Stereoelectronic properties of photosynthetic and related systems: Ab initio configuration interaction calculations on the ground and lower excited singlet and triplet states of magnesium chlorin and chlorin

Ab initio configuration interaction wavefunctions and energies are reported for the ground state and many low-lying singlet and triplet states of magnesium chlorin and chlorin, and are employed in an analysis of the electronic absorption spectra of these systems.In chlorin, the calculated visible spectrum consists of two ${}^1\text{(π, π}{}^1\text{)}$ states, the lower energy, y-polarized state exhibiting moderate absorption intensity in contrast to the very weak absorption of the higher energy x-polarized state. The configurational composition of both states is well described by the four-orbital model. Five ${}^1\text{(π, π}{}^1\text{)}$ states are responsible for the Soret band envelope. A moderately intense y-state lies under the low energy edge of the band envelope, while two x-polarized states of moderate and strong intensity, respectively, are responsible for the band maximum. The final two ${}^1\text{(π, π}{}^1\text{)}$ states lie at the high energy edge of the Soret band and introduce a measure of asymmetry into the band envelope. Two ${}^1\text{(n, π}{}^1\text{)}$ states of very weak oscillator strength are also found in this region of the spectrum. All the Soret states are of complex configurational composition, and several of the higher lying states contain contributions from doubly excited configurations.The calculated visible spectrum of magnesium chlorin also consists of two ${}^1\text{(π, π}{}^1\text{)}$ states, with the weakly absorbing x-polarized state lying approximately 200 cm^?1 lower in energy than the moderately intense y-polarized state. The configurational composition of both states is well described by the four-orbital model. Four ${}^1\text{(π, π}{}^1\text{)}$ states constitute the bulk of the intensity in the Soret band envelope. In distinction to chlorin, the moderately intense ${}^1\text{(π, π}{}^1\text{)}$ state at the low energy edge of the band envelope is x-polarized. Two intense ${}^1\text{(π, π}{}^1\text{)}$ states of y- and x-polarization, respectively, constitute the band maximum region, and a single x-polarized state of moderately strong intensity can be assigned to the high energy shoulder of the band envelope. Two other weakly absorbing ${}^1\text{(π, π}{}^1\text{)}$ states are also found in this region, along with another weakly absorbing state of mixed in-plane and out-of-plane polarization. No clearly defined ${}^1\text{(n, π}{}^1\text{)}$ states are observed. As was the case for chlorin, all the Soret states are of complex configurational composition, and some of the higher energy states contain significant contributions from doubly excited configurations.Chlorin and magnesium chlorin both possess three ${}^3\text{(π, π}{}^1\text{)}$ states which lie below S₁ and a single ${}^3\text{(π, π}{}^1\text{)}$ which lies slightly above S₂. All four of the low-lying ${}^3\text{(π, π}{}^1\text{)}$ states in each molecule are well described by the four-orbital model, with T₁ being essentially a single configuration in each case. The remainder of the ${}^3\text{(π, π}{}^1\text{)}$ states are clustered in the same energetic region as the comparable ${}^1\text{(π, π}{}^1\text{)}$ Soret states, with comparably complex configurational compositions.Dipole moments and charge distributions for low-lying singlet and triplet states are also reported, and are used to rationalize chemical reactivity characteristics.     

Propagation of ion acoustic solitons in plasma density gradients

Experimental observations of propagation of ion acoustic solitons in a plasma with density gradients are presented. Soliton amplitude and velocity change as $\text{N}\text{x}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and $\text{N}\text{x}{}^{\mathrm{<mtext>-1</mtext><mtext>2</mtext>}}$ respectively where Nx is the local density.     

Devil's attractors and chaos of a driven impact oscillator

The motion of a driven elastic impact oscillator: $\text{x}\text{?}\text{+ 0.4}\text{x}\text{?}\text{+ x =}\text{cos}\text{(ωt)}$, x > 0 and $\text{x}\text{?}\text{(t}{}^{\mathrm{+}}\text{) = -}\text{x}\text{?}\text{(t}{}^{\mathrm{?}}\text{)}$ at x = 0, is studied for ω ≈ 2?4. The oscillator exhibits Feigenbaum's bifurcations (computed δ ≈ 4.70), the Feigenbaum and intermittent transitions to chaos, crises in chaos and a strong hysteresis region for ω ≈ 3.18–3.20 where the impact/period ratios of a group of attractors show the Devil's staircase behaviour with locking values between $\text{3}\text{5}$ and $\text{3}\text{4}$.     

