\item$Z_1$, $M_1$ are the charge and mass numbers of the projectile
\item$Z_2$, $M_2$ are the charge and mass numbers of the target
\item$\mu=\frac{M_1 M_2}{M_1+ M_2}$ is the reduced mass number
\item$E_{\gamma}$ is the $\gamma$-ray energy in MeV
\item$E_{\text{i}}$ is the energy of relative motion of the projectile and target in the c.m.\ frame in the initial state in MeV$^{\ast}$
\item$\omega=\frac{(2J_f+1)(2l_{\text{i}}+1)}{(2J_1+1)(2J_2+1)(2l_{\text{f}}+1)}$ is the spin statistical weight factor
\item$\left( l_{\text{i}}010\vert l_{\text{f}}0\right)$ is the Clebsch-Gordan coefficient
\item$J_1$, $J_2$, $J_f$ are the spins of the projectile, target, and final state
\item$l_{\text{i}}$, $l_{\text{f}}$ are the orbital angular momenta in the initial and final state
\item$R_{l_{\text{i}}1 l_{\text{f}}}$ is the radial integral in units of fm$^{3/2}$
\end{itemize}
$^{\ast}$Note that Rolfs is a little unclear on which energy should be used here. It is either the energy of the relative motion in the c.m.\ frame or the energy of the projectile in the c.m.\ frame. These energies differ by a factor of $M_2/(M_1+M_2)$.
\vspace{0.5cm}
\noindent The ``experimental`` cross section is then found as,
\item$r$ is the projectile-target separation in fm
\item$\mathcal{O}_{\text{E}1}(r)=\left[(\rho^2-2)\sin\rho+2\rho\cos\rho\right]3r /\rho^3$ is the E1 multipole operator and $\rho= k_{\gamma}r$ where $k_{\gamma}=\tfrac{E_{\gamma}}{\hbar c}$
\item$u_{\text{c}}(r)$ is the initial-state (continuum) radial wave function
\item$u_{\text{b}}(r)$ is the final-state (bound) radial wave function
\end{itemize}
Note that $u_{\text{c}}(r)$ has units of fm$^{-1}$, $u_{\text{b}}(r)$ has units of fm$^{-3/2}$, and $\mathcal{O}_{\text{E}1}(r)$ has units of fm, so the integrand has units of fm$^{1/2}$ and the integral has units of fm$^{3/2}$.
\item$R_0= r_0(M_1^{1/3}+ M_2^{1/3})$ is the nuclear radius, where the value $r_0=1.36$~fm is used
\item$j_{l_{\text{f}}}$ is the regular spherical Bessel function of order $l_{\text{f}}$
\item$F_{l_{\text{i}}}$, $G_{l_{\text{i}}}$ are the spherical Coulomb functions
\item$K_{\text{i}}=[2m(E_{\text{i}}+V_0)]^{1/2}/\hbar$, where $m=\mu m_{\text{u}}$ is the reduced mass, $E_{\text{i}}>0$ is the energy of relative motion of the projectile and target in the c.m.\ frame in the initial (continuum) state, and $V_0>0$ is the depth of the square-well potential
\item$k_{\text{i}}=(2mE_{\text{i}})^{1/2}/\hbar$
\item$\sigma_{l_{\text{i}}}-\sigma_0$ is the usual Coulomb phase difference
\item$\delta_{l_{\text{i}}}$ is the nuclear phase shift$^{\ast}$
\item$A$ is a normalisation constant which is adjusted so that the wave function is continuous at $r=R_0$
\end{itemize}
$^{\ast}$Note that Rolfs assumed the nuclear phase shifts to be given by the hard-sphere phase shifts at the nuclear radius $R_0$.
The bound radial wave function has units of fm$^{-3/2}$ and is given by,
\begin{equation}
u_{\text{b}}(r) \; = \;\frac{u_{l_{\text{f}}}(r)}{r}\; = \; A
\begin{cases}
\; j_{l_{\text{f}}} (K_{\text{f}}r) \; , & r \leq R_0 \\
B \; W_{\eta, l_{\text{f}}} (\kappa_{\text{f}} r) / r \; , & r > R_0
\end{cases}
\end{equation}
where,
\begin{itemize}
\item$j_{l_{\text{f}}}$ is the regular spherical Bessel function of order $l_{\text{f}}$
\item$W_{\eta, l_{\text{f}}}$ is the Whittaker function
\item$K_{\text{f}}=[2m(E_{\text{f}}+V_0)]^{1/2}/\hbar$, where $m=\mu m_{\text{u}}$ is the reduced mass, $E_{\text{f}}<0$ is the energy of relative motion of the projectile and target in the c.m.\ frame in the final (bound) state, and $V_0>0$ is the depth of the square-well potential
\item$A$, $B$ are normalisation constants which are adjusted so that the wave function is continuous at $r=R_0$ and $\int_0^{\infty} u^{\ast}_{l_{\text{f}}}(k_{\text{f}} r) u_{l_{\text{f}}}(k_{\text{f}} r)\;\text{d}r =1$
\end{itemize}
\vspace{0.5cm}
\noindent The depth of the square-well potential, $V_0$, is adjusted to reproduce the binding energy of the final state, i.e., so that the logarithmic derivatives of the interior and exterior wave functions match at the channel radius,
