Contours of constant pseudo-Brewster angle in the complex є plane and an analytical method for the determination of optical constants

The locus of all points in the complex plane of the dielectric function є[єr + jєi = |є| exp(jθ)], that represent all possible interfaces characterized by the same pseudo-Brewster angle θpB of minimum p reflectance, is derived in the polar form: |є| = l cos(ζ/3), where l = 2(tan2ΦpB)k, ζ = arccos(- cosθ cos2ΦpB/k3), and k = (1 - 2/3 sin2ΦpB)½. Families of iso-ΦpB contours for (I) 0° ≤ ΦpB ≤ 45° and (II) 45° ≤ ΦpB ≤ 75° are presented. In range I, an iso-ΦpB contour resembles a cardioid. In range II, the contour gradually transforms toward a circle centered on the origin as ΦpB increases. However, the deviation from a circle is still substantial. Only near grazing incidence (ΦpB \u3e 80°) is the iso-ΦpB contour accurately approximated as a circle. We find that |є| \u3c 1 for ΦpB \u3c 37.23°, and |є| \u3e 1 for ΦpB \u3e 45°. The optical constants n,k (where n + jk = є½ is the complex refractive index) are determined from the normal incidence reflectance R0 and ΦpB graphically and analytically. Nomograms that consist of iso-R0 and iso-ΦpB families of contours in the nk plane are presented. Equations that permit the reader to produce his own version of the same nomogram are also given. Valid multiple solutions (n,k) for a given measurement set (R0,φpB) are possible in the domain of fractional optical constants. An analytical solution of the (R0,ΦpB) → (n,k) inversion problem is developed that involves an exact (noniterative) solution of a quartic equation in |є|. Finally, a graphic representation is developed for the determination of complex є from two pseudo-Brewster angles measured in two different media of incidence

Contours of constant pseudo-Brewster angle in the complex є plane and an analytical method for the determination of optical constants

The locus of all points in the complex plane of the dielectric function є[єr + jєi = |є| exp(jθ)], that represent all possible interfaces characterized by the same pseudo-Brewster angle θpB of minimum p reflectance, is derived in the polar form: |є| = l cos(ζ/3), where l = 2(tan2ΦpB)k, ζ = arccos(- cosθ cos2ΦpB/k3), and k = (1 - 2/3 sin2ΦpB)½. Families of iso-ΦpB contours for (I) 0° ≤ ΦpB ≤ 45° and (II) 45° ≤ ΦpB ≤ 75° are presented. In range I, an iso-ΦpB contour resembles a cardioid. In range II, the contour gradually transforms toward a circle centered on the origin as ΦpB increases. However, the deviation from a circle is still substantial. Only near grazing incidence (ΦpB \u3e 80°) is the iso-ΦpB contour accurately approximated as a circle. We find that |є| \u3c 1 for ΦpB \u3c 37.23°, and |є| \u3e 1 for ΦpB \u3e 45°. The optical constants n,k (where n + jk = є½ is the complex refractive index) are determined from the normal incidence reflectance R0 and ΦpB graphically and analytically. Nomograms that consist of iso-R0 and iso-ΦpB families of contours in the nk plane are presented. Equations that permit the reader to produce his own version of the same nomogram are also given. Valid multiple solutions (n,k) for a given measurement set (R0,φpB) are possible in the domain of fractional optical constants. An analytical solution of the (R0,ΦpB) → (n,k) inversion problem is developed that involves an exact (noniterative) solution of a quartic equation in |є|. Finally, a graphic representation is developed for the determination of complex є from two pseudo-Brewster angles measured in two different media of incidence

Angular range for reflection of p-polarized light at the surface of an absorbing medium with reflectance below that at normal incidence

The range of incidence angle, 0 \u3c φ \u3c φe, over which p-polarized light is reflected at interfaces between transparent and absorbing media with reflectance below that at normal incidence is determined. Contours of constant φe in the complex plane of the relative dielectric constant ε are presented. A method for determining the real and imaginary parts of the complex refractive index, ε1/2 = n + jk, which is based on measuring φe and the pseudo-Brewster angle φpB, is viable in the domain of fractional optical constants, n, k \u3c 1

Diversifying molecular and topological space via a supramolecular solid-state synthesis: a purely organic mok net sustained by hydrogen bonds

