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Feng, Gilmore and Deans 10 discussed the IBM phase structure in terms of a first-order phase transition terminating in an isolated point of a second-order phase transition. Recently, it was shown 11,12 that the model exhibits an additional, previously unrecognized, first-order prolate-oblate phase transition. Here we will show that the general structure of the phase transitions is given by the Landau theory. Let us consider a standard two-dimensional parametrization of the IBM1 Hamiltonian: H(N,r,,x) = r)nd+1^Qx-Qx, (1) where fid is the d-boson number operator and Qx = tfs + s^d + x[d* x d\W the quadrupole operator.

A693 (2001) 533 P. Woods and C. Davids, Ann. Rev. Nucl. Part. Sci. 47 (1997) 541 W. Nazarewicz, Nucl. Phys. A A 6 5 4 (1999) 195c H. Abele, S. Baessler, J. Reich, V. V. Nesvizhevski and O. Zimmer, ILL Ann. Rept. (2001) 78 FIFTY YEARS OF N E U T R O N CAPTURE R O B E R T E. C H R I E N Brookhaven National Laboratory A half century of neutron capture is reviewed. The development of this field and its personal impact on one research scientist are discussed. 1. Introduction Fifty years have passed since capture reaction studies, and especially the neutron capture techniques with high resolution, began to impact the study of nuclei.

2. Extent of the X(5) Region at N = 9 0 Originally, it was thought that 152 Sm was a unique example of phase coexistence and of a nucleus at the phase transitional point (what we call the critical point). The reasoning was based on a particular observable, B(E2 : 2f -> 0^) which is forbidden in the phase coexistence picture since it corresponds to a 2-phonon to zero phonon transition in the anharmonic vibrator set of levels based on the Oj level. This B(E2) value, whose small value was the original clue to the structure of 152 Sm, is 1-2 orders of magnitude smaller in 152 Sm than in other N=90 nuclei where it is known.

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