Measurement of the orthopositronium confinement energy in mesoporous thin films

In this paper, we present measurements of the ortho-positronium (ortho-Ps) emission energy in vacuum from mesoporous films using the time-of-flight technique. We show evidence of quantum mechanical confinement in the mesopores that defines the minimal energy of the emitted Ps. Two samples with different effective pore sizes, measured with positron annihilation lifetime spectroscopy, are compared for the data collected in the temperature range $50–400$ K. The sample with smaller pore size exhibits a higher minimal energy ($73\pm 5$ meV), compared to the sample with bigger pores ($48\pm 5$ meV), due to the stronger confinement. The dependence of the emission energy with the temperature of the target is modeled as ortho-Ps being confined in rectangular boxes in thermodynamic equilibrium with the sample. We also measured that the yield of positronium emitted in vacuum is not affected by the temperature of the target.

Figure 1

Experimental setup for the TOF measurements (the scale is in mm). The dashed line is the trajectory of the incoming positrons (blue) and the dotted line is the one of the secondary electrons (red).

Figure 2

Yield of Ps emitted in vacuum ($Y_v$) and total yield of Ps ($I_{\mathrm{tot}}=I_2+I_3$) for F (top plot) and C samples (bottom plot) at room temperature and 50 K.

Figure 3

TOF spectra of the F sample for positron implantation energies of 0.7, 1, 4, and 10 keV.

Figure 4

Positronium mean emission energy $\langle E_z\rangle$ as a function of the implantation voltage at a target temperature of 300 K. The triangles represents the energy extracted with the maximum analysis method (MA); the squares are after the subtraction of the nonthermalized part [maximum analysis method after correction of the spectra (MA-CS)].

Figure 5

(Top plot) The solid line is the TOF spectra without correction, the diamonds show the contribution from the target, and the crosses the sum of the contribution from the target and the nonthermalized part. (Bottom plot) The TOF spectra after the correction of the target and the nonthermalized components.

Figure 6

Ps mean emission energy $\langle E_z\rangle$ as a function of the positron implantation energy for C and F samples at 300 K.

Figure 7

(Top plot) Ps mean energy $\langle E_z\rangle$ for implantation energies higher than 2 keV at 50 and 300 K for the C sample. (Bottom plot) Ps mean energy as a function of the implantation energies higher than 4 keV at 50 and 300 K for the F sample.

Figure 8

(Top plot) Comparison between the data of the C sample at 6 keV and the MC simulating mono-energetic Ps emitted isotropically from the film surface. (Bottom plot) Comparison between the data of the C sample at 6 keV and the MC simulating mono-energetic Ps emitted perpendicular from the film surface. In both cases, the measured nonthermalized part (called 2-keV correction in the legend) was added to the MC.

Figure 9

Positronium mean energy as a function of the mesoporous film temperature. Those results are obtained at 6 keV for the C and 10 keV for the F sample. The solid lines are the results of using Eq. (7) with the pore side lengths $a$,$b$,$c$ left as free parameters. The dashed lines were obtained fitting with Eq. (7) with a single side length free $a=b=c$ (cubic box pores).