Imaginary-time method for ααn radiative capture reaction rates

The ααn process plays a crucial role in bridging the A = 5, 8 gap in a neutron-rich environment, determining its reaction rate highly significant in nuclear astrophysics. Using the imaginary-time approach, we calculated the ααn reaction rate over a very large spatial domain, fully accounting for the three-body effect without solving directly scattering problems. Although employing the same Hamiltonian as the transformed harmonic oscillator method, our calculated rate differs by more than ten orders of magnitude in the extremely low-temperature region but aligns well with the NACRE rate across all temperatures. A sufficiently large spatial domain is required at low temperatures to obtain accurate reaction rates, indicating the indispensability of direct three-body capture in this temperature regime.