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.
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