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.

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.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 AMar 1, 200643 citations

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

F. Robicheaux, James D. Hanson

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.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.

Physical Review AJan 27, 200449 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.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 PhysicsJan 3, 20077 citations

Radiative cascade of highly excited hydrogen atoms in strong magnetic fields

Türker Topçu, F. Robicheaux

We have studied the radiative decay of atomic hydrogen in strong magnetic fields of up to $4\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ . We have followed the radiative cascade from completely $l,m$ mixed distributions of highly excited states as well as from distributions that involve highly excited states with $\ensuremath{\mid}m\ensuremath{\mid}\ensuremath{\sim}n$. We have found that the time it takes to populate the ground state is not affected by the magnetic field for the initial states with $n\ensuremath{\lesssim}20$. For higher $n$ manifolds, the electrons in the most negative $m$ states are substantially slowed down by the magnetic field resulting in a much longer lifetime. We show that less than 10% of the antihydrogen atoms with $n\ensuremath{\sim}35$ generated in antihydrogen experiments at $4\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ will decay to their ground states before they hit the wall of the vacuum container unless they are trapped. We have also found that the decay time is mainly determined by the fraction of atoms that were initially in highest negative $m$ states due to the fact that only $\ensuremath{\mid}\ensuremath{\Delta}m\ensuremath{\mid}+\ensuremath{\mid}\ensuremath{\Delta}\ensuremath{\pi}\ensuremath{\mid}=1$ transitions are allowed in the magnetic field. We give a semiclassical method for calculating the decay rates for circular states and show that when the initial states have high-$\ensuremath{\mid}m\ensuremath{\mid}$, semiclassical rates agree with the full quantum mechanical rates within a couple of percent for states with effective $n\ensuremath{\gtrsim}20$.We have studied the radiative decay of atomic hydrogen in strong magnetic fields of up to $4\phantom{\rule{0.3em}{0ex}}\mathrm{T}$. We have followed the radiative cascade from completely $l,m$ mixed distributions of highly excited states as well as from distributions that involve highly excited states with $\ensuremath{\mid}m\ensuremath{\mid}\ensuremath{\sim}n$. We have found that the time it takes to populate the ground state is not affected by the magnetic field for the initial states with $n\ensuremath{\lesssim}20$. For higher $n$ manifolds, the electrons in the most negative $m$ states are substantially slowed down by the magnetic field resulting in a much longer lifetime. We show that less than 10% of the antihydrogen atoms with $n\ensuremath{\sim}35$ generated in antihydrogen experiments at $4\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ will decay to their ground states before they hit the wall of the vacuum container unless they are trapped. We have also found that the decay time is mainly determined by the fraction of atoms that were initially in highest negative $m$ states due to the fact that only $\ensuremath{\mid}\ensuremath{\Delta}m\ensuremath{\mid}+\ensuremath{\mid}\ensuremath{\Delta}\ensuremath{\pi}\ensuremath{\mid}=1$ transitions are allowed in the magnetic field. We give a semiclassical method for calculating the decay rates for circular states and show that when the initial states have high-$\ensuremath{\mid}m\ensuremath{\mid}$, semiclassical rates agree with the full quantum mechanical rates within a couple of percent for states with effective $n\ensuremath{\gtrsim}20$.

Physical Review AApr 10, 200631 citations

Strongly Magnetized Antihydrogen and Its Field Ionization

D. Vrinceanu, Brian Granger, Robert E. Parrott +5 more

Internal orbits of experimentally analyzed antihydrogen (H) atoms depend as much on an external magnetic field as on the Coulomb force. A circular "guiding center atom" model is used to understand their field ionization. This useful model, assumed in the theory of three-body H recombination so far, ignores the important coupling between internal and center-of-mass motion. A conserved pseudomomentum, effective potential, saddle point analysis, and numerical simulation show where the simple model is valid and classify the features of the general case, including "giant dipole states."Internal orbits of experimentally analyzed antihydrogen (H) atoms depend as much on an external magnetic field as on the Coulomb force. A circular "guiding center atom" model is used to understand their field ionization. This useful model, assumed in the theory of three-body H recombination so far, ignores the important coupling between internal and center-of-mass motion. A conserved pseudomomentum, effective potential, saddle point analysis, and numerical simulation show where the simple model is valid and classify the features of the general case, including "giant dipole states."

