Coherent Absorption Dynamics: The Dual Role of Off-Diagonal Couplings in Weakly Bound Nuclei

TL;DR

This work derives a generalized CDCC optical theorem that decomposes total absorption into direct, breakup, and interference components, σ_A = σ_D + σ_B + σ_int, where σ_int arises from off-diagonal imaginary couplings and is typically negative and sizable. The authors demonstrate that full non-diagonal couplings both redistribute flux and create interference that constrains the reaction probability, a feature absent in models that neglect W_1j. Numerical studies for d+^{93}Nb and Li-6+Co/Pb-208 illustrate that ignoring off-diagonal couplings overestimates σ_A and underestimates breakup absorption, while the full calculation enhances breakup channels on heavy targets and preserves flux balance through destructive interference. The findings imply that experimental analyses based on incoherent sums are biased and that full-coupling CDCC is essential for mechanism-resolved extraction of absorption cross sections in weakly bound systems; the generalized theorem and component analysis should apply to broader coupled-channel problems, including transfer channels.

Abstract

Disentangling reaction mechanisms in weakly bound nuclei remains a long-standing challenge, often compounded by the treatment of absorption as an incoherent sum of channel contributions. Within the Continuum-Discretized Coupled-Channels (CDCC) framework, we derive a generalized coupled-channel optical theorem and show that the total absorption cross section, $σ_{\mathrm A}\propto -\langleΨ|W|Ψ\rangle$, decomposes as $σ_{\mathrm A}=σ_{\mathrm D}+σ_{\mathrm B}+σ_{\mathrm{int}}$, where $σ_{\mathrm{int}}$ is a coherent interference term between channel components. For the systems and fragment-target optical potentials considered, $σ_{\mathrm{int}}$ is negative and comparable in magnitude to the direct absorption terms. The off-diagonal imaginary couplings play a dual role, redistributing flux among channels and generating $σ_{\mathrm{int}}$, which is required for flux-balance consistency. Calculations for $d+{}^{93}\mathrm{Nb}$ and ${}^{6}\mathrm{Li}+{}^{59}\mathrm{Co}/{}^{208}\mathrm{Pb}$ show that retaining the full non-diagonal coupling matrix substantially enhances breakup-channel absorption for heavy targets while reducing the total absorption through interference effects. Neglecting off-diagonal imaginary couplings therefore leads to a systematically biased physical picture, overestimating total absorption and severely underestimating breakup contributions, implying that experimental analyses based on incoherent-sum models inherit this bias. Full-coupling CDCC calculations are thus essential for consistent, mechanism-resolved extraction of absorption cross sections in weakly bound systems.

Figures (5)

• Figure 1: Elastic scattering cross sections from CDCC calculations (comparing the full calculation and the approximation with $W_{1j}=0$) for the $d + ^{93}\mathrm{Nb}$ reaction at 25.5 MeV.
• Figure 2: Comparison of absorption cross-section matrices for d+$^{93}$Nb at 25.5 MeV ($l=0$ bins). Left: Full coupling calculation. Right: Approximation with $W_{1j}=0$. The negative off-diagonal values in the full calculation (left) indicate coherent interference flux loss, which is artificially removed in the approximation (right).
• Figure 3: Decomposition of the total absorption cross section $\sigma_\mathrm{A}$ for $^6$Li+$^{59}$Co at 21.5 MeV. Red indicates positive contributions, while blue indicates negative contributions.
• Figure 4: Decomposition in the different bin energies of the total absorption cross section $\sigma_\mathrm{A}$ for $^6$Li+$^{59}$Co at 21.5 MeV. Red indicates positive contributions, while blue indicates negative contributions.
• Figure 5: Decomposition of the total absorption cross section $\sigma_\mathrm{A}$ for $^6$Li+$^{208}$Pb at 33 MeV.