A further contribution to the theory of the transient hot-wire technique for thermal conductivity measurements

We study the density of states of a one-dimensional tightbinding electron model with random hopping elements. The Hamiltonian is $\text{H = -∑}{}_{\mathrm{i}}\text{J}{}_{\mathrm{<mtext>i+</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{(a}{}^{\mathrm{+}}{}_{\mathrm{i}}\text{a}{}_{\mathrm{i+1}}\text{+a}{}^{\mathrm{+}}{}_{\mathrm{i+1}}\text{a}{}_{\mathrm{i}}\text{)}$, where the $\text{J}{}_{\mathrm{<mtext>i+</mtext><mtext>1</mtext><mtext>2</mtext>}}$'s are independent identically distributed random variables. It is proved that the single particle density of states D(E) diverges near E = 0 as $\text{1}\text{|(E}\text{log}{}^3\text{|E|)|}$.     

Stark effect in the torsio-rotational spectrum of propargyl mercaptan and SH bond moment determination

The Stark effect of rotational and torsio-rotational transitions of propargyl mercaptan has been analyzed. Assuming a dependence of the dipole moment components on the internal rotation angle of the type: $\text{μ}{}_{\mathrm{a}}\text{= μ}{}_{\mathrm{a}}{}^0\text{+ μ}{}_{\mathrm{a}}{}^{\mathrm{(1)}}\text{cos}\text{α}$, $\text{μ}{}_{\mathrm{b}}\text{= μ}{}_{\mathrm{b}}{}^0\text{+ μ}{}_{\mathrm{b}}{}^{\mathrm{(1)}}\text{cos}\text{α}$, and $\text{μ}{}_{\mathrm{c}}\text{= μ}{}_{\mathrm{c}}{}^{\mathrm{(1)}}\text{sin}\text{α}$, the following values of the determinable quantities were obtained: $\text{μ}{}_{\mathrm{a}}{}^{\mathrm{<mtext>eff</mtext>}}\text{= 0.718 ± 0.003}\text{D}$, $\text{μ}{}_{\mathrm{b}}{}^{\mathrm{<mtext>eff</mtext>}}\text{= 0.495 ± 0.010}\text{D}$, and $\text{μ}{}_{\mathrm{c}}{}^{\mathrm{(1)}}\text{= 0.809 ± 0.015}\text{D}$.The SH bond moment was also evaluated from $\text{μ}{}_{\mathrm{c}}{}^{\mathrm{(1)}}$ and compared with the SH bond moment of similar molecules.     

On the super symmetry charges in the theory of scalar and spinor free fields

It is shown that for spinorial charges Q^(L))_α (α = 1, 2, L = 1, …, S) satisfying the commutation relations

$\text{{Q}{}^{\mathrm{(L)}}{}_{\mathrm{\alpha }}\text{, Q}{}^{\mathrm{(M)}}{}_{\mathrm{\beta }}\text{} = ε}{}_{\mathrm{\alpha }}\text{βa}{}^{\mathrm{LM}}\text{Q,}$

$\text{{Q}{}^{\mathrm{(L)}}{}_{\mathrm{\alpha }}\text{, Q}{}^{\mathrm{(M)+}}{}_{\mathrm{\beta }}\text{} = cσ}{}^{\mathrm{\mu }}{}_{\mathrm{\alpha \beta }}\text{P}{}_{\mathrm{\mu }}\text{δ}{}^{\mathrm{LM}}\text{,}$

$\text{[Q}{}^{\mathrm{(L)}}\text{)}{}_{\mathrm{\alpha }}\text{, P}{}^{\mathrm{\mu }}\text{] = 0,}$

where Q is a scalar charge commuting with the spinor charges as well aswith the energy- momentum vector Pμ, there can exist several different multiplets for free massive scalar and spinor fields.     

