Adiabatic formation of quasibound states of antihydrogen

Abstract

The classical trajectory of an initially unbound positron within the electric field of an antiproton and a uniform magnetic field is simulated in three dimensions. Several simulations are run incorporating experimental parameters used for antihydrogen production, which has been achieved by two different groups [M. Amoretti, Nature (London) 419, 456 (2002); G. Gabrielse, Phys. Rev. Lett. 89, 213401 (2002)]. The simulations indicate that temporary bound states of antihydrogen can form at positive energies, where the energy of the system is defined to be zero when the positron and antiproton are at rest with infinite separation. Such quasibound states, which form only when the magnetic field is present, are typically smaller than in a dimension perpendicular to the magnetic field. An analytical model is developed for a formation cross section, and it is found that quasibound states may form more frequently than stable Rydberg states.

Completely bound motion of a positive-energy electron in the coulomb field of a motionless nucleus and a uniform magnetic field

“…and coincides with the cyclotron-rotation velocity since the electric-drift velocity 2 |p ϕ |/(2 |p ϕ | +z 2 t max ) 3/2 is much smaller than velocity (33) under conditions (10) and (16) of applicability of Eq. (24).…”

“…The best agreement between the analytical estimate and numerical calculations is reached in the region given in formulas (10) and (16), where Eq. (24) can be used:…”

“…The bound states of an electron in a hydrogen atom [1][2][3] and the Coulomb collisions of free particles [4][5][6][7][8][9][10][11][12] significantly vary under conditions of the photospheres of the white dwarfs with the temperature T ≈ 10 4 K and a strong magnetic field B ≥ 10 7 G. For example, the electron motion during collisions with the positively charged nuclei becomes irregular (stochastic) in both classical [7][8][9][10] and quantum limits [11,12]. Stochastic motion of a free particle emerges under the conditions where the Larmor radius r B = v T /ω B of the electron becomes smaller than the characteristic impact parameter r s = Ze 2 /(mv 2 T ) of the close collisions in the absence of a magnetic field: …”

“…Analytical approximation (36) of the boundary of the considered region is shown by the corresponding thick lines 1 -4 . The solid parts of the thick lines are in the region where |z t max | >ρ = 2 |p ϕ | > min[1, 2Ẽ], which corresponds to conditions(10) and(16)of the applicability of Eqs. (24) and (36).…”

The Role of Antihydrogen Formation in the Radial Transport of Antiprotons in Positron Plasmas

“…A number of authors have performed simulations and theoretical analyses of various aspects of antihydrogen formation, as applied to the experimental situations [19][20][21][22][23][24][25][26][27][28][29][30], and as summarised by Robicheaux [17]. The methodology used here has previously been described in [18,30], so we give only a very brief outline.…”