RF Separators and Separated Beams at SLAC
It has been shown that with momenta above -5 GeV/c, the only effective means of separation by particle mass in secondary beams is using RF deflectors. 192 Particle separation at proton synchrotrons requires the use of two RF deflectors. The beam structure at SLAC permits the use of a single deflector. second RFS to intercept the unwanted particles. For wanted particles the phase at the second RFS relative to that at the first is A& given in (4). The net deflection can range from Introduction
Relative Velocity Measurements of Electrons and gamma Rays at 15-GeV
J. M. Durand, J. C. Faivre, J. M. Fontaine, D. Garreta, D. Legrand, J. Saudinos, J. Thirion, R. Bertini, F. Brochard, and F, Hibou, Phys. Rev, Lett. 32, 839 (1974). Y. Hahn and D. W. Rule, to be published; Y. Hahn, Phys. Rev. A 9, 2014, 2024 (1974), and Phys. Rev. C 10, 585 (1974). M. L. Goldberger and K. M. Watson, collision Theo~ (Wiley, New York, 1964). 'OT. A. Murray, L. Riddiford, G. H. Grayer, T. W. Jones, and Y. Tanimura, Nuovo Cimento 49A, 261 (1967); &. A. Nikitin, in Particles and 1clei, edited by N. N. Bog»yubov (Consultants Bureau, New pork, 1972), Vol. I, Pt. 1, p. 2. "D. W. Rule, thesis, University of Connecticut, 1975 (unpublished); D. W. Rule and Y. Hahn, to be published. O. Kofoed Hanson, Lectures given at the International School of Subnuclear Physics, Erice, Italy, 1974, CERN Report No. CERN-TH1860 (to be published). ' See the discussions in R. H. Bassel and M. Rosen, Phys. Rev. C 10, 928 (1974); see also A. M. Saperstein, Phys. Rev. Lett. 30, 1259 (1973).
Asymptotic Properties of Solutions to Second-Order Difference Equations of Volterra Type
<jats:p>We consider the discrete Volterra type equation of the form <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi mathvariant="normal">Δ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mi mathvariant="normal">Δ</mml:mi><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:msubsup><mml:mo stretchy="false">∑</mml:mo><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mn mathvariant="normal">1</mml:mn></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup><mml:mrow><mml:mi>K</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>n</mml:mi><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mrow><mml:mi>x</mml:mi></mml:mrow><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:math>. We present sufficient conditions for the existence of solutions with prescribed asymptotic behavior. Moreover, we study the asymptotic behavior of solutions. We use <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi mathvariant="normal">o</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mrow><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msup><mml:mo stretchy="false">)</mml:mo></mml:math>, for given nonpositive real <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:math>, as a measure of approximation.</jats:p>