  The entanglement properties in an antiferromagnetic dimerized Heisenberg
spin-1/2 chain are investigated. The entanglement gap, which is the difference
between the ground-state energy and the minimal energy that any separable state
can attain, is calculated to detect the entanglement. It is found that the
entanglement gap can be increased by varying the alternation parameter. Through
thermal energy, the witness of the entanglement can determine a characteristic
temperature below that an entangled state can be obtained. The entanglement
detected by the energy can provide a lower bound for that determined by the
concurrence. If the alternation parameter is smaller than a critical value,
there is always no inter-dimer entanglement in the chain.
