  A new technique to search for new scalar and tensor interactions at the
sub-micrometer scale is presented. The technique relies on small shifts of
nuclear gamma lines produced by the coupling between matter and the nuclei in
the source or absorber of a Mossbauer spectrometer. Remarkably, such energy
shifts are rather insensitive to electromagnetic interactions that represent
the largest background in searches for new forces using atomic matter. This is
because nuclei are intrinsically shielded by the electron clouds. Additionally,
electromagnetic interactions cause energy shifts by coupling to nuclear moments
that are suppressed by the size of the nuclei, while new scalar interactions
can directly affect these shifts. Finally, averaging over unpolarized nuclei,
further reduces electromagnetic interactions. We discuss several possible
configurations, using the traditional Mossbauer effect as well as nuclear
resonant absorption driven by synchrotron radiation. For this purpose, we
examine the viability of well known Mossbauer nuclides along with more exotic
ones that result in substantially narrower resonances. We find that the
technique introduced here could substantially improve the sensitivity to a
variety of new interactions and could also be used, in conjunction with
mechanical force measurements, to corroborate a discovery or explore the new
physics that may be behind a discovery.
