Elastic Anomalies of Crystalline 4He at T=0

Elastic constants for hcp He-4 are investigated at zero temperature, from close to the melting pressure up to 14 MPa approximately. Well known relations of these quantities are used to analyze the results. A reliable model wave function is used in the calculations. We show that the linear compressibility has a non-isotropic character in a range of densities rather than the expected isotropic behavior. A fact that suggests that the relation among elastic constants that depends on a constant value of the structure parameters ratio c/a for hcp quantum crystals should not be used to extract an elastic constant from experimental data.