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:

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The population inversion in a three-level atomic system, interacting with two coherent laser pulses, occurs from the first level to the third level at the optimal detunings of the laser frequencies near the two-photon resonance. An examination is performed to see whether the energy density and time-delay of the photoionizing laser can significantly influence the ion yield for the case where the atom interacts with two coherent pulses and one photoionizing pulse incoherently coupled. The well-known three-colour, three-step, three-photon ionization scheme, which is available for the selective photoionization of 168Yb, is chosen for use in this research with the Bloch equation. It is revealed that the proper time-delay and energy density enable us to achieve higher efficiency for the selective photoionization of 168Yb, regardless of the Doppler-broadening, though the efficiency and selectivity of coherent excitation are prominently enhanced by applying the optimal detunings.

A principle for the e%cient excitation of a three-level medium in a selective photoionization method is examined. It is shown that with special detunings for a given set of the laser-atom interaction the third-level population can be maximized. The expression of the optimal detunings is derived near the two-photon resonance region. It is shown that if the optimal detuning method is applied to three-level systems of Yb and Ca, the first-level populations are inverted to their corresponding third levels by about 100% and 86%, respectively. Application of this method to a Doppler-broadened medium is discussed and it is found that the optimal detuning method with counterpropagating waves will be very effective for selective ionization of wanted atoms.PACS number(s): 32.80.Fb, 32.80.8x

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.