The transmission of a Dirac particle through a high (V0>E+m) square electrostatic potential barrier is investigated further. As is well known, the transmission coefficient is nonzero even as V0 goes to infinity. As well as reproducing the usual wave mechanics approach, a detailed fermion–antifermion multiple scattering calculation and an S-matrix calculation are examined to provide additional insight into the problem. The origin of the curious behavior is found to be the result of pair creation and annihilation events.The transmission of a Dirac particle through a high (V0>E+m) square electrostatic potential barrier is investigated further. As is well known, the transmission coefficient is nonzero even as V0 goes to infinity. As well as reproducing the usual wave mechanics approach, a detailed fermion–antifermion multiple scattering calculation and an S-matrix calculation are examined to provide additional insight into the problem. The origin of the curious behavior is found to be the result of pair creation and annihilation events.

American Journal of PhysicsApr 1, 199113 citations

Passage of fermions through a potential barrier

I. K. Karpenko

Jan 1, 19750 citations

Role of the slope of realistic potential barriers in preventing relativistic tunneling in the Klein zone

P. Christillin, Emilio d’Emilio

The transmission of fermions of mass $m$ and energy $E$ through an electrostatic potential barrier of rectangular shape (i.e., supporting an infinite electric field), of height $U>E+m{c}^{2}$ ---due to the many-body nature of the Dirac equation evidentiated by the Klein paradox---has been widely studied. Here we exploit the analytical solution, given by Sauter for the linearly rising potential step, to show that the tunneling rate through a more realistic trapezoidal barrier is exponentially depressed, as soon as the length of the regions supporting a finite electric field exceeds the Compton wavelength of the particle---the latter circumstance being hardly escapable in most realistic cases.The transmission of fermions of mass $m$ and energy $E$ through an electrostatic potential barrier of rectangular shape (i.e., supporting an infinite electric field), of height $U>E+m{c}^{2}$---due to the many-body nature of the Dirac equation evidentiated by the Klein paradox---has been widely studied. Here we exploit the analytical solution, given by Sauter for the linearly rising potential step, to show that the tunneling rate through a more realistic trapezoidal barrier is exponentially depressed, as soon as the length of the regions supporting a finite electric field exceeds the Compton wavelength of the particle---the latter circumstance being hardly escapable in most realistic cases.

arXiv:0706.2266Physical Review AOct 4, 200710 citations

Fermion transfer by vortex tunneling

Johan Nilsson

Bulletin of the American Physical SocietyMar 17, 20100 citations

Making Contact with Strongly Interacting Fermions

Anonymous

PhysicsMay 23, 20190 citations

Tunnel Effect of the Micro Particle

Cui-Lan Zhao

In this paper,transmission coefficient that the micro particle penetrate two potential barriers successively is calculated by solving the stationary schrodinger equation.Our numerical results show that the micro particle could penetrate potential barriers no matter energy of particle is taller or smaller than the height of potential barriers.But the transmission coefficient varies in several different circumstances.Particularly,it may arise resonance transmission in conditions.In a word,the transmission coefficient could changes with the height and width of two potential barriers,and have nothing to do with the distance between two potential barriers.In this paper,transmission coefficient that the micro particle penetrate two potential barriers successively is calculated by solving the stationary schrodinger equation.Our numerical results show that the micro particle could penetrate potential barriers no matter energy of particle is taller or smaller than the height of potential barriers.But the transmission coefficient varies in several different circumstances.Particularly,it may arise resonance transmission in conditions.In a word,the transmission coefficient could changes with the height and width of two potential barriers,and have nothing to do with the distance between two potential barriers.

Journal of Inner Mongolia University for the NationalitiesJan 1, 20070 citations

The transmission of fermions of mass

m

and energy

E

through an electrostatic potential barrier of rectangular shape (i.e., supporting an infinite electric field), of height

U>E+m{c}^{2}

---due to the many-body nature of the Dirac equation evidentiated by the Klein paradox---has been widely studied. Here we exploit the analytical solution, given by Sauter for the linearly rising potential step, to show that the tunneling rate through a more realistic trapezoidal barrier is exponentially depressed, as soon as the length of the regions supporting a finite electric field exceeds the Compton wavelength of the particle---the latter circumstance being hardly escapable in most realistic cases.