On investigating the structure of hadrons: Lattice Monte Carlo measurements of colour magnetic and electric fields and the topological charge density inside glueballs

We present some techniques for elucidating hadronic structure via lattice Monte Carlo calculations. Applying these techniques, we measure the fluctuations of colour magnetic and electric fields as well as the topological charge density inside and outside the lowest lying 0⁺ and 2⁺ glueballs in the SU(2) non-abelian lattice gauge theory. This gives us a picture of the glueball structure. We also obtain, as a by-product, an estimate of the gluon condensate ($\text{α}{}_{\mathrm{<mtext>s</mtext>}}\text{/π)〈π|F}{}_{\mathrm{\mu \nu }}{}^{\mathrm{a}}\text{F}{}_{\mathrm{\mu \nu }}{}_{\mathrm{a}}\text{|Ω〈}$ and an estimate of the 0^? glueball mass which agrees with our previous estimates.     

Necessary and sufficient conditions for the existence of a lagrangian. The case of quasi-linear field equations

Necessary and sufficient conditions for the existence of the Lagrangian associated with given field equations of motion are investigated. For the quasi-linear equations A_ab^μν(x^λ, φ^c, φ_?^c)φ_μν^b + B_a(x^μ, φ^b, φ_ν^b) = 0, the complete necessary and sufficient conditions are obtained, resorting to the formalism of an exterior derivative. It is emphasized that, to find expressions of these conditions, the anti-symmetric parts of the second derivatives of a Lagrangian, $\text{R}{}_{\mathrm{\mu \nu }}{}^{\mathrm{ab}}\text{= (}\text{?}{}^2\text{L}\text{?φ}{}_{\mathrm{\mu }}{}^{\mathrm{a}}\text{?φ}{}_{\mathrm{\nu }}{}^{\mathrm{b}}\text{?}\text{?}{}^2\text{L}\text{?φ}{}_{\mathrm{\nu }}{}^{\mathrm{a}}\text{?φ}{}_{\mathrm{\mu }}{}^{\mathrm{b}}\text{)/2}$, which disappear in the field equations, take an important role. The procedure to construct the Lagrandian associated with the field equations is also presented.     

The axial anomaly and anti-symmetric tensor fields

Spin-$\text{1}\text{2}$ fermions are coupled to external axial vector and rank-2 anti-symmetic tensor fields. The chiral U(1) Ward identity is shown to have anomalous structure given by $\text{F}{}_{\mathrm{\mu \nu }}\text{F}\text{?}{}^{\mathrm{\mu \nu }}$ only with F_μν the axial vector field strength tensor. No Additional axial anomalied are introduced due to the presence of the anti-symmetric tensor fields.     

The spectrum and structure of the He2 molecule: Characterization of the triplet states associated with the UAO's 4pσ, 5pσ, and 6pσ

The emission spectrum of the He₂ molecule has been rephotographed in the ～3200–4100 Å region and the $\text{4pσ g}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{→ 2s a}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$, $\text{5pσ k′}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{→ 2s a}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$, and $\text{6pσ n}{}^3\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}\text{→ 2s a}{}^3\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}$ transitions analyzed. The g, k′, and n states, which have not been reported previously, are characterized through v = 1, 2, and 1, respectively. Several small accidental perturbations have been observed in the rotational manifolds of the k′ and n states.     

Chiral ward identities,effective actions and meson-glueball mixing

The low-energy spectrum of 1⁺ and 0^? mesons in one-flavour QCS is investigated. It is shown that there exist two light pseudoscalar mesons, which are linear combinations of pure quark and pure glueball states. Simple relations implied by the axial anomaly for their decay constants are confirmed. The mass generation mechanism for the lightest pseudoscalar meson is identified as due to the mixing of the operators $\text{i}\text{ψ}\text{γ}{}_5\text{ψ}$ and $\text{(?}\text{g}{}^2\text{16π}{}^2\text{)}{}^1\text{F}{}_{\mathrm{\mu \nu }}{}^{\mathrm{a}}\text{F}{}^{\mathrm{a\mu \nu }}$, and the U(1) problem in this model is resolved. To establish these results, new functional methods are developed to determine the effective action for the appropriate fields in a low-energy approximation. A novel feature of our work is the introduction of a “symmetric” effective action, defined using a non-standard Legendre transform. The anomalous chiral Ward identities imply a simple invariance property for this functional, enabling it to be constructed in a particularly systematic way. Finally, the relation of our general results to the literature on effective lagrangians in the $\text{1}\text{N}$ approximation is discussed.     

