In a previous analysis , Maurin et al .
( 2001 ) have constrained several parameters of the cosmic ray diffusive propagation ( the diffusion coefficient normalization K _ { 0 } and its spectral index \delta , the halo half-thickness L , the Alfvén velocity V _ { a } , and the galactic wind V _ { c } ) using stable nuclei .
In a second paper ( Donato et al. , 2001 ) , these parameters were shown to reproduce the observed antiproton spectrum with no further adjustment .
In the present paper , we extend the analysis to the \beta -radioactive nuclei ^ { 10 } Be , ^ { 26 } Al and ^ { 36 } Cl .
These species will be shown to be particularly sensitive to the properties of the local interstellar medium ( lism ) .
As studies of the lism suggest that we live in an underdense bubble of extent r _ { hole } \sim 50 - 200 \mbox { pc } , this local feature must be taken into account .
We present a modified version of our diffusion model which describes the underdensity as a hole in the galactic disc ; we believe some of the formulæ presented here are new .
It is found that the presence of the bubble leads to a decrease in the radioactive fluxes which can be approximated by a simple factor \exp ( - r _ { hole } / l _ { rad } ) where l _ { rad } = \sqrt { K \gamma \tau _ { 0 } } is the typical distance travelled by a radioactive nucleus before it decays .
We find that each of the radioactive nuclei independently points towards a bubble of radius \lesssim 100 \mbox { pc } .
If these nuclei are considered simultaneously , only models with a bubble radius r _ { hole } \sim 60 - 100 \mbox { pc } are marginally consistent with data .
In particular , the standard case r _ { hole } = 0 \mbox { pc } is disfavored .
Our main concern is about the consistency of the currently available data , especially ^ { 26 } Al/ ^ { 27 } Al .