Two spherical stars A and B have densities ${\rho }_A$ and ${\rho }_B$, respectively. A and B have the same radius, and their masses M_A and M_B are related by M_B = 2M_A. Due to an interaction process, star A loses some of its mass, so that its radius is halved, while its spherical shape is retained, and its density remains ${\rho }_A$. The entire mass lost by A is deposited as a thick spherical shell on B with the density of the shell being ${\rho }_A$. If v_A and v_B are the escape velocities from A and B after the interaction process, the ratio
$\frac{v_B}{v_A}=\sqrt{\frac{10n}{{15}^{\frac{1}{3}}}}$
The value of n is ______.