welldeformed

Welldeformed, often written as well-deformed, is a term used in nuclear physics to describe atomic nuclei whose ground-state shape differs significantly from a sphere, typically taking a prolate or oblate ellipsoidal form. This contrasts with spherical nuclei and with soft or transitional nuclei that do not sustain a stable deformation. In the collective model, well-deformed nuclei have a relatively large quadrupole deformation parameter (beta2) and exhibit a characteristic rotational behavior.

In well-deformed nuclei, the intrinsic shape supports a sequence of rotational states that form band structures. The energy levels of these bands follow a pattern close to E(I) ≈ (ħ2/2I) I(I+1), and E2 transitions within the band are typically strong. Experimental signatures include large B(E2) values for transitions such as 0+ → 2+, and the ratio of energies R4/2 = E(4+)/E(2+) lying near the rotor value of about 3.3 to 3.5. The moment of inertia tends to be larger and changes smoothly with spin, reflecting the stable deformation.

Common regions where well-deformed nuclei are found include the rare-earth elements around A ≈ 150–160 and certain actinides. Examples often cited include isotopes of Nd, Sm, Gd, and Dy, which display clear rotational spectra and strong collective behavior. The concept aids understanding of collective motion, shape coexistence, and the evolution of nuclear deformation with neutron or proton number. The term is relative and model-dependent, and deformations can vary with spin, temperature, or external conditions.