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.     

Electrical transport and magnetic properties of Nd2(WO4)3

Measurements of the molar magnetic susceptibility (X_m) of a powdered sample of Nd₂(WO₄)₃ in the temperature range 300–900 K, and the electrical conductivity (σ) and dielectric constant (?$\text{)}\text{?}$ of pressed pellets of the compound in the temperature range 4.2–1180 K are reported. X_m obeys the Curie-Weiss law with a Curie constant C= 3.13 K/mole, a paramagnetic Curie temperature θ= ?60 K and a moment of Bohr magnetons, p= 3.49 for the Nd³⁺ ion. The electrical conductivity data can be explained in terms of the usual band model and impurity levels. Both the σ and ?$\text{\$}\text{?}$data indicate some sort of phase transition round 1025 K. The conductivity follows Mott's law $\text{σ = A exp (?B/T}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{)}$ in the temperature range $\text{200 < T < 3000}\text{K with}\text{B = 45.00 (}\text{K}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{and}\text{A = 1.38 × 10}{}^{\mathrm{?5}}\text{Ω}{}^{\mathrm{?1}}\text{cm}{}^{\mathrm{?1}}$. The dielectric constant increases slowly up to 600 K, as is usual for ionic solids. The increase becomes much faster above 600 K, which is attributed to space-charge polarization of thermally generated charge carriers.     

Excited vibrational state microwave spectra,structure, and force-field of trifluorosilane

The J = 2?1 microwave spectrum of six isotopic species of HSiF₃ has been observed and assigned in excited states of five of the six fundamental vibrations. The assignment is based on relative intensities, double resonance experiments, and trial anharmonic force constant calculations. Analysis of the spectra leads to experimental values for five of the $\text{α}{}_{\mathrm{r}}{}^{\mathrm{B}}$ constants, all three l-doubling constants q_t, one Fermi resonance constant φ₂₃₃, and one zeta constant $\text{ζ}{}_{\mathrm{6,\; 6}}{}^{\mathrm{(z)}}$.The harmonic force field has been refined to all the available data on vibration wavenumbers, centrifugal distortion constants, and zeta constants. The cubic anharmonic force field has been refined to the data on $\text{α}{}_{\mathrm{r}}{}^{\mathrm{B}}$ and q_t constants, using two models: a valence force model with two cubic force constants for SiH and SiF stretching, and a more sophisticated model. With the help of these calculations, the following equilibrium structure has been determined: $\text{r}{}_{\mathrm{e}}\text{(}\text{SiH}\text{) = 1.4468(±5)}\text{A}\text{?}$, $\text{r}{}_{\mathrm{e}}\text{(}\text{SiF}\text{) = 1.5624(±1)}\text{A}\text{?}$, ∠HSiF = 110.64(±3)°,     

A study of 3He capture in light nuclei

Excitation functions at θ = 90° have been measured for ${}^{16}\text{O}\text{(}{}^3\text{He}\text{, γ}{}_{\mathrm{0?2,\; 3?5,\; 6}}\text{)}{}^{19}\text{Ne}$, ${}^{15}\text{N}\text{(}{}^3\text{He}\text{, γ}{}_{\mathrm{0,\; 1?4}}\text{)}{}^{18}\text{F}\text{,}{}^{14}\text{N}\text{(}{}^3\text{He}\text{, γ}{}_{\mathrm{0,\; 1,2,3}}\text{)}{}^{17}\text{F}$, and ${}^{20}\text{Ne}\text{(}{}^3\text{He}\text{, γ}{}_{\mathrm{0\; +\; 1}}\text{)}{}^{23}\text{Mg}$, in the range E_{3He = 3–19 MeV}. The first reaction has also been studied at θ = 40°. Excitation functions at 90° have also been measured for and ${}^4\text{He}\text{(}{}^3\text{He}\text{, γ}{}_{\mathrm{0\; +\; 1}}\text{)}{}^7\text{Be}$ for E_3He = 19–26 MeV. Angular distributions have been measured for the first four reactions.For the most excitation functions, a broad peak is observed, several MeV wide, centred at about E_x≈ 20 MeV. Superimposed on this, in some cases, are narrower peaks, with width ≈ 1 MeV. Energies and widths have been extracted for all resonances.Cluster-model calculations have been carried out, using methods similar to those which have proved successful for low-lying states in A= 18–19 nuclei. No satisfactory correspondence with the present results was found. The shell model has been used to calculate Γ_3He and Γ_γ for 1?ω excitations in the final nuclei. These generally show good agreement with the trends of the experimental data. The results are consistent with the excitation of the giant dipole resonance in ³He capture, but much more weakly than in proton capture.     

