In agreement with Titchmarsh’s theorem, we prove that dispersion relations are just the Fourier-transform of the identity, g(x′)=±Sgn(x′)g(x′), which defines the property of being a truncated functions at the...In agreement with Titchmarsh’s theorem, we prove that dispersion relations are just the Fourier-transform of the identity, g(x′)=±Sgn(x′)g(x′), which defines the property of being a truncated functions at the origin. On the other hand, we prove that the wave-function of a generalized diffraction in time problem is just the Fourier-transform of a truncated function. Consequently, the existence of dispersion relations for the diffraction in time wave-function follows. We derive these explicit dispersion relations.展开更多
A production representation of partial-wave S matrix is utilized to construct low-energy elastic pion-nucleon scattering amplitudes from cuts and poles on complex Riemann sheets. Among them, the contribution of left-h...A production representation of partial-wave S matrix is utilized to construct low-energy elastic pion-nucleon scattering amplitudes from cuts and poles on complex Riemann sheets. Among them, the contribution of left-hand cuts is estimated using the ■(p^3) results obtained in covariant baryon chiral perturbation theory within the extendedon-nass-shell scheme. By fitting to data on partial-wave phase shifts, it is indicated that the existences of hidden poles in S11 and P11 channels, as conjectured in our previous paper [Eur. Phys. J. C, 78(7): 543(2018)], are firmly established. Specifically, the pole mass of the S11 hidden resonance is determined to be(895±81)-(164±23)i MeV,whereas,the virtual pole in the P11 channel locates at(966±18) MeV. It is found that analyses at the■(p^3) level improves significantly the fit quality, comparing with the previous■(p^2) one. Quantitative studies with cautious physical discussions are also conducted for the other S-and P-wave channels.展开更多
This paper addresses the formulae and numerical issues related to the possibility that fast wave may be grown when a relativistic electron beam through an ion channel in a cylindrical metal waveguide. To derive the di...This paper addresses the formulae and numerical issues related to the possibility that fast wave may be grown when a relativistic electron beam through an ion channel in a cylindrical metal waveguide. To derive the dispersion equations of the beam-wave interaction, it solves relativistic Lorentz equation and Maxwell＇s equations for appropriate boundary conditions. It has been found in this waveguide structure that the TM0m modes are the rational operating modes of coupling between the electromagnetic modes and the betatron modes. The interaction of the dispersion curves of the electromagnetic TM0m modes and the upper betatron modes is studied. The growth rates of the wave are obtained, and the effects of the beam radius, the beam energy, the plasma frequency, and the beam plasma frequency on the wave growth rate are numerically calculated and discussed.展开更多
文摘In agreement with Titchmarsh’s theorem, we prove that dispersion relations are just the Fourier-transform of the identity, g(x′)=±Sgn(x′)g(x′), which defines the property of being a truncated functions at the origin. On the other hand, we prove that the wave-function of a generalized diffraction in time problem is just the Fourier-transform of a truncated function. Consequently, the existence of dispersion relations for the diffraction in time wave-function follows. We derive these explicit dispersion relations.
基金Supported in part by National Nature Science Foundations of China(NSFC)(10925522,11021092)the Spanish Ministerio de Economía y Competitividad(MINECO)the European Regional Development Fund(ERDF)(FIS2017-84038-C2-1-P,FIS2017-84038-C2-2-P,SEV-2014-0398)
文摘A production representation of partial-wave S matrix is utilized to construct low-energy elastic pion-nucleon scattering amplitudes from cuts and poles on complex Riemann sheets. Among them, the contribution of left-hand cuts is estimated using the ■(p^3) results obtained in covariant baryon chiral perturbation theory within the extendedon-nass-shell scheme. By fitting to data on partial-wave phase shifts, it is indicated that the existences of hidden poles in S11 and P11 channels, as conjectured in our previous paper [Eur. Phys. J. C, 78(7): 543(2018)], are firmly established. Specifically, the pole mass of the S11 hidden resonance is determined to be(895±81)-(164±23)i MeV,whereas,the virtual pole in the P11 channel locates at(966±18) MeV. It is found that analyses at the■(p^3) level improves significantly the fit quality, comparing with the previous■(p^2) one. Quantitative studies with cautious physical discussions are also conducted for the other S-and P-wave channels.
基金Project supported in part by the National Natural Science Foundation of China (Grant Nos. 10775100 and 90503008)the Science Foundation of China Academy of Engineering Physics (Grant No. 10576019)the Fund of Theoretical Nuclear Physics Center,National Laboratory of Heavy Ion Accelerator Facility of Lanzhou
文摘This paper addresses the formulae and numerical issues related to the possibility that fast wave may be grown when a relativistic electron beam through an ion channel in a cylindrical metal waveguide. To derive the dispersion equations of the beam-wave interaction, it solves relativistic Lorentz equation and Maxwell＇s equations for appropriate boundary conditions. It has been found in this waveguide structure that the TM0m modes are the rational operating modes of coupling between the electromagnetic modes and the betatron modes. The interaction of the dispersion curves of the electromagnetic TM0m modes and the upper betatron modes is studied. The growth rates of the wave are obtained, and the effects of the beam radius, the beam energy, the plasma frequency, and the beam plasma frequency on the wave growth rate are numerically calculated and discussed.
