Bethe–Bloch Stopping Power Calculator

Example Data Table

Values are illustrative and depend on chosen corrections and material parameters.

Formula Used

How to Use This Calculator

1. Select a projectile preset, or choose “Custom projectile”.
2. Pick a material preset, or switch to “Custom material”.
3. Enter the kinetic energy in MeV and verify all fields.
4. If you know correction terms, enter δ and C; otherwise keep them zero.
5. Press Calculate to view results immediately under the header.
6. Use the download buttons to export the last result as CSV or PDF.

Tip: For compounds, use effective Z, A, and I from a trusted reference.

Notes and Good Practices

• Bethe–Bloch applies to moderately relativistic heavy charged particles in matter.
• At very low energies, additional corrections may be required for accurate results.
• For extremely high energies, provide a reasonable density correction δ to avoid overestimation.

Understanding Bethe–Bloch Stopping Power

1) What the calculator reports

This tool estimates the mean collisional energy loss of heavy, charged particles as they traverse matter. Results are shown as mass stopping power (MeV·cm²/g) and linear stopping power (MeV/cm). The first is material‑density independent, while the second directly scales with density and is useful for thickness calculations.

2) Inputs that matter most

The projectile charge z raises stopping power roughly with z², so heavier ions can deposit energy much more strongly. Kinetic energy controls the relativistic factors β and γ, which set both the 1/β² rise and the logarithmic growth inside the bracket term.

3) Material parameters and typical ranges

The absorber enters via Z/A, density ρ, and the mean excitation energy I. Many solids have I on the order of 100–300 eV, while high‑Z materials can be several hundred eV. If you are modeling compounds, use effective values from a trusted database.

4) Why the correction terms exist

At high energies, polarization of the medium reduces the logarithmic rise; this is captured by the density effect correction δ. At lower energies, atomic shell structure modifies the stopping power; the optional shell term is represented here using C/Z. When unknown, leaving both at zero provides a reasonable baseline.

5) Maximum energy transfer (Tmax)

The calculator computes Tmax, the maximum kinetic energy transferable to an electron in a single collision. For heavy projectiles, Tmax depends mainly on β²γ² and remains well below the projectile energy, which supports the “continuous slowing down” picture in many detector and shielding estimates.

6) Using mass stopping power for thickness

A quick design workflow is: use the mass stopping power to compare materials, then multiply by density to obtain MeV/cm for a specific medium. For a slab of thickness x, the mean energy loss is roughly ΔE ≈ (−dE/dx)·x in the regime where stopping power does not change rapidly with energy.

7) Practical applications

Stopping power is central to particle detectors, calorimetry, radiation damage estimates, and medical beam planning. Engineers also use it to select absorber materials, compare sensor substrates, and estimate heating or dose deposition when charged particles pass through structural components.

8) Interpreting results responsibly

Bethe–Bloch describes the mean collisional loss; it does not model straggling, nuclear interactions, or radiative losses for electrons. For very low energies, additional corrections may be necessary. For precision work, cross‑check with validated stopping power tables and ensure the chosen I and δ reflect your material and energy range.

FAQs

1) What does “mass stopping power” mean?

It is the energy loss per distance normalized by density, reported in MeV·cm²/g. It lets you compare materials without committing to a specific density, then convert to MeV/cm by multiplying by ρ.

2) Which inputs most strongly affect the result?

Projectile charge z and speed (via β) dominate. Stopping power scales roughly with z² and includes a 1/β² factor, while material dependence is mainly through Z/A, I, and any correction terms you provide.

3) What should I enter for I if I don’t know it?

Use a material preset if possible. Otherwise, start with 100–300 eV for many solids, then refine using a trusted reference for your exact material or compound to improve agreement with published tables.

4) When should I use the density correction δ?

At higher energies, δ becomes important because medium polarization reduces the logarithmic rise. If you are working in the multi‑hundreds of MeV to GeV range, supplying δ can prevent overestimation.

5) Why can results differ from published tables?

Tables may include additional corrections, different I values, or mixture rules for compounds. Small changes in I and δ can noticeably shift results. Use consistent material definitions and verify units before comparing.

6) Does this apply to electrons?

This implementation targets heavy charged particles where the Bethe–Bloch form is commonly used. Electrons require different treatment because of identical‑particle effects and significant radiative losses at higher energies.

7) Can I estimate energy loss through a thickness?

Yes. Convert to linear stopping power (MeV/cm), multiply by thickness for a first estimate, and remember stopping power changes with energy. For large losses, iterate: reduce energy, recompute, and sum over steps.