The scaling of the bond-bond correlation function $C(s)$ along linear polymer chains is investigated with respect to the curvilinear distance, $s$, along the flexible chain and the monomer density, $rho$, via Monte Carlo and molecular dynamics simulations. % Surprisingly, the correlations in dense three dimensional solutions are found to decay with a power law $C(s) sim s^{-omega}$ with $omega=3/2$ and the exponential behavior commonly assumed is clearly ruled out for long chains. % In semidilute solutions, the density dependent scaling of $C(s) approx g^{-omega_0} (s/g)^{-omega}$ with $omega_0=2-2 u=0.824$ ($ u=0.588$ being Florys exponent) is set by the number of monomers $g(rho)$ contained in an excluded volume blob of size $xi$. % Our computational findings compare well with simple scaling arguments and perturbation calculation. The power-law behavior is due to self-interactions of chains on distances $s gg g$ caused by the connectivity of chains and the incompressibility of the melt. %
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