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1.
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(π, π1) 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(π, π1) 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(π, π1) states lie at the high energy edge of the Soret band and introduce a measure of asymmetry into the band envelope. Two 1(n, π1) 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(π, π1) 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(π, π1) states constitute the bulk of the intensity in the Soret band envelope. In distinction to chlorin, the moderately intense 1(π, π1) state at the low energy edge of the band envelope is x-polarized. Two intense 1(π, π1) 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(π, π1) 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(n, π1) 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(π, π1) states which lie below S1 and a single 3(π, π1) which lies slightly above S2. All four of the low-lying 3(π, π1) 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(π, π1) states are clustered in the same energetic region as the comparable 1(π, π1) 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.  相似文献   

2.
Experimental observations of propagation of ion acoustic solitons in a plasma with density gradients are presented. Soliton amplitude and velocity change as Nx12 and Nx-12 respectively where Nx is the local density.  相似文献   

3.
The motion of a driven elastic impact oscillator: x? + 0.4x? + x = cos(ωt), x > 0 and x?(t+) = -x? (t?) 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 35 and 34.  相似文献   

4.
Using new data from 100 GeVc π? interactions, we find the energy dependence of the invariant cross-section in the target fragmentation (central) region to be consistent with an A + Bs?12(C + Ds?14) 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.  相似文献   

5.
Excitation functions for the reactions 197Au(3He, xn)200?xTl (x = 3, … 7) and 181Ta(3He, xn)184?xRe (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.  相似文献   

6.
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 n43 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, n53 and n43 terms. We find the experimental evidence for the occurence of n53 and n43 contributions for the first time.  相似文献   

7.
A new 710 ns isomer in 179W is found to decay directly into backbending region of the 72-(514) gorund-state band. The i132 band is observed up to spin 412 and shows no evidence for backbending at core rotational frequencies, where the effect is observed in the 179W and 180W ground-state bands.  相似文献   

8.
Regge's action for a discrete lattice is derived from Einstein's continuum formula ?√ |g| R dDx in general relativity.  相似文献   

9.
10.
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 t14 instead of the usual simple exponential law.  相似文献   

11.
Predissociations in the y1Πg and x1Σg? Rydberg states of N2 (configurations u?14pσ and u?13pπ, 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 x1Σg? state and with another, 1Σ+, state of the same electron configuration as x, is analyzed. From this analysis the location of the (unobserved) 1Σg+ 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 3Σg? state dissociating to 4S + 2P atoms: combined, however, with perturbation of the y state by the k1Πg Rydberg state (configuration g?14dπ), whose Π+ levels are completely predissociated.  相似文献   

12.
The Callan-Gross relation is shown to be consistent with MIT-SLAC data for σL(Q2)σT(Q2) 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 σLσT at small x.  相似文献   

13.
We present an infinite set of exact solutions and eigenvalues for the one-dimensional Schrödinger equation involving the potential x2 + λx2(1 + gx2). Comparison with numerical methods is made.  相似文献   

14.
The transverse spin pair correlation function pxn=<SxmSxm+n>=<SxmSxm+n> is calculated exactly in the thermodynamic limit of the system described by the one-dimensional, isotropic, spin-12, XY Hamiltonian
H=?2Jl=1N(SxlSxl+1+SylSyl+1)
. It is found that at absolute zero temperature (T = 0), the correlation function ρxn for n ≥ 0 is given by
ρx2p=142π2pΠj=1p?14j24j2?12p?2jif n=2p
,
ρx2p+1142π2p+1Πj=1p4j24j2?12p+2jif 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 |?xn| at T = 0 is derived to be xn| ~ an with a = 0.147088?. For finite temperatures, ρxn is calculated numerically. By using the results for ?xn, the transverse inverse correlation length and the wavenumber dependent transverse spin pair correlation function are also calculated exactly.  相似文献   

15.
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 12? [521], 52? [512], and the 72+ mixed positive-parity (mainly 72+ [633]) bands were observed in 173Hf and 175Hf while the 72? [514], 92+ (mainly 92+[624]), and the 3QP(K = 232+) 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.  相似文献   

16.
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
x?(t)+2ξωnx?(t)+ω2n=Ce(t)pV20(t)DL/2m (i)
C?e(t)+{α ? βC2e(t)+γC4e(t)}C?e(t)+ω20Ce(t)=bx?(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 Cl(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 x?(t) into equation (ii). This equation is then used to derive the Fokker-Planck equation for the process Cl(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].  相似文献   

17.
A red-degraded band head, normally badly overlapped by the gamma system, A3Φ - X′ 3Δ, 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 1Π - X 1Σ+ system of zirconium oxide is confirmed by rotational analysis where the following constants (cm?1) are obtained for 90Zr16O:
B0′(R,P) = 0.40142 D0′(R,P) = 3.51 × 10?7
B0′(Q) = 0.40166 D0′(Q) =3.52 × 10?7
B0″ = 0.42263 D0″ =3.19 × 10?7
ν0 = 15383.81s
The Λ-type doubling in the 1Π state and the question of whether X 1Σ+ or X′ 3Δ is the true ground state of ZrO are discussed.  相似文献   

18.
19.
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 Δ = Σi=1n?2?Xi2, 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, ?d2dx2 + x2 + l(l + 1)x2 + λ|x|, 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.  相似文献   

20.
Thermogravimetric measurements were performed on nonstoichiometric CeO2?x in the temperature range 750–1500°C and from oxygen pressures of 10?2 to 10?26 atm. From this data the deviation from stoichiometry x = x(T, Po2) was determined. The thermodynamic quantities ΔHo2 and ΔSo2 were calculated in the region 0.001? x ? 0.3 and found to be independent of temperature.In the composition region 0.001< x < 0.006, the variation of ΔSo2 with x is consistent with a defect model involving randomly distributed doubly ionized oxygen vacancies. The experimental Po2-15 dependence of x and σ (electrical conductivity) is shown to be consistent with this model as ΔHo2 (≈ -10 eV) exhibits a slight dependence on x. It is postulated that the variation in ΔHo2 may result from lattice parameter increases with x, while the defects remain essentially randomly distributed.In the composition region 0.006 < x < 0.1, xPo2?1n with 1 < n < 5, and in the region 0.1 < x < 0.3, xPo2?1n with n increasing rapidly with x to n? 30. This behavior is believed to result from increasing defect interaction with increasing departures from stoichiometry. It is interesting to note that the ordered phase observed by Bevan and Kordis between CeO1·72 and CeO1·70 was not observed in this study at temperatures between 1300° and 1500°C.  相似文献   

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