A. Putze et al.: An MCMC technique to sample transport and source parameters of Galactic cosmic rays. II. fluxes and other quantities derived from the propagation parameters. In the first paper of this series (Paper I), we focused on the phenomenologically well-understood LBM to ease the implementation of the MCMC. In contrast, here we have analysed a more realistic DM. In agreement with previous studies, when B/C only is considered, we have confirmed that a model with diffusion/convection/reacceleration is more likely than the diffusion/reacceleration case. The for- mer would imply that δ ∼ 0 . 8, whereas the latter would imply that δ ∼ 0 . 2. This result does not depend on the halo size: we provided simple parameterisations to obtain the value of the transport parameters for any halo size L . If mere eye inspection of the published AMS-01 data shows consistency with the HEAO-3 data (covering the same en- ergy region), a B/C analysis based on AMS-01 data (instead of HEAO-3) also indicates that convection and reaccelera- tion is required, but now providing a diffusion slope δ ∼ 0 . 5, closer to theoretical expectations. Data from PAMELA or high-energy data from CREAM and TRACER are required to help solving the long-standing uncertainty in the value for δ . A second important topic of this paper has been the halo size L of the Galaxy and the impact of the underdense medium in the solar neighbourhood. The determination of L is for instance crucial to predictions of antimatter fluxes from dark matter annihilations. The size of the local un- derdense medium is as important, as it can bias the de- termination of L . We provided a step-by-step study of the various radioactive clocks at our disposal. Our detailed ap- proach can serve as a guideline as how to take advantage of future high-precision measurements that will soon become available (e.g., from AMS). The main conclusions about the constraints provided by the radioactive species are, in diffu- sion/reacceleration models, L ∼ 4 kpc and no underdense local bubble is necessary to match the data. For the best-fit model, which requires diffusion/convection/reacceleration, L ∼ 8 kpc with r$_{h}$ ∼ 120 pc. For both models, the halo size found is an increasing function of the diffusion slope δ . A striking feature is that in models with convection, the best-fit value for r$_{h}$ remains ∼ 100 pc for any δ ≳ 0 . 3. For instance, the B/C AMS-01 data (which implies that δ ∼ 0 . 5) and the radioactive ratios are consistent with a wind and a local underdense bubble. This very value of r$_{h}$ ∼ 100 pc is also supported by direct observation of the LISM (see Appendix B). As emphasised in this study, the determination of the value of L and r$_{h}$ strongly depends on the value of δ . For all these parameters, high-energy data of secondary-to- primary ratios, data in the ∼ 1 GeV/n − 10 GeV/n range for isotopic ratios (of radioactive species), and/or data for The equation is even in z so that it is enough to solve it in the upper-half plane. The use of the standard boundary condition N ( z = L ) = 0 and continuity of the density and the current at the disc crossing completely characterises the solution. iii) R ( z ) = Γ $^{r}$→s $_{decay}$N $^{r}$( z, E ) described a contribution from a radioactive nucleus r , decaying into s ′ in both the disc and the halo. i) P ( z ) = 2 hδ ( z ) × q s $_{0}$Q ( E ) is the standard primary source term for sources located in the thin disc. The quantity q s 0 is the source abundance of nucleus j whose source spectrum is Q ( E ) ∝ β $^{η}$R − $^{α}$. ii) S ( z ) = 2 hδ ( z ) × Γ $^{p}$→s tot N $^{p}$( z = 0 , E ) is the standard sec- ondary source term (also in the disc), where Γ $^{p}$→s tot = nvσ $^{p}$→s is the production cross-section of nucleus p into s . This simple form originates from the straight-ahead approximation used when dealing with nuclei (see, e.g., Maurin et al. 2001 for more details). In this equation, N is the differential density of a given CR species, Γ$_{rad}$ = 1 / ( γτ ) is its decay rate, and Γ$_{tot}$ = ∑ $_{ISM}$n$_{ISM}$ vσ$_{ISM}$ is its destruction rate in the thin gaseous disc ( n$_{ISM}$ =H, He). The right-hand side (r.h.s) of the equa- tion is a generic source term, that contains one of the fol- lowing three contributions, i.e., Q ( z ) = P ( z )+ S ( z )+ R ( z ): The starting point is the transport equation (Berezinskii et al. 1990). We assume that the diffusion coefficient K does not depend on spatial coordinates. A constant wind V$_{c}$ blows the particle away from the Galactic disc, along the z direction. In the thin-disc approximation (e.g., Webber et al. 1992), the diffusion/convection for the 1D–model (discarding energy redistributions) is The derivation of these solutions is very similar and has no additional difficulties to those experienced by Maurin et al. (2001), to which we refer the reader for more details. As both frameworks (1D and 2D) exhibit similar forms, formulae are written for the 1D model only. Formulae for the 2D case are obtained by replacing some 1D quantities by their 2D counterparts, as specified below. We provide below the solutions for the diffusion equation with a constant wind V$_{c}$ and a single diffusion coefficient K ( E ) in the whole Galaxy. In the 1D version of the model (e.g., Jones et al. 2001), the source distribution and the gas density do not depend on r , so that the propagated fluxes depend only on z . Acknowledgements. We thank C. Combet for a careful reading of the paper. A. P is grateful for financial support from the Swedish Research Council (VR) through the Oskar Klein Centre. We acknowledge the support of the French ANR (grant ANR-06-CREAM). the radioactive elemental ratios in the 1 − 100 GeV/n en- ergy range are necessary. This is within reach of several fly- ing and forthcoming balloon-borne projects and satellites (PAMELA, AMS). A.1. 1D–model Appendix A: Solutions of the diffusion equation 16 Table 8. Best-fit parameters on B/C+ $^{10}$Be/$^{9}$Be$^{26}$+Al/$^{27}$Al +$^{36}$Cl/Cl: 1D vs 2D DM. Config. K 0 × 10 2 δ V c V a L r h χ $^{2}$/ d.o.f (kpc $^{2}$Myr $^{$_{−}$1}$) (km s $^{$_{−}$1}$) (kpc) 1D-II- L 15.4 0.23 · · · 92.5 6.2 · · · 3.09 2D-II- L 14.9 0.24 · · · 90.8 8.8 · · · 3.04 1D-III- Lr h 1.90 0.83 18.9 73.5 13.6 0 . 13 1.43 2D-III- Lr h 5.24 0.85 18.3 123. 4.3 0 . 16 1.48