A note on the momentum distribution function for an electron gas

The one-electron momentum distribution function $\text{〈a}{}_{\mathrm{k\sigma }}{}^2\text{a}{}_{\mathrm{k\sigma }}\text{〉}$ for an electron gas is investigated by a diagrammatic analysis of perturbation theory. It is shown that $\text{〈a}{}_{\mathrm{k\sigma }}{}^2\text{a}{}_{\mathrm{k\sigma }}\text{〉}$ has the following exact asymptotic form for large k (k ? p_F; p_F, the Fermi momentum): $\text{〈a}{}_{\mathrm{k\sigma }}{}^2\text{a}{}_{\mathrm{k\sigma }}\text{〉 =}\text{4}\text{9}\text{(}\text{αr}{}_{\mathrm{s}}\text{π}\text{)}{}^2\text{×(}\text{p}{}_{\mathrm{<mtext>F</mtext>}}{}^8\text{k}{}^8\text{) g?(0) + ?}$, where g?(0) is the zero-distance value of the spin-up-spin-down pair correlation function. The physical implications of the above asymptotic form are discussed.     

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.     

Nonlinear temperature and velocity distributions in the two-dimensional Bénard problem

The nonlinear temperature and velocity profiles of a two-dimensional Boussinesq fluid heated from below are shown to be the sum or terms with periodicity $\text{Λ}\text{cr}\text{n}$, with n = 1, 2, 3; their amplitudes are a function of $\text{? =}\text{(R}{}_{\mathrm{<mtext>a</mtext>}}\text{? R}{}^{\mathrm{<mtext>cr</mtext>}}{}_{\mathrm{<mtext>a</mtext>}}\text{)}\text{R}{}^{\mathrm{<mtext>cr</mtext>}}{}_{\mathrm{<mtext>a</mtext>}}$. The results are in agreement with the observations of Bergé and Dubois.     

Observed and calculated interactions between valence states of the NO molecule

No perturbation between two valence states of NO has ever been identified, although many valence-Rydberg and several Rydberg-Rydberg perturbations have been extensively studied. The first valence-valence crossing to be experimentally documented for NO is reported here and occurs between the ¹⁵N¹⁸O B²Π (v = 18) and B′²Δ (v = 1) levels. No level shifts larger than the detection limit of 0.1 cm^?1 are observed at the crossings near $\text{J = 6.5 [B}{}^2\text{Π}\text{(F}{}_1\text{) ～ B′}{}^2\text{Δ}\text{(F}{}_2\text{)]}$ and $\text{J = 12.5 [B}{}^2\text{Π}\text{(F}{}_1\text{) ～ B′}{}^2\text{Δ}\text{(F}{}_1\text{)]}$; two crossings involving higher rotational levels could not be examined. Semi-empirical calculations of spin-orbit and Coriolis perturbation matrix elements indicate that although the electronic part of the $\text{B}{}^2\text{Π}\text{～ B′}{}^2\text{Δ}$ interaction is large, a small vibrational factor renders the ¹⁵N¹⁸O B (v = 18) ? B′ (v = 1) perturbation unobservable. Semi-empirical estimates are given for all perturbation matrix elements of the operators $\text{Σ}{}_{\mathrm{i}}\text{a}\text{?}{}_{\mathrm{i}}\text{l}{}_{\mathrm{i}}\text{·s}{}_{\mathrm{i}}$ and $\text{B(L}{}_{\mathrm{\pm }}\text{S}{}_{\mathrm{?}}\text{? J}{}_{\mathrm{\pm }}\text{L}{}_{\mathrm{?}}\text{)}$ which connect states belonging to the configurations $\text{(σ2p)}{}^2\text{(π2p)}{}^4\text{(π}{}^1\text{2p)}$, $\text{(σ2p)(π2p)}{}^4\text{(π}{}^1\text{2p)}{}^2$, and $\text{(σ2p)}{}^2\text{(π2p)}{}^3\text{(π}{}^1\text{2p)}{}^2$.     

