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The radiative branching ratio of the Hoyle state is crucial to estimate the triple-$\alpha$ reaction rate in stellar environments at medium temperatures. Knowledge of the $\gamma$-decay channel is critical as this is the dominant radiative decay channel for the Hoyle state. A recent study by Kib\'edi et al. [Phys. Rev. Lett. 125, 182701 (2020)] has challenged our understanding of this astrophysically significant branching ratio and its constraints. The objective of this work was to perform a new measurement of the $\gamma$-decay branching ratio of the Hoyle state to deduce the radiative branching ratio of the Hoyle state. An additional objective was to independently verify aspects of the aforementioned measurement conducted by Kib\'edi et al. For the main experiment of this work, the Hoyle state was populated by the $^{12}\textrm{C}(p,p')$ reaction at 10.8 MeV at the Oslo Cyclotron Laboratory. The $\gamma$-decay branching ratio was deduced through triple-coincidence events, each consisting of a proton ejectile corresponding to the Hoyle state, and the subsequent $\gamma$-ray cascade. In the main experiment of this work, a $\gamma$-decay branching ratio of the Hoyle state of $\Gamma_{\gamma}/\Gamma=4.0(4)\times 10^{-4}$ was determined, yielding a corresponding radiative branching ratio of $\Gamma_{\textrm{rad}}/\Gamma=4.1(4) \times 10^{-4}$, which is in agreement with several recent studies, as well as the previously adopted ENSDF average of $\Gamma_{\textrm{rad}}/\Gamma=4.16(11)\times 10^{-4}$. Aspects of the analysis performed by Kib\'edi et al. were verified in this work and the source of discrepancy between the results of this work and that of Kib\'edi et al. could not be determined. Further independent and innovative studies for the radiative width of the Hoyle state will substantiate whether the discrepant result by Kib\'edi et al. should be excluded from future evaluations.

The $g$ factors of $11/2^-$ isomers in semimagic $^{109}$Sn and $^{111}$Sn (isomeric lifetimes $\tau = 2.9(3)$ ns and $\tau = 14.4(7)$ ns, respectively) were measured by an extension of the Time Differential Perturbed Angular Distribution technique, which uses \LaBr detectors and the hyperfine fields of a gadolinium host to achieve precise measurements in a new regime of short-lived isomers. The results, $g(11/2^-; {^{109}\textrm{Sn}}) = -0.186(8)$ and $g(11/2^-; {^{111}\textrm{Sn}}) = -0.214(4)$, are significantly lower in magnitude than those of the $11/2^-$ isomers in the heavier isotopes and depart from the value expected for a near pure neutron $h_{11/2}$ configuration. Broken-symmetry density functional theory calculations applied to the sequence of $11/2^-$ states reproduce the magnitude and location of this deviation. The $g(11/2^-)$ values are affected by shape core polarization; the odd $0h_{11/2}$ neutron couples to $J^{\pi}=2^+,4^+,6^+...$ configurations in the weakly-deformed effective core, causing a decrease in the $g$-factor magnitudes., Comment: 8 pages, 7 figures. Accepted in Physics Letters B

The only proposed observation of a discrete, hexacontatetrapole ($E6$) transition in nature occurs from the T$_{1/2}$ = 2.54(2)-minute decay of $^{53m}$Fe. However, there are conflicting claims concerning its $\gamma$-decay branching ratio, and a rigorous interrogation of $\gamma$-ray sum contributions is lacking. Experiments performed at the Australian Heavy Ion Accelerator Facility were used to study the decay of $^{53m}$Fe. For the first time, sum-coincidence contributions to the weak $E6$ and $M5$ decay branches have been firmly quantified using complementary experimental and computational methods. Agreement across the different approaches confirms the existence of the real $E6$ transition; the $M5$ branching ratio and transition rate have also been revised. Shell model calculations performed in the full $pf$ model space suggest that the effective proton charge for high-multipole, $E4$ and $E6$, transitions is quenched to approximately two-thirds of the collective $E2$ value. Correlations between nucleons may offer an explanation of this unexpected phenomenon, which is in stark contrast to the collective nature of lower-multipole, electric transitions observed in atomic nuclei., Comment: 9 pages, 4 figures, to be published in Physical Review Letters

