The Spin-Orbit Staircase

Plate 50 speaks for itself: “Magic landings.”

The Physics

Nuclei with certain numbers of protons or neutrons are extra stable. A strong spin–orbit term in the nuclear potential splits each level into j = ℓ ± ½ and opens large gaps at the magic numbers.

U = V(r) − V_ls(r) ℓ·s

• U: single-nucleon potential, J
• V(r): central potential, J
• V_ls(r): spin–orbit strength, J
• ℓ: orbital angular momentum (units of ħ)
• s: spin (units of ħ)

Spin-orbit splits levels: j = ℓ ± 1/2. Big gaps at 2, 8, 20, 28, 50, 82, 126.

Sources

• M. G. Mayer, Phys. Rev. 75, 1969 (1949).
• O. Haxel, J. H. D. Jensen, H. E. Suess, Phys. Rev. 75, 1766 (1949).

On the poster

Plate 050, “The Spin-Orbit Staircase”: the pixel-art plate with its slogan “Magic landings.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.