α(Q2) corrections to particle multiplicity ratios in gluon and quark jets

The order $\text{α(Q}{}^2\text{)}$ correction to the particle multiplicity ratio in gluon and quark jets is calculated in QCD. We find

$\text{r=}\text{9}\text{4}\text{1?}\text{αC}{}_{\mathrm{<mtext>A</mtext>}}\text{2π}\text{1}\text{3}\text{+}\text{N}{}_{\mathrm{?}}\text{3C}{}_{\mathrm{<mtext>A</mtext>}}\text{?}\text{2N}{}_{\mathrm{?}}\text{C}{}_{\mathrm{<mtext>F</mtext>}}\text{3C}{}^2{}_{\mathrm{<mtext>A</mtext>}}$

with r=〈n〉_{gluon jet}/〈n〉_{quark jet}. The method used is systematic and could be used for an order α(Q²) calculation.     

Optical-optical double-resonance spectroscopy of BaF: The E2Σ+ and F2Π states

Sub-Doppler optical-optical double-resonance excitation spectra of BaF were recorded using two single-mode cw dye lasers. In the 30 000-cm^?1 region, the electronic states observed were E²Σ⁺ and F²Π. The latter had been previously assigned as the “F²Σ⁺” state by Fowler [Phys. Rev.59, 645–652 (1941)]. The (3, 0) and (4, 0) bands of the E²Σ⁺-B²Σ⁺ transition and the (1, 0) and (2, 0) bands of the F²Π-B²Σ⁺ transition were rotationally analyzed. The molecular constants suggest inferences about the dominant atomic orbital character of the Rydberg molecular orbitals responsible for the E²Σ⁺ and F²Π electronic states. A new electronic state, the $\text{E′}{}^2\text{Π}$, is predicted. The molecular parameters obtained (in cm^?1, 1σ uncertainty in parentheses) are

     

6.

Deep inelastic sum rules at fixed hadron energy     

C. Lopez  F.J. Yndurain 《Nuclear Physics B》1982,194(3):397-402

Experimentally, it is much easier to measure structure functions at fixed hadron energy E_h, rather than at fixed Q². We prove the sum rules

,

$\text{h}{}_{\mathrm{NS}}\text{=}\text{4}\text{3}\text{(}\text{1}\text{6}\text{π}{}^2\text{?}\text{5}\text{8}\text{),}$

$\text{h}{}_{\mathrm{S}}\text{=}\text{4}\text{16+3n}{}_{\mathrm{<mtext>f</mtext>}}\text{(2π}{}^2\text{+}\text{1}\text{6}\text{π}{}^2\text{n}{}_{\mathrm{<mtext>f</mtext>}}\text{?}\text{65}\text{12}\text{?}\text{5}\text{72}\text{n}{}_{\mathrm{<mtext>f</mtext>}}\text{).}$

Here s = 2m_pE_h and F_2,3 are the standard functions for scattering of neutrinos on an isoscalar target. K is an unknown constant, and the corrections to the sum rules are O(α_s²), O(α_s^1.75), respectively.     

7.

Deperturbation study of the 0_u⁺ symmetry states of As₂ observed in the energy range 39 000–45 000 cm⁻¹     

Pierre Perdigon  Françoise Martin 《Journal of Molecular Spectroscopy》1980,83(1):40-63

The mutual perturbations of the A¹Σ_u⁺ and b0_u⁺ states of As₂ are due to a strong spin-orbit interaction. The numerical treatment of these perturbations leads to the following parameters:

