(c) (Rl Grounded) (Rl Positive) Net e from break-up

200 400 600 800 1000

Channel Number

Figure 5.2 Typical time-of-flight spectra fo r (a) residual positron and Ps, (b) transmitted Ps and (c) net residual positrons.

Chapter 5 - Ps Break-Up in Collision with He Atoms 121

5.2.2 Magnetic Field Measurements

In order to ensure that all positrons from Ps break-up were extracted from the scattering cell, the magnitude of the magnetic field, B, in the scattering region was adjusted such that the Larmor radius of the residual positrons plus the radius of the Ps beam was smaller than the radius of the exit aperture of the scattering cell. This was checked by verifying signal saturation with increasing values of B Figure 5.3 shows results obtained for different B-field intensities around the scattering cell for the break-up positron yield. Ye \ defined as

T. = (5.4) & 2 B Field (m T ) b) 18eV a) 13eV .a i

I

I

1

Figure 5.3 Residual positron yields fo r differing B-field intensities fo r the four incident Ps energies a) ISeVy b) 18eV, c) 25eVand d) 33eV.

At the two higher incident energies, the relative break-up-cross-section appears to saturate within errors with increasing magnetic field, indicating insufficient confinement of the residual positrons at the lower magnetic fields. At 25eV and 33eV,

Chapter 5 - Ps Break-Up in Collision with He Atoms 122

the break-up-cross-section was obtained from the weighted mean of the values above 15mT. At 18eV, the residual positron yield does not display a significant B-field dependence, indicating that the lower B-field values are sufficient to confine the residual positrons. This would also appear to be the case at 13eV, although the experimental uncertainties are larger. For both lower energies, the relative break-up- cross-section was obtained from the weighted average of all the B-field measurements.

Measurements were also taken at various He gas pressures (shown in appendix C), to check the linearity of signal with pressure. Within the pressure range of this study, no attenuation of the break-up flux was found to be occurring in the target gas. Figure 5.4 shows the residual positron yield values obtained in this study.

•a .2 10 10 8 6 4 15 20 25 30 E n e r g y ( e V )

Figure 5.4 Residual positron yields versus incident Ps energy.

35

As can be seen from figure 5.4, the residual positron yield is approximately constant at the lower energies, but almost doubles at 33eV. In the next few sections the correction factors (given in Equation 5.1) are calculated and are used to determine the absolute break-up cross-section.

Chapter 5 - P s Break-Up in Collision with He Atoms__________________________123

5.2.3 Survival Probability of Ps Atoms

In order to determine the absolute values o f the break-up-cross-section, we need to know the number of Ps atoms traversing the scattering cell. More Ps atoms are available to break-up within the scattering cell than are detected at CEMA2, due to in- flight-decay. To correct for this effect, we have to scale the measured scattered Ps flux, {Np^scatt, by calculating the average fraction of the incident Ps beam passing through the scattering cell. The total number of Ps atoms, Nav, available to break-up in the scattering cell is given by

^ (5.5)

where S is the survival probability factor and is given by ^ ^ S(CEMA2)

{S(ScattCell)}

and S(CEMA2) corresponds to the fraction of Ps atoms that reach the detector - taken directly from the corresponding Ps decay curve (see section 4.5.3). <S(ScattCell)> is the average fraction of Ps atoms along the scattering cell, calculated using

1 /2 ±(

{s{ScattCelij) = ^ ^ Je " d x, (5.7)

where x corresponds to the Ps flight length, t is the o-Ps lifetime, E is the Ps kinetic energy and m is the mass of a positron. The limits for the Ps flight length, through the scattering cell, are //= 0.073m and h= 0.139m. These distances correspond to the flight-length from the middle of the production cell to the middle o f the scattering cell, plus or minus half of the scattering cell length (see section 3.3.3). Table 5.2 shows the survival probability factors determined for each Ps energy used in this study.

Chapter 5 - Ps Break-Up in Collision with He Atoms 124

Energy (eV) Flight Length (cm) S(CEMA2) <S(ScattCell)> S 33 0.393 0.314 0.690 0.455 27 0.393 0.267 0.661 0.404 18 0.293 0.314 0.620 0.506 13 0.293 0.249 0.571 0.436

Table 5.2 Ps survival probability correction factors.

5.2.4 Geometric Ps Faetor

The Ps break-up study was undertaken mostly using a scattering cell with cylindrical apertures of radius 4mm. The Ps detection pencil angle, 0pencii (light purple region of figure 5.6) is defined by the exit aperture of the scattering cell. Only Ps atoms within this pencil angle will be detected at CEMA2. Ps atoms can enter the scattering cell outside of the Ps detection pencil angle (cyan region inside the scattering cell). As the residual positrons are magnetically confined, any Ps atoms that break-up in the cyan region of figure 5.5 can lead to positrons that are confined to reach CEMA2, leading to a greater break-up signal than that from the possible break­ up of the detectable Ps.

Ps Beam

Scattering Cell