Continuous Slowing Down Approximation Range¶
CSDA range integrates reciprocal total stopping power to estimate a charged particle's path length while treating energy loss as continuous rather than fluctuating.
Core Idea¶
CSDA range estimates a charged particle's traveled path from its initial energy to rest. It assumes a smooth local energy-loss rate given by total stopping power and integrates the reciprocal of that rate over energy. This suppresses collision-by-collision energy fluctuations; the output is an approximation to average path length, not the distance every particle travels.[^ref-2031a147f136]
Scope of Application¶
NIST provides CSDA range tables for electrons (ESTAR), protons (PSTAR) and helium ions (ASTAR). A checked PSTAR row for a 10 MeV proton in liquid water gives total stopping power 45.67 MeV cm²/g, CSDA mass range 0.1230 g/cm² and separate projected range 0.1228 g/cm². A checked ESTAR default-table row for a 1 MeV electron in aluminum gives total stopping power 1.486 MeV cm²/g and CSDA mass range 0.5546 g/cm². Both outputs depend on the full species/material stopping curve, not merely the stopping-power value at the stated starting energy.[ref-d5d395c73df1][ref-c877634b5f50][ref-480b406dcd18][ref-b1f53e3a44e8]
Clarity¶
Track length and forward penetration are different when scattering bends a particle's route. CSDA represents path length; projected range represents depth. NIST tabulates some ranges as mass thickness (g/cm²), not automatically centimeters.[ref-2031a147f136][ref-c877634b5f50]
Manages Complexity¶
One integral compresses many microscopic losses into a reproducible comparison scale. It does not provide the spread of actual stopping depths or account for every transport detail.
Abstract Reasoning¶
Given total stopping power \(S(E)\), integrate \(1/S(E)\) from zero to initial energy. A high local stopping power contributes less path for a given energy loss. For a shielding-depth question, use directional transport information rather than relabeling the CSDA number.
Knowledge Transfer¶
The same computation transfers among charged-particle species when the correct stopping curve is supplied. It does not automatically describe neutral-particle attenuation or other processes called “slowing.” No prime parent is asserted from the generic word range.
[^ref-2031a147f136]: NIST, STAR appendix, definitions of CSDA range, projected range and detour factor.
[^ref-d5d395c73df1]: NIST, STAR introduction, species and table scope of ESTAR/PSTAR/ASTAR.
[^ref-c877634b5f50]: NIST, PSTAR/ASTAR program description, total stopping power, mass-range outputs and separate projected-range method.
[^ref-480b406dcd18]: NIST, PSTAR text-only program, submitted 2026-10-01 with Water, Liquid and 10 MeV (default energies off); official result row T=1.000E+01, total stopping 4.567E+01, CSDA 1.230E-01, projected 1.228E-01. The POST result URL is not stable; these inputs reproduce it.
[^ref-b1f53e3a44e8]: NIST, ESTAR text-only program, submitted 2026-10-01 with 13: Aluminum and default energies; official 1.000E+00 MeV row, total stopping 1.486E+00, CSDA 5.546E-01. The POST result URL is not stable; these inputs reproduce it.
Neighborhood in Abstraction Space¶
Continuous Slowing Down Approximation Range sits in a sparse region of the domain-specific corpus (83rd percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Unclustered & Miscellaneous (2551 abstractions)
Nearest neighbors
- Bethe formula — 0.84
- Momentum-Transfer Cross Section — 0.83
- Lorden's Inequality — 0.82
- Residence Time (Statistics) — 0.82
- Brownian Skorokhod Embedding — 0.81
Computed from structural-signature embeddings · 2026-10-08