Complex-Scaling Calculation of Three-Body Resonances Using Complex-Range Gaussian Basis Functions --- Application to 3$\alpha$ resonances in 12C ---

Understand

We propose to use the complex-range Gaussian basis functions, {r^l e^{-(1 \pm i\omega)(r/r_n)^2}Y_{lm}(\hat{r}); r_n in a geometric progression}, in the calculation of three-body resonances with the complex-scaling method (CSM) in which use is often made of the real-range Gaussian basis functions, {r^l e^{-(r/r_n)^2}Y_{lm}(\hat{r})}, that are suitable for describing the short-distance structure and the asymptotic decaying behavior of few-body systems.

• The former basis set is more powerful than the latter when describing the resonant and nonresonant continuum states with highly oscillating amplitude at large scaling angles \theta.
• We applied the new basis functions to the CSM calculation of the 3\alpha resonances with J=0^+, 2^+ and 4^+ in 12C.
• The eigenvalue distribution of the complex scaled Hamiltonian becomes more precise and the maximum scaling angle becomes drastically larger (\theta_{max}=16 deg.