Positron stopping times

The actual eigenstates are equal admixtures of the two unperturbed pure spin states when the field is exactly at the value at which the crossing would have occurred (v,m = 0). Since initially (when the muon stops) the system is in a well defined muon spin state, i.e., one of the two unperturbed pure spin states, the system oscillates at the frequency vT between the muon spin being along and opposite to the field, as implied by Eqs. 10 and 11. Thus, upon time averaging the positron counts the forward-backward asymmetry is reduced. 

The penetrating abilities of the particles and rays are proportional to their energies. Beta particles and positrons are about 100 times more penetrating than the heavier and slower-moving alpha particles. They can be stopped by a g-inch-thick (0.3 cm) aluminum... 

The Na source is placed between two identical samples. Two XP 2020 photomultipliers equipped with scintillators are attached directly to the two samples. The pulses from the photomultipliers are used as start and stop pulses for the TCSPC module. The pulses from PMT 2 are delayed by a few nanoseconds so that a stop pulse arrives after the corresponding start pulse. Eaeh y quantum generates a large number of photons in the scintillator. Therefore, the PMT pulses are multiphoton signals, and the time resolution can be better than the transit time spread of the PMTs. Moreover, the amplitudes of the photomultiplier pulses are proportional to the energy of the particle that caused the scintillation. Therefore the amplitudes can be used to distinguish between the 511 keV events of the positron decay and the 1.27 MeV events from the Na. The discriminator thresholds for start and stop are adjusted in a way that the stop channel sees all, the start channel only the larger Na events. The rate of the Na events is of the order of a few kHz or below. 

Therefore it is unlikely that a time measurement is started and stopped by two successive 1.27 MeV quanta of the Na decay. The by far most likely start-stop event is the detection of a 1.27 MeV quantum in the start PMT followed by the detection of a positron in the stop PMT. The histogram of these events gives the desired positron lifetime distribution. A typical result is shown in Fig. 5.140. 

P (beta) radiation, positively or negatively charged particles (electrons and positrons) of around 0 to 4 MeV. Generally, they require about 1000 times more mass than alpha particles to stop them. A 1 MeV beta particle will travel about 4m in air, but only 5cm in water. 

In the course of the positronium lifetime measurements, radioactive isotopes of positron decay serve as sources, e.g., sodium-22, copper-64. At the moment of the emission of the positron from this source a y-photon is also released. (In the case of, e.g., sodium-22 its energy is 1.28 MeV.) This y-photon serves as the start signal in the coincidence equipment used. The y-photon produced by the 2y-annihilation process to be studied (0.51 MeV) is the stop signal. The magnitude of the time measured between the start and stop signals (the positronium lifetime) is in the range 10 —10 s. To get a lifetime curve of adequate statistics, the apparatus repeats the time measurement about 10 — 10 times. For the details of the experimental technique see, e.g., refs. [De 53, Fe 56, Go 71a]. 

The nucleons consist mainly of photons, electrons, and positrons, and compose about 10 percent of the cosmic radiation at sea level. A fraction of muons and nucleons are absorbed while traversing the atmosphere. Variations in absorber thickness (air mass) are proportional to variations in barometric pressure. The absorption length for cosmic-ray muons at sea level in the atmosphere is 4,000 g/cm (Cocconl, 1951), and for cosmic nucleons, 120 g/cm (Hayakawa, 1969). Thus, it is clear that muons have significantly higher penetrating power than nucleons, about 33 times in the air. The probability of absorption rapidly increases with the atomic number, Z. In terms of lead shielding, these muons can penetrate a meter or more, while nucleons can be stopped in several inches of lead. 

In the case of extremely short half-lives, the starting point of decay-constant determination is still something like Eq. (7.8), but special tricks/equipment (coincidence circuit, time-to-amplitude converter, multichannel analyzer) as well as special conditions (available start and stop signals informing of the birth and death, respectively, of individual nuclei/particles) are also needed. The waiting-time distribution shown in Fig. 9.13 of Chap. 9 in Vol. 1 has also been obtained with such an apparatus, which is the standard equipment of Positron Annihilation Spectroscopy (PAS) measurements (see Chap. 27 in Vol. 3). 

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