Browsing by Author "Duck, Ian M."
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Item A first-quantized proof of the symmetrization postulate(1971) Wagoner, Donald Edward; Duck, Ian M.Methods used to prove the existence of superselection rules are studied in detail. It is shown that the known methods of proving superselection rules are applicable only if the superselecting operator is an observable. In particular, place permutations are not observables, so the fact that place permutations commute with all observables does not lead to a superselection rule between vectors of different symmetry types. It is shown that if states not having a definite symmetry type can exist, then it is possible to have several different states which are eigenstates of the same observables with the same eigenvalues. In this case a maximal set of observables does not exist. Therefore a proof of the Symmetrization Postulate (SP) which assumes a maximal set of observables actually presupposes part of what is to be proved. A rigorous proof of the SP must depend only on the weaker assumption of a non-degenerate set of observables. The usual formulation of the Transition Probability Postulate (TPP) is used to construct a trivial proof of the assertion that physical states are represented by unique rays in Hilbert space; however the feature of the TPP which is essential to this proof is not essential to the TPP itself. The features of the TPP which are essential for computing transition probabilities are identified. These essential features of the TPP are then used to prove that states are represented by unique rays. The difficulties involved in rigorously defining the interchange operator Pij are discussed and a careful definition of Pij is given. The uniqueness of the ray is then used to show that states of systems containing several indistinguishable particles must be eigenstates of Pij and must satisfy the Symmetrization Postulate. Finally, the SP is used to prove the slightly stronger result that a given state must have the same symmetry type for each pair of the same species of particles.Item A Monte Carlo study of high transverse energy triggers in PP collisions at Plab=400 Gev/c(1983) Naudet, Charles Joseph.; Mietinen, Hannu E.; Duck, Ian M.; Hannon, James P.We have studied the properties of typical inelastic final states in pp collisions at =4 Gev/c under triggering conditions similar to those used in actual jet experiments . The events were generated by a Monte Carlo method 'which employed experimentally observed multiplicity and inclusive momentum distributions and constrained all the events to conserve momentum and energy. We find that a requirement of high transverse energy in a given solid angle selects mostly very high multiplicity events. Some experimentally observed momentum correlations seem to be of kinematical orgin and the triggered events have a similar transverse energy spectrum, but a less coplanar event structure than what is observed in experimental data.Item A nuclear study utilizing the Faddeev equations(1968) McMahan, Clyde Alex; Duck, Ian M.The Faddeev equations with separable two-body scattering amplitudes are used to calculate the binding energy of the three-alpha system. We find a value of the binding energy in reasonable agreement with the experiment value. Using separable potentials of the Yamaguchi, Tabakin, and Barbour-Schult types to generate the S-wave scattering amplitudes, we find the three-body bound state is not extremely sensitive to the form of the two-body interaction. We also find the admixed D-state contributes little to the three-body binding energy. With a view to future studies, a set of separable potentials is presented to describe neutron-alpha scattering.Item A phenomenological study of proton-proton elastic shattering near 700 MeV(1982) Turpin, Stephen E.; Duck, Ian M.; Roberts, Jabus B.; Miettinen, Hannu E.Proton-proton elastic scattering experiments are now of sufficient number and quality below 8 MeV to tightly constrain almost all isovector phase shifts which are significantly sensitive to elastic scattering parameters. A study of the sensitivity of various experimental observables to small changes in the phase parameter indicates which experiments might be most profitable in further constraining the phase shifts. There exists drastic disagreement between the measurements of Aj at 7 MeV in a recent experiment and current phase shift solutions, and since reasonable variations of the phase parameters do not produce significant improvement in the fit, the suspicion of some normalization error in the experiment is raised.Item Application of Hartree-Fock theory to finite nuclei(1969) Hughes, Henry Grady; Duck, Ian M.The Hartree-Fock equations are derived and generalized to the case of nuclear matter using the Brueckner reaction matrix. The Fourier transform of the nonlocal term in the resulting integral-differential equation is expanded to second-order terms, and the equation is reduced to a differential equation. An iterative method is used to obtain a self-consistent solution. Several expansion procedures were tried, and in all cases the iterations converged to reasonable values for potentials, wave functions, and binding energies for 016.Item Current algebras and pion Lagrangians(1969) Hu, Chenyou; Duck, Ian M.The theory of weak interactions of non-strange and strange particles is reviewed. The algebra of currents is discussed briefly and applied to the soft pion calculations. The phenomenological non-linear Lagrangians of pions are developed in