A Geometrical Method of Decoupling

The computation of tunes and matched beam distributions are essential steps in the analysis of circular accelerators. If certain symmetries - like midplane symmetrie - are present, then it is possible to treat the betatron motion in the horizontal, the vertical plane and (under certain circumstances) the longitudinal motion separately using the well-known Courant-Snyder theory, or to apply transformations that have been described previously as for instance the method of Teng and Edwards. In a preceeding paper it has been shown that this method requires a modification for the treatment of isochronous cyclotrons with non-negligible space charge forces. Unfortunately the modification was numerically not as stable as desired and it was still unclear, if the extension would work for all thinkable cases. Hence a systematic derivation of a more general treatment seemed advisable. In a second paper the author suggested the use of real Dirac matrices as basic tools to coupled linear optics and gave a straightforward recipe to decouple positive definite Hamiltonians with imaginary eigenvalues. In this article this method is generalized and simplified in order to formulate a straightforward method to decouple Hamiltonian matrices with eigenvalues on the real and the imaginary axis. It is shown that this algebraic decoupling is closely related to a geometric "decoupling" by the orthogonalization of the vectors $\vec E$, $\vec B$ and $\vec P$, that were introduced with the so-called "electromechanical equivalence". We present a structure-preserving block-diagonalization of symplectic or Hamiltonian matrices, respectively. When used iteratively, the decoupling algorithm can also be applied to n-dimensional systems and requires ${\cal O}(n^2)$ iterations to converge to a given precision.Comment: 13 pages, 1 figur

Updated Report Acceleration of Polarized Protons to 120-150 GeV/c at Fermilab

The SPIN@FERMI collaboration has updated its 1991-95 Reports on the acceleration of polarized protons in Fermilab's Main Injector, which was commissioned by Fermilab. This Updated Report summarizes some updated Physics Goals for a 120-150 GeV/c polarized proton beam. It also contains an updated discussion of the Modifications and Hardware needed for a polarized beam in the Main Injector, along with an updated Schedule and Budget.Comment: 30 pages, 12 figure

The pp -> K^+Sigma^+n cross section from missing mass spectra

We utilize existing inclusive data on K^+ meson momentum spectra of the reaction pp -> K^+X at T_p = 2.3 - 2.85 GeV to deduce total cross sections for pp -> K^+\Sigma^+n. The method used to extract those cross sections is explained and discussed in detail. Our result for T_p = 2.85 GeV is consistent with the data point from a direct measurement at the same beam energy. The cross section obtained for T_p = 2.3 GeV is with 13.7\pm2.3 \mu b considerably smaller than the value found in a recent experiment by the COSY-11 Collaboration at a somewhat lower beam energy, indicating that the pp -> K^+\Sigma^+n reaction cross section could exhibit a rather unusual energy dependence.Comment: 12 pages, 8 figure

The d' dibaryon in the quark-delocalization, color-screening model

We study the questions of the existence and mass of the proposed $d' (IJ^P=00^-)$ dibaryon in the quark-delocalization, color-screening model (QDCSM). The transformation between physical and symmetry bases has been extended to the cases beyond the SU(2) orbital symmetry. Using parameters fixed by baryon properties and $NN$ scattering, we find a mild attraction in the $IJ^P=00^-$ channel, but it is not strong enough to form a deeply bound state as proposed for the $d'$ state. Nor does the (isospin) I=2 N$\Delta$ configuration have a deeply bound state. These results show that if a narrow dibaryon $d'$ state does exist, it must have a more complicated structure.Comment: 12 pp. latex, no figs., 2 tables, additional refs., Report-no was adde

A Precision Measurement of pp Elastic Scattering Cross Sections at Intermediate Energies

We have measured differential cross sections for \pp elastic scattering with internal fiber targets in the recirculating beam of the proton synchrotron COSY. Measurements were made continuously during acceleration for projectile kinetic energies between 0.23 and 2.59 GeV in the angular range $30 \leq \theta_{c.m.} \leq 90$ deg. Details of the apparatus and the data analysis are given and the resulting excitation functions and angular distributions presented. The precision of each data point is typically better than 4%, and a relative normalization uncertainty of only 2.5% within an excitation function has been reached. The impact on phase shift analysis as well as upper bounds on possible resonant contributions in lower partial waves are discussed.Comment: 23 pages 29 figure