Dielectric susceptibility and correlation length of one-dimensional CDW with impurties. II. weak disorder

Dependence of static dielectric susceptibility and correlation length of charge density waves (CDW) with weak defects on parameter of incommensurability with lattice is investigated. In almost commensurate phase (h?h_ch_c), $\text{χ ～ (h?h}{}_{\mathrm{c}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{In}{}^{\mathrm{<mtext>-4</mtext><mtext>3</mtext>}}\text{h}{}_{\mathrm{c}}\text{/h?h}{}_{\mathrm{c}}$ and R_c ～ (h ? h_c)^{$\text{2}\text{3}$}. In${}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{h}{}_{\mathrm{c}}\text{/h ? h}{}_{\mathrm{c}}$. Far from commensurability $\text{(h?h}{}_{\mathrm{c}}\text{) χ～ (a+h}{}^2{}_{\mathrm{c}}\text{/h}{}^2\text{)}{}^{\mathrm{<mtext>-2</mtext><mtext>3</mtext>}}$, $\text{R}{}_{\mathrm{c}}\text{～ (a + h}{}^2{}_{\mathrm{c}}\text{/h}{}^2\text{)}{}^{\mathrm{<mtext>-2</mtext><mtext>3</mtext>}}$, where a is the dimensionless ratio of random potential intensities, corresponding to backward and forward scattering impurities.     

The spectrum and structure of the He2 molecule: Multichannel quantum defect analyses of the triplet levels associated with (1σg)2(1σu)npλ

Emission spectra for the electronic transitions $\text{6–17pπ}{}^3\text{Π}{}_{\mathrm{g}}\text{-2s a}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ and $\text{7–16pσ}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{-2s a}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ of He₂ are reported and the electronic structures of $\text{npπ}{}^3\text{Π}{}_{\mathrm{g}}{}^{\mathrm{?}}$ and $\text{np(}{}^2\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{)}$ characterized. The energy levels associated with $\text{(1σ}{}_{\mathrm{g}}\text{)}{}^2\text{(1σ}{}_{\mathrm{u}}\text{)np(}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{)}$ exhibit extensive channel mixing, which leads to a breakdown of conventional band models for the higher n¹-members of these Rydberg “series.” However, a model based on multichannel quantum defect theory quantitatively correlates the observed level structures. The higher-energy ($\text{n}{}^1\text{> ～5}$) portions of the $\text{np(}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{)}$ channels can be represented by two eigen-quantum defects μ₁ = 0.225 and μ₂ = 0.930 and the close- to loose-coupling matrix elements $\text{U}{}_{11}\text{= U}{}_{22}\text{= [N(2N + 1)}{}^{\mathrm{?1}}\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ and $\text{U}{}_{12}\text{= ?U}{}_{21}\text{= [(N + 1)(2N + 1)}{}^{\mathrm{?1}}\text{]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. The inclusion of energy dependence in the μ_α's leads to quantitative correlations for all n¹-values.     

The A′(3Π2) state of ICl

Although $\text{A′(}{}^3\text{Π}{}_2\text{) ← X(}{}^1\text{Σ}{}^{\mathrm{+}}\text{)}$ is forbidden in near case c molecules the A′ ← X transition can be efficiently accomplished by the three-step sequence $\text{A′(}{}^3\text{Π}{}_2\text{) ← D′(2) ← A(}{}^3\text{Π}{}_1\text{) ← X(}{}^1\text{Σ}{}^{\mathrm{+}}\text{)}$. Transitions to a range of levels of A′, v_A′ = 2–38, have been recorded by this means, using J-selective polarization-labeling spectroscopy. Principal constants of the A′ state of I³⁵Cl are T_e = 12682.05, ω_e = 224.57, ω_eχ_e = 1.882, ω_ey_e = ?0.0107, B_e = 0.08653, and α_e = 0.000675 cm^?1. The A′ state is therefore similar in its physical characteristics to two other (relatively) deep states, $\text{A(}{}^3\text{Π}{}_1\text{)}$ and $\text{B(}{}^3\text{Π}{}_0\text{+)}$, of the 2431 configuration.     

