arXiv:1206.5171

Internal and external dynamics of antihydrogen in electric and magnetic fields of arbitrary orientation

Michal Špaček, V. Petráček

Published Jun 22, 2012• 1 citation

Abstract

We have studied the motion of antihydrogen atoms in electric and magnetic fields of arbitrary orientation. Our aim was to find an exact model of external (centre-of-charge) and internal dynamics which would allow us to describe antihydrogen motion in a realistic way. After analysing the kinematics of the charge exchange reaction producing antihydrogen and of antihydrogen deexcitation, we discuss the dynamics in cases of special fields configurations. Finally, we propose an expression for the force acting on an antihydrogen atom when the field configuration is arbitrary. The general formula -- when reduced in the special field configurations -- matches the results which we obtained independently before. The focus is both on the centre of charge dynamics and on the accurate internal quantum characteristics.

DOI: 10.48550/arxiv.1206.5171

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arXiv:1206.5171

Internal and external dynamics of antihydrogen in electric and magnetic fields of arbitrary orientation

Michal Špaček, V. Petráček

Published Jun 22, 2012• 1 citation

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.1206.5171

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arXiv:1608.02785Physical Review AAug 30, 201643 citations

A theoretical comparison of the behavior of the antihydrogen

(\overline{\mathrm{H}})

and hydrogen

(\mathrm{H})

atoms in external electric and magnetic fields is made. It is shown that observable differences arise in the spectroscopic properties of

\mathrm{H}

and

\overline{\mathrm{H}}

atoms in parallel electric and magnetic fields of the order of 475 V∕cm and 0.12 T, respectively.

The antihydrogen formation by charge exchange between cold antiprotons and Rydberg positronium

{\text{P}}_{s}^{*}

is studied by using the classical trajectory Monte Carlo method. In the absence of external magnetic field the cross section scaled by the fourth power of the

{\text{P}}_{s}^{*}

principal quantum number

{n}_{{\text{P}}_{s}}

shows a universal behavior as a function of the ratio

{k}_{v}

between the velocity of the

{\text{P}}_{s}

center of mass and that of the positron in the classical circular orbit. At low velocity, below about ${k}_{v}\ensuremath{\simeq}0.2--0.3$, we show for Rydberg positronium that the cross section increases as

1/{k}_{v}^{2}

or, in an equivalent way, as

1/{E}_{{\text{P}}_{s}}^{\text{cm}}

with

{E}_{{\text{P}}_{s}}^{\text{cm}}

being the

{\text{P}}_{s}^{*}

center-of-mass energy. In this regime the distribution of the principal quantum number of the antihydrogen state is narrow and it shows a peak at about

\sqrt{2}{n}_{{\text{P}}_{s}}

while at higher

{k}_{v}

values a broad distribution of antihydrogen states is produced. The study of the collision process in the presence of moderate magnetic field (0.5--2 T) shows that there is an experimentally interesting region of

{k}_{v}

with the cross section slightly higher than that in the absence of field. However the presence of a magnetic field changes significantly the cross section behavior as a function of

{k}_{v}

, especially at low velocities, where reductions of the cross sections and deviations from the

1/{k}_{v}^{2}

(

1/{E}_{{\text{P}}_{s}}^{\text{cm}}

) are observed. Our calculations show a dependance of the cross section upon the angle between the magnetic field and the flight direction of the incoming

{\text{P}}_{s}^{*}