Measurement of Spin Correlation Parameters ANN_{NN}, ASS_{SS}, and A_SL{SL} at 2.1 GeV in Proton-Proton Elastic Scattering

At the Cooler Synchrotron COSY/J\"ulich spin correlation parameters in elastic proton-proton (pp) scattering have been measured with a 2.11 GeV polarized proton beam and a polarized hydrogen atomic beam target. We report results for A$_{NN}$, A$_{SS}$, and A_${SL}$ for c.m. scattering angles between 30$^o$ and 90$^o$. Our data on A$_{SS}$ -- the first measurement of this observable above 800 MeV -- clearly disagrees with predictions of available of pp scattering phase shift solutions while A$_{NN}$ and A_${SL}$ are reproduced reasonably well. We show that in the direct reconstruction of the scattering amplitudes from the body of available pp elastic scattering data at 2.1 GeV the number of possible solutions is considerably reduced.Comment: 4 pages, 4 figure

Analysis of optical flow models in the framework of calculus of variations

In image sequence analysis, variational optical flow computations require the solution of a parameter dependent optimization problem with a data term and a regularizer. In this paper we study existence and uniqueness of the optimizers. Our studies rely on quasiconvex functionals on the spaces W¹,P(Ω, IRd), with p > 1, BV(Ω, IRd), BD(&Omeag;). The methods that are covered by our results include several existing techniques. Experiments are presented that illustrate the behavior of these approaches

Measurement of the pn→ppπ0π−pn \to pp\pi^0\pi^- Reaction in Search for the Recently Observed Resonance Structure in dπ0π0d\pi^0\pi^0 and dπ+π−d\pi^+\pi^- systems

Exclusive measurements of the quasi-free $pn \to pp\pi^0\pi^-$ reaction have been performed by means of $pd$ collisions at $T_p$ = 1.2 GeV using the WASA detector setup at COSY. Total and differential cross sections have been obtained covering the energy region $\sqrt s$ = (2.35 - 2.46) GeV, which includes the region of the ABC effect and its associated resonance structure. No ABC effect, {\it i.e.} low-mass enhancement is found in the $\pi^0\pi^-$-invariant mass spectrum -- in agreement with the constraint from Bose statistics that the isovector pion pair can not be in relative s-wave. At the upper end of the covered energy region $t$-channel processes for Roper, $\Delta(1600)$ and $\Delta\Delta$ excitations provide a reasonable description of the data, but at low energies the measured cross sections are much larger than predicted by such processes. Adding a resonance amplitude for the resonance at $m$=~2.37 GeV with $\Gamma$ =~70 MeV and $I(J^P)=~0(3^+)$ observed recently in $pn \to d\pi^0\pi^0$ and $pn \to d\pi^+\pi^-$ reactions leads to an agreement with the data also at low energies

Search for the eta-mesic 4He with WASA-at-COSY detector

An exclusive measurement of the excitation function for the dd->3Heppi- reaction was performed at the Cooler Synchrotron COSY-Juelich with the WASA-at-COSY detection system. The data were taken during a slow acceleration of the beam from 2.185 GeV/c to 2.400 GeV/c crossing the kinematic threshold for the eta meson production in the dd->4He-eta reaction at 2.336 GeV/c. The corresponding excess energy with respect to the 4He-eta system varied from -51.4MeV to 22MeV. The integrated luminosity in the experiment was determined using the dd->3Hen reaction. The shape of the excitation function for the dd->3Heppi- was examined. No signal of the 4He-eta bound state was observed. An upper limit for the cross-section for the bound state formation and decay in the process dd->(4He-eta)bound->3Heppi- was determined on the 90% confidence level and it varies from 20nb to 27nb for the bound state width ranging from 5MeV to 35MeV, respectively.Comment: 8 pages, 9 figure