Nucleon-nucleon scattering with the complex scaling method and realistic interactions

We demonstrate the validity of the complex scaling method for realistic strong, nonlocal, nucleon-nucleon interactions by comparing the deuteron bound state and nucleon-nucleon scattering phase shifts with results from other high-precision methods. This opens a pathway for the simultaneous ab initio solutions of the nuclear bound and scattering problems within a unified framework.

Figure 1

Eigenvalues of the CS coupled-channel Hamiltonian (1) for the (a) ${\mathrm{N}}^2{\mathrm{LO}}_{\mathrm{opt}}$ and (b) JISP16 realistic potentials. The deuteron bound state (indicated by the arrows) is shown to be invariant under complex rotations of momenta and coordinates.

Figure 2

${}^3{P}_1$ and ${}^3{D}_2$ channel phase shifts obtained with the CSM with the JISP16 interaction, as compared with the exact solution and the Nijmegen data [40]. We observe an independence of the results starting already for values of $\theta$ as small as 0.2 rad. Even for $\theta =0.1$ rad the phase-shift fluctuations are fairly small and follow the trend of the exact phase shift.

Figure 3

Same as Fig. 2 but for the ${}^3{F}_3$ and ${}^3{G}_4$ channel phase shifts.

Figure 4

${}^3\mathrm{P}{}_0$ channel phase shift calculated with the CSM with the ${\mathrm{N}}^3\mathrm{LO}$ SRG $(\lambda ={2.0\mathrm{fm}}^{-1})$ and the ${\mathrm{N}}^2{\mathrm{LO}}_{\mathrm{opt}}$ realistic interactions. ${\mathrm{N}}^2{\mathrm{LO}}_{\mathrm{opt}}$ phase-shift data are from [46].