Binding energies of λλ hypernuclei and the λλ interaction

The binding energies of the ΛΛ hypernuclei ¹⁰_ΛΛBe and ⁶_ΛΛHe are calculated variationally with a 2α + 2Λ and with an α + 2Λ model, respectively. For ¹⁰_ΛΛBe the integrations were made with Monte Carlo techniques while for ⁶_ΛΛHe direct numerical methods were used. A wide range of phenomenological ΛΛ potentials based on meson-exchange models was considered. An approximately universal linear relation between the calculated values of $\text{B}{}_{\mathrm{\Lambda \Lambda }}\text{(}{}^{10}{}_{\mathrm{\Lambda \Lambda }}\text{Be}\text{)}$ and of $\text{B}{}_{\mathrm{\Lambda \Lambda }}\text{(}{}^6{}_{\mathrm{\Lambda \Lambda }}\text{He}\text{)}$ is obtained. For the experimental value of $\text{B}{}_{\mathrm{\Lambda \Lambda }}\text{(}{}^{10}{}_{\mathrm{\Lambda \Lambda }}\text{Be}\text{) = 17.7 ± 0.1}\text{MeV}$ this relation predicts a much too small value of $\text{B}{}_{\mathrm{\Lambda \Lambda }}\text{(}{}^6{}_{\mathrm{\Lambda \Lambda }}\text{He}\text{)}$, well below the lower limit of the quoted experimental value of 10.9 ± 0.6 MeV. For ΛΛ potentials with repulsive cores the relations, for a given $\text{B}{}_{\mathrm{\Lambda \Lambda }}\text{(}{}^{10}{}_{\mathrm{\Lambda \Lambda }}\text{Be}\text{)}$, between the low-energy ΛΛ scattering parameters a, r₀ and the intrinsic range b are both approximately universal and independent of the detailed potential shape. For the experimental value of $\text{B}{}_{\mathrm{\Lambda \Lambda }}\text{(}{}^{10}{}_{\mathrm{\Lambda \Lambda }}\text{Be}\text{)}$ the preferred values are 2.5 ? ?a ? 3.5 fm, 2.6 ? r₀ ? 3.1 fm. The large and negative values of a correspond to conditions not too far from a bound ¹S₀ ΛΛ state and could indicate a 6-quark dibaryon state with the same quantum numbers and above the ΛΛ threshold.     

How to continue the predictions of perturbative QCD from the spacelike region where they are derived to the timelike regime where experiments are performed

The predictions of perturbative QCD are derived in the deep euclidean region, whereas the physical region for most observables is timelike. The confrontation of these predictions with experiment thus necessitates an analytic continuation. This we find introduces large higher order corrections in terms of α_s(|Q²|), the usual choice ofperturbative expansion parameter. These corrections are naturally absorbed by changing to the expansion parameter $\text{a}\text{(Q}{}^2\text{) = |α}{}_{\mathrm{<mtext>s</mtext>}}\text{(Q}{}^2\text{)|(}\text{Re}\text{α}{}_{\mathrm{<mtext>s</mtext>}}\text{(Q}{}^2\text{)/|α}{}_{\mathrm{<mtext>s</mtext>}}\text{(Q}{}^2\text{)|)}{}^{\mathrm{<mtext>(n?2)</mtext><mtext>3</mtext>}}$, where α_s(Q²)ⁿ is the leading term in the spacelike region. For the intermediate range of Q² experimentally accessible at present, where $\text{a}\text{(Q}{}^2\text{)}$ is significantly smaller than α_s(|Q²|), we find the resulting phenomenology is improved. In particular, we demonstrate how the values of $\text{Λ}{}_{\mathrm{<mtext>MS</mtext>}}$ obtained from analyses of quarkonium decays become consistent.     

Neutron-proton shell model multiplets in 88Y and 90Y from a study of the (α, nγ) reaction

The non-selective nature of the (α, nγ) reaction has been used to complement information from charged-particle reactions on the level structure of ⁸⁸Y and ⁹⁰Y. The γ-ray spectra were recorded with a 25 cm³ Ge(Li) detector at 90° to the beam using primarily targets of ⁸⁵Rb₂CO₃ and ⁸⁷Rb₂CO₃ and α-particle energies of 11.8, 12.2 and 13.0 MeV. The resulting transitions were accommodated in level schemes that involved primarily the following shell model configurations: $\text{(π}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}^1\text{(ν}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?1}}$, $\text{(π}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?1}}\text{(ν}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}^1$, $\text{(π}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}^1\text{(ν}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?1}}$, $\text{(π}\text{f}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?1}}\text{(ν}\text{g}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}^{\mathrm{?1}}$ in ⁸⁸Y and $\text{(π}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}^1\text{(ν}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)}{}^1$, $\text{π}\text{g}\text{(}{}_{\mathrm{<mtext>9</mtext><mtext>2</mtext>}}\text{)}{}^1\text{(ν}\text{d}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}\text{)}{}^1$,$\text{(π}\text{p}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}^1\text{(ν}\text{s}{}_{\mathrm{<mtext>1</mtext><mtext>2)</mtext>}}\text{)}{}^1$ in ⁹⁰Y.     

