  Using imaginary-time theory, it is shown that the triple-alpha reaction rate
can be reliably calculated without the need to solve scattering problems
involving three charged particles. The calculated reaction rate is found to
agree well with the empirical NACRE rate, which is widely adopted in stellar
evolution calculations. The reason for this is explained using $R$-matrix
theory. Extremely slow convergence is found to occur when a coupled-channel
expansion is introduced, which helps to explain the very different reaction
rates obtained using different theoretical approaches.