	$\text{v′}{}_{\mathrm{E}}$	$\text{E}{}^2\text{Σ}{}^{\mathrm{+}}$	$\text{v′}{}_{\mathrm{F}}$	$\text{F}{}^2\text{Π}$
$\text{T}{}_{\mathrm{v\prime 0}}$	3	29 767.32(1)	1	29 997.29(1)
$\text{Δ}\text{G}{}_{\mathrm{<mtext>v\prime \; +\; </mtext><mtext>1</mtext><mtext>2</mtext>}}$	3	522.841(27)	1	522.553(2)
$\text{B}{}_{\mathrm{e}}$		0.22990(22)		0.22931(8)
$\text{α}{}_{\mathrm{e}}$		0.00113(14)		0.00108(2)
$\text{A}{}_{\mathrm{v\prime }}$			1	56.9840(12)
$\text{p}{}_{\mathrm{v\prime }}$			1	?0.02426(6)
$\text{γ}{}_{\mathrm{v\prime }}$	3	?0.17367(46)

     

8.

νW₂ at small ω′ and resonance form factors in a quark model with broken SU(6)     

F.E. Close 《Physics letters. [Part B]》1973,43(5):422-426

The small ω′ behaviour of F₂^en/F₂^ep and the apparent difference in the q² dependences of the magnetic form factor of the proton and of the transition to Δ⁺(1236) are quantitatively correlated in a model where nucleon consistes of a quarks and a scalar or vector core. The proton and Δ transition form factors suggest that only the scalar core contributes at large q² and small ω′. As a result the ω′ dependence of $\text{F}{}_2{}^{\mathrm{<mtext>en</mtext>}}\text{F}{}_2{}^{\mathrm{<mtext>ep</mtext>}}$ is obtained for ω′ < 3 and predictions for the weak structure functions and polarisation asymmetries at smallω′ are presented. We predict $\text{F}{}^{\mathrm{<mtext>\nu </mtext><mtext>p</mtext>}}\text{F}{}^{\mathrm{<mtext>\nu </mtext><mtext>n</mtext><mtext>\omega \prime \to 1</mtext><mtext>0</mtext>}}$ asymmetries $\text{ω′→1}\text{1}$ and also expect that $\text{G}{}_{\mathrm{<mtext>m</mtext>}}{}^{\mathrm{<mtext>n</mtext>}}\text{G}{}_{\mathrm{<mtext>m</mtext>}}{}^{\mathrm{<mtext>p</mtext>}}\text{→}\text{?1}\text{2}$ as q²→∞.     

9.

Silver-compensated germanium center in α-quartz     

F.C. Laman  J.A. Weil 《Journal of Physics and Chemistry of Solids》1977,38(9):949-956

A synthetic germanium-doped crystal of α-quartz was subjected to an electro-diffusion process $\text{ca. 600}\text{V}\text{cm}$, 625°K), in which Ag⁺ ions were introduced along the crystal's optic axis (c). A 9800MHz electron paramagnetic resonance spectrum at room temperature, taken after room temperature x-irradiation, revealed the presence of a silver-compensated germanium center A_Ge?Ag with large, almost isotropic ¹⁰⁷Ag and ¹⁰⁹Ag hyperfine splittings (26.078, 30.112 mT for magnetic field B∥c). Measurement of the spin-Hamiltonian (i.e. matrices $\text{g}$, $\text{A}{}^{73}{}_{\mathrm{<mtext>Ge</mtext>}}$, $\text{A}{}^{107}{}_{\mathrm{<mtext>Ag</mtext>}}$ and $\text{A}{}^{109}{}_{\mathrm{<mtext>Ag</mtext>}}\text{)}$ discloses that a suitable model for the observed center utilizes germanium, substituted for silicon, with the accompanying silver interstitial in a nearby c-axis channel, and with electronic structure in which an appreciable admixture Ge⁴⁺?Ag⁰ to Ge³⁺?Ag⁺ exists. Estimates of the unpaired electron orbital are presented.     

10.

Flavor symmetry,K0–K̄0 mixing and new physics effects on CP violation in D± and D±s decays     

《Physics letters. [Part B]》1999,450(4):405-411

     

11.

Wavelets on the 2-sphere and related manifolds     

《Reports on Mathematical Physics》1999,43(1-2):13-24

     

12.

