The Bragg curve is a graphical representation of how ionizing radiation, specifically heavy charged particles, deposits energy as it travels through a medium. Named after the British physicist William Henry Bragg, the curve plots the rate of energy loss—often called stopping power or linear energy transfer (LET)—against the depth of penetration in the absorbing material.
When a heavy charged particle, such as an alpha particle or a proton, penetrates matter, it interacts with the electron clouds of the target atoms through coulomb forces. This process leads to excitation and ionization of the medium.
At high velocities (initial entry into the medium), the particle's interaction time with any given atom is brief, resulting in a relatively low and constant rate of energy loss. As the particle travels deeper, it loses kinetic energy and slows down. According to the Bethe-Bloch formula:
where is energy, is distance, is the particle's charge, and is its velocity. As the velocity decreases, the stopping power increases dramatically. Consequently, the rate of ionization peaks sharply just before the particle comes to a complete rest. This localized spike in energy deposition is known as the Bragg peak. Once the particle's kinetic energy is entirely depleted, the ionization rate drops abruptly to zero.
Different types of ionizing radiation exhibit distinct energy deposition profiles:
The Bragg peak is of fundamental importance in radiation oncology, particularly in proton beam therapy and heavy-ion therapy. By tuning the initial energy of the proton beam, medical physicists can position the Bragg peak precisely within a deep-seated tumor, delivering a lethal dose of radiation to the cancer cells while sparing the surrounding healthy tissue. This highly targeted deposition is a significant advantage over conventional X-ray or gamma therapies.