Appendix

In this section we list some standard results used in the analysis in this paper [4].

$$j_{\ell + 1}(x) = {\ell \over x} j_{\ell}(x) - j_{\ell}'(x)$$ (38)

$$j_{\ell - 1}(x) = {{\ell + 1} \over x} j_{\ell}(x) + j_{\ell}'(x)$$ (39)

$$\mathrm{e}^{{\mathrm{i}} {\bf k} \cdot {\bf r}} = 4 \pi \sum_{\el... ...\ell}(k r)~{\bar Y}_{\ell m} (\Omega_{\bf k})~{\bar Y}_{\ell m}(\Omega_{\bf r})$$ (40)

$$\int_{a}^{b} j_{\ell}(mx) j_{\ell}(nx) x^2 \mathrm{d}x$$

$$\qquad = \frac{1}{m^2 - n^2} \left[ x^2 \left\{ n j_{\ell}(m x) j_{\ell-1}(n x) - m j_{\ell-1}(m x) j_{\ell}(n x) \right\} \right]_{a}^{b}$$ (41)

$$\int_{a}^{b} j_{\ell}^2 (m x) x^2 \mathrm{d}x = {\textstyle{1 \ov... ...biggl[ x^2 \biggl\{ x j_{\ell}^2 (m x) + x j_{\ell - 1}^2 (m x) \biggr. \biggr.$$

$$\biggl. \biggl. \qquad - {2\ell + 1 \over m} j_{\ell - 1} (m x) j_{\ell} (m x) \biggr\} \biggr]_{a}^{b}$$ (42)