Nucleon Pole Research Articles

The role of the neutron electric form factor ind(e, e? N) N including polarization observables

The influence of the neutron electric form factor on various observables in two-body break-up of deuterons by electrons such as differential cross section, beam, target and beam-target asymmetries and outgoing nucleon polarization as well is investigated for different kinematic regions. The electron-deuteron vector asymmetryAedV and the outgoing nucleon polarization component P′x(n) are the most promising observables in and off the quasi-free region for a determination ofGEn. Also the single polarization observablesAdT and Py0(p) and the double polarization observable P′z(n) show significant influences fromGEn.

Surviving and Spurious Yukawa Couplings in the Skyrmion Model

1. It has been pointed out/H) within the present quantization algorithm of the Skyrmion model, that a pion-Skyrmion Yukawa coupling term vanishes from the pion-Skyrmion effective Lagrangian, where an asymptotically free pion field is introduced as quantum fluctuation about a classical Skyimion configuration. It was Skyrme himself who first pointed out this.4) If we have no ~oupling terms linear in the pion field at all, the iI state ~annot decay into N7r, and P-wave pion-nucleon scattering amplitudes do not develop nucleon poles. In order to construct a state with definite spin and isospin values such as Nand ii, we have to rotate the Skyrmion and project it on a definite spin and isospin state. The rotated Skyrmion described in terms of collective coordinates is not an exact solution of the equations of motion. Due to this breaking of the equations of motion at order Nc - a term linear in the pion field survives at order Nc -3/2. The surviving linear term has been regarded as the missing Yukawa coupling which gives rise to the iI decay,5)-8) while the present author9) has claimed that it is hard to regard such a surviving Yukawa coupling as the proper Yukawa couplings which are determined by experiments. On the other hand, there is an argumeneO),ll) that the Yukawa couplings of order INc exist also in a soliton model, but due to the cancellation between the leading terms the resultant Born terms become order 1. If this is the case, the defect of the vanishing Yukawa coupling is an illusion: But, the Born terms appear only as a result of the inadequate application of the reduction formula) to meson-soliton scattering amplitudes. In this paper we give additional arguments against the validity of the surviving Yukawa coupling and also of the spurious Born terms.

Particle polarizations in decays of5He? and4H?hypernuclei

Nucleon polarizations are examined in the hypernucleus decays5HeΛ, →4He + p + π−,4HΛ, →3H + p + π−, and4HΛ, →3He + n + π−. The effect of the strong interaction in the final state is taken into account. A significant role is predicted for the resonance interaction in the p-4He system in the formation of the proton polarization in the5HeΛ decay. It is also shown that in the4HΛ, →3H + p + π− decay the proton-polarization components should attain significant magnitudes, while in the charge-exchange decay4HΛ, →3He + n + π−, the neutron polarization is expected to be not too large.

The role of the neutron electric form factor ind(e, e? N)N including polarization observables

The influence of the neutron electric form factor on various observables in two-body break-up of deuterons by electrons such as differential cross section, beam, target and beam-target asymmetries and outgoing nucleon polarization as well is investigated for different kinematic regions. The electron-deuteron vector asymmetryA ed V and the outgoing nucleon polarization component P′x(n) are the most promising observables in and off the quasi-free region for a determination ofG En. Also the single polarization observablesA d T and Py 0(p) and the double polarization observable P′z(n) show significant influences fromG En.

On the P11 problem in π-deuteron scattering

In the study of the π-deuteron system the proper treatment of the P 11 π-nucleon channel has remained a problem. When the P 11 channel is broken up into the nucleon pole term and a background term the nucleon pole term is Pauli blocked leading to a poorer fit to the data. In this work it is shown that there is a diagram which largely cancels the diagram responsible for the Pauli blocking. It is expected that the inclusion of this diagram will lead to better agreement with the data and cure the P 11 problem.

Two-body deuteron photodisintegration above pion threshold with a dynamical treatment of δ degrees of freedom

The two-body photo break-up of the deuteron above pion threshold is calculated treating the final state interaction in a coupled channel approach with inclusion of Δ degrees of freedom. For the electromagnetic interaction nucleon, isobar and meson exchange currents are taken into account. Various observables (total and differential cross sections, γ-asymmetry and nucleon polarization) are influenced by the dynamical treatment of Δ degrees of freedom. Especially for the proton polarization it leads to an improved agreement with experiment. However, the situation for the shape of the differential cross section remains problematic.

Helicity-amplitude relations for vector-meson production from a skyrmion model.

