Nucleon Pole Research Articles

Backward pion-nucleon scattering and fermion-exchange mechanisms

It is shown that interference of the N α and N γ fermion trajectories offers an alternative explanation of the dip observed in the high-energy backward π +p differential cross sections at u ≈ −0.15 (GeV/ c) 2. It is also shown that this mechanism predicts a nucleon polarization P which, in general, oscillates as a function of u and attains rather large values (|P| ⪆ 0.35); this is in contrast with the mechanism of dominance by N α exchange [3], which at high energy necessarily leads to a small P(⪅ 0.1), smoothly varying with u.

New Phase-Shift Parametrization Based on a Phase-Shift Dispersion Relation

The dispersion relation for the phase shift used by Ball and Frazer is generalized to include the effects of zeros and poles in the $S$ matrix. For complex $S$-matrix zeros near the physical cut, one obtains a new parametrization for a resonant state. For $l=0$, the usual Breit-Wigner phase shift is found. The method is easily extended to resonances in higher partial waves (in terms of two parameters for the case of pure elastic unitarity). The results are used to describe three partial waves in $\ensuremath{\pi}N$ scattering: ${P}_{33}$, ${D}_{13}$, and ${P}_{11}$. Excellent agreement with the published ${P}_{33}$ phase shifts is obtained by using our resonant form plus the integral over the inelastic cut. The inelastic contribution to the phase shift is small at low energies but becomes important for ${E}_{L}>300$ MeV (${E}_{L}$ is the incident-pion kinetic energy). Inelastic effects in the ${D}_{13}$ partial wave can account for almost all of the phase shift up to ${E}_{L}=500$ MeV. A narrow resonance plus inelasticity gives a good fit to the phase shifts up to ${E}_{L}=900$ MeV. Our fit to the ${P}_{11}$ phase shift depends on the nucleon pole, the Roper resonance, a zero in the $S$ matrix below the elastic threshold, and inelastic effects. A good fit to the low-energy phase shifts can be obtained only if one assumes large inelasticity above 1 BeV; however, the model does account for the qualitative behavior of the ${P}_{11}$ phase shift.

Phenomenological Analysis of Pion Nucleon Scattering at High Energies

Pion nucleon scattering in the multi-Ge V region is analyzed in a purely phenomenological way in the sense that any specific theoretical model is not introduced. The scattering amplitude including the spin flip part is appropriately parametrized and the numerical values of these parameters are determined. In particular, it is to be emphasized that the hitherto unknown parameter f3 (the real to imaginary ratio of the spin flip amplitude) is uniquely determined within the present experimental knowledge ((:W>=0.7 for the rc+p and sc->=0.8 for the re-p). Furthermore, an empirical formula for the scattering amplitude is proposed. This formula is valid for all angles and is able to explain most of the presently available data in the multi-Ge V region. For example, polarization data on elastic scattering are fairly well reproduced. Complete phase shift analysis is also performed and behaviours of the phase shifts and the absorption parameters are discussed. § l. Introduction Recently experimental data on the pion nucleon scattering' at high energies have been rapidly accumulated. 1 > Among these data the values of the recoil nucleon polarization for elastic rc+j), n-j) and charge exchange n-·p scattering 2 > enable us to discuss quantitatively a behaviour of the spin flip amplitudes for these processes. Furthermore, a very precise measuremene> of the real to im­ aginary ratios of the forward scattering amplitude gives also useful· information on the real amplitude. Nevertheless, the present experimental knowledge is still far from a complete determination of the whole scattering amplitude. It is, however, worthwhile for a further development of the theory to investigate to what extent we can get detailed information on the amplitude and to try to obtain an empirical expression for the amplitude at the present stage. Here we will, therefore, treat pion nucleon scattering in the multi-Ge V region purely phenomenologically. This means that in this paper we do not refer to any specific theoretical models such as the Regge theory, the statistical model, the quark model, etc. In § 2 the s-dependence of the amplitude at t = 0 is discussed by expanding the amplitude as a power series of 1/ Is (s and t are the usual Mandelstam vari­ ables, s = (centre-of-mass total energyy and t = (four-momentum transferY). Numerical values of the coefficients of the series are given to the order of 1/ vs- for the spin nonflip amplitude.

…also of Interest: Albany, Michigan State, Germanium

The State University of New York, Albany expects to install a 4‐MeV Dynamitron in the academic year 1968–69 that will produce intense beams of positive ions for the study of low‐yield neutron and proton capture reactions. The research program, directed by Jagadish Garg, will include nucleon polarization studies and high‐resolution neutron and gamma spectroscopy… Michigan State University will soon have a TRIGA Mark 1 reactor that will operate at 250 thermal kW… J. C. McGroddy and M. I. Nathan of IBM find that bulk germanium in a high electric field can modulate a direct current with high‐frequency oscillations in the gigahertz range.