detail.Item Gravitational radiation theory(1974) Wilson, Thomas L.; Duck, Ian M.A survery is presented of current research in the theory of gravitational radiation. Ironically, theoretical work on gravitational radiation first appears in the electromagnetic (vector) theories of gravitation - where it has since been forgotten. This is in part due to an over enchantment with the more general tensor theory of radiation, although such enchantment is warranted in the sense that it may be the proper solution to the problems in radiation theory. Special care is taken to stay away from the metaphysics of gravitation theory and to stick with the mathematical structure of gravitational radiation. Furthermore, the radiation problem is treated in a fashion entirely divorced from other problems in gravitation. The development proceeds candidly through three points of view -- scalar, vector, and tensor radiation theory - and the corresponding results are stated.Item Kinetic Energy Oscillations in Annular Regions of an Ultracold Neutral Plasma(2005) Laha, Sampad; Killian, Thomas C.; Dunning, F. Barry; Duck, Ian M.A study of ion oscillations in the annular regions of a strontium plasma is reported._x000D_ An ultracold neutral plasma is formed by photoionizing the 1 P 1 electrons using a_x000D_ pulsed dye laser' and absorption spectroscopy is done on the 2 S ½ - 2 P ½ transitionItem L-changing in Na(Ns, Np)-Xe collisions(1984) McIntire, John P.; Dunning, F. Barry; Jeys, Thomas H.; Duck, Ian M.A crossed atomic beam/pulsed laser technique and electric field ionization have been used to study Na(nS,nP)-Xe collisions for 28 =< n =< 52. The predominate mode for destruction of the parent nS,nP atoms is l-changing. The time evolution of the A-mixed population is monitored at several times after laser fire and fit to a rate equation to determine the rate constants for l-changing. The data can be qualitatively explained by appealing to the free electron model and applying simple energy transfer arguments to the Rydberg electron-target interaction. Present results are compared to other experimental data.Item Measurement of spin parameters A and Ann in np and pp elastic scattering at 6 G3V/c(1981) Calkin, Mark M.; Mietinen, Hannu E.; Duck, Ian M.; Roberts, Jabus B.The spin parameters A and Ann have been measured for np and pp elastic scattering at 6 GeV/c using a 12 GeV/c polarized deuteron beam and a polarized proton target at the Argonne ZGS. The recoil proton was measured by a conventional magnetic spectrometer, while the scattered neiitron/proton was detected in a brass-scintillator neutron converter/detector. Clean elastic signals were seen in both reactions. Our results on pp elastic scattering show that A and Ann are small and positive, in agreement with previous measurements. In np elastic scattering, we find that Ann -1% over the t-range .25<-t<.6 (GeV/c)2.Item Monte Carlo study of multiple hard scattering effects in proton-nucleus interactions at high transverse energies(1985) Hage, George; Duck, Ian M.; Phillips, Gerald C.; Corcoran, Marjorie D.All experimental data for proton-nucleus collisions at ultrarelativistic energies confirms the "Anomalous nuclear enhancement" phenomena, which gives a cross section dependence upon the atomic number A as oPA = oppA^a with a greater than 1. This power law dependence cannot be explained by QCD parton-models if only a single proton-nucleon hard collision is assumed, for then a power of 1 would emerge. The effect of multiple-hard scattering of partons inside the nucleus is studied in this thesis. E^T cross sections and other variables, such as planarity and multiplicity, are studied within the multiple scattering model using Monte Carlo techniques. The results are compared with data for two different un-biased triggers, the global trigger and the two-high trigger. Judgments on the importance of multiple scattering are made.Item On the theory of tachyons(1970) Phillippi, Elmer Joseph; Duck, Ian M.Hypothetical particles, called tachyons, which travel faster than the speed of light, are studied both as classical particles subject to the mathematical restrictions of special relativity theory and as particles described by a many-particle quantum field quantized according to Fermi-Dirac statistics. Negative-energy particles appear in the theory but are interpreted physically as positive-energy particles with the opposite momentum. We find that the total number of particles present is not Lorentz invariant, but (for charged tachyons) the total charge is. It is possible to contrive causal, paradoxes leading to causal loops (effect precedes cause) but such difficulties can be remedied by defining a cosmological preferred frame and postulating that emission and absorption of tachyons can only take place between members of some restricted class of observers with velocities less than some critical value relative to the preferred inertial reference frame. The causality of tachyon signal transmission is considered in terms of entropy flux, and we find that we must reinterpret signals carrying positive entropy backward in time as signals carrying negative entropy forward in time. Several experiments have been conducted to find tachyons, both charged and neutral, but all have been unsuccessful.Item [Pi]-D scattering using the Foldy-Walecka optical model(1976) Brown, Johnny M.; Duck, Ian M.We discuss the possibility of producing a bound state of the pi-D system assuming that the only important interaction in the tr-N system below = 3 MeV is the 3-3 resonance. We find that the combined