0820033

We propose to observe Her~X-1 during INTEGRALs AO-8 for a total observingtime of 600 ksec: covering one Main-On with two INTEGRAL orbitsthe first near the maximum of the Main-On the second during its decay plus oneINTEGRAL}orbit during the following Short-On. Our prime objectives are tosystematically measure the centroid energy of the fundamental cyclotron lineE_cyc as a function of time X-ray flux 35 day phase and 1.24 s phaseand to study the variation of the shape of the pulse profile with 35 day phase.These observations will contribute to answering the following questions: Is there a slow seculardecrease in the value of E_cyc with time? Does E_cyc depend on 35 day phase?How stable is the positive correlation of the value of E_cyc with the X-ray luminosity?Does the neutron star itself really show precession?The results will yield infomation about fundamental physics in this disk-accreting binary pulsarwith respect to: the structure of the magnetic field at the polar caps the physics of sub-Eddingtonaccretion the generation of spectra and pulse profiles. [truncated! Please see actual data for full text]