Solving the Coulomb scattering problem using the complex scaling method

Based on the work of Nuttall and Cohen [Phys. Rev. {\bf 188} (1969) 1542] and Resigno et al{} [Phys. Rev. A {\bf 55} (1997) 4253] we present a rigorous formalism for solving the scattering problem for long-range interactions without using exact asymptotic boundary conditions. The long-range interaction may contain both Coulomb and short-range potentials. The exterior complex scaling method, applied to a specially constructed inhomogeneous Schr\"odinger equation, transforms the scattering problem into a boundary problem with zero boundary conditions. The local and integral representations for the scattering amplitudes have been derived. The formalism is illustrated with numerical examples.Comment: 3 pages, 3 figure

Predicting participation in group parenting education in an Australian sample: The role of attitudes, norms, and control factors

We examined the theory of planned behavior (TPB) in predicting intentions to participate in group parenting education. One hundred and seventy-six parents (138 mothers and 38 fathers) with a child under 12 years completed TPB items assessing attitude, subjective norms, perceived behavioral control (PBC), and two additional social influence variables (self-identity and group norm). Regression analyses supported the TPB predictors of participation intentions with self-identity and group norm also significantly predicting intentions. These findings offer preliminary support for the TPB, along with additional sources of social influence, as a useful predictive model of participation in parenting education

Comparison of Methods for the Purification of Alpha-1 Acid Glycoprotein from Human Plasma

Alpha-1 acid glycoprotein (AGP) is a highly glycosylated, negatively charged plasma protein suggested to have anti-inflammatory and/or immunomodulatory activities. Purification of AGP could be simplified if methods that exploit its high solubility under chemically harsh conditions could be demonstrated to leave the protein in its native conformation. Procedures involving exposure of AGP to hot phenol or sulphosalicylic acid (SSA) were compared to solely chromatographic methods. Hot phenol-purified AGP was more rapidly cleared from mice in vivo following intravenous injection than chromatographically purified AGP. In contrast, SSA-purified AGP demonstrated an identical in vivo clearance profile and circular dichroism spectrum to chromatographically purified AGP. Similarly, no differences in susceptibility to enzymatic deglycosylation or reactivity with Sambucus nigra lectin were detected between AGP purified via the two methods. Incorporation of the SSA step in the purification scheme for AGP eliminated the need for a large (4 mL resin/mL of plasma) initial chromatographic step and simplified its purification without causing any detectable distortion in the conformation of the protein. Confirmation that this procedure is nondenaturing will simplify AGP purification and investigation of its possible biological roles in laboratory animals

In Vivo Clearance of Alpha-1 Acid Glycoprotein Is Influenced by the Extent of Its N-Linked Glycosylation and by Its Interaction with the Vessel Wall

Alpha-1 acid glycoprotein (AGP) is a highly glycosylated plasma protein that exerts vasoprotective effects. We hypothesized that AGP's N-linked glycans govern its rate of clearance from the circulation, and followed the disappearance of different forms of radiolabeled human AGP from the plasma of rabbits and mice. Enzymatic deglycosylation of human plasma-derived AGP (pdAGP) by Peptide: N-Glycosidase F yielded a mixture of differentially deglycosylated forms (PNGase-AGP), while the introduction of five Asn to Gln mutations in recombinant Pichia pastoris-derived AGP (rAGP-N(5)Q) eliminated N-linked glycosylation. PNGase-AGP was cleared from the rabbit circulation 9-fold, and rAGP-N(5)Q, 46-fold more rapidly than pdAGP, primarily via a renal route. Pichia pastoris-derived wild-type rAGP differed from pdAGP in expressing mannose-terminated glycans, and, like neuraminidase-treated pdAGP, was more rapidly removed from the rabbit circulation than rAGP-N(5)Q. Systemic hyaluronidase treatment of mice transiently decreased pdAGP clearance. AGP administration to mice reduced vascular binding of hyaluronic acid binding protein in the liver microcirculation and increased its plasma levels. Our results support a critical role of N-linked glycosylation of AGP in regulating its in vivo clearance and an influence of a hyaluronidase-sensitive component of the vessel wall on its transendothelial passage

Norm estimates of complex symmetric operators applied to quantum systems

This paper communicates recent results in theory of complex symmetric operators and shows, through two non-trivial examples, their potential usefulness in the study of Schr\"odinger operators. In particular, we propose a formula for computing the norm of a compact complex symmetric operator. This observation is applied to two concrete problems related to quantum mechanical systems. First, we give sharp estimates on the exponential decay of the resolvent and the single-particle density matrix for Schr\"odinger operators with spectral gaps. Second, we provide new ways of evaluating the resolvent norm for Schr\"odinger operators appearing in the complex scaling theory of resonances

Resonance Lifetimes from Complex Densities

The ab-initio calculation of resonance lifetimes of metastable anions challenges modern quantum-chemical methods. The exact lifetime of the lowest-energy resonance is encoded into a complex "density" that can be obtained via complex-coordinate scaling. We illustrate this with one-electron examples and show how the lifetime can be extracted from the complex density in much the same way as the ground-state energy of bound systems is extracted from its ground-state density

Non-Equilibrium Dynamics in Two-Color, Few-Photon Dissociative Excitation and Ionization of D2_2

D$_2$ molecules, excited by linearly cross-polarized femtosecond extreme ultraviolet (XUV) and near-infrared (NIR) light pulses, reveal highly structured D$^+$ ion fragment momenta and angular distributions that originate from two different 4-step dissociative ionization pathways after four photon absorption (1 XUV + 3 NIR). We show that, even for very low dissociation kinetic energy release $\le$~240~meV, specific electronic excitation pathways can be identified and isolated in the final ion momentum distributions. With the aid of {\it ab initio} electronic structure and time-dependent Schr\"odinger equation calculations, angular momentum, energy, and parity conservation are used to identify the excited neutral molecular states and molecular orientations relative to the polarization vectors in these different photoexcitation and dissociation sequences of the neutral D$_2$ molecule and its D$_2^+$ cation. In one sequential photodissociation pathway, molecules aligned along either of the two light polarization vectors are excluded, while another pathway selects molecules aligned parallel to the light propagation direction. The evolution of the nuclear wave packet on the intermediate \Bstate electronic state of the neutral D$_2$ molecule is also probed in real time.Comment: 11 pages including 6 figure

Noncommutative Differential Forms on the kappa-deformed Space

We construct a differential algebra of forms on the kappa-deformed space. For a given realization of the noncommutative coordinates as formal power series in the Weyl algebra we find an infinite family of one-forms and nilpotent exterior derivatives. We derive explicit expressions for the exterior derivative and one-forms in covariant and noncovariant realizations. We also introduce higher-order forms and show that the exterior derivative satisfies the graded Leibniz rule. The differential forms are generally not graded-commutative, but they satisfy the graded Jacobi identity. We also consider the star-product of classical differential forms. The star-product is well-defined if the commutator between the noncommutative coordinates and one-forms is closed in the space of one-forms alone. In addition, we show that in certain realizations the exterior derivative acting on the star-product satisfies the undeformed Leibniz rule.Comment: to appear in J. Phys. A: Math. Theo