Gamow shell model description of ${}^4\mathrm{He}(d,d)$ elastic scattering reactions

Structure of weakly bound/unbound light nuclei is often related to the low-energy decay channels involving composite particles like deuteron or $\alpha$ particle. These channels are essential to understand the appearance of light nuclei in the Big Bang nucleosynthesis or the helium fusion. We generalize the Gamow shell model (GSM) in coupled-channel (GSM-CC) representation to include reaction channels with the composite particles. In the core + valence particle formulation, this unified microscopic approach for structure and reactions involving weakly bound/unbound nuclei can be also applied to study low-energy properties of heavy nuclei. As the first application of this generalized GSM-CC approach, we describe the structure of ${}^6\mathrm{Li}$ and deuteron-$\alpha$-particle elastic scattering using the same effective Furutani-Horiuchi-Tamagaki (FHT)-type nucleon-nucleon interaction. Asymptotically, the deuteron structure including its continuum is described using the ${\mathrm{N}}^3\mathrm{LO}$ chiral force. The bulk of the data, including low-energy spectrum of ${}^6\mathrm{Li}$, asymptotic normalization coefficients, and angular differential cross sections are satisfactorily described.

Figure 1

Energies (given with respect to ${}^4\mathrm{He}$ core) and widths (in MeV) of the $T=0$ spectrum of ${}^6\mathrm{Li}$ calculated in GSM-CC approach using FHT(E) and FHT(ANC) interactions and denoted as GSM-CC(E) and GSM-CC(ANC), respectively, are compared to evaluated energy centroids and widths of Ref. [51].

Figure 2

Phase shifts of the ${}^4\mathrm{He}(d,d)$ elastic scattering reaction calculated using the FHT(E) interaction (dotted lines) and the FHT(ANC) interaction (solid lines) are compared to results of the $R$-matrix analyses of experimental data (symbols) [56, 57]. $E_d$ is the kinetic energy of the incoming deuteron and is expressed in the laboratory frame.

Figure 3

Center-of-mass frame angular distributions of the ${}^4\mathrm{He}(d,d)$ elastic scattering reaction calculated at four different energies (laboratory frame) using both the FHT(E) (dashed line) and FHT(ANC) (solid line) interactions are compared with the experimental data (symbols) [60, 61].

Figure 4

Center-of-mass frame angular differential distributions for ${}^4\mathrm{He}(d,d)$ elastic scattering reaction at deuteron backscattered angles 164.5 and 167 degrees, calculated with the FHT(E) (dotted line) and the FHT(ANC) (solid line) interactions at different deuteron kinetic energies $E_d$ in the laboratory frame. The experimental data is depicted by symbols [58, 59].