[en] The proposed objectives of this project were: 1. Reliable determination of the ¹S₀ gap energy of low-density neutron matter as a function of the neutron density. 2. Determination of phase diagram of the neutron matter at those densities. 3. Clarification of crossover properties of the neutron matter of these densities, which are caused by Bose-Einstein condensate. The NSAC Long Range Plan for nuclear science identified the research area central to the mission of nuclear physics as five agenda. This project has addressed the second agenda: What is the structure of nucleonic matter? The basic approach used was to determine the nucleon-nucleon potential on a simple cubic lattice by applying the method of effective field theory, and using the potential on the same lattice, carry out quantum Monte Carlo calculations of thermal properties of neutron matter. The project was an application of the effective field theory on a many nucleon system. The proposed objectives have been achieved, and two manuscripts were written in collaboration with T. Abe. The manuscripts include most of the results and represent the achievements of the project. They are: (1) ''Lattice calculation of thermal properties of low-density neutron matter with pionless NN effective field theory,'' in Physical Review C, vol. 79, 054002 (2009). (2) ''From low-density neutron matter to the unitary limit,'' in Physical review C, vol. 79, 054003 (2009). The contents of the manuscripts are summarized, describing the work and accomplishments that have been made.