Applications of local chiral N$^2$LO three-nucleon interaction to nuclear structure and reactions

We overview recent results obtained with the three-nucleon (NNN) interaction derived within the chiral effective field theory at the N$^2$LO order regulated with a magnitude of the momentum transfer [1]. The regulated NNN interaction is then local in the coordinate space, which is an advantage for some many-body techniques. This interaction in combination with a chiral N$^3$LO nucleon-nucleon potential [2] proved to be successful in describing $A$=3 and 4 binding energies, radii [3,4] and scattering lengths [4], the structure of mid-$p$-shell nuclei [3], photo-disintegration of $^4$He [5], and $n-^3$H and A=3 scattering [6,7]. [1] P. Navratil, Few Body Syst. 41, 117 (2007). [2] D. R. Entem and R. Machleidt, Phys. Rev. C 68, 041001(R) (2003). [3] P. Navratil, V. G. Gueorguiev, J. P. Vary, W. E. Ormand, A. Nogga, Phys. Rev. Lett. 99, 042501 (2007). [4] A. Kievsky {\it et al.}, J. Phys. G 35, 063101 (2008). [5] S. Quaglioni and P. Navratil, Phys Lett B 652, 370 (2007). [6] M. Viviani {\it et al.}, arXiv:0812.3547 [nucl-th]. [7] L. E. Marcucci {\it et al.}, arXiv:0905.3306 [nucl-th].