= Solution
Define the positive mass <collision stopping power> as $S_{\rm col}/\rho=-(1/\rho)dT/dx$. For a projectile of charge $ze$, mass $M\gg m_e$, speed $v=\beta c$ and <Lorentz factor> $\Gamma=(1-\beta^2)^{-1/2}$, the <Bethe stopping formula> can be written
$$
\boxed{\frac{S_{\rm col}}\rho=4\pi N_A r_e^2m_ec^2\frac{Z}{A}\frac{z^2}{\beta^2}\left[\frac12\ln\!\left(\frac{2m_ec^2\beta^2\Gamma^2T_{\max}}{I^2}\right)-\beta^2-\frac\delta2-\frac CZ\right].}
$$
Here $Z$ is the absorber <atomic number>, $A$ its molar <mass>, $I$ its mean excitation <energy>, $r_e=e^2/(4\pi\epsilon_0m_ec^2)$, and $N_A$ the <Avogadro constant>. Also
$$
T_{\max}=\frac{2m_ec^2\beta^2\Gamma^2}{1+2\Gamma m_e/M+(m_e/M)^2}.
$$
The optional $\delta$ and $C/Z$ represent density and shell corrections. For a very heavy projectile $T_{\max}\simeq2m_ec^2\beta^2\Gamma^2$, and the bracket reduces to $\ln(2m_ec^2\beta^2\Gamma^2/I)-\beta^2$ when those corrections are neglected. If $T$ denotes remaining projectile <kinetic energy>, the printed $dT/(\rho dx)$ is negative; the conventional positive <stopping power> has the minus sign above.<PSTAR and ASTAR database methods by NIST>[Section 3.5, use of Bethe theory at high energies and measured low-energy stopping powers]{ref}
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