Generalized gauge-space rotations in atomic nuclei: A critical insight

Abstract

We critically reexamine the concepts of pairing rotations and moments of inertia in gauge space extracted from experimental binding energies. Our analysis focuses on pairing correlations among like nucleons, neutron-proton pairing, and $α$-type correlations. By investigating $α$ separation energies and binding-energy differences along chains of fixed isospin projection and subtracting macroscopic contributions, we reveal a remarkably smooth and nearly universal behavior in the residual $α$ correlation energy. These results exhibit the parabolic trends characteristic of collective rotations in gauge space. We demonstrate that the standard definition of the gauge-space moment of inertia for like-nucleon pairing is dominated by macroscopic contributions from Coulomb and symmetry energies. Once these are removed, the remaining moment of inertia becomes negative. This suggests that the observed behavior reflects the loss of correlation energy due to Pauli-blocking effect. Our results indicate that $α$ correlations constitute a genuine collective mode associated with quartetting dynamics arising from the coherent coupling of two superfluid components.

Figures (3)

• Figure 1: Systematics of the $\alpha$-correlation energy $E_{\alpha}$ in the ground states of heavy nuclei as a function of neutron number, extracted from experimental atomic masses wang2021ame. Data points with the same isospin are connected by solid lines. (a) $E_{\alpha}$ obtained directly from experimental binding energies. (b) $E_{\alpha}$ after subtracting Coulomb and liquid-drop contributions from the total binding energy. (c) Same as panel (b), but shown for $Z\leq82$ relative to the mid-shell, taking particle--hole conjugation into account. (d) Same as panel (c), but for $Z\geq84$.
• Figure 2: Left: Quadratic residual energy (in MeV) extracted from experimental binding energies (solid symbol) for even-even Sn and Pb isotopes and $N=82$ isotones. Right: Same as left but with the macroscopic symmetry energy and Coulomb energy subtracted from the binding energy. We adopt the sign convention used in Refs. PapHinohara2016. Because of this choice, the trends shown here are the inverse of those in Fig. \ref{['dssd']}: a concave-upward curve in the left panels indicates enhanced extra binding energy for nuclei near the center value $A_0$. In contrast, concave-downward curves (right) show enhanced binding energy for systems with fewer pairs as they move away from $A_0$.
• Figure 3: Quadratic residuals (solid symbols) extracted from experimental binding energies after subtracting the Coulomb contribution for various $\alpha$ chains with fixed isospin projection. Upper panel: The $T=0$ chain is plotted relative to $^{56}$Ni. Lower panel: Heavy isobar chains are plotted relative to their corresponding Pb isotopes. The gain in extra quadratic energy as $\alpha$ particles or holes are added to the Pb core is consistent with the $E_{\alpha}$ systematics shown in Figs. \ref{['dssd']}c and \ref{['dssd']}d.