Physical Review LettersMar 31, 200437 citations

Motion of Guiding Center Drift Atoms in the Electric and Magnetic Field of a Penning Trap.

S. G. Kuzmin, Thomas M. O’Neil

The ApparaTus for High precision Experiment on Neutral Antimatter and antihydrogen TRAP collaborations have produced antihydrogen atoms by recombination in a cryogenic antiproton-positron plasma. This paper discusses the motion of the weakly bound atoms in the electric and magnetic field of the plasma and trap. The effective electric field in the moving frame of the atom polarizes the atom, and then gradients in the field exert a force on the atom. An approximate equation of motion for the atom center of mass is obtained by averaging over the rapid internal dynamics of the atom. The only remnant of the atom internal dynamics that enters this equation is the polarizability for the atom. This coefficient is evaluated for the weakly bound and strongly magnetized (guiding center drift) atoms understood to be produced in the antihydrogen experiments. Application of the approximate equation of motion shows that the atoms can be trapped radially in the large space charge field near the edge of the positron column. Also, an example is presented for which there is full three-dimensional trapping, not just radial trapping. Even untrapped atoms follow curved trajectories, and such trajectories are discussed for the important class of atoms that reach a field ionization diagnostic. Finally, the critical field for ionization is determined as an upper bound on the range of applicability of the theory.The ApparaTus for High precision Experiment on Neutral Antimatter and antihydrogen TRAP collaborations have produced antihydrogen atoms by recombination in a cryogenic antiproton-positron plasma. This paper discusses the motion of the weakly bound atoms in the electric and magnetic field of the plasma and trap. The effective electric field in the moving frame of the atom polarizes the atom, and then gradients in the field exert a force on the atom. An approximate equation of motion for the atom center of mass is obtained by averaging over the rapid internal dynamics of the atom. The only remnant of the atom internal dynamics that enters this equation is the polarizability for the atom. This coefficient is evaluated for the weakly bound and strongly magnetized (guiding center drift) atoms understood to be produced in the antihydrogen experiments. Application of the approximate equation of motion shows that the atoms can be trapped radially in the large space charge field near the edge of the positron column. Also, an example is presented for which there is full three-dimensional trapping, not just radial trapping. Even untrapped atoms follow curved trajectories, and such trajectories are discussed for the important class of atoms that reach a field ionization diagnostic. Finally, the critical field for ionization is determined as an upper bound on the range of applicability of the theory.

APSNov 1, 20040 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{\rightarrow}\mathrm{H}+e

B=0

case, strong

B

B=0

case, strong

B

We have studied the radiative decay of atomic hydrogen in strong magnetic fields of up to

4\phantom{\rule{0.3em}{0ex}}\mathrm{T}

. We have followed the radiative cascade from completely

l,m

mixed distributions of highly excited states as well as from distributions that involve highly excited states with $\ensuremath{\mid}m\ensuremath{\mid}\ensuremath{\sim}n$. We have found that the time it takes to populate the ground state is not affected by the magnetic field for the initial states with $n\ensuremath{\lesssim}20$. For higher

n

manifolds, the electrons in the most negative

m

states are substantially slowed down by the magnetic field resulting in a much longer lifetime. We show that less than 10% of the antihydrogen atoms with $n\ensuremath{\sim}35$ generated in antihydrogen experiments at

4\phantom{\rule{0.3em}{0ex}}\mathrm{K}

will decay to their ground states before they hit the wall of the vacuum container unless they are trapped. We have also found that the decay time is mainly determined by the fraction of atoms that were initially in highest negative

m

states due to the fact that only $\ensuremath{\mid}\ensuremath{\Delta}m\ensuremath{\mid}+\ensuremath{\mid}\ensuremath{\Delta}\ensuremath{\pi}\ensuremath{\mid}=1$ transitions are allowed in the magnetic field. We give a semiclassical method for calculating the decay rates for circular states and show that when the initial states have high-$\ensuremath{\mid}m\ensuremath{\mid}$, semiclassical rates agree with the full quantum mechanical rates within a couple of percent for states with effective $n\ensuremath{\gtrsim}20$.