Momentum Distribution Sum Rule for Angle-Resolved Photoemission

Within a spectral function A(k,ω) interpretation of angle-resolved photoemission (ARPES), the intensity obeys the sum rule ∫dωf(ω)A(k,ω)0ex0ex=0ex0exn(k), where f is the Fermi function and n(k) the momentum distribution. We show the usefulness of this sum rule for analyzing ARPES data. The integrated intensity in Bi₂Sr₂CaCu₂{O}₈$ at ${k}F$ is independent of temperature even though the spectrum is strongly $T$ dependent. We also demonstrate the possibility of measuring $n(k)$ using ARPES for YB${a}₂C{u}₄O₈.