Effects of Eu3+  Fe3+ exchange interaction on the spin Hamiltonian parameters of Fe3+ in EuGaG

The anisotropic exchange $\text{1}\text{3}\text{a}{}_{\mathrm{\mu \nu }}\text{Y}{}_{\mathrm{\mu \nu }}\text{(L}{}_{\mathrm{<mtext>Eu</mtext>}}\text{)S}{}_{\mathrm{<mtext>Eu</mtext>}}\text{· S}{}_{\mathrm{<mtext>Fe</mtext>}}\text{(0 < μ ? 6)}$ is incorporated with the isotropic exchange ?2 a₀₀S_Eu · S_Fe to interpret the observed spin-Hamiltonian parameters g and D of Fe³⁺ doped into EuGaG. Calculations from the observed g shifts yield a value of a₀₀ equal to 0.01 K. In order to explain the observed D shift, it is concluded that the spherical harmonics Y_μν(L_Eu) with μ > 2 are of dominant importance.     

Energies and orbital sizes for some Rydberg and valence states of the nitrogen molecule

Accurate SCF computations are reported on the Rydberg states of N₂ of electron configurations $\text{---1π}{}_{\mathrm{u}}{}^3\text{2π}{}_{\mathrm{u}}$, $\text{---1π}{}_{\mathrm{u}}{}^3\text{3σ}{}_{\mathrm{u}}$, and ---3σ_g2π_g, also on the valence states of the configuration $\text{---1π}{}_{\mathrm{u}}{}^3\text{1π}{}_{\mathrm{g}}$. The Rydberg state calculations supplement those of Lefebvre-Brion and Moser. A comparison is made between the $\text{---1π}{}_{\mathrm{u}}{}^3\text{2π}{}_{\mathrm{u}}$ states and the parallel set of states of the $\text{1π}{}_{\mathrm{u}}{}^3\text{1π}{}_{\mathrm{g}}$ configuration. This comparison shows a sharp difference in the ¹Σ⁺ states of the two configurations, the ¹Σ⁺ state being very high in the latter but relatively low in the former configuration. Recknagel coefficients are given for the several states of the two configurations; as expected, these are much smaller for the $\text{1π}{}_{\mathrm{u}}{}^3\text{2π}{}_{\mathrm{u}}$ configuration. Also, the ¹Δ state is relatively lower for the latter configuration.     

Measurement of Debye-Waller factors by Raman scattering from inter-term excitons and exciton-multiphonon states in FeF2

We have observed inter-term Raman scattering from ⁵T_2g→⁵E_g Frenkel excitons in antiferromagnetic FeF₂. It differs qualitatively from previously observed intra-term scattering in a sharply reduced zero-phonon cross section and the appearance of relatively strong exciton-phonon scattering. Since the Raman process is fully allowed, it is possible to measure excited state Debye-Waller factors, D, and we find $\text{D(Λ}{}_3{}^{\mathrm{+}}\text{+ Λ}{}_4{}^{\mathrm{+}}\text{,}{}^5\text{E}{}_{\mathrm{g}}\text{) = 0.04}$ and $\text{D(Λ}{}_1{}^{\mathrm{+}}\text{,}{}^5\text{E}{}_{\mathrm{g}}\text{) = 0.03}$.     

Gluon condensate and the interquark potential

We construct a potential for qurkonium systems using as the basic ingredients the gluon condensate, i.e., 〈0∥G_μν^aG_μν^a∥0〉 ≠ 0 to incorporate nonperturbative effects and using quark screening. The potential is able to account satisfactorily for the s$\text{s}$, c$\text{c}$ and b$\text{b}$ bound states with a flavor independent, essentially constant value for the effective coupling constant $\text{(}\text{α}{}_{\mathrm{<mtext>S</mtext>}}\text{≈ 0.45)}$. We also investigate heavier quark systems with the constant $\text{α}{}_{\mathrm{S}}$ and find that for quark mass ? 20 GeV the potential is essentially coulombic.     

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.     