Hyperfine structure of CH3OH

Hyperfine structure of the (0, 0, 1) - (1, 0, 1) transition of methanol has been investigated by beam absorption and of the (J, 1, 3?) → (J, 1, 3+) transitions for J = 2, 3, and 6 by beam-maser spectroscopy. The best-fit results for the spin-rotation and spin-spin coupling constants $\text{C}{}_{\mathrm{JK\tau \pm }}{}^{\mathrm{(i)}}$ and $\text{D}{}_{\mathrm{JK\tau \pm }}{}^{\mathrm{(i)}}$, respectively, are in kHz¹: $\text{C}{}_{101}{}^{\mathrm{(1)}}\text{= 2.4(10)}$, $\text{C}{}_{101}{}^{\mathrm{(2)}}\text{= ?0.6(10)}$, $\text{D}{}_{101}{}^{\mathrm{(1)}}\text{= ?13.8(9)}$, $\text{D}{}_{101}{}^{\mathrm{(2)}}\text{= 7.0(9)}$, $\text{C}{}_{\mathrm{213?}}{}^{\mathrm{(1)}}\text{= ?5.0(10)}$, $\text{C}{}_{\mathrm{213?}}{}^{\mathrm{(2)}}\text{= ?5.5(10)}$ and ($\text{C}{}_{\mathrm{J13?}}{}^{\mathrm{(2)}}\text{- C}{}_{\mathrm{J13+}}{}^{\mathrm{(2)}}\text{) = 0.98(9)}$.     

The measurement of the rotational relaxation times of OCS from the nutation signals

The time dependence of microwave absorption was measured for the J = 2-1 and J = 3-2 transitions of OCS under on- and off-resonant conditions utilizing Stark and source modulation, respectively. The two effective pressure parameters obtained under the two conditions, which correspond to $\text{(T}{}_2{}^{\mathrm{?1}}\text{+ T}{}_1{}^{\mathrm{?1}}\text{)}\text{4πP}$ and $\text{(2πT}{}_2\text{P)}{}^{\mathrm{?1}}$, respectively, according to the Bloch equation, are different beyond experimental error; the difference $\text{(T}{}_2{}^{\mathrm{?1}}\text{? T}{}_1{}^{\mathrm{?1}}\text{)}\text{2πP}$ is 0.94 ± 0.38 (2.5σ) MHz/Torr for J = 2?1. This difference was also determined to be 1.19 ± 0.30 MHz/Torr from the dependence of the nutation frequency on the microwave power.     

The ultraviolet absorption spectrum of thioformaldehyde

The spectra of H₂CS and D₂CS were surveyed over the wavelength region from 230 to 180 nm and four distinct absorptions were identified. These are assigned to transitions from the $\text{X}\text{?}{}^1\text{A}{}_1$ ground state to the $\text{B}\text{?}{}^1\text{A}{}_1\text{(π, π}{}^1\text{)}$, $\text{C}\text{?}{}^1\text{B}{}_2\text{(n, 3s)}$, $\text{D}\text{?}{}^1\text{A}{}_1\text{(n, 3p}{}_{\mathrm{y}}\text{)}$, and $\text{E}\text{?}{}^1\text{B}{}_2\text{(n, 3p}{}_{\mathrm{z}}\text{)}$ electronic states. A vibrational and rotational analysis of the second system was undertaken. The results indicate that the molecule is planar in the $\text{C}\text{?}{}^1\text{B}{}_2\text{(n, 3s)}$ state and that while the CH and CS bond lengths remain near their ground-state values, the HCH angle increases substantially.     