Study of the energy and charged multiplicity dependence of inclusiveπ− production in π−p interactions up to fermilab energies

Using new data from 100 $\text{GeV}\text{c π}{}^{\mathrm{?}}$ interactions, we find the energy dependence of the invariant cross-section in the target fragmentation (central) region to be consistent with an $\text{A + Bs}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{(C + Ds}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>4</mtext>}}\text{)}$ behavior. The leading particle peak near x = + 1 exhibits a width in x which becomes smaller with increasing energy and an integrated cross section which is approximately energy independent.     

Analysis of (particle,xn) reactions on tantalum and gold: (II). 181Ta, 197Au(3He,xn) excitation functions and equilibrium statistical model analysis

Excitation functions for the reactions ${}^{197}\text{Au}\text{(}{}^3\text{He}\text{, x}\text{n}\text{)}{}^{\mathrm{200?x}}\text{Tl}\text{(x = 3, … 7)}$ and ${}^{181}\text{Ta}\text{(}{}^3\text{He}\text{, x}\text{n}\text{)}{}^{\mathrm{184?x}}\text{Re}\text{(x = 3, … 7)}$ were measured at bombarding energies up to 75 MeV. The data are compared to the results of an equilibrium statistical model calculation including angular momentum conservation and γ-ray competition. Satisfactory agreement was found except for the high energy tails.     

Recombination in electron-hole droplets in polar and non-polar indirect band gap semiconductors and carrier concentration power law

The dependence of the recombination relaxation rate on the carrier concentration, n, is examined in detail. It is found that in polar indirect band gap semiconductors the phonon-induced recombination rate varies as $\text{n}{}^{\mathrm{<mtext>4</mtext><mtext>3</mtext>}}$ at low temperatures. This is a new power law. On the other hand, in the non-polar materials, the relaxation rate varies as a linear combination of n², $\text{n}{}^{\mathrm{<mtext>5</mtext><mtext>3</mtext>}}$ and $\text{n}{}^{\mathrm{<mtext>4</mtext><mtext>3</mtext>}}$ terms. We find the experimental evidence for the occurence of $\text{n}{}^{\mathrm{<mtext>5</mtext><mtext>3</mtext>}}$ and $\text{n}{}^{\mathrm{<mtext>4</mtext><mtext>3</mtext>}}$ contributions for the first time.     

Connection between backbending and high-spin isomer decay in 179W

A new 710 ns isomer in ¹⁷⁹W is found to decay directly into backbending region of the $\text{7}\text{2}{}^{\mathrm{-}}\text{(514)}$ gorund-state band. The $\text{i}{}_{\mathrm{<mtext>13</mtext><mtext>2</mtext>}}$ band is observed up to spin $\text{41}\text{2}$ and shows no evidence for backbending at core rotational frequencies, where the effect is observed in the ¹⁷⁹W and ¹⁸⁰W ground-state bands.     

Derivation of Regge's action from Einstein's theory of general relativity

Regge's action for a discrete lattice is derived from Einstein's continuum formula $\text{?√ |g| R}\text{d}{}^{\mathrm{D}}\text{x}$ in general relativity.     

The theory of the instability of a planar interface in a process of the phrase transformation

The theory of the instability of a planar interface during an isothermal phase transformation is developed. It is shown that for large times only perturbations with large wave length are essential. The amplitude of the deviation from a planar interface grows with time as an exponent, the argument of which is proportional to $\text{t}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$ instead of the usual simple exponential law.     

Predissociation and Λ-doubling in the even-parity Rydberg states of the nitrogen molecule

Predissociations in the y¹Π_g and $\text{x}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ Rydberg states of N₂ (configurations $\text{1π}{}_{\mathrm{u}}{}^{\mathrm{?1}}\text{4pσ}$ and $\text{1π}{}_{\mathrm{u}}{}^{\mathrm{?1}}\text{3pπ}$, respectively) and their likely causes, are discussed. Peaking of rotational intensity at unusually low J values, without sharp breaking off, is interpreted as due to case c^? or case cⁱ predissociation. Λ doubling in the y state, attributed to interactions with the $\text{x}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ state and with another, ¹Σ⁺, state of the same electron configuration as x, is analyzed. From this analysis the location of the (unobserved) ${}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ state, here labeled x′, is obtained. It is concluded that the predissociation in the Π⁺ levels of the y state is an indirect one mediated by the interaction with x′ coupled with predissociation of x′ by a ${}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{?}}$ state dissociating to ${}^4\text{S +}{}^2\text{P}$ atoms: combined, however, with perturbation of the y state by the k¹Π_g Rydberg state (configuration $\text{3σ}{}_{\mathrm{g}}{}^{\mathrm{?1}}\text{4dπ}$), whose Π⁺ levels are completely predissociated.     

