Semiclassical treatment of Wannier's theory when the exponent diverges

We consider a non-standard application of the Wannier model. A physical example is the single ionization of a hydrogenic beryllium ion with a fully stripped beryllium ion, where the ratio of the charge of the third particle to the charges of the escaping particles is 1/4; we investigate the single ionization by an electron of an atom comprising an electron and a nucleus of charge 1/4. An infinite exponent is obtained suggesting that this process is not tractable within the Wannier model. A modified version of Crothers' uniform semiclassical wavefunction for the outgoing particles has been adopted, since the Wannier exponents and are infinite for an effective charge of Z = 1/4. We use Bessel functions to describe the Peterkop functions u and u and derive a new turning point ?. Since u is well behaved at infinity, there exists only the singularity in u at infinity, thus we employ a one- (rather than two-) dimensional change of dependent variable, ensuring that a uniform solution is obtained that avoids semiclassical breakdown on the Wannier ridge. The regularized final-state asymptotic wavefunction is employed, along with a continuum-distorted-wave approximation for the initial-state wavefunction to obtain total cross sections on an absolute scale. © 2006 IOP Publishing Ltd.

Allogenic Peripheral Blood Derived Mesenchymal Stem Cells (MSCs) Enhance Bone Regeneration in Rabbit Ulna Critical-Sized Bone Defect Model

Mesenchymal stem cells (MSCs) were demonstrated to exist within peripheral blood (PB) of several mammalian species including human, guinea pig, mice, rat, and rabbit. Whether or not the PB derived MSCs (PBMSCs) could enhance the regeneration of large bone defects have not been reported. In this study, rabbit MSCs were obtained from mononuclear cells (MNCs) cultures of both the PB and bone marrow (BM) origin. The number of PBMSCs was relatively lower, with the colony forming efficiency (CFE) ranging from 1.2-13 per million MNCs. Under specific inductive conditions, PBMSCs differentiated into osteoblasts, chondrocytes, and adipocytes, showing multi- differentiation ability similar to BMMSCs. Bilateral 20 mm critical-sized bone defects were created in the ulnae of twelve 6-month old New Zealand white rabbits. The defects were treated with allogenic PBMSCs/Skelite (porous calcium phosphate resorbable substitute), BMMSCs/Skelite, PBMNCs/Skelite, Skelite alone and left empty for 12 weeks. Bone regeneration was evaluated by serial radiography, peripheral quantitative computed tomography (pQCT), and histological examinations. The x-ray scores and the pQCT total bone mineral density in the PBMSCs/Skelite and BMMSCs/Skelite treated groups were significantly greater than those of the PBMNCs/Skelite and Skelite alone groups (p