Observation of the v = 0–13 levels of Na₂b³Π_u by OODR ³Λ_g-b³Π_u fluorescence spectroscopy     

Li Li  S.F. Rice  R.W. Field 《Journal of Molecular Spectroscopy》1984,105(2):344-350

The absolute vibrational numbering of the Na₂b³Π_u state has been established by direct observation of the v = 0–13 levels. These b³Π_u levels appear as the lower levels in rotationally resolved fluorescence spectra resulting from OODR excitation of ³Π_g, ³Δ_g, and ³Σ_g⁺ states via b³Π_u ～ A¹Σ_u⁺ mixed intermediate levels. The molecular constants for the Na₂b³Π_u state are (in cm^?1, one standard error in parentheses)

	$\text{T}{}_{\mathrm{e}}\text{(}\text{cm}{}^{\mathrm{?1}}\text{)}$	$\text{ω}{}_{\mathrm{e}}\text{(}\text{cm}{}^{\mathrm{?1}}\text{)}$	$\text{ω}{}_{\mathrm{e}}\text{x}{}_{\mathrm{e}}\text{(}\text{cm}{}^{\mathrm{?1}}\text{)}$	$\text{B}{}_{\mathrm{e}}\text{(}\text{cm}{}^{\mathrm{?1}}\text{)}$
$\text{A}{}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$	40 806 (3)	297 (2)	5.1 (2)	0.0798 (12)
$\text{b0}{}_{\mathrm{u}}{}^{\mathrm{+}}$	38 884 (3)	422 (1)	8.8 (1)	0.0783 (12)

     

13.

Matthiessen's rule and its variation for cyclotron resonance width in two and three dimensions     

M. Prasad  S. Fujita 《Physics letters. A》1977,63(2):147-148

Based on the proper connected diagram expansion, we calculated cyclotron resonance widths Γ_n associated with neighboring Landau states (n, n +1) for free electrons in interaction with more than one kind of impurities. In 3D usual Matthiessen's rule Γ_n=Γ⁽¹⁾_n+Γ⁽²⁾_n+…where Γ⁽ⁱ⁾_n represent widths calculated separately for each kind, is obtained. In 2D a new rule: is obtained.     

14.

Discrete series of lie superalgebras     

Jouko Mickelsson 《Reports on Mathematical Physics》1980,18(2):197-210

Let $\text{g}$ denote the Lie superalgebra $\text{sl}\text{(n, 1)}$. Its even part is the Lie algebra $\text{g}{}_0\text{=}\text{gl}\text{(n)}$ of n×n complex matrices. Let

denote the reductive subalgebra $\text{gl}\text{(p)⊕}\text{gl}\text{(q)}$ in $\text{g}{}_0\text{, p+q=n}$. We show that for a certain set Λ⁺₀ of irreducible finite dimensional

-modules there exists, for each λ?Λ⁺₀, an irreducible

-finite g-module (which is unique up to equivalence) with minimal

- type λ.     

15.

Anomalous stoner enhancements in amorphous systems     

R. Oppermann 《Solid State Communications》1982,44(8):1297-1299

An n-orbital model describing both elastic impurity scattering and exchange interaction is examined near its instability for itinerant ferromagnetism. At the critical point and at zero temperature, long range spin fluctuations cause anomalous enhancements of the density of states near the Fermi energy with $\text{?(E) - ?(E}{}_{\mathrm{F}}\text{) ∝ |E ? E}{}_{\mathrm{F}}\text{|}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$ in three-dimensions (3D) and with ln²|E ? E_F| in 2D. An estimation of the conductivity $\text{σ(Ω)}$ in a continuum analog model reveals Ω^{$\text{1}\text{4}$} -and ln²$\text{|Ω}{}_{\mathrm{\tau }}\text{|}$-corrections in 3D and 2D respectively.     

16.

