We continue our study of the stability of designer gravity theories, where one considers anti-de Sitter gravity coupled to certain tachyonic scalars with boundary conditions defined by a smooth function W . It has recently been argued that there is a lower bound on the conserved energy in terms of the global minimum of W , if the scalar potential arises from a superpotential P and the scalar reaches an extremum of P at infinity. We show, however, that there are superpotentials for which these bounds do not hold.PACS number:

The experimental results on the laser isotope separation of the neodimium, samarium, europium, gadolinium, dysprosium, and erbium by the selective two-step photoionization are given. The rare earth elements have been chosen for the investigation because they constitute a good series of the very similar but different atoms that are heavy enough and allow experiments to be carried out that are representative enough. The experimental technique developed for the laser isotope separation experiments has been applied to measure the excitation energy transfer cross sections at the collisions in the gas of the same atoms ((153)Eu ? (151)Eu, sigma = 1.4 x 10(-13) cm(2)). The combination of the selective two-step photoionization and ion mass filtration allowed us to develop a very convenient technique for the precise measurement of hyperfine structure in the spectrum of odd isotopes. The examples of dysprosium and erbium are given. The technique is good for the rare and unstable isotopes as well. The ionization cross sections for the transition starting off the excited level have been estimated ( approximately 10(-17) cm(2)). For the example of gadolinium the possibility of creating neutral atomic vapor dense enough for laser isotope separation by the electron-beam evaporation technique has been demonstrated.

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