Scaling violation,the Callan Gross relation,and color excitation in electroproduction

The Callan-Gross relation is shown to be consistent with MIT-SLAC data for $\text{σ}{}_{\mathrm{<mtext>L</mtext>}}\text{(Q}{}^2\text{)}\text{σ}{}_{\mathrm{<mtext>T</mtext>}}\text{(Q}{}^2\text{)}$ for x ? 0.33 in deep inelastic eN scattering, despite the fact that these data are taken in the large Q² region where F₁ and F₂ individually exhibit scaling violation. Comparison is made with asymptotic freedom predictions, and color excitation is proposed to explain large values of $\text{σ}{}_{\mathrm{<mtext>L</mtext>}}\text{σ}{}_{\mathrm{<mtext>T</mtext>}}$ at small x.     

On the Schrödinger equation for the x2 + λx2(1 + gx2) interaction

We present an infinite set of exact solutions and eigenvalues for the one-dimensional Schrödinger equation involving the potential $\text{x}{}^2\text{+}\text{λx}{}^2\text{(1 + gx}{}^2\text{)}$. Comparison with numerical methods is made.     

Transverse spin correlation function of the one-dimensional spin-12 XY model

The transverse spin pair correlation function p^x_n=<S^x_mS^x_m+n>=<S^x_mS^x_m+n> is calculated exactly in the thermodynamic limit of the system described by the one-dimensional, isotropic, spin-$\text{1}\text{2}$, XY Hamiltonian

$\text{H=?2J}\text{∑}\text{l=1}\text{N}\text{(S}{}^{\mathrm{x}}{}_{\mathrm{l}}\text{S}{}^{\mathrm{x}}{}_{\mathrm{l+1}}\text{+S}{}^{\mathrm{y}}{}_{\mathrm{l}}\text{S}{}^{\mathrm{y}}{}_{\mathrm{l+1}}\text{)}$

. It is found that at absolute zero temperature (T = 0), the correlation function ρ^x_n for n ≥ 0 is given by

$\text{ρ}{}^{\mathrm{x}}{}_{\mathrm{2p}}\text{=}\text{1}\text{4}\text{2}\text{π}{}^{\mathrm{2p}}\text{Π}\text{j=1}\text{p?1}\text{4j}{}^2\text{4j}{}^2\text{?1}{}^{\mathrm{2p?2j}}\text{if}\text{n=2p}$

,

$\text{ρ}{}^{\mathrm{x}}{}_{\mathrm{2p+1}}\text{=±}\text{1}\text{4}\text{2}\text{π}{}^{\mathrm{2p+1}}\text{Π}\text{j=1}\text{p}\text{4j}{}^2\text{4j}{}^2\text{?1}{}^{\mathrm{2p+2j}}\text{if}\text{n=2p+1}$

, where the plus sign applies when J is positive and the minus sign applies when J is negative. From these the asymptotic behavior as n → ∞ of |?^x_n| at T = 0 is derived to be $\text{|ρ}{}^{\mathrm{x}}{}_{\mathrm{n}}\text{| ～}\text{a}\text{n}$ with a = 0.147088?. For finite temperatures, ρ^x_n is calculated numerically. By using the results for ?^x_n, the transverse inverse correlation length and the wavenumber dependent transverse spin pair correlation function are also calculated exactly.     

Rotational bands in odd hafnium nucleides

Rotational bands up to high-spin members in odd-neutron Hf nucleides are studied by in-beam spectroscopy using (α, xn) reactions on isotopically enriched Yb targets. The $\text{1}\text{2}{}^{\mathrm{?}}$ [521], $\text{5}\text{2}{}^{\mathrm{?}}$ [512], and the $\text{7}\text{2}{}^{\mathrm{+}}$ mixed positive-parity (mainly $\text{7}\text{2}{}^{\mathrm{+}}$ [633]) bands were observed in ¹⁷³Hf and ¹⁷⁵Hf while the $\text{7}\text{2}{}^{\mathrm{?}}$ [514], $\text{9}\text{2}{}^{\mathrm{+}}$ (mainly $\text{9}\text{2}{}^{\mathrm{+}}$[624]), and the $\text{3}\text{QP}\text{(K =}\text{23}\text{2}$⁺) bands were studied in ¹⁷⁷Hf. The analysis of the band structure within the Nilsson model is extended to also include adjacent odd Hf nuclei making it possible to follow these bands through five isotopes of Hf.     

