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sion/convection/reacceleration). For model II, the size of r$_{h}$ suddenly jumps to ∼ 100 pc. But for δ ≳ 0 . 3, it returns to the pure diffusion regime, r$_{h}$ decreasing abruptly (to a non-vanishing value) and L becoming vanishingly small. In this regime, the thin-disc approximation is no longer valid and nothing can be said about it. For model III, the plateau r$_{h}$ ∼ 100 pc is stable for all δ ≳ 0 . 2. The under- dense bubble also stabilises the value of the halo size L . The way of understanding this trend is as for the stan- dard DM, but now the flux of the radioactive species reads N rad r$_{h}$ (0) ∝ exp( − r$_{h}$$_{/}$√$_{Kγτ}$$_{0}$$_{)}$$_{/}$ √$_{Kγτ}$$_{0}$$_{. The weaker depen-}$ dence of L with δ must be represented by this formula. We underline that for all best-fit configurations leading to r$_{h}$ ̸ = 0, the improvement is statistically meaningful com- pared to the case r$_{h}$ = 0. 

## 5.2. Isotopic versus elemental measurements 

A similar analysis can be carried out using elemental ra- tios instead of isotopic ones. As before, the best-fit values of well-chosen combinations of the transport parameters { K$_{0}$, δ, V$_{c}$, V$_{a}$ } are left unchanged when radioactive species are added to the fit (same values as in Fig. 11). 

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## 5.2.1. General dependence of L with δ 

For the standard DM ( r$_{h}$ = 0), the dependence of the diffu- sive halo size L on the diffusion slope δ is shown in Fig. 12, 

