Electric Monopole Transition from the Superdeformed Band in ${}^{40}\mathrm{Ca}$

The electric monopole ($E0$) transition strength ${\rho }^2$ for the transition connecting the third $0^{+}$ level, a “superdeformed” band head, to the “spherical” $0^{+}$ ground state in doubly magic ${}^{40}\mathrm{Ca}$ is determined via $e^{+}{e}^{-}$ pair-conversion spectroscopy. The measured value ${\rho }^2(E0;0_3^{+}\to 0_1^{+})=2.3(5)\times {10}^{-3}$ is the smallest ${\rho }^2(E0;0^{+}\to 0^{+})$ found in $A<50$ nuclei. In contrast, the $E0$ transition strength to the ground state observed from the second $0^{+}$ state, a band head of “normal” deformation, is an order of magnitude larger ${\rho }^2(E0;0_2^{+}\to 0_1^{+})=25.9(16)\times {10}^{-3}$, which shows significant mixing between these two states. Large-scale shell-model (LSSM) calculations are performed to understand the microscopic structure of the excited states and the configuration mixing between them; experimental ${\rho }^2$ values in ${}^{40}\mathrm{Ca}$ and neighboring isotopes are well reproduced by the LSSM calculations. The unusually small ${\rho }^2(E0;0_3^{+}\to 0_1^{+})$ value is due to destructive interference in the mixing of shape-coexisting structures, which are based on several different multiparticle-multihole excitations. This observation goes beyond the usual treatment of $E0$ strengths, where two-state shape mixing cannot result in destructive interference.

Figure 1

(a) The $\gamma$-ray energy spectrum measured by the HPGe detector, (b) $e^{+}{e}^{-}$ pair coincidence spectrum, (c) and $e^{+}{e}^{-}$ spectrum after background subtraction. Peaks at 5.212, 5.249, and 5.629 MeV are labeled, as are single-escape (SE) and double-escape (DE) contaminant peaks.

Figure 2

Partial level scheme of ${}^{40}\mathrm{Ca}$ [29].

Figure 3

Systematics of the ${\rho }^2(E0;0^{+}\to 0_1^{+})$ values of even-even $A<50$ nuclei (filled circles) [34]. The ${\rho }^2(E0;0_{3,2}^{+}\to 0_1^{+})$ in ${}^{40}\mathrm{Ca}$ from this Letter are shown as open and filled triangles.

Figure 4

Systematics of the ${\rho }^2(E0)$ values for ${}^{36}\mathrm{S}$, ${}^{38}\mathrm{Ar}$, ${}^{42}\mathrm{Ca}$, and ${}^{40}\mathrm{Ca}$. Open triangles are experimental values from Refs. [34, 40] and this Letter; filled circles are LSSM calculations.

Figure 5

(a) Overlap ${\xi }_{if}(m)$ and (b) $E0$ matrix element $M_{if}(m)$ for each $m$ value of the $mp\text{−}mh$ excitation. The summed $E0$ matrix elements ${\sum }_{m^{\prime }\le m}{M}_{if}(m^{\prime })$ and the total values are shown by the open and filled triangles, respectively.