The dual of supersymmetric SU(2k) with an antisymmetric tensor and composite dualities     

《Nuclear Physics B》1995,452(3):513-525

     

17.

Transverse spin correlation function of the one-dimensional spin-$\text{1}\text{2}$ XY model     

Takashi Tonegawa 《Solid State Communications》1981,40(11):983-986

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.     

18.

The study of Ba 6p1/2nd (J = 1, 3) autoionizing states     

《Journal of Electron Spectroscopy and Related Phenomena》2004,136(3):273-280

     

19.

The spectrum and structure of the He2 molecule: Characterization of the triplet states associated with the UAO's 4pπ and 5pπ     

F.B Orth  M.L Ginter 《Journal of Molecular Spectroscopy》1977,64(2):223-232

The He₂ band systems $\text{4pπ i}{}^3\text{Π}{}_{\mathrm{g}}\text{→ 2s a}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ and $\text{5pπ l}{}^3\text{Π}{}_{\mathrm{g}}\text{→ 2s a}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ are described in detail, and the i and l states characterized. A number of significant perturbations in the i and l states are identified, and the possible perturber states discussed. The following molecular constants (cm^?1) are reported:

$\text{T}{}_{\mathrm{e}}$	13 517.2 (1.3)	$\text{B}{}_{\mathrm{e}}$	0.1434 (0.0027)
$\text{ω}{}_{\mathrm{e}}$	153.6 (1.1)	$\text{α}{}_{\mathrm{e}}$	9×10?5 (4×10?4)
$\text{ω}{}_{\mathrm{e}}\text{ξ}{}_{\mathrm{e}}$	0.47 (0.09)	$\text{r}{}_{\mathrm{e}}$	3.20 (0.03) Å
$\text{A}{}_{\mathrm{e}}$	7.85 (0.60)	$\text{α}{}_{\mathrm{A}}$	0.19 (0.16)

     

20.

On the ratio Σ⁰/Λ in electroproduction off protons     

Otto Nachtmann 《Nuclear Physics B》1974,74(3):422-428

Recent experimental results on electroproduction off protons show that the ratio σ(ep → eK⁺Σ⁰)/σ(ep → eK⁺Λ) decreases strongly with increasing Q². A simple argument is given in the framework of the quark parton model which could provide a qualitative understanding of this fact. The decrease of the Σ⁰/Λ ratio is related to the decrease of the ratio $\text{F}{}_1{}^{\mathrm{<mtext>\gamma </mtext><mtext>n</mtext>}}\text{/F}{}_1{}^{\mathrm{<mtext>\gamma </mtext><mtext>p</mtext>}}$ as Q² increases, where $\text{F}{}_1{}^{\mathrm{<mtext>\gamma </mtext><mtext>p</mtext>}}\text{and F}{}_1{}^{\mathrm{<mtext>\gamma </mtext><mtext>n</mtext>}}$ are the usual structure functions for deep inelastic electron-nucleon scattering.     

State	$\text{ω}{}_{\mathrm{e}}$	$\text{xω}{}_{\mathrm{e}}$	$\text{B}{}_{\mathrm{e}}$	$\text{α}{}_{\mathrm{e}}$	$\text{r}{}_{\mathrm{e}}\text{(}\text{A}\text{?}\text{)}$
$\text{i}{}^3\text{Π}{}_{\mathrm{g}}$	1707.95	35.00	7.242g	0.222	1.0782
$\text{l}{}^2\text{Π}{}_{\mathrm{g}}$	1703.86	34.97	7.2264	0.2188	1.0794

Deep inelastic sum rules at fixed hadron energy

Experimentally, it is much easier to measure structure functions at fixed hadron energy E_h, rather than at fixed Q². We prove the sum rules

,

$\text{h}{}_{\mathrm{NS}}\text{=}\text{4}\text{3}\text{(}\text{1}\text{6}\text{π}{}^2\text{?}\text{5}\text{8}\text{),}$

