Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Three-body recombination for protons moving in a strong magnetic field

F. Robicheaux, James D. Hanson

Published Jan 27, 2004• 49 citations
Publisher

Abstract

Using a classical Monte Carlo method, we have computed the three-body recombination (two free electrons and a proton scattering into one free electron and a hydrogen atom: $e+e+\stackrel{\ensuremath{\rightarrow}}{p}\mathrm{H}+e)$ in strong magnetic fields. The proton is allowed its full motion whereas the motion of the electron is given by the guiding center approximation. We investigate recombination for temperatures and fields similar to those used in recent experiments that generated anti-hydrogen. When the proton has the same temperature as the electrons, the recombination rate for the more elaborate equations of motion is roughly 60% larger than for the $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\infty}$ approximation. The recombination rate decreases as the proton speed approaches the electron thermal speed; the variation of this rate has implications for the directionality of the anti-atoms formed in recent experiments. We report on several properties of the atoms formed by three-body recombination in strong magnetic fields.

DOI
10.1103/physreva.69.010701

Related papers

Three body recombination for electrons in a strong magnetic field: magnetic moment

F. Robicheaux

Using a classical Monte Carlo method, we have computed the three-body recombination (two free electrons and a proton scattering into one free electron and a hydrogen atom, $e+e+p\ensuremath{\rightarrow}\mathrm{H}+e$) in strong magnetic fields. The proton is fixed in space but the electrons are allowed their full, three-dimensional motion. We investigate recombination for temperatures and fields similar to those used in recent experiments that generated antihydrogen. The present rate is compared to that when the electrons' motion is given by the guiding center approximation, validating previous results at low temperature and demonstrating the breakdown of this approximation at higher temperature. Unlike the $B=0$ case, strong $B$ gives preferential recombination to atoms with positive magnetic moment. Also, the canonical angular momentum in the field direction is often negative even when the magnetic moment is negative. Both results affect the trapping of antihydrogen using spatially dependent magnetic fields.

Bulletin of the American Physical Society•May 19, 2006•0 citations

Three-body recombination for electrons in a strong magnetic field: Magnetic moment

F. Robicheaux

Using a classical Monte Carlo method, we have computed the three-body recombination (two free electrons and a proton scattering into one free electron and a hydrogen atom, $e+e+p\ensuremath{\rightarrow}\mathrm{H}+e$) in strong magnetic fields. The proton is fixed in space but the electrons are allowed their full, three-dimensional motion. We investigate recombination for temperatures and fields similar to those used in recent experiments that generated antihydrogen. The present rate is compared to that when the electrons' motion is given by the guiding center approximation, validating previous results at low temperature and demonstrating the breakdown of this approximation at higher temperature. Unlike the $B=0$ case, strong $B$ gives preferential recombination to atoms with positive magnetic moment. Also, the canonical angular momentum in the field direction is often negative even when the magnetic moment is negative. Both results affect the trapping of antihydrogen using spatially dependent magnetic fields.

Physical Review A•Mar 1, 2006•43 citations

Three-body recombination with mixed sign light particles

F. Robicheaux

Using a classical trajectory Monte Carlo method, we have computed the three-body recombination (two free positrons and an anti-proton scattering into one free positron and an anti-hydrogen atom: e+ + e+ + p ̄ → ¯H + e+) in the presence of electrons. By simply reversing the sign of all of the particles, these results can be applied to three-body recombination of matter in the presence of positrons. An important parameter is the fraction of light particles which are of the opposite sign; we performed calculations for several values of this parameter and find a substantial effect even for small fractions. We have also included a strong magnetic field in the calculation since this seems the most likely way to have mixed sign light particles in the same region of space. Our results will be useful for future anti-hydrogen experiments. We identify the main mechanisms controlling the recombination process. 1.

Journal of Physics B Atomic Molecular and Optical Physics•Jan 3, 2007•7 citations

Temperature and Magnetic Field Dependence of Three-Body Recombination in Spin-Polarized Hydrogen

Harald F. Hess, David A. Bell, Gregory P. Kochanski +2 more

The three-body recombination rate in spin-polarized hydrogen has been measured at temperatures from 0.25 to 0.60 K in magnetic fields from 5 to 9 T. In contrast to theoretical expectation, the three-body rate is a weakly decreasing function of field in this region. At 7.6 T the gas and surface three-body rate constants are ${L}_{g}=7.5(3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}39}$ ${\mathrm{cm}}^{6}$ ${\mathrm{s}}^{\ensuremath{-}1}$ and ${L}_{s}=2.0(6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}$ ${\mathrm{cm}}^{4}$ ${\mathrm{s}}^{\ensuremath{-}1}$. The large value of ${L}_{s}$ can account for effects previously attributed to an anomalously large surface two-body nuclear relaxation rate.

