Possible interpretation of the complex expectation values associated with resonances

TL;DR

This paper introduces a scheme to interpret complex expectation values of nuclear resonances using Green's functions, explaining peak shifts and applying it to various nuclear states including the Hoyle state.

Contribution

It presents a novel interpretation method for complex expectation values of resonances, linking them to the Breit-Wigner distribution and applying it to nuclear systems with complex scaling.

Findings

The real part of the expectation value corresponds to the integral of the Breit-Wigner distribution.

The imaginary part accounts for the peak shift in the resonance strength.

Application to nuclear resonances reveals unique energy dependence of the strength function.

Abstract

We propose a possible scheme to interpret the complex expectation values associated with resonances having the complex eigenenergies. Using the Green's function for resonances, the expectation value is basically described by the Breit-Wigner distribution as a function of the real excitation energy. In the expression of the complex expectation values for resonances, the real part brings the integral value of the distribution, while the imaginary part produces the deviation from the Breit-Wigner distribution,which explains a shift of the peak in the strength from the resonance energy. We apply the present scheme to the several nuclear resonances of $^{12}$C including the Hoyle state, and neutron/proton-rich nuclei of $^6$He, $^6$Be, $^8$He, and $^8$C. In these nuclei, many-body resonances are obtained as the complex-energy eigenstates under the correct boundary condition using the complex scaling method, and their nuclear radii are uniquely evaluated. We discuss the peculiar energy dependence of the strength function of the square radius for the resonances in these nuclei.