Mattis has derived six relations among the partial-wave amplitudes for the reaction $\ensuremath{\pi}N\ensuremath{\rightarrow}\ensuremath{\rho}N$. From these relations we deduce that the six independent helicity amplitudes for the $t$-channel isospin-0 reaction may be simply expressed in terms of one unknown function. This leads to definite predictions for the $\ensuremath{\rho}$-meson density matrix and the absence of nucleon polarization effects, which can be tested directly, without recourse to partial-wave analysis.

Information on photonuclear transition matrix elements from measuring the emitted nucleon polarization in the reaction plane.

A compact general expression for the differential cross section of the photonuclear reaction (..gamma.., N), in which the incident photon is circularly polarized and any polarization of the emitted nucleon observed, is presented. Angular distribution coefficients relevant to the nucleon polarization in the scattering plane are expressed as bilinear combinations of matrix elements for a special case of the /sup 16/O(..gamma..,N/sub 0/) reaction. The polarization P/sub x/, calculated within the direct-semidirect model at E/sub ..gamma../ = 60 MeV, is shown as an example of the theoretical result.

Mechanism of 3He( pi -,pn) reaction.

The ${\ensuremath{\pi}}^{\mathrm{\ensuremath{-}}}$ absorption by $^{3}\mathrm{He}$ is investigated in a model study based on the nucleon pole mechanism \ensuremath{\pi}NN\ensuremath{\rightarrow}NN\ensuremath{\rightarrow}NN. We find that the amplitude of the three-body rescattering mechanism can have a strong interference effect with the amplitude of the direct two-body absorption process even in the region where the two-body process dominates. The main experimental signature of this important coherent effect is a sharp peak near the high energy end of the proton spectrum measured in a coincident experiment. Our results suggest that in order to extract the isospin dependence of pion absorption by a pair of nucleons from the recent $^{3}\mathrm{He}$(${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$,NN) data, the three-nucleon rescattering amplitude must be calculated accurately and included coherently in the analysis.

General analysis of two-body nucleon decays

An effective nucleon decay theory has been developed by Weinberg and Wilczek-Zee consistent with low-energy phenomenology. This theory, together with the SU(6) quark model, is used to derive two-body nucleon decay branching ratios. Scalar boson exchange effects are included and lead to non-trivial modifications of the pure vector boson exchange results. Contributions from both spectator and nucleon pole diagrams are considered.

Desirability of measurements on the asymmetry function at low energies in theH2(γ,n)H1reaction

Theoretical results on the asymmetry function are provided to encourage measurements to further test the recent unexpected conclusion that nucleon polarization measurements in the photodisintegration of the deuteron at low gamma-ray energies do not appear to require the two-body exchange current contributions.

Two-body effects and deuteron photodisintegration with polarized and unpolarized gamma rays

Employing the two-body charge effects owing to $\ensuremath{\pi}$ exchange and the current effects owing to $\ensuremath{\pi}$-, $\ensuremath{\rho}$-, and $\ensuremath{\omega}$-exchange processes, the angular distribution, asymmetry function, and polarization of nucleons from the $^{2}\mathrm{H}{(\ensuremath{\gamma},n)}^{1}\mathrm{H}$ reaction are investigated. The cross section and polarization parameters are reported for the Paris, Yale, super-soft-core B, and Hamada-Johnston potentials. The changes in the parameters owing to exchange effects are found to be nearly the same for all the potentials, and all the potentials are found to reproduce the low energy angular distribution data provided a suitable normalization factor is chosen.[NUCLEAR REACTIONS $^{2}\mathrm{H}{(\ensuremath{\gamma},n)}^{1}\mathrm{H}$. Two-body exchange effects, total and differential cross section, polarization, asymmetry function with realistic nucleon-nucleon interactions.]

Proton pole contribution in proton decay

We show that nucleon pole terms contribute significantly to proton decay, increasing the branching ratio for e + π 0 and ν R π + modes. The total lifetime is decreased to the point where keeping the SU(5) value of the lifetime below the experimental upper bound forces us to the choice of QCD scale parameter and proton radius parameter which are near the edge of the allowed region.

Chew-Low model and the potential description of theπNinteraction

The inverse scattering problem for the Chew-Low model is solved and the solution is used to construct three different forms for the off-shell $\ensuremath{\pi}N$ $T$ matrix. The three forms differ in their treatment of the nucleon pole and the crossing cut. One of the forms is shown to be equivalent to a separable potential model with an energy dependent strength. The analysis gives some insight into the question of the range of the $\ensuremath{\pi}N$ interaction.NUCLEAR REACTIONS Inverse problem for Chew-Low model; relation between field theory and potential descriptions of $\ensuremath{\pi}N$ interaction.

