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Quantum tunneling in many-body systems is the subject of many experimental and theoretical studies in fields ranging from cold atoms to nuclear physics. However, theoretical description of quantum tunneling with strongly interacting particles, such as nucleons in atomic nuclei, remains a major challenge in quantum physics. An initialvalue approach to tunneling accounting for the degrees of freedom of each interacting particle is highly desirable. Inspired by existing methods to describe instantons with periodic solutions in imaginary time, we investigate the possibility to use an initial value approach to describe tunneling at the mean-field level. Real-time and imaginarytime Hartree dynamics are compared to the exact solution in the case of two particles in a two-well potential. Whereas real-time evolutions exhibit a spurious self-trapping effect preventing tunneling in strongly interacting systems, the imaginary-time-dependent mean-field method predicts tunneling rates in excellent agreement with the exact solution. Being an initial-value method, it could be more suitable than approaches requiring periodic solutions to describe realistic systems such as heavy-ion fusion.

Background: In stellar environments, carbon is produced exclusively via the 3α process, where three α 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. While not directly measurable, the radiative width can be deduced by combining three separately measured quantities, one of which is the E 0 decay branching ratio. The E 0 branching ratio can be measured by exciting the Hoyle state in the 12 C(p, p ) reaction and measuring the pair decay of both the Hoyle state and the first 2 + state of 12 C. Purpose: We aim 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 E 0 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 • < θ < 158 • in 14 small energy steps between 10.20 and 10.70 MeV with a thin (60 μg/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 xtheir ratio, the equivalent population ratio can be extracted applicable for any thick 12 C target that may be used in pairconversion measurements. This equivalent ratio agreed with a direct measurement performed with a thick target. 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 E 0 branching ratio in 12 C. Implications for future measurements are discussed, as well as possible applications of this data set for investigating cluster structures in 13 N.

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