Lifetimes of Radioactive Heavy Ion Beams

Abstract

In the previous chapter, it was discussed that for non-radioactive ion beams, the lifetimes depend on the atomic charge-changing interactions between the ion beam and residual-gas components. In the case of radioactive ion beams, the mean lifetimes depend in addition on the nuclear properties of accelerated ions, and hence, the total mean lifetime comprises both atomic and nuclear components:

$$\begin{aligned} \frac{1}{\tau } = \frac{1}{\tau _{\mathrm{atomic}}} + \frac{1}{\tau _{\mathrm{nuclear}}}, \end{aligned}$$

(10.1)

or equivalently:

$$\begin{aligned} \lambda = \lambda _{\mathrm{atomic}} + \lambda _{\mathrm{nuclear}}, \end{aligned}$$

(10.2)

where $\lambda = 1/\tau$ is the total decay rate. Each decay components may have several terms, which correspond to different decay channels (e.g., $\alpha -, \,\,\beta ^+-, \,\,\beta ^--$decay, fission, etc.) and/or state transitions (e.g., nuclear ground-ground state transitions, ground-excited state transitions, etc.), so one can define:

$$\begin{aligned} \lambda _{\mathrm{nuclear}} = \sum _{\mathrm{all\,\, channels\,\, }i} \lambda _{i}. \end{aligned}$$

(10.3)

The individual decay rate depends on the underlying processes. In the following sections, we describe mechanisms of the decay rates, or mean lifetimes, due to the nuclear reactions.