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Felix Bloch helped explain how particles slow in matter

In Copenhagen in the early 1930s, Felix Bloch refined Hans Bethe’s theory of how charged particles lose energy in matter, work remembered in the Bethe–Bloch formula.

Felix Bloch
Felix Bloch · 1905–1983
Person
Felix Bloch
Lived
1905–1983
Field
Physics
From
Swiss-American

The story

When a fast charged particle, such as a proton or an alpha particle, passes through a material, it gradually loses energy by exciting and ionising the atoms along its path. How quickly it slows down, a quantity called stopping power, was one of the central questions of early nuclear physics. Niels Bohr had written a famous classical treatment of the problem in 1913, and he spent years hoping to bring theory into closer agreement with experiment.

In the autumn of 1931 Felix Bloch, then a young theorist who had already made his name with the quantum theory of metals, arrived at Bohr's institute in Copenhagen on an Oersted fellowship. In long conversations Bohr gradually drew him into the stopping problem. There was a puzzle to solve. Bohr's classical calculation predicted larger energy losses than were seen for alpha and beta particles, while Hans Bethe had produced a more accurate, fully quantum mechanical result in 1930. It was not clear why the two approaches disagreed.

Bloch resolved the discrepancy. He showed that the Bohr and Bethe formulas were opposite limiting cases of a single, more general result, depending on how the phase of the interaction changed as the particle passed close to an atom. Bohr was pleased. Bloch finished the paper after returning to Leipzig as a lecturer in 1932, and it appeared in the Annalen der Physik in 1933. Late in 1932 he added a second, very practical refinement: using the Thomas–Fermi model of the atom, he showed that the average excitation energy of an atom, the one number that describes the material in Bethe's theory, is roughly proportional to its atomic number. That paper appeared in the Zeitschrift für Physik in 1933.

Bethe's equation combined with Bloch's estimate became widely known as the Bethe–Bloch formula, and a further term that improves its accuracy is still called the Bloch correction. Within months of this work Hitler came to power, and Bloch, who was Jewish, left Leipzig for good.

The formula served for decades as the basis for more refined calculations that added screening and straggling effects, and its modern descendants predict stopping power to within a few percent at higher energies. Physicists rely on them to design particle detectors and to work out how beams of protons and heavier ions deposit their energy in the body, knowledge of great practical importance for radiation therapy against cancer.

Why it matters

Knowing how charged particles lose energy is essential for designing particle detectors and for planning radiation treatments that use proton and ion beams.

About Felix Bloch

Swiss-born physicist who laid the quantum foundations of solid-state physics, discovered nuclear magnetic resonance – the basis of MRI – and became CERN’s first director-general.

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Felix Bloch
1905–1983 · Physics
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Another act of tikkun olam. This is part of tikkun olam, the Jewish idea of repairing the world, and every one of us can add to it.

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