Organizational procedure for the study of pion production and absorption processes on nuclei

For nuclear processes involving pions, such as pion production/absorption or exchange currents, it is shown that a natural organization involves adoption of the $\ensuremath{\pi}\mathrm{NN}$ vertex function ${g}_{\ensuremath{\pi}}({q}^{2}){\ensuremath{\gamma}}_{5}{\ensuremath{\tau}}_{\ensuremath{\alpha}}$, where $q$ is the pion four-momentum and ${g}_{\ensuremath{\pi}}({{m}_{\ensuremath{\pi}}}^{2})\ensuremath{\simeq}13.4$ is the renormalized pion-nucleon coupling constant. The result is independent of the form and details of any fundamental interaction Lagrangian. The difference between ${g}_{\ensuremath{\pi}}({q}^{2}){\ensuremath{\gamma}}_{5}{\ensuremath{\tau}}_{\ensuremath{\alpha}}$ and the fully-dressed $\ensuremath{\pi}\mathrm{NN}$ vertex function contributes to amplitudes involving more bosons, e.g., scattering amplitudes ($\ensuremath{\pi}N\ensuremath{\rightarrow}\ensuremath{\pi}N$), production amplitudes ($\ensuremath{\pi}N\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}N$), etc. Such contributions are mediated through either seagull-like terms or $P11$ intermediate states. It is pointed out that it is neither necessary nor practical to calculate these partial contributions to scattering and production amplitudes. One can always exploit other approaches, theoretical and phenomenological, to make reasonably good models for the full amplitudes. The usual procedure of including the effects of negative energy parts of the nucleon propagator in interaction potentials, exchange currents, etc., is easily included in the present organization. The result is that from scattering amplitudes, etc; the positive energy nucleon poles are deleted but $Z$ graphs are included.NUCLEAR REACTIONS Theoretical, organization scheme, pion reactions with nuclei, effective $\ensuremath{\pi}\mathrm{NN}$ vertex.

Cross section and polarization in deuteron photodisintegration: General formulas

The differential cross section and the outgoing nucleon polarization in the disintegration of unpolarized deuterons by polarized photons are given as expansions in Legendre functions.NUCLEAR REACTIONS $d(\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\gamma}}, n)p$. Differential cross section and polarization. Legendre function expansion.

Polarization of the secondary nucleons in thepp → ppπ 0 andpp→npπ+ reactions at 1000 MeV

The calculation of the secondary nucleons polarization in thepp→ppπ0 andpp→npπ+ reactions at 1000 MeV is effected in the framework of the one-pion exchange model. It is shown that polarization is due to the interference of the resonant amplitude with the non-resonant amplitudes of theπN virtual scattering. The angular dependence of the polarization is sensitive to the behaivour of theπN scattering amplitudes off the mass shell.

Nucleon polarization and the nuclear charge operator

Effects of nucleon polarization on the nuclear charge operator have been evaluated in a constituent quark model. At momentum transfer q ≈ 4 fm −1 monopole, dipole and quadrupole excitations are of equal importance. In a harmonic oscillator model for 3He all multipolarities give negative contributions, leading to an overall contribution comparable to the relativistic pair effect. The influence of realistic wave functions, coupling constants and off-shell form factors is discussed.

Separable potential model for the off-shellπNamplitude

A simple model is used to reproduce modern $\ensuremath{\pi}N$ phase shifts in the $S$, $P$, $D$, and $F$ waves for ${T}_{\ensuremath{\pi}}l2$ GeV (except ${P}_{11}$). In these channels a rank one, two-channel separable potential model is used and the inverse scattering problem is solved directly. In the ${P}_{11}$ channel the phase shifts are fit with a separable $t$ matrix which contains a pole at the nucleon mass and an explicit sign change in the phase shift. This model is intended for use in theories of the low and medium energy pion-nucleus interaction where it supersedes the obsolete LT and LMM potentials. The explicit pole in the ${P}_{11}$ channel should facilitate the inclusion of pion annihilation into the many body problem.[NUCLEAR REACTIONS ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}N$; 0-2 GeV phase shifts reproduced; $S$, $P$, $D$, $F$ waves; separable potential with inverse scattering problem; nucleon pole and sign change in ${P}_{11}$.]

Inversion procedure for a pion-nucleonTmatrix

The solution of the inverse scattering problem for a separable model of the pion-nucleon $T$ matrix is obtained. The model is based on the Feshbach-Villars Hamiltonian formulation of the Klein-Gordon equation, and includes the left hand cut in the complex energy plane associated with crossing, as well as the direct and crossed nucleon poles. Numerical results are given for the four $P$-wave channels.[NUCLEAR REACTIONS Pion-nucleon elastic scattering; inversion procedure for separable $T$ matrix; contains nucleon poles and crossing cut.]