Extending the QCD leading logs up to reggeon field theory

The deep inelastic structure function D(ω, q²) is calculated in the leading log approximation for $\text{(}\text{Nβ}{}_2\text{π}{}^2\text{)α}{}^2{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}_0{}^2\text{) 1}\text{n}\text{ω < 0.84 1}\text{n}\text{(}\text{1}\text{α}{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}^2\text{))}$. For larger ω up to ( the influence of reggeon cuts proves to slow down the growth of the structure function. A reggeon diagram technique is developed, and D is calculated up to a pre-exponent O(1), leading to D(ω, q²) ∝ q² for $\text{(}\text{Nβ}{}_2\text{π}{}^2\text{)α}{}^2{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}^2{}_0\text{) 1}\text{n}\text{ω ? 0.42}\text{α}{}^2{}_{\mathrm{<mtext>S</mtext>}}\text{(q}{}_0{}^2\text{)}\text{α}{}_{\mathrm{<mtext>S</mtext>}}{}^2\text{(q}{}^2\text{)}$. By assuming the reggeon diagrams when ω is still greater, one can expect to obtain a strong coupling behaviour: D(ω, q²) ∝ q²(ln ω)^η (η <2).     

Classical integrable finite-dimensional systems related to Lie algebras

During the last few years many dynamical systems have been identified, that are completely integrable or even such to allow an explicit solution of the equations of motion. Some of these systems have the form of classical one-dimensional many-body problems with pair interactions; others are more general. All of them are related to Lie algebras, and in all known cases the property of integrability results from the presence of higher (hidden) symmetries. This review presents from a general and universal viewpoint the results obtained in this field during the last few years. Besides it contains some new results both of physical and mathematical interest.The main focus is on the one-dimensional models of n particles interacting pairwise via potentials V(q) = g²ν(q) of the following 5 types: $\text{ν}{}_{\mathrm{<mtext>I</mtext>}}\text{(q)=q}{}^{\mathrm{?2}}\text{, ν}{}_{\mathrm{<mtext>II</mtext>}}\text{(q)=a}{}^{\mathrm{?2}}\text{sinh}{}^2\text{(aq), ν}{}_{\mathrm{<mtext>III</mtext>}}\text{(q)=a}{}^2\text{/}\text{sin}\text{2(aq), ν}{}_{\mathrm{<mtext>IV</mtext>}}\text{=a}{}^2\text{P}\text{(aq), , ν}{}_{\mathrm{<mtext>V</mtext>}}\text{(q)=q}{}^{\mathrm{?2}}\text{+ω}{}^2\text{q}{}^2$. Here $\text{P}$(q) is the Weierstrass function, so that the first 3 cases are merely subcases of the fourth. The system characterized by the Toda nearest-neighbor potential, g_j²exp[-a(q_j?q_j+1)], is moreover considered. Various generalizations of these models, naturally suggested by their association with Lie algebras, are also treated.     

Spectrum and structure of the He2 molecule: Characterization of the triplet states associated with (1σg)2(1σu)nsσ, ndσ, ndπ, and ndδ (n = 5–12)

