 conformal field theory description a D-brane is an object with a well-defined position, in the full string field theory appropriate for incorporating quantum fluctuations in its position, a D-brane is regarded as an object with thickness of the order of the string scale. In particular, as discussed in [@li], an analysis of the tachyonic lump solution in the string field theory, which may be considered as a D-brane [@Moeller:2000jy], suggests that the widths of the D-brane in the transverse dimensions are about $1.55\ell_s$. In the setting of [@li], there are open strings between the D7-branes and D3-branes that satisfy Neumann (N) and Dirichlet (D) boundary conditions, respectively, which we call ND particles. Their gauge couplings with the gauge fields on the D7-branes are $$\frac{1}{g_{37}^2} = \frac{V}{g_7^2}~,~\,
 \label{coupl}$$ where $g_7$ is the gauge coupling on the D7-branes, and $V$ denotes the volume of the extra four spatial dimensions of the D7 branes transverse to the D3-branes [@giveon]. If there were no D-particle foam, the Minkowski space dimensions would be non-compact, in which case $V$ in (\[coupl\]) would approach infinity and $g_{37} \to 0$. In such a case, Standard Model particles would have no interactions with the ND-particles on the compactified D3-brane (D-particle’). Thus, our Ansatz for the gauge couplings between the gauge fields on the D7-branes and the ND-particles is [@li] $$\frac{1}{g_{37}^2} = \frac{V_{A3} R'}{(1.55\ell_s)^4}
\frac{\ell_s^4}{g_7^2} = \frac{V_{A3} R'}{(1.55)^4} \frac{1}{g_{7}^2}~.~\,
 \label{coupl-N}$$ where $R'$ is the radius of the fourth space dimension transverse to the D3-branes. We remind the reader that the D7-brane gauge couplings are such that $g_7^2 \propto g_s$, in accordance with general properties of D-branes and their equivalence at low energies to gauge theories [@giveon].

The amplitudes describing the splitting and capture of a photon state by a D-particle may be calculated in this picture using the standard techniques outlined in [@ben