$\text{h}{}_{\mathrm{S}}\text{=}\text{4}\text{16+3n}{}_{\mathrm{<mtext>f</mtext>}}\text{(2π}{}^2\text{+}\text{1}\text{6}\text{π}{}^2\text{n}{}_{\mathrm{<mtext>f</mtext>}}\text{?}\text{65}\text{12}\text{?}\text{5}\text{72}\text{n}{}_{\mathrm{<mtext>f</mtext>}}\text{).}$

Here s = 2m_pE_h and F_2,3 are the standard functions for scattering of neutrinos on an isoscalar target. K is an unknown constant, and the corrections to the sum rules are O(α_s²), O(α_s^1.75), respectively.     

Deperturbation study of the 0u+ symmetry states of As2 observed in the energy range 39 000–45 000 cm−1

The mutual perturbations of the A¹Σ_u⁺ and b0_u⁺ states of As₂ are due to a strong spin-orbit interaction. The numerical treatment of these perturbations leads to the following parameters:

νW2 at small ω′ and resonance form factors in a quark model with broken SU(6)

The small ω′ behaviour of F₂^en/F₂^ep and the apparent difference in the q² dependences of the magnetic form factor of the proton and of the transition to Δ⁺(1236) are quantitatively correlated in a model where nucleon consistes of a quarks and a scalar or vector core. The proton and Δ transition form factors suggest that only the scalar core contributes at large q² and small ω′. As a result the ω′ dependence of $\text{F}{}_2{}^{\mathrm{<mtext>en</mtext>}}\text{F}{}_2{}^{\mathrm{<mtext>ep</mtext>}}$ is obtained for ω′ < 3 and predictions for the weak structure functions and polarisation asymmetries at smallω′ are presented. We predict $\text{F}{}^{\mathrm{<mtext>\nu </mtext><mtext>p</mtext>}}\text{F}{}^{\mathrm{<mtext>\nu </mtext><mtext>n</mtext><mtext>\omega \prime \to 1</mtext><mtext>0</mtext>}}$ asymmetries $\text{ω′→1}\text{1}$ and also expect that $\text{G}{}_{\mathrm{<mtext>m</mtext>}}{}^{\mathrm{<mtext>n</mtext>}}\text{G}{}_{\mathrm{<mtext>m</mtext>}}{}^{\mathrm{<mtext>p</mtext>}}\text{→}\text{?1}\text{2}$ as q²→∞.     

Silver-compensated germanium center in α-quartz

A synthetic germanium-doped crystal of α-quartz was subjected to an electro-diffusion process $\text{ca. 600}\text{V}\text{cm}$, 625°K), in which Ag⁺ ions were introduced along the crystal's optic axis (c). A 9800MHz electron paramagnetic resonance spectrum at room temperature, taken after room temperature x-irradiation, revealed the presence of a silver-compensated germanium center A_Ge?Ag with large, almost isotropic ¹⁰⁷Ag and ¹⁰⁹Ag hyperfine splittings (26.078, 30.112 mT for magnetic field B∥c). Measurement of the spin-Hamiltonian (i.e. matrices $\text{g}$, $\text{A}{}^{73}{}_{\mathrm{<mtext>Ge</mtext>}}$, $\text{A}{}^{107}{}_{\mathrm{<mtext>Ag</mtext>}}$ and $\text{A}{}^{109}{}_{\mathrm{<mtext>Ag</mtext>}}\text{)}$ discloses that a suitable model for the observed center utilizes germanium, substituted for silicon, with the accompanying silver interstitial in a nearby c-axis channel, and with electronic structure in which an appreciable admixture Ge⁴⁺?Ag⁰ to Ge³⁺?Ag⁺ exists. Estimates of the unpaired electron orbital are presented.     

