Reconciling Coulomb Dissociation and Radiative Capture Measurements

We calculate the energy spectrum for ${}^8\mathrm{B}$ dissociation on a Pb target to all orders in the Coulomb and nuclear fields, and show that the slope of $S_{17}(E)$ obtained in previous analyses of Coulomb dissociation data is too steep, due to deficiencies in the conventional first-order analysis that was used. With a more complete theory that avoids the far-field approximation and includes $E2$, nuclear and dynamical projectile polarization, the disagreement between indirect and direct methods for determining the $S_{17}(E)$ slope and the extrapolated $S_{17}(0)$ values is reduced significantly.

Figure 1

Decay energy spectra for ${}^8\mathrm{B}$ on ${}^{208}\mathrm{P}\mathrm{b}$ at $51.9\mathrm{M}\mathrm{e}\mathrm{V}/n$ and impact parameter $b=20\mathrm{f}\mathrm{m}$. The FF approximation for $E1$ and $E2$ transitions is compared to the unrestricted first-order $E0$, $E1$, and $E2$ calculations in (a). The summed spectra are compared to dynamic calculations in (b).

Figure 2

Decay energy spectrum obtained in the full dynamic calculation at $51.9\mathrm{M}\mathrm{e}\mathrm{V}/n$ (solid curve) is compared to the results of first-order $E1$ and $E1+E2$ transitions in the far-field approximation. The minimum impact parameter is $b_{\min }=12\mathrm{f}\mathrm{m}$ in (a) and 30 fm in (b).

Figure 3

Measured and calculated angular distributions of the ${}^7\mathrm{B}\mathrm{e}+p$ center-of-mass system for a 0.5–0.75 MeV relative energy cut. The calculated distributions have been filtered by the experimental acceptance of the RIKEN experiment [2]. The dynamic calculation has been multiplied by a factor of 1.2.

Figure 4

Calculated ratio of relative energy spectra at $51.9\mathrm{M}\mathrm{e}\mathrm{V}/n$ obtained in the full calculation and in the first-order $E1$ FF approximation, for the three indicated values of the minimum impact parameter.