Motivated by a recent paper by Ekholm--Kowarik--Portmann, we analyze the semi-classical analysis of the ground state energy of the Dirichlet-Pauli operator. Tunneling effect can be measured with some analogy with the semi-classical analysis of the small eigenvalues of a Witten Laplacian, as analyzed in papers by Helffer-Sjöstrand, Helffer-Klein-Nier, Helffer-Nier,.... The presented works are in collaboration with Mikael Persson Sundqvist (Lund) and Hynek Kowarik (Brescia).