Spectroscopic aspects of subthreshold Siegert states

The Siegert states are approached in the framework of Bloch–Lane–Robson theory of quantum collisions. Both the bound and the quasi-stationary Siegert states are subject of the equation relating the channel R-matrix element to the logarithmic derivative. The Siegert state dependence on the decay channel parameters results in channel renormalization of reduced widths, especially near threshold. The neutron subthreshold and the electron Rydberg states are examples of subthreshold Siegert states. The Siegert approach results in Heisenberg’s S-matrix formula for the bound state and the subthreshold resonance. The Siegert state residue is a spectroscopic asymptotic normalization constant. The decay width of the electron Rydberg channel resonance is, up to a factor, the electron strength function.

THEORETICAL INVESTIGATIONS OF THE 12C(α,γ)16OE2 CROSS SECTION

The E2 component of the 12 C (α,γ)16 O cross section is investigated in three ways: by a microscopic cluster model, by R-matrix fits and by a combination of both. The microscopic calculation leads to an estimate of the S-factor at a typical energy of 300 keV of SE2(300 keV )≈ 50 keV-b for ground-state transitions. Cascade transitions to the [Formula: see text] and [Formula: see text] excited states of 16 O are also studied. Then the S-factor is analyzed in the phenomenological R-matrix theory. We show that the background term plays a crucial role, and cannot be determined without ambiguity. Consequently only an upper limit on the extrapolated S-factor can be obtained [SE2(300 keV )< 190 keV-b ]. Finally, we use the microscopic Asymptotic Normalization Constant (ANC) of the [Formula: see text] level, well known to be a cluster state to constrain the R-matrix analysis. This procedure strongly reduces the uncertainties on the R-matrix fits, and we end up with a recommended value of SE2(300 keV ) = 42 ± 2 keV-b .

Partly non-local potentials in the model triton

Binding energy, ET, wave function, form factor, and asymptotic normalization constant, CT, have been calculated for the model triton using two classes of phase equivalent potentials: partly non-local (PNL) potentials, and rank-two separable potentials. The results are compared with those of Fiedeldey. The binding energy is sensitive to the deuteron wave function and zero-energy wound integral. The triton form factors depend on ET and the deuteron wave function. CT is almost insensitive to variations in the PNL potentials, but increases with ET for the separable potentials.