Observation of proton emission following thermal neutron capture in 34.5 d 84Rb

Using a target prepared by on-line isotope separation, thermal neutron capture in ⁸⁴Rb (I^π = 2^?) has been shown to induce proton emission to the ground state (0⁺) and first excited state (2⁺) of ⁸⁴Kr. The branching ratio was measured as $\text{Γ}{}_{\mathrm{<mtext>p</mtext>}}\text{(0}{}^{\mathrm{+}}\text{)}\text{Γ}{}_{\mathrm{<mtext>p</mtext>}}\text{(2}{}^{\mathrm{+}}\text{)}\text{= 4.7 ± 0.7}$, favouring a $\text{3}\text{2}{}^{\mathrm{?}}$ assignment of the capturing state without excluding $\text{5}\text{2}{}^{\mathrm{?}}$, and the (n_th, p) cross section as 12 ± 2 b. The energy available for the process was determined to be 3.45 ± 0.01 MeV, in agreement with other mass data in the region.     

The electronic spectrum of gaseous SnS

Observations of the spectrum of SnS excited in chemiluminescence have led to the characterization of two low-lying excited states of SnS, $\text{a}\text{Ω}\text{1(}{}^3\text{Σ}{}^{\mathrm{+}}\text{)}$, with T_e = 18 143.9 cm^?1, and $\text{A0}{}^{\mathrm{+}}\text{(}{}^3\text{Π}\text{)}$, with T_e = 22 021.3 cm^?1. Extended rotational analyses of the perturbed bands observed in the absorption spectrum enable assignments to be suggested for the components $\text{Ω}\text{0}{}^{\mathrm{+}}$ and 1 of ³Σ^? and $\text{Ω}\text{1}$ of ³Π.     

Inclusive K10(890) production in π−p interactions at 16 GeV/c

Inclusive $\text{K}{}^{10}$ production is studied in π^?p interactions at 16 GeV/c with x_? > 0.2. The $\text{K}{}^{10}$ is found to be pre-dominantly centrally produced with cross section $\text{σ(}\text{K}{}^{10}\text{) = (72 ± 12) μb}$ for x_? > 0.2 and compares closely to data on $\text{K}{}^{10}$ production in π⁺p interactions at the same energy.     

Coriolis intensity perturbations in the SO2 molecule: Experimental determination of the relative signs of (∂μ∂Qi)

The Coriolis interactions between ν₁ and ν₃, and between ν₂ and ν₃ in SO₂ have been analyzed to obtain the signs of the products $\text{ζ}{}_{3.1}{}^{\mathrm{c}}\text{(}\text{?μ}{}^{\mathrm{a}}\text{?Q}{}_3\text{)(}\text{?μ}{}^{\mathrm{b}}\text{?Q}{}_1\text{)}$ and $\text{ζ}{}_{3.2}{}^{\mathrm{c}}\text{(}\text{?μ}{}^{\mathrm{a}}\text{?Q}{}_3\text{)(}\text{?μ}{}^{\mathrm{b}}\text{?Q}{}_2\text{)}$. It has been found that both of the signs of these products are positive. Then, relative signs of ($\text{?μ}\text{?Q}{}_1$) have been determined using the calculated values of the Coriolis zeta constants for the present definition of the normal coordinates. The obtained sign combination of ($\text{?μ}\text{?Q}{}_{\mathrm{i}}$) is ±(+?+), which agrees with the one predicted by the molecular orbital calculations. Using the sign combination (+?+), the polar tensors of S and O atoms were also calculated.     

Thermochemistry of azide salts and the azide ion using direct minimisation equations to obtain the lattice energy of the univalent azide salts

The opportunity to test a new equation for the computation of the lattice energy and at the same time examine a disparity in the literature data for the enthalpy of formation of the azide ion, $\text{ΔH}{}^{\mathrm{\theta }}{}_{\mathrm{?}}\text{(}\text{N}{}_3{}^{\mathrm{?}}\text{) (}\text{g}\text{)}$ was the motivation for this study. The results confirm our earlier calculation and show the new equation to be reliable. Thermodynamic data produced in the study take values: $\text{ΔH}{}^{\mathrm{\theta }}{}_{\mathrm{?}}\text{(}\text{N}{}_3{}^{\mathrm{?}}\text{)(}\text{g}\text{) = 144}\text{kJ mor}{}^{\mathrm{?1}}$ΔH^θ_hyd(N₃^?) = ?315 KJ mol^?1 or ΔH^θ_hyd(N₃^?) = ?295 KJ mol^?1U_POT(NaN₃) = 732 kJ mol^?1U_POT(KN₃) = 659 kJ mol^?1U_POT(RbN₃) = 637 kJ mol^?1U_POT(CsN₃) = 612 kJ mol^?1U_POT(TIN₃) = 689 kJ mol^?1. The lattice energies of azides whose enthalpies of formation are documented have been calculated as well as the enthalpy of formation of the azide radical.     

