We solve the Klein-Gordon equation in the presence of a spatially one-dimensional WoodsSaxon potential. The scattering solutions are obtained in terms of hypergeometric functions and the condition for the existence of transmission resonances is derived. It is shown how the zeroreflection condition depends on the shape of the potential.

We solve the Klein-Gordon equation in the presence of a spatially one-dimensional cusp potential. The bound state solutions are derived and the antiparticle bound state is discussed.

The coalescence of liquid drops induces a higher level of complexity compared to the classical studies about the aggregation of solid spheres. Yet, it is commonly believed that most findings on solid dispersions are directly applicable to liquid mixtures. Here, the state of the art in the evaluation of the flocculation rate of these two systems is reviewed. Special emphasis is made on the differences between suspensions and emulsions. In the case of suspensions, the stability ratio is commonly evaluated from the initial slope of the absorbance as a function of time under diffusive and reactive conditions. Puertas and de las Nieves (1997) developed a theoretical approach that allows the determination of the flocculation rate from the variation of the turbidity of a sample as a function of time. Here, suitable modifications of the experimental procedure and the referred theoretical approach are implemented in order to calculate the values of the stability ratio and the flocculation rate corresponding to a dodecane-in-water nanoemulsion stabilized with sodium dodecyl sulfate. Four analytical expressions of the turbidity are tested, basically differing in the optical cross section of the aggregates formed. The first two models consider the processes of: a) aggregation (as described by Smoluchowski) and b) the instantaneous coalescence upon flocculation. The other two models account for the simultaneous occurrence of flocculation and coalescence. The latter reproduce the temporal variation of the turbidity in all cases studied (380 ≤ [NaCl] ≤ 600 mM), providing a method of appraisal of the flocculation rate in nanoemulsions.

We solve the Klein-Gordon equation in the presence of a spatially one-dimensional cusp potential. The scattering solutions are obtained in terms of Whittaker functions and the condition for the existence of transmission resonances is derived. We show the dependence of the zero-reflection condition on the shape of the potential. In the low momentum limit, transmission resonances are associated with half-bound states. We express the condition for transmission resonances in terms of the phase shifts.PACS numbers: 03.65. Pm, 03.65.Nk, 03.65.Ge The study of low-momentum scattering of nonrelativistic particles by one-dimensional potentials is a well studied and understood problem [1]. Here we have that, as momentum goes to zero, the reflection coefficient goes to unity unless the potential V (x) supports a zero energy resonance. In this case the transmission coefficient goes to unity, becoming a transmission resonance [2]. Recently, this result has been generalized to the Dirac equation [3], showing that transmission resonances at k = 0 in the Dirac equation take place for a potential barrier V = V (x) when the corresponding potential well V = −V (x) supports a supercritical state. Kennedy [4] has shown that this result is also valid for a Woods-Saxon potential. More recently, transmission resonances and half-bound states have been discussed for a Dirac particle scattered by a cusp potential [5,6] as well as for a class of short range potentials [7]. The bound states for scalar relativistic particles satisfying the Klein-Gordon equation are qualitatively different from the previous case. Here, for short-range attractive potentials the Schiff-Snyder effect [8,9,10,11,12,13,14] takes place, i.e for a given potential strength two bound states appear, one with positive norm and another with negative norm. Such states can be associated with a particle-antiparticle creation process. No antiresonant states appear [11,12].The absence of resonant overcritical states for the Klein-Gordon equation in the presence of short-range potential interactions does not prevent the existence of transmission resonances for given values of the potential.Quantum effects associated with scalar particles in the presence of external potentials have been extensively discussed in the literature [10,14]. Among quantum effects, we have that transmission resonance is one of the most interesting phenomena. For given values of the energy and the proper choice of the shape of the effective barrier, the probability of transmission reaches a maximum such as that obtained in the study of superradiance [14], where the amplitude of the scattered solutions by a rotating Kerr black hole is even larger than the amplitude of the incident wave. Analogous phenomena can also be obtained due to the presence of strong electromagnetic potentials [15].Recently, transmission resonances for the Klein-Gordon equation in the presence of a Woods-Saxon potential barrier have been computed [16]. The transmission coefficient as a function of the energy and the potential am...

The phase-integral approximation devised by Fröman and Fröman, is used for computing cosmological perturbations in the power-law inflationary model. The phase-integral formulas for the scalar and tensor power spectra are explicitly obtained up to ninth-order of the phase-integral approximation. We show that, the phase-integral approximation exactly reproduces the shape of the power spectra for scalar and tensor perturbations as well as the spectral indices. We compare the accuracy of the phase-integral approximation with the results for the power spectrum obtained with the slow-roll and uniform approximation methods.