Background: In stars, carbon is produced exclusively via the $3\alpha$ process, where three $\alpha$ particles fuse to form $^{12}$C in the excited Hoyle state, which can then decay to the ground state. The rate of carbon production in stars depends on the radiative width of the Hoyle state. The radiative width can be deduced by combining three separately measured quantities, one of which is the $E0$ decay branching ratio. The $E0$ branching ratio can be measured by exciting the Hoyle state in the $^{12}$C$(p,p')$ reaction and measuring the pair decay of its Hoyle state and first $2^+$ state. Purpose: To reduce the uncertainties in the carbon production rate in the universe by measuring a set of proton angular distributions for the population of the Hoyle state ($0^+_2$) and $2^+_1$ state in $^{12}$C in $^{12}$C$(p,p')$ reactions between 10.20 and 10.70 MeV, used in the determination of the $E0$ branching ratio of the Hoyle state. Method: Proton angular distributions populating the ground, first $2^+$, and the Hoyle states in $^{12}$C were measured in $^{12}$C(p,p') reactions with a silicon detector array covering $22^\circ<\theta<158^\circ$ in 14 energy steps between 10.20 and 10.70 MeV with a thin ($60\ \mu$g/cm$^2$) $^{nat}$C target. Results: Total cross-sections for each state were extracted and the population ratio between the $2^+_1$ and Hoyle state determined at each energy step. By appropriately averaging these cross-sections and taking their ratio, the equivalent population ratio can be extracted applicable for any thick $^{12}$C target used in pair-conversion measurements. Conclusions: We present a general data set of high-precision $^{12}$C$(p,p')$ cross-sections that make uncertainties resulting from the population of the $2^+_1$ and $0^+_2$ states by proton inelastic scattering negligible for any future measurements of the $E0$ branching ratio in $^{12}$C., Comment: 11 pages, 7 figures

Isomers in $^{66}$Ga, $^{67}$Ge, and $^{69}$Ge were recoil-implanted into ferromagnetic hosts of iron and gadolinium at $\approx 6$~K, and the hyperfine magnetic fields were determined by Time Differential Perturbed Angular Distribution (TDPAD) measurements. The hyperfine field strengths at $\approx 6$~K are compared to the results of previous higher-temperature measurements and the amplitudes of the $R(t)$ functions are compared to empirical expectations. The results show that gadolinium can be a suitable host for high-precision in-beam $g$-factor measurements. The results of new $g$-factor measurements for isomers in $^{66}$Ga and $^{67}$Ge are $g(^{66}$Ga$,7^{-}) = +0.126(4)$, supporting a $[\pi_{f5/2} \otimes \nu g_{9/2}]_{7^-}$ configuration assignment, and $g(^{67}$Ge$,\frac{9}{2}^{+})=-0.1932(22)$, derived from a new measurement of the ratio $g(^{67}\mathrm{Ge})/g(^{69}\mathrm{Ge}) = 0.869(9)$. These values are in agreement with previous results. The $R(t)$ amplitudes indicate that the nuclear alignment produced in the isomeric states was significantly lower than the empirically expected $\sigma/I \approx 0.35$., Comment: 10 pages, 10 figures

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 $^{40}$Ca has been determined via $e^+e^-$ pair-conversion spectroscopy. The measured value, $\rho^2(E0; 0^+_3 \to 0^+_1)~=~2.3(5)\times10^{-3}$, 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 were performed to understand the microscopic structure of the excited states, and the configuration mixing between them; experimental $\rho^2$ values in $^{40}$Ca and neighboring isotopes were 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.