Model calculation of the electronic structure and spectroscopy of Hg2

Energy curves and transition moments of the excited valence states of Hg₂ were obtained in a model calculation based on calculated Mg₂ energy levels and the assumption that the asymptotic spin-orbit matrix elements for the Hg atom are applicable to the molecular states. The spin-orbit and orbital-rotational interaction of the excited states of Hg₂ is analyzed in both a Hund's case (c) and (a) representation. The intermediate (a) → (c) transition moments are obtained as a function of the internuclear distance. The effect of the orbital-rotational interaction which introduces Hund's case (b) and (e) couplings is found to be small for transitions among excited states under the conditions normally encountered for populating excimer states.Using the energy level positions and transition moments, the observed spectra and predicted spectra are compared for both radiative transitions including the ground state and among the excited states. The lifetime of the $\text{1}{}_{\mathrm{u}}\text{(}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{)}$ excimer state is calculated to be 1.4 μsec with the 335 nm band assigned to the $\text{1}{}_{\mathrm{u}}\text{→ X}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ transition. The 485 nm bands cannot be assigned to any Hg₂ transitions. Strong bound-continuum absorptions are predicted for the 485 nm bands. On the other hand, the 335 nm emission is predicted to be absorbed by bound-bound transitions only.     

Parity violation in pion-proton scattering

Parity-violating pion-proton scattering is strongly dominated by so-called penguin operators. These operators are due to the presence of the neutral current, and their strength is further enhanced by the QCD renormalization effects. Without such contributions the elastic asymmetry (A_l) would be an order of magnitude smaller (up to 150 MeV of the pion laboratory kinetic energy). Possible contributions from the resonance poles (?-meson, ($\text{1}\text{2}{}^{\mathrm{+}}\text{)}{}^1\text{-}\text{reson}$) have been also included. Thus pion scattering on the polarized proton can test the commonly-used effective QCD renormalized weak hamiltonian.     

New potential energy function for alkali halide molecules

A new repulsive term in the ionic interaction potential for computing the lattice energy, the rotational constant (α₀) and the vibrational constant (w₀x₀) of alkali halide molecules has been proposed as $\text{ψ(r) = Af}{}^{\mathrm{n}}\text{r}{}^{\mathrm{-n}}\text{e}{}^{\mathrm{<mtext>?r</mtext><mtext>\lambda </mtext>}}$, which apart from being generalised, dimensionally homogenous and physically sound yields better values for lattice energy, α₀ and w₀x₀ than the previously reported potentials models.     

Interference effects in 12C(p, γ)13N and direct capture to unbound states

Excitation functions of the capture reaction ¹²C(p, γ₀)¹³N have been obtained at θ_γ = 0° and 90° and E_p = 150–2500 keV. The results can be explained if a direct radiative capture process, E1(s and d → p), to the ground state in ¹³N is included in the analysis in addition to the two well-known resonances in this beam energy range $\text{[E}{}_{\mathrm{p}}\text{= 457(}\text{1}\text{2}{}^{\mathrm{+}}\text{)}$ and 1699 $\text{(}\text{3}\text{2}{}^{\mathrm{?}}\text{) keV]}$. The direct capture component is enhanced through interference effects with the two resonance amplitudes. From the observed direct capture cross section, a spectroscopic factor of C²S(l = 1) = 0.49 ± 0.15 has been deduced for the $\text{1}\text{2}{}^{\mathrm{?}}$ ground state in ¹³N. Excitation functions for the reaction ${}^{12}\text{C(p,γ}{}_1\text{p}{}^1\text{)}{}^{12}\text{C}$ have been obtained at θ_γ = 0° and 90° and E_p = 610–2700 keV. Away from the 1699 keV resonance the capture γ-ray yield is dominated by the direct capture process E1 (p → s) to the $\text{2366 (}\text{1}\text{2}{}^{\mathrm{+}}\text{) keV}$ unbound state. Above E_p = 1 MeV, the observed excitation functions are well reproduced by the direct capture theory to unbound states (bremsstrahlung theory). Below E_p = 1 MeV, i.e., E_p → 457 keV, the theory diverges in contrast to observation. This discrepancy is well known in bremsstrahlung theory as the “infrared problem”. From the observed direct capture cross sections at $\text{E}{}_{\mathrm{p}}\text{? 1 MeV}$, a spectroscopic factor of C²S(l = 0) = 1.02 ± 0.15 has been found for the $\text{2366 (}\text{1}\text{2}{}^{\mathrm{+}}\text{) keV}$ unbound state. A search for direct capture transitions to the $\text{3512 (}\text{3}\text{2}{}^{\mathrm{?}}\text{)}$and $\text{3547 (}\text{5}\text{2}{}^{\mathrm{+}}\text{) keV}$ unbound states resulted in upper limits of C²S(l = 1) ≦ 0.5 and C²S(l = 2) ? 1.0, respectively. The results are compared with available stripping data as well as shell-model calculations. The astrophysical aspect of the ¹²C(p, γ₀)¹³N reaction also is discussed.     

