  We present the results of a series of XMM-Newton EPIC and OM observations of
Her X-1, spread over a wide range of the 35 day precession period. We confirm
that the spin modulation of the neutron star is weak or absent in the low state
- in marked contrast to the main or short-on states. During the states of
higher intensity, we observe a substructure in the broad soft X-ray modulation
below ~1keV, revealing the presence of separate peaks which reflect the
structure seen at higher energies. The strong fluorescence emission line at
~6.4keV is detected in all observations (apart from one taken in the middle of
eclipse), with higher line energy, width and normalisation during the main-on
state. In addition, we report the detection of a second line near 7keV in 10 of
the 15 observations taken during the low-intensity states of the system. This
feature is rather weak and not significantly detected during the main-on state,
when the strong continuum emission dominates the X-ray spectrum. Spin resolved
spectroscopy just after the rise to the main-on state shows that the variation
of the Fe Kalpha line at 6.4 keV is correlated with the soft X-ray emission.
This confirms our past finding based on the XMM-Newton observations made
further into the main-on state, and indicates the common origin for the thermal
component and the Fe Kalpha line detected at these phases. We also find that
the normalisation of the 6.4keV line during the low state is correlated with
the binary orbital phase, having a broad maximum centered near phi_(orbit) ~
0.5. We discuss these observations in the context of previous observations,
investigate the origin of the soft and hard X-rays and consider the emission
site of the 6.4keV and 7keV emission lines.
