The underlying structure of low-lying collective bands of atomic nuclei is discussed from a novel perspective on the interplay between single-particle and collective degrees of freedom, by utilizing state-of-the-art configuration interaction calculations on heavy nuclei. Besides the multipole components of the nucleon-nucleon interaction that drive collective modes forming those bands, the monopole component is shown to control the resistance against such modes. The calculated structure of 154 Sm corresponds to coexistence between prolate and triaxial shapes, while that of 166 Er exhibits a deformed shape with a strong triaxial instability. Both findings differ from traditional views based on β/γ vibrations. The formation of collective bands is shown to be facilitated from a self-organization mechanism.The structure of atomic nuclei exhibits single-particle as well as collective-mode aspects created by the protons and neutrons (nucleons). The former has been characterized by the shell structure shown initially by Mayer [1] and Jensen [2], while the latter has presented a variety of nuclear shapes following Rainwater [3], and Bohr and Mottelson [4][5][6]. The two aspects lead to "the problem of reconciling the simultaneous occurrence of single-particle and collective degrees of freedom ..." [7]. This is one of the most important basic questions in nuclear structure research, and it remains open. For instance, G.E. Brown has addressed the question, "how single particle states can coexist with collective modes", throughout his life [8]. We discuss in this Letter this problem from a novel perspective.Nucleons in an atomic nucleus occupy single-particle orbits in various configurations. The effective nucleonnucleon (NN) interaction in nuclei induces multi-nucleon correlations by mixing such configurations. This mixing occurs, in many cases, basically for "valence" nucleons in single-particle orbits on top of the appropriate closed proton and neutron shell (inert core). The ellipsoidal shapes correspond to such correlations having the nature of quadrupole surface deformation from a sphere, driven by the quadrupole component of the NN interaction [9][10][11][12][13][14]. This gives rise to an interplay between collective mode and single-particle states (SPS's). If SPS's relevant to these correlations are separated by large gaps, the mixing between them and the resulting correlations are reduced. Thus, the SPS's can act as a "resistance" to (the formation of) collective modes. In this Letter, we first present how ellipsoidal shapes emerge from multi-nucleon systems by using the state-of-the-art Configuration Interaction (CI) simulations, called Monte Carlo Shell Model (MCSM) [15,16]. This allowed us to uncover a novel mechanism: the monopole component of the NN interaction shifts the single-particle energies (SPEs) effectively, weakening the "resistance" against deformation, and thus 2 + 4 + a b 0 1 2 E (MeV) N N 0 100 200 B(E2) (W.u.) 4+ calc. 2+ calc. 2+ exp. 4+ exp. -2 -1 0 Q (eb)c N 84 88 92 84 88 92 84 88 92 2+ calc...