We report a new measurement of the cross section for the production of isol
ated photons with transverse energies (E-T(gamma)) above 10 GeV and pseudor
apidities \eta\ < 2.5 in p (p) over bar collisions at root s = 1.8 TeV. The
results are based on a data sample of 107.6 pb(-1) recorded during 1992-19
95 with the D0 detector at the Fermilab Tevatron collider. The background,
predominantly from jets which fragment to neutral mesons, was estimated usi
ng the longitudinal shower shape of photon candidates in the calorimeter. T
he measured cross section is in good agreement with the next-to-leading ord
er QCD calculation for E-T(gamma) greater than or similar to 36 GeV.