  There is a large body of evidence that atomic nuclei can undergo octupole
distortion and assume the shape of a pear. This phenomenon is important for
measurements of electric-dipole moments of atoms, which would indicate CP
violation and hence probe physics beyond the standard model of particle
physics. Isotopes of both radon and radium have been identified as candidates
for such measurements. Here, we have observed the low-lying quantum states in
$^{224}$Rn and $^{226}$Rn by accelerating beams of these radioactive nuclei. We
report here additional states not assigned in our 2019 publication. We show
that radon isotopes undergo octupole vibrations but do not possess static
pear-shapes in their ground states. We conclude that radon atoms provide less
favourable conditions for the enhancement of a measurable atomic
electric-dipole moment.