Constraint on the Double-Pion-Production Amplitude in Pion-Nucleon Collisions Implied by a Partially Conserved Axial-Vector Current

A constraint between the "nonpole" part of the pion-production amplitude and the pion-nucleon elastic scattering amplitude has been derived using the hypothesis of partially conserved axial-vector current (PCAC). An attempt has been made to evaluate this nonpole part of the pion-production amplitude, at the unphysical values of the invariants, under the assumption that the important processes are the one-pion-exchange process and the processes involving at least one nucleon pole. This allows us to evaluate the off-mass-shell pion-pion amplitude. We have shown that in the isobaric-spin-1 and -2 states our evaluated off-shell pion-pion amplitudes are not inconsistent with those evaluated on the basis of the algebra of currents and PCAC. In the isobaric-spin-0 state our results, with our approximations, are at variance with those of the algebra of currents and PCAC. We have shown that if the nonpole pion-production amplitude were assumed to be dominated by the one-pion-exchange process alone our results would agree remarkably well with those obtained using algebra of currents and PCAC.

Relations between spin-correlation measurements in nucleon-deuteron elastic scattering if the channel spin is conserved

The nucleon-deuteron elastic scattering cross section with polarized beam and a polarized target is described by 18 quantities (unpolarized cross section, one parameter for the nucleon polarization, four parameters for the deuteron polarization and 12 spin correlation coefficients). The channel-spin conservation hypothesis gives eight relations between these 18 quantities. The experimental verification of these relations would check the validity of the hypothesis.

Effect of the Quasipole on theπ−NForward Scattering Amplitudes

It is shown that a quasipole plays an important role in low-energy meson-baryon scattering. The influence of this quasipole, which exists on the second Riemann sheet just below the elastic threshold and has a residue of the same order of magnitude as that of the nucleon pole, is analyzed by extrapolation of the data of the pion-nucleon scattering amplitude. Since the residue of the quasipole is related to the pion-nucleon coupling constant, this extrapolation gives an independent possibility for determining the coupling constant. The result is $\frac{{g}^{2}}{4\ensuremath{\pi}}=13.9$.

Diffusion élastique des nucléons par les noyaux légers

The cross section and polarization of nucleons of intermediate energies (100 to 300 MeV) elastically scattered by 4He and 12C have been calculated within the impulse approximation including multiple scattering terms. The method is valuable for small angles. Several results are presented, which show good agreement, without any adjustable parameter.

Reciprocal Bootstrap of theNandN*Using the Static-Model Bethe-Salpeter Equation

The Bethe-Salpeter equation is written down for the static model of $\ensuremath{\pi}N$ scattering. This equation satisfies unitarity exactly in the elastic region, but includes at least some inelasticity at higher energies. It is solved below the inelastic threshold by using the Noyes technique, and then making a Pagels-type approximation. It is applied to the reciprocal bootstrap problem of Chew, where ${N}^{*}$ exchange is assumed to provide the dominant force for binding the $N$, and $N$ exchange for giving rise to the ${N}^{*}$. Experimental values are used for the crossed-channel masses and couplings. The cutoff is adjusted to give the correct position for the direct-channel nucleon pole. This gives an output ${N}^{*}$ mass and residues which are in rough agreement with experiment.

Two-Channel Model ofP11 π−NPartial-Wave Amplitude

A simple two-channel model of the ${P}_{11} \ensuremath{\pi}\ensuremath{-}N$ channel and a phenomenological second channel, the $\ensuremath{\sigma}\ensuremath{-}N$, is constructed. It is shown that this model reproduces the detailed structure of the $\ensuremath{\pi}\ensuremath{-}N$ phase shift and produces the nucleon pole as a dynamical bound state with the proper residue. On the basis of this model it is argued that the forces required in the second channel are comparable to those in the $\ensuremath{\pi}\ensuremath{-}N$ channel, and a significant portion of the binding of the nucleon is produced by the $\ensuremath{\sigma}\ensuremath{-}N$ channel. Finally, it is observed that the Roper resonance (600 MeV) corresponds to a pole in the $S$ matrix, and should be fitted into an ${\mathrm{SU}}_{3}$ multiplet.

K −−p charge exchange scattering at 1.51 and 1.7 GeV/c

It is shown that the dσ/ dΩ for K −− p charge exchange scattering at 1.5 - 1.7 GeV/ c can be well described in terms of the direct resonance amplitudes and the ϱ-exchange amplitude. The polarization of recoil nucleons is predicted with the same model.

N * (1518) as a regge pole and pion-nucleon scattering phase-shift inT=1/2,J=3/2 state

TheD13 pion-nucleon scattering phase-shifts are calculated using the Khuri representation suitably modified in order to exhibit explicitly the isolated nucleon pole in theu-channel. The results of the calculation are compared with the phase-shift analysis ofRoper.

Polarized Proton Targets and Low‐Energy Nucleon‐Nucleon Experiments

AbstractThe possible use of a polarized proton target in the investigation of low‐energy nucleon‐nucleon interactions is reviewed. The reconstruction of the scattering matrix and verification of P‐, T‐and isotopical invariances are briefly discussed. Possible sources and detectors of polarized particles are considered. The problem of phase‐shift analysis and nucleon‐nucleon potentials are treated in the appendices. Tables of experimental values are given for the polarization of nucleons scattered on nucleons. Experimental quantities determined from the phase‐shift analysis are given in graphs for the energies 14.5 and 23.1 MeV.

