Two-potential formula continued off-the-energy-shell

We derive an off-energy-shell generalization of the two-potential formula by using a coordinate-space approach and apply the formalism to construct algorithms for studying spatial behaviour of the fully off-shellT matrix. We also suggest some future applications of the proposed theory.     

Many-body theory for simultaneous photoionization and photoexcitation of helium

Brueckner-Goldstone many-body perturbation theory is applied to study the simultaneous photoionization and photoexcitation (SSP) of helium. The results are used to examine the validity and limitations of other approaches to the problem. The oscillator strengths ($\text{d}\text{?}\text{?}$) for the transition 1s²→(2s ?p)¹P and 1s²→(2p ?s)¹P are compared with the results of Brown. The cross section for SPP at the photoexcitation threshold (65.399 eV) is found to be in agreement with the experimental result of Samson.     

Incoherent X-ray scattering by K-shell electrons

Values of the incoherent scattering function S_K for scattering of photons from K-shell electrons are computed for ₂He, ₃Li, ₄Be and ₅B at photon energies 6, 10, 14, and 18 keV by using screened hydrogenic wavefunctions. The screening has been taken into account by the Thomas-Fermi model of the neutral atom. Unlike the previous calculations we have used a distorted Coulomb wavefunction for the ejected electron. The effects of Coulomb distortion and of screening corrections are discussed. It is shown that the screening correction and the Coulomb distortion in the ejected electron wavefunction play significant roles in the study of incoherent X-ray scattering by bound electrons.     

Asymmetric Synthesis of Densely Functionalized Medium‐Ring Carbocycles and Lactones through Modular Assembly and Ring‐Closing Metathesis of Sulfoximine‐Substituted Trienes and Dienynes

An asymmetric synthesis of densely functionalized 7–11‐membered carbocycles and 9–11‐membered lactones has been developed. Its key steps are a modular assembly of sulfoximine‐substituted C‐ and O‐tethered trienes and C‐tethered dienynes and their Ru‐catalyzed ring‐closing diene and enyne metathesis (RCDEM and RCEYM). The synthesis of the C‐tethered trienes and dienynes includes the following steps: 1) hydroxyalkylation of enantiomerically pure titanated allylic sulfoximines with unsaturated aldehydes, 2) α‐lithiation of alkenylsulfoximines, 3) alkylation, hydroxy‐alkylation, formylation, and acylation of α‐lithioalkenylsulfoximines, and 4) addition of Grignard reagents to α‐formyl(acyl)alkenylsulfoximines. The sulfoximine group provided for high asymmetric induction in steps 1) and 4). RCDEM of the sulfoximine‐substituted trienes with the second‐generation Ru catalyst stereoselectively afforded the corresponding functionalized 7–11‐membered carbocyles. RCDEM of diastereomeric silyloxy‐substituted 1,6,12‐trienes revealed an interesting difference in reactivity. While the (R)‐diastereomer gave the 11‐membered carbocyle, the (S)‐diastereomer delivered in a cascade of cross metathesis and RCDEM 22‐membered macrocycles. RCDEM of cyclic trienes furnished bicyclic carbocycles with a bicyclo[7.4.0]tridecane and bicyclo[9.4.0]pentadecane skeleton. Selective transformations of the sulfoximine‐ and bissilyloxy‐substituted carbocycles were performed including deprotection, cross‐coupling reaction and reduction of the sulfoximine moiety. Esterification of a sulfoximine‐substituted homoallylic alcohol with unsaturated carboxylic acids gave the O‐tethered trienes, RCDEM of which yielded the sulfoximine‐substituted 9–11‐membered lactones. RCEYM of a sulfoximine‐substituted 1,7‐dien‐10‐yne showed an unprecedented dichotomy in ring formation depending on the Ru catalyst. While the second‐generation Ru catalyst gave the 9‐membered exo 1,3‐dienyl carbocycle, the first‐generation Ru catalyst furnished a truncated 9‐membered 1,3‐dieny carbocycle having one CH₂ unit less than the dienyne.     

A chromenoquinoline-based fluorescent off-on thiol probe for bioimaging

A new chromenoquinoline-based fluorescent off-on thiol probe 2 is reported. In aqueous buffer solutions at physiological pH, the probe exhibited 223-fold enhancement in fluorescence intensity by a Michael addition of cysteine to the maleimide appended to a chromenoquinoline. Cell permeability and live cell imaging of thiols are also demonstrated.     

Low-Valent Titanium Mediated Deprotection of N-Allyl/Benzyl Amines: A New Approach

A novel low-valent titanium (LVT) mediated cleavage of N-allyl/benzyl amines is reported. Regio- and chemo-selective cleavages were also observed.     

Optical theorem and Aharonov-Bohm scattering

A rigorous derivation of the optical theorem (OT) from the conservation of probability flux (CPF) is presented for scattering on an arbitrary spherically symmetric potential inN-spatial dimensions (ND). The constructed expression for the OT is found to yield the corresponding well-known results for two- and three-dimensional cases in a rather natural way. The Aharonov-Bohm (AB) effect is considered as a scattering event of an electron by a magnetic field confined in an infinitely long shielded solenoid and a similar derivation is attempted for an appropriate optical theorem. Our current understanding of the scattering theory is found to be inadequate for the purpose. The reason for this is discussed in some detail.