Scaling behavior of the ground-state antihydrogen yield as a function of positron density and temperature from classical-trajectory Monte Carlo simulations

Antihydrogen production has reached such a level that precision spectroscopic measurements of its properties are within reach. In particular, the ground-state level population is of central interest for experiments aiming at antihydrogen spectroscopy. The positron density and temperature dependence of the ground-state yield is a result of the interplay between recombination, collisional, and radiative processes. Considering the fact that antihydrogen atoms with the principal quantum number $n=15$ or lower quickly cascade down to the ground state within 1 ms, the number of such states is adopted as a measure of useful antihydrogen atoms. It has been found that the scaling behavior of the useful antihydrogen yield is different depending on the positron density and positron temperature.

Figure 1

Antihydrogen bound-state level population distribution after evolution of $10 \mu \mathrm{s}$ (circle), $20 \mu \mathrm{s}$ (square), and $50 \mu \mathrm{s}$ (triangle) and the thermal equilibrium level population distribution (solid line) for positron temperature of $T_e=50\text{K}$ and positron density $n_e={10}^{14}{\mathrm{m}}^{-3}$.

Figure 2

Antihydrogen bound-state level population distribution after evolution of $10 \mu \text{s}$ for various magnetic field strengths $0\le B\le 3$ T, and the thermal equilibrium level population distribution (solid line) for positron temperatures $T_e=50$ K (a) and $T_e=100$ K (b) and positron density $n_e={10}^{14}{\mathrm{m}}^{-3}$.

Figure 3

Contour plot of the number of ground-state antihydrogen atoms for various positron temperatures (vertical axis) and density values (horizontal axis).

Figure 4

Contour plot of the number of ground-state antihydrogen atoms for various positron temperatures (vertical axis) and density values (horizontal axis) after $10 \mu \mathrm{s}$ interaction and 1 ms of flight.

Figure 5

Dependence of ground-state antihydrogen atoms on positron temperature (a) and density (b) for various positron density and temperature values (respectively) after $10 \mu \mathrm{s}$ of mixing. The $\propto n_e^2{T}_e^{-4.5}$ (solid line) and $\propto n_e^{1.6}{T}^{-2.0}$ (dashed line) scaling behaviors are indicated for reference.

Figure 6

Dependence of ground-state antihydrogen atoms on positron temperature (a) and density (b) for various positron density and temperature values (respectively) after 1 ms of flight. The $\propto n_e^2{T}_e^{-4.5}$ (solid line) and $\propto n_e^{1.3}{T}^{-2.0}$ (dashed line) scaling behaviors are indicated for reference.