A possible test for the nuclear shell model and the impulse approximation

A study is made of the polarization and angular distribution of the emitted nucleon in certain nuclear disintegration processes initiated by inelastic scattering or photoproduction of pions. The result can be used as a test of the nuclear shell model or alternatively of the validity of the impulse approximation.

Polarization effects in photonuclear reactions

We derive explicit formulae for angular asymmetries and longitudinal and transverse polarizations of nucleons emitted from nuclei in the (γ, N) reaction, corresponding to linearly or circularly polarized as well as unpolarized incident photons. The reaction is assumed to proceed in two stages, namely, by photo-excitation of a single nuclear level and its subsequent decay via nucleon emission. Our expressions are given in terms of the nuclear transverse multipole form factors for the excitation and of the reduced matrix elements corresponding to the decay. The results are illustrated by obtaining nucleon angular distributions and transverse polarizations following photo-excitation of the giant dipole resonance in 16O, using Gillet's model and R-matrix theory. The comparison of these results with experiment is satisfactory.

Nucleon polarization in elastic lepton or antilepton production by high-energy neutrino or antineutrino

The degrees of polarization of the final nucleon in the processes ν+n→p+μ− and\(\bar \nu + p \to n + \mu ^ + \) are calculated for an unpolarized target nucleon. Three models for this elementary interaction are considered as numerical examples. The degrees of polarization, two transverse and one longitudinal, turn out to be crucial observables to distinguish these models.

Self-Consistent Determination of the Position and Width of the 33πNResonance

Using the procedure discussed in the preceding paper, we determine the approximate position ${M}^{*}$ and width $\ensuremath{\Gamma}$ of the 33 $\ensuremath{\pi}N$ resonance. The $\frac{N}{D}$ formalism is used to generate a unitary $I=J=\frac{3}{2} \ensuremath{\pi}N$ $p$-wave amplitude. The nucleon pole parameters are taken from experiment and the nearby left-hand-cut contribution is assumed to be accurately given by crossing symmetry with only the 33 physical-scattering contribution to the crossing relation retained. Distant left-hand singularities are accounted for by two Bal\'azs poles whose residues are determined by requiring the crossing relation for the real part of the amplitude to be satisfied on the nearby left-hand cut. The real part crossing relation is also assumed to be dominated by the 33 contribution. Self-consistency between the 33 amplitude determined by the $\frac{N}{D}$ calculation and that used to evaluate the crossing relations is obtained by an iterative procedure. We find ${M}^{*}=1.22$ and $\ensuremath{\Gamma}=0.11$ in units of the physical-nucleon mass, compared with the experimental values of ${M}^{*}=1.32$ and $\ensuremath{\Gamma}=0.11$, respectively.

Analysis and Model of Low-EnergyΛK0Production

The low-energy $\ensuremath{\Lambda}{K}^{0}$ production data are analyzed under the assumption of a ${K}^{*}$-exchange background. A new interesting result is found; namely, that the observed anomaly in the polarization and slight shoulder in the cross section at 829 MeV is apparently due to a narrow ${F}_{\frac{5}{2}}$ resonance located at 1647 MeV. The parameters of this resonance are determined from the data by adding its contribution to a model proposed previously by the author, which gave fairly good results above and below the energy of the anomaly, after modifying the contribution from a ${P}_{\frac{1}{2}}$ resonance included in that model by taking into account the proper threshold behavior. Fits to all the data up to 1.03 BeV/c (900 MeV) (the region of validity of the previous model) are given. The result obtained for the product of relative partial widths agrees remarkably well with that predicted by unitary symmetry for a member of an octet with an asymmetry parameter of 0.674 (Carruther's model). It is also found that the ${P}_{\frac{1}{2}}$ resonance (if it exists) cannot be a member of an octet, but it has to belong to either a $\overline{1}\overline{0}$ or 27 representation, if the ${F}_{\frac{5}{2}}$ resonance belongs to an octet. Experiments which might confirm or deny the existence of these resonances are suggested. Further, our method of analysis is extended to a more general type of background which includes contributions from the nucleon pole and baryon exchange terms.

Polarization of recoil nucleons in ?0-photoproduction on protons below 500 MeV. I

Using the model of pion photoproduction recently discussed byBall andSchmidt a prediction for the polarization of the recoil protons is given for unpolarized photons. The strong dependence on the assumed values ofE 0+ andM 1− is shown. Taking into account this result and assuming thatM 1+ and the higher multipoles are sufficiently known, the possibility of determining the small multipoles from measurements is discussed.

On the theory of pion production

We express the matrix element and the cross-section for single-pion production in pion-nucleon collisions in terms of four scalar invariant amplitudes. The contributions to these amplitudes from the nearest singularities in thet andu channels forT=J=3/2 isobar production and from the nucleon pole of thes-channel are calculated. Pion-pion scattering is also included. Full account is taken of the virtuality of the different intermediate states. The model provides a natural explanation of the 1512 MeVD13 resonance, which should be accompanied by aP11 resonance at roughly the same energy.