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The proton matrix element of the isovector-scalar density,$<p|\overline{u}u-\overline{d}d|p>/2M_p$, is calculated by evaluating thenucleon current correlation function in an external isovector-scalar fieldusing the QCD sum-rule method. In addition to the usual chiral and gluoncondensates of the QCD vacuum, the response of the chiral condensates to theexternal isovector field enters the calculation. The latter is determined bytwo independent methods. One relates it to the difference between the up anddown quark chiral condensates and the other uses the chiral perturbationtheory. To first order in the quark mass difference $\delta m=m_d-m_u$, thenon-electromagnetic part of the neutron-proton mass difference is given by theproduct $\delta m <p|\overline{u}u-\overline{d}d|p>/2M_p$; the resulting valueis in reasonable agreement with the experimental value.Comment: 16 pages in revtex (3 figures avaible under request), UMD preprint  #94-08

Calculation of 〈p‖u¯u-d¯d‖p〉 from QCD sum rules and the neutron-proton mass difference