File:Shape deformations 1.jpg

Summary

Regions of deformed nuclei.

The nuclei, for which both N and Z are even numbers (called even-even nuclei), have ground-state spin-parity 0+, without exception. The overwhelming majority of these has 2+ first excited state. Writing the excitation energies of the lowest-lying 2+ and 4+ states as E(2+1) and E(4+1), the filled circle represents even-even nuclei, in which E(4+1)/E(2+1) > 2.7. The data are taken from http://www.nndc.bnl.gov/ensdf/. The line of β stability is indicated by the thin long-dashed curve. The thin straight lines parallel to the x and y axes show the magic numbers of protons and neutrons, which are known in nuclei along the β stability line. Except for very light nuclei (Z ≤ 8) the neutron drip line, at which nuclei become unstable for neutron emission, is not known experimentally. The boarder of deformed nuclei shown for the neutron-rich region of medium-heavy nuclei is often equal to the boarder of neutron-rich nuclei, for which the energy of the 4+1 state is presently known. The criterion of deformed even-even nuclei can be made in one of the following four ways; (i) the excitation spectra exhibit an approximate I(I+1) energy dependence indicating rotational structure. In the figure the (rather arbitrary) criterion E(4+1)/E(2+1) > 2.7 is chosen. (ii) B(E2) values are much larger than single particle or collective vibrational estimates. (iii) The excitation energy of the first excited 2+ state is especially low, say by a factor of at least 5, compared with twice the odd-even mass difference, 2Δ. We note that the ratio, E(2+1)/2Δ, has the mass-number dependence of about A1/6. (iv) The ratio, Q(2+1)2/B(E2;2+1→0+gr), where Q(2+1) expresses the quadrupole moment of the lowest 2+ state while B(E2) denotes the reduced probability of electric-quadrupole transitions, is approximately equal to 4.10, which is the value for the ideal collective rotation.

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