potentials of the two nucleons in the deuteron system are not sufficient to induce binding with the pion. However, the 3-3 resonance does produce a pi-D resonance at a lower energy and with a narrower half-width than the pi-N resonance. We use the approach of Foldy and Walecka^ to generate the equations describing the pi-D interaction. This approach neglects both the three body interactions in the pi-D system and the momentum exchanged between the pion and the deuteron. This enables us to describe the pi-D interaction in terms of partial waves knowing only the form of the pi-N scattering amplitude and the potential describing the Tr-N interaction. An S-wave resonance is forced to occur in the pi-N system so that the effects of the parity and A values of the Tr-D partial waves on the overall pi-D S-wave interaction can be clearly seen. The resonance in the pi-D interaction caused by the S-wave pi-N resonance indicates that the nucleons in the deuteron are weakly coupled together. Assuming this to be true in the P-wave pi-D interaction, we make a second order Born approximation of the P-wave matrix equations produced from the FoldyWalecka approach to simplify the numerical computations. We use both the rather simple pi-N scattering amplitudes and the TT-N scattering amplitudes derived from the Foldy-Walecka approach to describe the S-wave and P-wave pi-N resonances. Both forms of the pi-N scattering amplitudes give similar results when inserted into the Foldy-Walecka equations describing the pi-D interaction. The method used by Foldy and Walecka seems to be useful in describing the pi-D interaction, especially since the equations are easily expanded in a multiple scattering series. However, we believe their method would be too cumbersome as we have applied it for systems of larger size or higher angular momenta. We neglect spin and isospin, assume infinite masses for the nucleons in the pi-D system, and discuss forward scattering only. We find that if spin, isospin, or other refinements are included in our description of the pi-D interaction, the time required for the numerical computation of the Foldy-Walecka equations increases dramatically.Item The calculation of neutron-deuteron scattering by the K-matrix method(1972) Reed, James Farr; Duck, Ian M.Item The coupling through unitarity of the NN and NN* channels(1969) Bruno, Daniel Ruben O; Duck, Ian M.We present a formalism to calculate the nucleon-nucleon interaction with contributions from the NN-pi channel in the isobar approximation for the N-pi system. In order to write dispersion relations for the T = 1, J = 0 amplitudes, we study the complex singularities that are present in the Born amplitude for the production process. We use the N/D coupled channels method for the helicity partial wave amplitudes and write the explicit equations for the T = 1, J = 0 amplitudes taking into account, through a simplified model, the contributions of the complex singularities.Item The peratization approximation(1966) Gale, William Arthur; Duck, Ian M.The peratization program is investigated in the field of singular potential scattering, as an analog to the unrenormalizable field theories. We review some known results on the scattering amplitude, and establish the applicability of the commonly used regularizations. A general argument for peratization is presented. Several examples are considered. The results for weak types of singularities offer an unresolved contradiction.Item The quark-Skyrme nucleon(1990) Mattingly, Alan Charles; Duck, Ian M.We construct a quark-soliton model of the nucleon which interpolates between the MIT bag model of arbitrarily confined relativistic quarks and the Skyrme model in which the nucleon is a topological knot in the pion field. Confinement is achieved using the color dielectric model. The field equations are solved numerically for the so called hedgehog state for which the field equations reduce to radial ones. Nucleon observables are calculated by projecting the quark-soliton hedgehog ground state onto spin-isospin eigenstates, which are taken to be variationally best nucleon and nucleon isobar states.Item Theory of single pion production in nucleon-nucleon scattering(1981) Umland, Eric Alexander; Duck, Ian M.; Baker, Stephen D.; Mutchler, Gordon S.We have developed a phenomenological theory for the reaction NN+NNir based on the peripheral model and the formation and decay of dibaryon resonances. The peripheral graphs include one pion exchange with a monopole form factor at the TTNN vertex and the full TTN elastic scattering amplitude obtained from phase shift analyses and including off-shell corrections. Interfering with the one pion exchange graphs are one rho exchange graphs. Similiar monopole form factors are included at the pNN and pNA vertices. All form factors possess one adjustable parameter. We also study effects due to the still speculative J = 3~ and 2+ dibaryon resonances. The highly inelastic nature of these objects suggests that a single pion production reaction of the form NN+R+NA+NNTr presents the best opportunity for observing dibaryon manifestations. We calculated the fifth order spin dependent differential cross sections d+ (beam polarized up) and cr (beam polarized down) and the asymmetry (c+-c)/(a +). The peripheral model alone gives generally poor agreement with the kinematically-complete, beam polarized data of Hancock. Inclusion of the diproton amplitudes results in a general improvement in the fits, supporting the notion of such resonances in the 3 and 1D2 partial waves of the NN channel.