Underlying Structure of Collective Bands and Self-Organization in Quantum Systems

Abstract

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...

Shape Coexistence at Zero Spin in Ni64 Driven by the Monopole Tensor Interaction

“…As demonstrated in Fig. 4(b), by deactivating components of the monopole interaction (i.e., monopole frozen [6]), a nearly vanishing prolate minimum would reside at even higher excitation, in line with mean-field predictions [24][25][26][27][28].…”

“…In contrast, recent Monte Carlo shell-model (MCSM) calculations [11] indicate coexistence of spherical and deformed oblate and prolate 0 þ states already in 62;64 Ni. This coexistence originates from the action of the monopole tensor force which shifts effective single-particle energies, already at the valley of stability, weakening resistance against deformation [6,11,12]. This Letter reports extensive tests of these MCSM predictions.…”

“…The concept was originally introduced by Jahn and Teller who demonstrated that, in nonlinear molecules, coupling between degenerate electronic states and collective vibrations can destroy the system's original symmetry [1]. In atomic nuclei, the appearance of ellipsoidal deformation is a realization of this effect with specific superpositions of spherical singleparticle states (e.g., Nilsson model [2]) induced by deformed mean potentials (mean-field approaches) [3,4], or by quadrupole correlations (shell-model descriptions) [5,6], highlighting the interplay between single-particle states and collective modes.…”

“…Over the past two decades, studies of neutron-rich nuclei have highlighted the contribution of the monopole component of the tensor force to the evolution of the structure of exotic nuclei [6,9], especially in the change in single-particle (or shell) structure with neutron excess, with some magic numbers vanishing and other, new ones appearing [10]. Besides such single-particle properties, its role in driving the nuclear shape was subsequently identified [6,[11][12][13][14][15], specifically in connection with shape coexistence.…”

“…4. 64 Ni potential energy surfaces with (a) full, original interaction used in MCSM calculations [11], and (b) monopolefrozen interaction (i.e., the monopole component is subtracted from the proton-neutron interaction, and single-particle energies are adjusted to original effective values of the spherical minimum [6]).…”