A three-dimensional hydrogen-bonded network based on a rare mok topology has been constructed using an organic molecule synthesized in the solid state. The molecule is obtained using a supramolecular protecting-group strategy that is applied to a solid-state [2+2] photodimerization. The photodimerization affords a novel head-to-head cyclobutane product. The cyclobutane possesses tetrahedrally disposed cis-hydrogen-bond donor (phenolic) and cis-hydrogen- bond acceptor (pyridyl) groups. The product self-assembles in the solid state to form a mok network that exhibits twofold interpenetration. The cyclobutane adopts different conformations to provide combinations of hydrogen-bond donor and acceptor sites to conform to the structural requirements of the mok net

Virtual Pion Scattering

We propose a theory which exploits the charge-exchange reactions ($^3$He,$^3$H$\pi^+$) and (p,n$\pi^+$) as effective sources of virtual pions. We consider processes in which the creation of virtual pions is followed by conventional coupled-channel pion scattering to discrete nuclear states. This picture allows us to incorporate successful theories of pion scattering and utilize virtual pions as probes of the nuclear matter. For coherent pion production we clearly demonstrate that the shift of the coherent peak position in the excitation function of $^3$He-A relative to $^3$He-N scattering is determined entirely by the pion nucleus rescattering.Comment: 10 pages, revtex 3, 2 figures attached in file figures.u

The extraction of nuclear sea quark distribution and energy loss effect in Drell-Yan experiment

The next-to-leading order and leading order analysis are performed on the differential cross section ratio from Drell-Yan process. It is found that the effect of next-to-leading order corrections can be negligible on the differential cross section ratios as a function of the quark momentum fraction in the beam proton and the target nuclei for the current Fermilab and future lower beam proton energy. The nuclear Drell-Yan reaction is an ideal tool to study the energy loss of the fast quark moving through cold nuclei. In the leading order analysis, the theoretical results with quark energy loss are in good agreement with the Fermilab E866 experimental data on the Drell-Yan differential cross section ratios as a function of the momentum fraction of the target parton. It is shown that the quark energy loss effect has significant impact on the Drell-Yan differential cross section ratios. The nuclear Drell-Yan experiment at current Fermilab and future lower energy proton beam can not provide us with more information on the nuclear sea quark distribution.Comment: 17 pages, 4 figure

Statistics of Coulomb blockade peak spacings for a partially open dot

We show that randomness of the electron wave functions in a quantum dot contributes to the fluctuations of the positions of the conductance peaks. This contribution grows with the conductance of the junctions connecting the dot to the leads. It becomes comparable with the fluctuations coming from the randomness of the single particle spectrum in the dot while the Coulomb blockade peaks are still well-defined. In addition, the fluctuations of the peak spacings are correlated with the fluctuations of the conductance peak heights.Comment: 13 pages, 1 figur

g_{\pi \Lambda \Sigma} and g_{K \Sigma \Xi} from QCD sum rules

The coupling constants g_{\pi \Lambda \Sigma} and g_{K \Sigma \Xi} are calculated in the QCD sum rule approach using the three-point function method and taking into account the SU(3) symmetry breaking effects. The pattern of SU(3) breaking appears to be different from that based on SU(3) relations.Comment: revtex, 9 page

Elastic Scattering of Pions From the Three-nucleon System

We examine the scattering of charged pions from the trinucleon system at a pion energy of 180 MeV. The motivation for this study is the structure seen in the experimental angular distribution of back-angle scattering for pi+ 3He and pi- 3H but for neither pi- 3He nor pi+ 3H. We consider the addition of a double spin flip term to an optical model treatment and find that, though the contribution of this term is non-negligible at large angles for pi+ 3He and pi- 3H, it does not reproduce the structure seen in the experiment.Comment: 15 pages + 5 figure

Three-body decay of the d* dibaryon

Under certain circumstances, a three-body decay width can be approximated by an integral involving a product of two off-shell two-body decay widths. This ``angle-average'' approximation is used to calculate the $\pi NN$ decay width of the $d^*(J^\pi=3^+, T=0)$ dibaryon in a simple $\Delta^2$ model for the most important Feynman diagrams describing pion emissions with baryon-baryon recoil and meson retardation. The decay width is found to be about 0.006 (0.07, 0.5) MeV at the $d^*$ mass of 2065 (2100, 2150) MeV for input dynamics derived from the Full Bonn potential. The smallness of this width is qualitatively understood as the result of the three-body decay being ``third forbidden''. The concept of $\ell$ forbiddenness and the threshold behavior of a three-body decay are further studied in connection with the $\pi NN$ decay of the dibaryon $d'(J^\pi=0^-, T=0 or 2)$ where the idea of unfavorness has to be introduced. The implications of these results are briefly discussed.Comment: 15 pages, RevTeX, two-column journal style, six figure