  Consider an N-Boson system interacting via a two-body repulsive short-range
potential $V$ in a three dimensional box $\Lambda$ of side length $L$. We take
the limit $N, L \to \infty$ while keeping the density $\rho = N / L^3$ fixed
and small. We prove a new lower bound for its ground state energy per particle
$$\frac{E(N, \Lambda)}{N} \geq 4 \pi a \rho [ 1 - O(\rho^{1/3} |\log \rho|^3)
],$$ as $\rho \to 0$, where $a$ is the scattering length of $V$.