Statistical flow-oscillator modeling of vortex-shedding

The very important engineering problem of modeling the fluid-structure interaction occurring during the shedding of vortices has defied, and will probably continue to defy, a closed form exact solution for the foreseeable future. Therefore, an attempt must be made to extract relevant information about the process in order to be able to have a basic understanding of it for the purpose of analysis. A useful method involves the flow-oscillator concepts of Hartlen and Currie [1] redefined here for stochastic processes. The fluid-structure system is assumed to be governed by the cross-coupled equations

$\text{x}\text{?}\text{(t)+2ξω}{}_{\mathrm{n}}\text{x}\text{?}\text{(t)+ω}{}^2{}_{\mathrm{n}}\text{=C}{}_{\mathrm{e}}\text{(t)pV}{}^2{}_0\text{(t)DL/2m (i)}$

$\text{C}\text{?}{}_{\mathrm{e}}\text{(t)+{α ? βC}{}^2{}_{\mathrm{e}}\text{(t)+γC}{}^4{}_{\mathrm{e}}\text{(t)}}\text{C}\text{?}{}_{\mathrm{e}}\text{(t)+ω}{}^2{}_0\text{C}{}_{\mathrm{e}}\text{(t)=b}\text{x}\text{?}\text{(t), (ii)}$

where these equations govern the structure and fluid oscillators, respectively. The fluid damping is non-linear. These equations are taken as stochastic differential equations because of the many unpredictable, random effects that determine the loading and response. The lift coefficient C_$\text{l}$(t) is assumed to be a zero mean, narrow band process and the velocity V₀, composed of a uniform, constant velocity current plus oscillating wave, a broad band process. The analysis is based on solving equation (i) for x(t) by using Duhamel's integral and substituting its derivative $\text{x}\text{?}\text{(t)}$ into equation (ii). This equation is then used to derive the Fokker-Planck equation for the process C_$\text{l}$(t). To obtain the Fokker-Planck equation, slowly varying variables are replaced by their long-time averages [2] and then the method of stochastic averaging is employed [3, 4]. The moment equation for the lift-oscillator process is derived from the Fokker-Planck equation and, as equation (ii) is non-linear, one finds the moment equation to be in terms of higher order moments. A truncation scheme [5] is used to derive the moment generating function. It is possible then to generate the first and second order statistics of the lift coefficient and the structure response in terms of the empirical parameters of fluid damping. This work was carried out in conjunction with an analysis of ocean wave-current forces with application to offshore fixed structures [6].     

The rotational analysis of the 1Π-X 1Σ+ system at 649.5 nanometers of zirconium oxide

A red-degraded band head, normally badly overlapped by the gamma system, $\text{A}{}^3\text{Φ}\text{- X′}{}^3\text{Δ}$, of zirconium oxide, appears in emission spectra of zirconium arcs and in absorption spectra of S-type stars and of frozen rare gas matrices containing zirconium. The emission band has been examined at high-resolution with the aid of separated zirconium isotopes. Identification of the band as 0-0 of a ${}^1\text{Π}\text{- X}{}^1\text{Σ}{}^{\mathrm{+}}$ system of zirconium oxide is confirmed by rotational analysis where the following constants (cm^?1) are obtained for ⁹⁰Zr¹⁶O:

$\text{B}{}_0\text{′(R,P) = 0.40142 D}{}_0\text{′(R,P) = 3.51 × 10}{}^{\mathrm{?7}}$

$\text{B}{}_0\text{′(Q) = 0.40166 D}{}_0\text{′(Q) =3.52 × 10}{}^{\mathrm{?7}}$

$\text{B}{}_0\text{″ = 0.42263 D}{}_0\text{″ =3.19 × 10}{}^{\mathrm{?7}}$

$\text{ν}{}_0\text{= 15383.81s}$

The Λ-type doubling in the ¹Π state and the question of whether $\text{X}{}^1\text{Σ}{}^{\mathrm{+}}$ or $\text{X′}{}^3\text{Δ}$ is the true ground state of ZrO are discussed.     

Singular perturbation potentials

This is a perturbative analysis of the eigenvalues and eigenfunctions of Schrödinger operators of the form ?Δ + A + λV, defined on the Hilbert space L²(Rⁿ), where $\text{Δ = Σ}{}_{\mathrm{i=1}}{}^{\mathrm{n}}\text{?}{}^2\text{?X}{}_{\mathrm{i}}{}^2$, A is a potential function and V is a positive perturbative potential function which diverges at some finite point, conventionally the origin. λ is a small real or complex parameter. The emphasis is on one-dimensional or separable problems, and in particular the typical example is the “spiked harmonic oscillator” Hamiltonian, $\text{?d}{}^2\text{dx}{}^2\text{+ x}{}^2\text{+}\text{l(l + 1)}\text{x}{}^2\text{+ λ|x|}{}^{\mathrm{?\alpha }}$, where α is a positive constant. When this kind of perturbation is very singular, the first-order Rayleigh-Schrödinger perturbative correction, (u₀, Vu₀), where u₀ is the unperturbed eigenfunction, diverges. This analysis constructs explicitly calculable terms in a modified perturbation series to a finite order, by using linear operator theory in concert with approximation methods for differential equations. Along the way a connection between a W-K-B type approximation and Bessel functions is exploited.