  In this paper, we propose an experiment for the precise measurements of very
forward particle production at RHIC. The proposal is to install a LHCf-like
calorimeter in the ZDC installation slot at one of the RHIC interaction points.
By installing a high-resolution electromagnetic calorimeter at this location we
measure the spectra of photons, neutrons and pi0 at pseudo rapidity eta above
6.
  The new measurements at 500 GeV p-p collisions contribute to improve the
hadronic interaction models used in the cosmic-ray air shower simulations.
Using a similar kinematic coverage at RHIC to that of the measurements at LHC,
we can test the Feynman scaling with a wide energy range and make the
extrapolation of models into cosmic-ray energy more reliable. Combination of a
high position resolution of the LHCf detector and a high energy resolution of
the ZDC makes it possible to determine pT of forward neutrons with the ever
best resolution. This enables us to study the forward neutron spin asymmetry
discovered at RHIC in more detail.
  Another new experiment expected at RHIC is world-first light-ion collisions.
Cosmic-ray interaction models have been so far tested with accelerator data,
but colliders have provided only p-p and heavy-ion collisions. To simulate the
interaction between cosmic-ray particles and atmosphere, collision of light
ions like nitrogen is a ultimate goal for the cosmic-ray physics. We propose
200 GeV p-N collisions together with 200 GeV p-p collisions to study the
nuclear effects in the forward particle production.
  The experiment can be performed by using the existing LHCf detector.
Considering the geometry and response of one of the LHCf detectors, we propose
some short dedicated operations. Ideal beam conditions are summarized in this
paper. Our basic idea is to bring one of the LHCf detectors to RHIC and then
operate from 2016 season at RHIC.