Observation of the v = 0–13 levels of Na2b3Πu by OODR 3Λg-b3Πu fluorescence spectroscopy

The absolute vibrational numbering of the Na₂b³Π_u state has been established by direct observation of the v = 0–13 levels. These b³Π_u levels appear as the lower levels in rotationally resolved fluorescence spectra resulting from OODR excitation of ³Π_g, ³Δ_g, and ³Σ_g⁺ states via b³Π_u ～ A¹Σ_u⁺ mixed intermediate levels. The molecular constants for the Na₂b³Π_u state are (in cm^?1, one standard error in parentheses)

Matthiessen's rule and its variation for cyclotron resonance width in two and three dimensions

Based on the proper connected diagram expansion, we calculated cyclotron resonance widths Γ_n associated with neighboring Landau states (n, n +1) for free electrons in interaction with more than one kind of impurities. In 3D usual Matthiessen's rule Γ_n=Γ⁽¹⁾_n+Γ⁽²⁾_n+…where Γ⁽ⁱ⁾_n represent widths calculated separately for each kind, is obtained. In 2D a new rule: is obtained.     

Discrete series of lie superalgebras

Let $\text{g}$ denote the Lie superalgebra $\text{sl}\text{(n, 1)}$. Its even part is the Lie algebra $\text{g}{}_0\text{=}\text{gl}\text{(n)}$ of n×n complex matrices. Let

denote the reductive subalgebra $\text{gl}\text{(p)⊕}\text{gl}\text{(q)}$ in $\text{g}{}_0\text{, p+q=n}$. We show that for a certain set Λ⁺₀ of irreducible finite dimensional

-modules there exists, for each λ?Λ⁺₀, an irreducible

-finite g-module (which is unique up to equivalence) with minimal

- type λ.     

Anomalous stoner enhancements in amorphous systems

An n-orbital model describing both elastic impurity scattering and exchange interaction is examined near its instability for itinerant ferromagnetism. At the critical point and at zero temperature, long range spin fluctuations cause anomalous enhancements of the density of states near the Fermi energy with $\text{?(E) - ?(E}{}_{\mathrm{F}}\text{) ∝ |E ? E}{}_{\mathrm{F}}\text{|}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$ in three-dimensions (3D) and with ln²|E ? E_F| in 2D. An estimation of the conductivity $\text{σ(Ω)}$ in a continuum analog model reveals Ω^{$\text{1}\text{4}$} -and ln²$\text{|Ω}{}_{\mathrm{\tau }}\text{|}$-corrections in 3D and 2D respectively.     

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.     

The spectrum and structure of the He2 molecule: Characterization of the triplet states associated with the UAO's 4pπ and 5pπ

The He₂ band systems $\text{4pπ i}{}^3\text{Π}{}_{\mathrm{g}}\text{→ 2s a}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ and $\text{5pπ l}{}^3\text{Π}{}_{\mathrm{g}}\text{→ 2s a}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ are described in detail, and the i and l states characterized. A number of significant perturbations in the i and l states are identified, and the possible perturber states discussed. The following molecular constants (cm^?1) are reported:

On the ratio Σ0/Λ in electroproduction off protons

Recent experimental results on electroproduction off protons show that the ratio σ(ep → eK⁺Σ⁰)/σ(ep → eK⁺Λ) decreases strongly with increasing Q². A simple argument is given in the framework of the quark parton model which could provide a qualitative understanding of this fact. The decrease of the Σ⁰/Λ ratio is related to the decrease of the ratio $\text{F}{}_1{}^{\mathrm{<mtext>\gamma </mtext><mtext>n</mtext>}}\text{/F}{}_1{}^{\mathrm{<mtext>\gamma </mtext><mtext>p</mtext>}}$ as Q² increases, where $\text{F}{}_1{}^{\mathrm{<mtext>\gamma </mtext><mtext>p</mtext>}}\text{and F}{}_1{}^{\mathrm{<mtext>\gamma </mtext><mtext>n</mtext>}}$ are the usual structure functions for deep inelastic electron-nucleon scattering.