Nuclear shapes

As we have seen, the nucleons reside in well-defined orbitals in the nucleus that can be understood in a relatively simple quantum mechanical model, the shell model. In this model, the properties of the nucleus are dominated by the wave functions of the one or two unpaired nucleons. Notice that the bulk of the nucleons, which may even number in the hundreds, only contribute to the overall central potential. These core nucleons cannot be ignored in reality and they give rise to large-scale, macroscopic behavior of the nucleus that is very different from the behavior of single particles. There are two important collective motions of the nucleus that we have already mentioned that we should address collective or overall rotation of deformed nuclei and vibrations of the nuclear shape about a spherical ground-state shape. 

Gisselsson, D., Bjork, J., Hoglund, M., Mertens, F., Cin, P. D., Akerman, M., and Mandahl, N. 2001. Abnormal nuclear shape in solid tumors reflects mitotic instability. Am. J. Pathol. 158 199-206. 

The structures of the neutron-rich isotopes 97Y, 98Y and 99Y reflect with special clearness the rapid change of the nuclear shape at neutron number 60. The discovery of a new isomer in 97Y has provided evidence for the shell-model character of this nucleus even at high excitation energies while 99Y shows the properties of a symmetric rotor already in the ground state. The level pattern of the intermediate isotope 98Y indicates shape coexistence. 

Y most probably has coexisting nuclear shapes with a well developed rotational band on the 495 keV level and other levels which seem to be rather of vibrational nature. 

Nuclear Shape Transitions and Dynamical Supersymmetries in the Pt Region... 

The 1S-2S transition frequency is so well known [18] that further precision at this time will not yield a better value for the Lamb shift and nuclear shape corrections. Nevertheless, further precision is desirable both for advancing the frontier of optical metrology, and because the transition has potential applications for... 

The spectrum of hydrogen is composed of a major structure, determined by the Rydberg constant, QED corrections like the Lamb shift and finally nuclear shape... 

Fig. 1. Nuclear shapes and nuclear quadrupole moments (a) prolate nucleus, I> 1, Q> 0 (b) spherical nucleus, I = 1/2. eQ — 0 (c) oblate nucleus, I> 1, eQ <0...

Toth, J.I., et al. (2005). Blocking protein farnesyltransferase improves nuclear shape in fibroblasts from humans with progeroid syndromes. Proc Natl Acad Sci USA 102 12873-12878. 

Thomas CH et al (2002) Engineering gene expression and protein synthesis by modulation of nuclear shape. Proc Natl Acad Sci USA 99(4) 1972-1977... 

The experimental data and nuclear shape calculations convincingly show that the well-deformed nuclei have axial symmetry at low and moderate angular momenta. At the same time in a wider neutron number region N = 84—120), departures were observed from axial symmetry in several Nd, Sm, Gd, Pt, and other nuclei. An analysis performed by Casten (2000) shows that the lack of axial symmetry is associated rather with y-softness than with stable triaxial deformation. 

Several other coexisting nuclear shapes have also been identified in Dy with different P and y deformation parameters (O Fig. 2.22b). 

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