The classification of diagrams in perturbation theory

The derivation of scattering equations connecting the amplitudes obtained from diagrammatic expansions is of interest in many branches of physics. One method for deriving such equations is the classification-of-diagrams technique of Taylor. However, as we shall explain in this paper, there are certain points of Taylor's method which require clarification. Firstly, it is not clear whether Taylor's original method is equivalent to the simpler classification-of-diagrams scheme used by Thomas, Rinat, Afnan and Blankleider (TRAB). Secondly, when the Taylor method is applied to certain problems in a time-dependent perturbation theory it leads to the over-counting of some diagrams. This paper first restates Taylor's method, in the process uncovering reasons why certain diagrams might be double-counted in the Taylor method. It then explores how far Taylor's method is equivalent to the simpler TRAB method. Finally, it examines precisely why the double-counting occurs in Taylor's method, and derives corrections which compensate for this double-counting.Comment: 50 pages, RevTeX. Major changes from original version. Thirty figures available upon request to [email protected]. Accepted for publication in Annals of Physic

Covariant four-dimensional scattering equations for the NN−πNNNN-\pi NN system

We derive a set of coupled four-dimensional integral equations for the $NN-\pi NN$ system using our modified version of the Taylor method of classification-of-diagrams. These equations are covariant, obey two and three-body unitarity and contain subtraction terms which eliminate the double-counting present in some previous four-dimensional $NN-\pi NN$ equations. The equations are then recast into a from convenient for computation by grouping the subtraction terms together and obtaining a set of two-fragment scattering equations for the amplitudes of interest.Comment: Version accepted for publication in ``Annals of Physics''. New section containing two new figures added. 58 pages, 20 figures. Uses RevTeX. For copies of figures email [email protected]

A covariant gauge-invariant three-dimensional description of relativistic bound-states

A formalism is presented which allows covariant three-dimensional bound-state equations to be derived systematically from four-dimensional ones without the use of delta-functions. The amplitude for the interaction of a bound state described by these equations with an electromagnetic probe is constructed. This amplitude is shown to be gauge invariant if the formalism is truncated at the same coupling-constant order in both the interaction kernel of the integral equation and the electromagnetic current operator.Comment: 17 pages, RevTeX, uses BoxedEPS.te

Determining the Shallow Surface Velocity at the Apollo 17 Landing Site

Many studies have been performed to determine the shallow surface velocity model at the Apollo 17 landing site. The Lunar Seismic Profiling Experiment (LSPE) had both an active component with eight explosive packages (EPs) and a passive experiment collecting data at various time intervals. Using the eight EPs, the initial shallow surface velocity model was determined to be 250 m/s in the first layer of depth 248 m, 1200 m/s with a depth of 927 m in the second layer, and 4000 m/s down to a depth of 2 km in the third layer. Have performed variations on this study to produce new velocity models shown. Recent studies have also been reanalyzing the passive LSPE data and have found three different thermal moonquake event types occurring at different times within the lunar day. The current goal of the project is to collocate the thermal moonquakes to physical surface features to determine the breakdown of lunar rocks. However, to locate shallow surface events, an accurate velocity model is needed. Presented a thermal moonquake location algorithm using first order approximation, including surface events only. To improve these approximations, a shallow surface velocity is needed

Using chiral perturbation theory to extract the neutron-neutron scattering length from pi- d -> n n gamma

The reaction pi- d -> n n gamma is calculated in chiral perturbation theory so as to facilitate an extraction of the neutron-neutron scattering length (a_nn). We include all diagrams up to O(Q^3). This includes loop effects in the elementary pi- p -> gamma n amplitude and two-body diagrams, both of which were ignored in previous calculations. We find that the chiral expansion for the ratio of the quasi-free (QF) to final-state-interaction (FSI) peaks in the final-state neutron spectrum converges well. Our third-order calculation of the full spectrum is already accurate to better than 5%. Extracting a_nn from the shape of the entire pi- d -> n n gamma spectrum using our calculation in its present stage would thus be possible at the +-0.8 fm level. A fit to the FSI peak only would allow an extraction of a_nn with a theoretical uncertainty of +-0.2 fm. The effects that contribute to these error bars are investigated. The uncertainty in the $nn$ rescattering wave function dominates. This suggests that the quoted theoretical error of +-0.3 fm for the most recent pi- d -> n n gamma measurement may be optimistic. The possibility of constraining the nn rescattering wave function used in our calculation more tightly--and thus reducing the error--is briefly discussed.Comment: 35 pages, 14 eps figures, references and figure added, discussions of errors extended and clarified, improved conclusions, typos corrected, to be published in PR