Analysis

Abstract

In this chapter, the analysis of the data is described in detail. First, a summary of the acquired data is described in Sect. 3.1. The data calibration and offline trigger selections are described in Sect. 3.2. The time-walks of the LaBr$_3$ crystal scintillator and plastic scintillator are also corrected. The transition signals are obtained after some event selections and are described in Sect. 3.3. In Sect. 3.4, the reaction cross-section ($\sigma (\omega )$) at one frequency point is obtained by comparing the signal rate with a Monte Carlo simulation. Then, $\sigma (\omega )$ is fitted with a Breit-Wigner function to obtain the Ps-HFS, the lifetime of p-Ps and Einstein’s A coefficient. Systematic errors are estimated in Sect. 3.5. The uncertainty associated with the power estimation of millimeter waves limits the precision of the measurement. Another dominant systematic uncertainty is from the Stark effect caused by the local electric fields of gas molecules used as electron donors in forming positronium. Finally, the results are presented in Sect. 3.6. This is the first direct determination of the Ps-HFS and the lifetime of p-Ps as well.