Physical Review Letters•Apr 23, 1984•59 citations

Relaxation and recombination in spin-polarized atomic hydrogen

D. A. Bell, Harald F. Hess, Greg Kochanski +5 more

We have studied relaxation and recombination processes in compressed, doubly polarized atomic hydrogen at temperatures from 0.13 to 0.60 K and magnetic fields from 3 to 9 T. The gas and surface dipole three-body recombination rate constants at a field of 7.6 T are measured to be, respectively, ${L}_{g}$=8.9(8)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}39}$ ${\mathrm{cm}}^{6}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ and ${L}_{s}$=1.2(4)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}24}$ ${\mathrm{cm}}^{4}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$. They decrease slowly with field and ${L}_{s}$ exhibits no significant angular dependence. The three-body recombination rate due to hyperfine mixing has also been measured. Electronic and nuclear relaxation rates have been measured; the b-c electronic relaxation rate constant in the gas is ${G}^{\mathrm{bc}}$=1.03(7)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$exp(-${E}_{\mathrm{bc}}$/${k}_{B}$T). The temperature and field dependence of the nuclear relaxation rate in the gas are observed to be in excellent agreement with recent theoretical calculations. Three-body surface recombination-rate measurements using $^{3}\mathrm{\ensuremath{-}}^{4}$He surfaces indicate that as little as one monolayer of $^{3}\mathrm{He}$ on the liquid $^{4}\mathrm{He}$ surface appreciably decreases the adsorption energy of atomic hydrogen. Densities achieved include 4.5\ifmmode\times\else\texttimes\fi{}${10}^{18}$ atoms${\mathrm{?}}^{\mathrm{\ensuremath{-}}3}$ at 0.55 K (pure $^{4}\mathrm{He}$ walls), and 1.4\ifmmode\times\else\texttimes\fi{}${10}^{18}$ atoms${\mathrm{?}}^{\mathrm{\ensuremath{-}}3}$ at 0.19 K (8 at. ? sup 3---He).

Physical review. B, Condensed matter•Dec 1, 1986•57 citations

Magnetic-field dependence of resonance recombination in spin-polarized atomic hydrogen

Isaac F. Silvera, Herman P. Godfried, E. R. Eliel +4 more

The two-body recombination rate of spin-polarized atomic hydrogen has been studied at fixed temperatures in low magnetic fields. Rates in excess of the surface rate are attributed to resonant recombination. The field dependence of the lifetime of the bound state has been approximated by the relation \ensuremath{\tau}=${\ensuremath{\tau}}_{0}$exp(-\ensuremath{\alpha}B), and values for ${\ensuremath{\tau}}_{0}$ and \ensuremath{\alpha} have been determined.