Emission spectra for the electronic transitions $\text{ndλ(}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{u}}\text{,}{}^3\text{Δ}{}_{\mathrm{u}}\text{) → 2pπ b}{}^3\text{Π}{}_{\mathrm{g}}\text{(n = 5–12)}$, $\text{nsσ}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 2pπ b}{}^3\text{Π}{}_{\mathrm{g}}\text{(n = 5–12)}$, $\text{ndλ(}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{u}}\text{,}{}^3\text{Δ}{}_{\mathrm{u}}\text{) → 3pσ c}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{(n = 5–10)}$, $\text{nsσ}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 3pσ c}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{(n = 5–11)}$, $\text{ndλ(}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{u}}\text{,}{}^3\text{Δ}{}_{\mathrm{u}}\text{) → 3pπ e}{}^3\text{Π}{}_{\mathrm{g}}\text{(n = 6–11)}$, $\text{nsσ}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 3pπ e}{}^3\text{Π}{}_{\mathrm{g}}\text{(n = 6–11)}$, $\text{nsσ}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{→ 4pσ g}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{(n = 9–11)}$, and $\text{10dδ}{}^3\text{Δ}{}_{\mathrm{u}}\text{→ 4pσ g}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ of ⁴He₂ are reported and the electronic structure of the triplet states associated with v = 0 of (1σ_g)²(1σ_u) nsσ and ndλ characterized. The energy levels comprising the $\text{(1σ}{}_{\mathrm{<mtext>g</mtext>}}\text{)}{}^2\text{(1σ}{}_{\mathrm{<mtext>u</mtext>}}\text{)ndλ(}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Δ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{)}$ and the $\text{(1σ}{}_{\mathrm{<mtext>g</mtext>}}\text{)}{}^2\text{(1σ}{}_{\mathrm{<mtext>u</mtext>}}\text{)ndλ(}{}^3\text{Π}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{,}{}^3\text{Δ}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{)}$ manifolds exhibit strong channel mixing, while the mixing of the $\text{(1σ}{}_{\mathrm{<mtext>g</mtext>}}\text{)}{}^2\text{(1σ}{}_{\mathrm{<mtext>u</mtext>}}\text{)nsσ}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ with the $\text{nd(}{}^3\text{λ}\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Δ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{)}$ channel structure is relatively minor. Models based on multichannel quantum defect theory are used to aid in the spectral assignments and to correlate the observed level structures. We show that three-limit and two-limit models adequately represent the bulk of the observed $\text{ndλ(}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Π}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{,}{}^3\text{Δ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{)}$ and $\text{ndλ(}{}^3\text{Π}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{,}{}^3\text{Δ}{}_{\mathrm{u}}{}^{\mathrm{?}}\text{)}$ channel structures, respectively.     

Self-adjointness of the minimal Schrödinger operator with potential belonging to L1, loc

Let $\text{0 ?q(x) ∈L}{}_{\mathrm{1,loc}}\text{(}\text{R}{}^{\mathrm{m}}\text{)}$,m? 1.Consider the operatorT₀ = ?Δ+q with domain consisting of all bounded measurable functions $\text{u(x), x ∈}\text{R}{}^{\mathrm{m}}$, having bounded support, for which the distribution ?Δu+qu belongs to $\text{L}{}_2\text{(}\text{R}{}^{\mathrm{m}}\text{)}$. The main result of the paper is essential self-adjointness of $\text{T}{}_0\text{in L}{}_2\text{(}\text{R}{}^{\mathrm{m}}\text{)}$. The proof is independent of a method due to Kato who recently established the self-adjointness of a maximal Schrödinger operator corresponding to such potential.     

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.     

Molecular structure of phosgene as studied by gas electron diffraction and microwave spectroscopy: The rz structure and isotope effect

The r_z structure of phosgene has been determined by a joint analysis of the electron diffraction intensity and the rotational constants as follows: $\text{r}{}_{\mathrm{z}}\text{(}\text{CO}\text{) = 1.1785 ± 0.0026}\text{A}\text{?}$, $\text{r}{}_{\mathrm{z}}\text{(}\text{CCl}\text{) = 1.7424 ± 0.0013}\text{A}\text{?}$, ∠_z;ClCCl = 111.83 ± 0.11°, where uncertainties represent estimated limits of experimental error. The effective constants representing bond-stretching anharmonicity have been obtained from an analysis of the isotopic differences in the r_z structure: $\text{a}{}_3\text{(}\text{CO}\text{) = 2.9 ± 0.9}\text{A}\text{?}{}^{\mathrm{?1}}$, $\text{a}{}_3\text{(}\text{CCl}\text{) = 1.6 ± 0.4}\text{A}\text{?}{}^{\mathrm{?1}}$. The equilibrium bond distances have been estimated from the r_z structure for the normal species and from the anharmonic constants to be $\text{r}{}_{\mathrm{e}}\text{(}\text{CO}\text{) = 1.1756 ± 0.0032}\text{A}\text{?}$, $\text{r}{}_{\mathrm{e}}\text{(}\text{CCl}\text{) = 1.7381 ± 0.0019}\text{A}\text{?}$.     

Derivation of the Gribov—Lipatov reciprocity relation in a scaling bootstrap model

The Gribov—Lipatov reciprocity relation $\text{ν}\text{W}{}_2\text{(ω) = ? ω}{}^{-3}\text{νW}{}_2\text{(ω}{}^{-1}\text{)}$ is shown to be valid in scaling bootstrap model under certain assumptions.