Ian Duck

Toward an understanding of the spin-statistics theorem

We respond to a recent request from Neuenschwander for an elementary proof of the Spin-Statistics Theorem. First, we present a pedagogical discussion of the results for the spin-0 Klein–Gordon field quantized according to Bose–Einstein statistics; and for the spin-12 Dirac field quantized according to Fermi–Dirac statistics and the Pauli Exclusion Principle. This discussion is intended to make our paper accessible to students familiar with the matrix solution of the quantum harmonic oscillator. Next, we discuss a number of candidate intuitive proofs and conclude that none of them pass muster. The reasons for their shortcomings are fully discussed. Then we discuss an argument, originally suggested by Sudarshan, which proves the theorem with a minimal set of requirements. Although we use Lorentz invariance in a specific and limited part of the argument, we do not need the full complexity of relativistic quantum field theory. Motivated by our particular use of Lorentz invariance, if we are permitted to eleva...

Three-body break-up in the d + d → d + p + n reaction

Abstract Neutron-charged-particle and charged-particle-charged-particle coincidence spectra from the d + d → d + p + n reaction were measured for θ 1 = −θ 2 = 20° at bombarding energies 6–13 MeV. Deuteron-neutron and deuteron-proton spectra for θ 1 = −θ 2 are dominated by a broad peak associated with deuteron-nucleon quasi-free scattering. The measured data were interpreted using the quasi-free scattering model. The constructed model describes the general behavior of the coincidence spectra rather well, although the calculated spectral shapes are broader than the measured ones. The limitations of the simple quasi-free scattering model are shown also by the fact that the model predicts an order of magnitude too high cross section and that the normalization constant to the measured peak cross section is energy dependent.

Proton-proton Bremsstrahlung

Abstract We calculate proton-proton Bremsstrahlung cross sections using the Tabakin separable potentials to generate off-shell nucleon-nucleon t-matrix elements in low partial waves and off-shell one-pion-exchange amplitudes for the higher partial waves. Our results are in good agreement with the experimental values reported by Warner, Halbert, Gottschalk and Thorndike at proton bombarding energies of 48, 62, 158 and 204 MeV, but are at the lower limit of the experimental results of Warner at 30 MeV and of Slaus at 46 MeV. The calculated cross sections in the Harvard geometry decrease monotonically to zero at zero proton energy. We have estimated the effect of rescattering corrections and of non-local corrections to the Bremsstrahlung amplitude and find these terms to be negligible for proton-proton Bremsstrahlung. Our results are insensitive to the choice of Tabakins “soft-core” or “hard-shell” 1S0 potential, and are insensitive to small changes in the P-wave potentials.

Quarks, gluons and the pion-nucleon coupling constant

Abstract A variant of the MIT bag model of confined quarks is used to express the pion-nucleon coupling constant ƒ π in terms of the Δ(1232)−N(938) mass difference ΔM. Both ΔM and ƒ π are supposed to occur via the exchange of a single magnetic gluon. The result, which scales with the 5 2 power of the proton charge radius Rp, produces about one half the experimental value for quark wave functions fitted to nucleon parameters.

Pion production in the reaction pd → tπ

Abstract The Yao-Barry model is extended to the reaction pd → tπ and provides a description of the cross section for incident proton energies from 340 to 670 MeV in terms of a single parameter, the triton nd wavefunction evaluated at the origin. The results are competitive with the predictions of the Ruderman model for the energy dependence of the forward cross section and show much larger backward cross sections.

N--N* INTERACTIONS WITH FADDEEV EQUATIONS.

Abstract We discuss the problem of whether a two-nucleon bound state or resonance can arise dynamically from the Peierls mechanism - the exchange of a real pion by two nucleons having a resonant interaction with the pion. We examine a number of low partial waves of the nucleon-nucleon-pion system to determine in which states the resonant pion exchange mechanism gives rise to significant attractive forces with the possibility of creating a bound state or resonance. Our principal tool is the non-relativistic Faddeev equation incorporating isospin and spin. We also use a relativistic extension of the Faddeev equations due to Lovelace. The pion-nucleon interaction is represented by a separable potential, but we investigate the sensitivity of the results to the exact form of this interaction. Our principal result for the NNπ system is that there will be no bound states but two broad resonances with isospin two indicated at an energy about 350 MeV above the nucleon-nucleon threshold. Spinless bosons of the nucleon mass would have a bound state in a non-relativistic model.

Angular distributions in C12 → 3α

Abstract Feynman diagram techniques are used to calculate angular distributions of C 12 → 3α for states in C 12 with spin 0 + , 1 − , 2 + . The breakup is assumed to proceed sequentially through the 0 + , 2 + states of Be 8 . The extent to which the sequential mode dominates provides a determination of the nature of the states of C 12 in terms of the cluster model. Pure sequential decay would indicate that these states in C 12 are well described as being cluster model states with an alpha particle bound to a Be 8 nucleus. Angular distributions are presented for unpolarized initial states and for 2 + states of arbitrary polarization. Application is made to states which have been studied experimentally.

THREE-ALPHA-PARTICLE RESONANCES VIA THE FADEEV EQUATION

Abstract We use the Fadeev equation with a separable two-particle scattering amplitude to search for stationary states of the three-alpha-particle system. With a two-particle scattering amplitude consisting of an S-wave resonance, we find a single low-energy resonance which can be driven to negative energy only by using unreasonable off-energy shell dependence of the two-particle scattering amplitude.

Polarization and asymmetry in 3He(d, p)4He

Abstract We analyse the polarization P, asymmetry A (for a polarized target) and angular distribution in 3He(d, p)4He in terms of the most general transition matrix allowed by the requirements of Galilean invariance and reflection invariance. We determine the conditions for which P = −A (in crude agreement with experiment). A multipole expansion of the amplitudes is presented and a fit to the lowest energy data available is obtained by considering S 1 2 , P 1 2 and P 3 2 angular momentum states only.

Three-alpha final state interactions

Abstract We use a soluble model of the decay of a 2 + particle into three identical strongly interacting 0 + particles to investigate the reaction 11 B(p, α)2∝ at a proton energy of 2.65 MeV through the 18.37 MeV state of 12 C. The strong final state interactions are described by Faddeev equations with separable two-body interactions to represent the ground and first excited states of 8 Be. It is necessary to use a mixed 12 C initial configuration to reproduce the experimentally observed interference effects. A fit to the data requires the approximate inclusion of the Coulomb phase shifts. The decay is dominated by final state interactions with little evidence for direct three-body decay.