Physical review. B, Condensed matter•Feb 1, 1988•6 citations
Using a classical Monte Carlo method, we have computed the three-body recombination (two free electrons and a proton scattering into one free electron and a hydrogen atom: e+e+p\ensuremath→H+e)e+e+\stackrel{\ensuremath{\rightarrow}}{p}\mathrm{H}+e)e+e+p\ensuremath→​H+e) in strong magnetic fields. The proton is allowed its full motion whereas the motion of the electron is given by the guiding center approximation. We investigate recombination for temperatures and fields similar to those used in recent experiments that generated anti-hydrogen. When the proton has the same temperature as the electrons, the recombination rate for the more elaborate equations of motion is roughly 60% larger than for the B\ensuremath→\ensuremath∞\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\infty}B\ensuremath→​\ensuremath∞ approximation. The recombination rate decreases as the proton speed approaches the electron thermal speed; the variation of this rate has implications for the directionality of the anti-atoms formed in recent experiments. We report on several properties of the atoms formed by three-body recombination in strong magnetic fields.
Using a classical Monte Carlo method, we have computed the three-body recombination (two free electrons and a proton scattering into one free electron and a hydrogen atom, $e+e+p\ensuremath{\rightarrow}\mathrm{H}+e$) in strong magnetic fields. The proton is fixed in space but the electrons are allowed their full, three-dimensional motion. We investigate recombination for temperatures and fields similar to those used in recent experiments that generated antihydrogen. The present rate is compared to that when the electrons' motion is given by the guiding center approximation, validating previous results at low temperature and demonstrating the breakdown of this approximation at higher temperature. Unlike the B=0B=0B=0 case, strong BBB gives preferential recombination to atoms with positive magnetic moment. Also, the canonical angular momentum in the field direction is often negative even when the magnetic moment is negative. Both results affect the trapping of antihydrogen using spatially dependent magnetic fields.
Using a classical Monte Carlo method, we have computed the three-body recombination (two free electrons and a proton scattering into one free electron and a hydrogen atom, $e+e+p\ensuremath{\rightarrow}\mathrm{H}+e$) in strong magnetic fields. The proton is fixed in space but the electrons are allowed their full, three-dimensional motion. We investigate recombination for temperatures and fields similar to those used in recent experiments that generated antihydrogen. The present rate is compared to that when the electrons' motion is given by the guiding center approximation, validating previous results at low temperature and demonstrating the breakdown of this approximation at higher temperature. Unlike the B=0B=0B=0 case, strong BBB gives preferential recombination to atoms with positive magnetic moment. Also, the canonical angular momentum in the field direction is often negative even when the magnetic moment is negative. Both results affect the trapping of antihydrogen using spatially dependent magnetic fields.
Using a classical trajectory Monte Carlo method, we have computed the three-body recombination (two free positrons and an anti-proton scattering into one free positron and an anti-hydrogen atom: e+ + e+ + p ̄ → ¯H + e+) in the presence of electrons. By simply reversing the sign of all of the particles, these results can be applied to three-body recombination of matter in the presence of positrons. An important parameter is the fraction of light particles which are of the opposite sign; we performed calculations for several values of this parameter and find a substantial effect even for small fractions. We have also included a strong magnetic field in the calculation since this seems the most likely way to have mixed sign light particles in the same region of space. Our results will be useful for future anti-hydrogen experiments. We identify the main mechanisms controlling the recombination process. 1.
The three-body recombination rate in spin-polarized hydrogen has been measured at temperatures from 0.25 to 0.60 K in magnetic fields from 5 to 9 T. In contrast to theoretical expectation, the three-body rate is a weakly decreasing function of field in this region. At 7.6 T the gas and surface three-body rate constants are ${L}_{g}=7.5(3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}39}$ cm6{\mathrm{cm}}^{6}cm6 ${\mathrm{s}}^{\ensuremath{-}1}$ and ${L}_{s}=2.0(6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}24}$ cm4{\mathrm{cm}}^{4}cm4 ${\mathrm{s}}^{\ensuremath{-}1}$. The large value of Ls{L}_{s}Ls​ can account for effects previously attributed to an anomalously large surface two-body nuclear relaxation rate.
We have studied relaxation and recombination processes in compressed, doubly polarized atomic hydrogen at temperatures from 0.13 to 0.60 K and magnetic fields from 3 to 9 T. The gas and surface dipole three-body recombination rate constants at a field of 7.6 T are measured to be, respectively, Lg{L}_{g}Lg​=8.9(8)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}39}$ cm6{\mathrm{cm}}^{6}cm6 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$ and Ls{L}_{s}Ls​=1.2(4)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}24}$ cm4{\mathrm{cm}}^{4}cm4 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$. They decrease slowly with field and Ls{L}_{s}Ls​ exhibits no significant angular dependence. The three-body recombination rate due to hyperfine mixing has also been measured. Electronic and nuclear relaxation rates have been measured; the b-c electronic relaxation rate constant in the gas is Gbc{G}^{\mathrm{bc}}Gbc=1.03(7)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}15}$ cm3{\mathrm{cm}}^{3}cm3 ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$exp(-Ebc{E}_{\mathrm{bc}}Ebc​/kB{k}_{B}kB​T). The temperature and field dependence of the nuclear relaxation rate in the gas are observed to be in excellent agreement with recent theoretical calculations. Three-body surface recombination-rate measurements using $^{3}\mathrm{\ensuremath{-}}^{4}$He surfaces indicate that as little as one monolayer of 3He^{3}\mathrm{He}3He on the liquid 4He^{4}\mathrm{He}4He surface appreciably decreases the adsorption energy of atomic hydrogen. Densities achieved include 4.5\ifmmode\times\else\texttimes\fi{}1018{10}^{18}1018 atoms${\mathrm{?}}^{\mathrm{\ensuremath{-}}3}$ at 0.55 K (pure 4He^{4}\mathrm{He}4He walls), and 1.4\ifmmode\times\else\texttimes\fi{}1018{10}^{18}1018 atoms${\mathrm{?}}^{\mathrm{\ensuremath{-}}3}$ at 0.19 K (8 at. ? sup 3---He).