Quadrupole transitions of $^{10}$C and their isospin symmetry with $^{10}$Be

TL;DR

The paper investigates the quadrupole properties of $^{10}$C and its mirror $^{10}$Be, focusing on isospin symmetry and an experimental anomaly in $B(E2)$ values. It employs a multicool extension of antisymmetrized molecular dynamics (AMD) to variationally optimize a large set of intrinsic configurations, including excited states generated with a pseudopotential that enforces approximate orthogonality to the ground ensemble. The results reproduce the energy spectra and reveal elongated linear-chain cluster states, while detailing monopole and quadrupole transitions for protons and neutrons; the study explains the $B(E2;2^+_1\to 0^+_1)$ anomaly by contrasting proton and neutron deformations in the two nuclei and confirms isospin symmetry through multiple observables. The work provides a coherent, unified description of mean-field and cluster phenomena in light mirror nuclei and suggests specific experimental tests to further validate the predicted transitions and deformations.

Abstract

We investigate the structures of $^{10}$C focusing on the quadrupole properties in comparison with the mirror nucleus $^{10}$Be. We describe $^{10}$C and $^{10}$Be in the variation of the multiple bases of the antisymmetrized molecular dynamics (AMD), in which the multiple AMD bases are optimized simultaneously in the total-energy variation. In the monopole transitions, we confirm the isospin symmetry between $^{10}$C and $^{10}$Be by exchanging protons and neutrons. In the quadrupole transitions, most cases show larger values in $^{10}$C than those of $^{10}$Be, except for the transition of $2^+_1\to 0^+_1$. The transition of $2^+_1\to 0^+_1$ shows similar values in the two nuclei in spite of the different proton numbers, which agrees with the experimental situation as an anomaly. This relation comes from the small proton deformation in $^{10}$C due to its subclosed nature and the large proton deformation in $^{10}$Be due to two-$α$ clustering. This property can also be seen in the quadrupole moments of the two nuclei. In the neutron deformations of $^{10}$C and $^{10}$Be, the opposite tendency of protons is confirmed and these results ensure the isospin symmetry between the two nuclei. We also confirm the large quadrupole transitions between the elongated linear-chain states. It would be desirable for future experiments to investigate the present characteristics of the transitions in the two nuclei.

Figures (5)

• Figure 1: Intrinsic energy (upper) and radius (lower) of $^{10}$C for positive parity state with the basis number $N_{\rm b}=16$ in the multicool calculation. The strength $\lambda$ of the pseudopotential changes.
• Figure 2: Intrinsic density distributions of the representative configurations of $^{10}$C for the ground state. Units of densities and axes are in fm$^{-3}$ and in fm, respectively. The lower label in each panel explains the configuration.
• Figure 3: Intrinsic density distributions of the representative configurations of $^{10}$C for the excited states with the pseudopotential. Units of densities and axes are in fm$^{-3}$ and in fm, respectively. The lower label in each panel explains the configuration.
• Figure 4: Energy spectra of $^{10}$C (left two panels) and $^{10}$Be (right two panels) in the experiments tilley04sobotka24 and the multicool calculation in units of MeV. In each spectrum, the left-hand and right-hand sides of the measures represent the total energies and the measures in the middle represent the excitation energy. The threshold energies are shown with the dotted horizontal lines for $\alpha$+$\alpha$+$N$+$N$, $^6$He/$^6$Be+$\alpha$ denoted as $E_{64}$, and $^9$Be+$n$/$^9$B+$p$ denoted as $E_{91}$.
• Figure 5: Proton density distributions of the representative configurations of the $2^+_1$ states of $^{10}$Be (upper four panels) and $^{10}$C (lower four panels). Units of densities and axes are in fm$^{-3}$ and in fm, respectively. The lower label in each panel explains the configuration. The deformation parameters $\beta$ of protons and the squared overlaps with the $2^+_1$ state in units of % are shown at the bottom of each panel.