm{Li}+\ensuremath{\gamma}$ process from being obtained from the breakup data. The astrophysical ${S}_{24}(E)$ factor has been calculated within the $\ensuremath{\alpha}\ensuremath{-}d$ two-body potential model with potentials determined from the fits to the $\ensuremath{\alpha}\ensuremath{-}d$ elastic scattering phase shifts. However, the scattering phase shift, according to the theorem of the inverse scattering problem, does not provide a unique $\ensuremath{\alpha}\ensuremath{-}d$ bound-state potential, which is the most crucial input when calculating the ${S}_{24}(E)$ astrophysical factor at astrophysical energies. In this work, we emphasize the important role of the asymptotic normalization coefficient (ANC) for ${}^{6}\mathrm{Li}\ensuremath{\rightarrow}\ensuremath{\alpha}+d$, which controls the overall normalization of the peripheral $\ensuremath{\alpha}+d\ensuremath{\rightarrow}{}^{6}\mathrm{Li}+\ensuremath{\gamma}$ process and is determined by the adopted $\ensuremath{\alpha}\ensuremath{-}d$ bound-state potential. Since the potential determined from the elastic scattering data fit is not unique, the same is true for the ANC generated by the adopted potential. However, a unique ANC can be found directly from the elastic scattering phase shift, without invoking intermediate potential, by extrapolation the scattering phase shift to the bound-state pole [Blokhintsev et al., Phys. Rev. C 48, 2390 (1993)]. We demonstrate that the ANC previously determined from the $\ensuremath{\alpha}\ensuremath{-}d$ elastic scattering $s$-wave phase shift [Blokhintsev et al., Phys. Rev. C 48, 2390 (1993)], confirmed by ab initio calculations, gives ${S}_{24}(E)$, which at low energies is about $38%$ less than the other one reported [Hammache et al., Phys. Rev. C 82, 065803 (2010)]. We recalculate also the reaction rates, which are lower than those obtained in that same study [Hammache et al., Phys. Rev. C 82, 065803 (2010)].

The stochastic variational method is used with a confining potential of the form $V=\ensuremath{\lambda}{r}^{12}$ to generate correlated basis sets capable of accurately describing low-energy elastic scattering. Stabilization concepts are then used to extract the phase shifts and other scattering observables. The method is applied to positron scattering from H and He, and Ps scattering from H and He. The results of the calculations are in uniformly good agreement with previous high quality calculations or with experiment. In particular, the scattering length for Ps-He scattering is found to be $1.566{a}_{0}$ while the zero-energy ${_{1}Z}_{\text{eff}}$ was 0.1157. The Ps-He $s$-wave phase shift is found to be incompatible with experimental momentum transfer cross sections obtained by the Doppler broadening technique.

We present a theoretical investigation for the nonlinear interaction between electron-acoustic shock waves in a nonextensive two-electron plasma. The interaction is governed by a pair of Korteweg-de Vries-Burgers equations. We focus on studying the colliding effects on the propagation of shock waves, more specifically, we have studied the effects of plasma parameters, i.e., the nonextensive parameter q, the “hot” to “cold” electron number density ratio α, and the normalized electron kinematic viscosity η0 on the trajectory changes (phase shifts) of shock waves. It is found that there are trajectory changes (phase shifts) for both colliding shock waves in the present plasma system. We also noted that the nonlinearity has no decisive effect on the trajectory changes, the occurrence of trajectory changes may be due to the combined role played by the dispersion and dissipation of the nonlinear structure. Our theoretical study may be beneficial to understand the propagation and interaction of nonlinear electrostatic waves and may brings a possibility to develop the nonlinear theory of electron-acoustic waves in astrophysical plasma systems.