  We studied the acceptance dependence of proton cumulants (up to fourth order)
and correlation functions in 0--5\% most central Au+Au collisions at
$\sqrt{s_\text{NN}}$=7.7, 11.5, 19.6, 27, 39, 62.4 and 200 GeV from UrQMD
model. We found that high order proton cumulants show suppressions at large
acceptance. By decomposing the proton cumulants into linear combination of
multi-proton correlation functions, we observed the two-proton correlation
functions always show negative values due to the effects of baryon number
conservations. The three and four-proton correlation functions are close to
zero and show negligible acceptance dependence. We further observed that the
proton cumulants and correlation functions follow similar trends and show a
scaling behavior when plotting the results versus mean number of protons. The
comparisons between experimental data and the UrQMD calculations show that the
non-monotonic energy dependence of proton correlation functions measured by
STAR experiment cannot be described by the UrQMD model. The UrQMD calculations
can provide us baselines for the experimental studies of the proton cumulants
and correlation functions. Finally, we propose to measure the rapidity
dependence of the reduced proton correlation functions to search for the QCD
critical point in heavy-ion collisions.