Nuclear polarization and signs of quadrupole moments of high-spin Gd isomers

Time-differential perturbed-angular-distribution (TDPAD) experiments have been performed on polarized intermediate- and high-spin isomers ${}^{144}\text{Gd}\text{(10}{}^{\mathrm{+}}\text{)}\text{and}{}^{147}\text{Gd}\text{(}\text{13}\text{2}{}^{\mathrm{+}}\text{,}\text{27}\text{2}{}^{\mathrm{?}}\text{,}\text{49}\text{2}{}^{\mathrm{+}}\text{)}$. Excited Gd nuclei populated by $\text{(}{}^{28}\text{Si}\text{, x}\text{n}\text{)}$ reactions were polarized by the tilted-multifoil technique and implanted in a Gd single-crystal host. Observation of the subsequent electric quadrupole interaction with the known electric field gradient yielded negative values of the sign of the deformation for all isomers studied. The magnitude of the induced nuclear polarization P_I was also determined from the TDPAD data and compared to model calculations in order to deduce the average atomic angular momentum and polarization of Gd ions at v/c ～ 0.018.     

Measurement of charge distributions for 229Th(nth,f) and 232U(nth,f)

A gas ΔE ? E_R telescope has been used to measure charge yields and their correlations with kinetic energies for ²²⁹Th and ²³²U. Even-charge yields are enhanced compared with odd-charge yields for both fissioning systems; this enhancement increases for events with higher kinetic energy. The mean odd-even effect $\text{δ}{}_{\mathrm{<mtext>p</mtext>}}\text{is}\text{= (40±4)\%}\text{for}{}^{229}\text{Th}$; it is $\text{(21 ± 3)\%}\text{for}{}^{232}\text{U-the same as for}{}^{233}\text{U}\text{((22.1±2.1)\%)}\text{and}{}^{235}\text{U}\text{((23.7±0.7)\%)}$. The energy-integrated δ_p and δ_p for different energy windows, vary strongly as a function of charge (Z) due to the underlying shells. The δ_p averaged over Z increases fast with kinetic energy, contrary to the existing results for ²³³U and ²³⁵U, where δ_p flattens off at low energies. For both systems, the most probable kinetic energy ē shows a strong odd-even stagger; the mean odd-even effect on energy, $\text{δE}{}_{\mathrm{<mtext>K</mtext>}}{}^{\mathrm{<mtext>o?e</mtext>}}\text{,}\text{is}\text{1.4 ± 0.3}\text{MeV for}{}^{229}\text{Th, and}\text{1.7±0.4}\text{MeV for}{}^{232}\text{U}\text{—}$ the latter is about twice the value for ${}^{233}\text{U}\text{(0.95 ± 0.09}\text{MeV}\text{)}\text{and}{}^{235}\text{U}\text{(0.7}\text{MeV}\text{)}$. These results are discussed in terms of the existing models.     

Intermittency of fully developed turbulence

The energy spectrum in the inertial range takes the form $\text{E(k)～ε}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}\text{k}{}^{\mathrm{<mtext>?5</mtext><mtext>3</mtext>}}\text{(kl}{}_0\text{)}{}^{\mathrm{<mtext>?\mu </mtext><mtext>3</mtext>}}$, where ε is the mean rate of energy transfer and l₀ is the length scale of the production range. The intermittency exponent μ is determined by introducing a new statistical hypothesis on the basis of the β-model recently proposed by Frisch, Sulem and Nelkin. The result is μ ≈ 0.341 which is in good agreement with the experiments, μ_exp=0.3–0.5.