Symmetry restoration and the background field method in gauge theories

Spontaneously broken gauge theories in a constant external electromagnetic field are shown to exhibit a first-order phase transition to a restored symmetry phase when the external field exceeds a certain critical value. The effects of fields characterized by various values of the two Lorentz invariants $\text{F}{}_1\text{=}\text{1}\text{2}\text{(B}{}^2\text{? E}{}^2\text{)}$ and F₂ = E · B are discussed. In a simple SU(2) model the critical field strength is found to be g_R²(F₁)_crit = 0.057 m_w⁴, m_w being the vector boson mass. A number of theoretical developments in the background field formalism are presented. A new gauge-fixing term, the background field R gauge, is introduced. The configuration space heat kernel method for evaluating functional determinants, extended to allow the use of dimensional regularization, is employed, and it is shown how to perform background field calculations in a gauge specified by an arbitrary parameter α. Further applications of these methods are discussed.     

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:

     

13.

Classical integrable finite-dimensional systems related to Lie algebras     

M.A. Olshanetsky  A.M. Perelomov 《Physics Reports》1981,71(5):313-400

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.     

14.

Local field theory of the dual string     

H.B. Nielsen  P. Olesen 《Nuclear Physics B》1973,57(2):367-380

We develop a (classical) local field theory which contains as a special solution the (classical) dual string recently discussed by Goddard, Goldstone, Rebbi and Thorn. The basic field is a gauge field F_μν(x), and the Lagrangian is given by $\text{(}\text{?1}\text{2α'}\text{)√F}{}^2$. We treat the case of closed strings (corresponding to the Shapiro-Virasoro model) where F_μν can be expressed in terms of potentials A_μ. Quantization of F_μν is briefly discussed, but a more thorough discussion is postponed.     

15.

A note on the momentum distribution function for an electron gas     

H. Yasuhara  Y. Kawazoe 《Physica A》1976,85(2):416-424

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.     

16.

Electronic spectrum of 1,5-naphthyridine: Vapor spectra     

Gad Fischer  I.G Ross 《Journal of Molecular Spectroscopy》1981,87(2):331-344

Analyses of the vapor spectra of 1,5-naphthyridine-d₀ and -d₆ are presented. The spectra are characterized by two principal origins, one the true electronic origin, magnetic dipole allowed, ${}^1\text{B}{}_{\mathrm{g}}\text{←}{}^1\text{A}{}_{\mathrm{g}}$, 27 598.5 cm^?1 (-d₆ 27 676.9), and the other a vibronic origin, electricd-dipole allowed, corresponding to the activity of a low-frequency vibration 6a_u, 183 cm^?1 (-d₆ 163). Extensive sequence structure is evident and the relative intensities of the sequence bands associated with the two origins provide the strongest argument for their assignments. The absence of 6a_u as a major source of intensity in the hot bands is in agreement with vibronic coupling calculations which propose that in absorption intensity “flows” to the lower-frequency vibrations.     

17.

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

Victor Elias 《Physics letters. [Part B]》1977,68(4):335-338

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.     

18.

Optical absorption and ESR study of F centres in BaClF and SrClF crystals     

M. Yuste  L. Taurel  M. Rahmani  D. Lemoyne 《Journal of Physics and Chemistry of Solids》1976,37(10):961-966

Magnetic and optical properties of two types of F centres, calledF(F^?) and F (Cl^?), created in BaClF and SrClF tetragonal crystals are described. The experimerttal position of the absorption bands and the [g] principal values of each centre are the following at 78K. In BaClF, $\text{F(}\text{Cl}{}^{\mathrm{?}}\text{): λ}{}_{\mathrm{}}\text{=438}\text{nm}\text{, λ}{}_{\mathrm{\perp }}\text{=550}\text{nm}\text{, g}{}_{\mathrm{\parallel }}\text{=1.9690 ± 0.0003, g}{}_{\mathrm{\perp }}\text{=1.9798±0.0003; F(}\text{F}{}^{\mathrm{?}}\text{): λ}{}_{\mathrm{\parallel }}\text{=532}\text{nm}\text{, λ}{}_{\mathrm{\perp }}\text{=}\text{430}\text{nm}\text{446}\text{nm}\text{, g}{}_{\mathrm{\parallel }}\text{=1.9836 ± 0.0003, g}{}_{\mathrm{\perp }}\text{=1.9695±0.0003.}\text{In SrCIF}\text{, F(}\text{Cl}{}^{\mathrm{?}}\text{): γ}{}_{\mathrm{\parallel }}\text{=380}\text{nm}\text{, λ}{}_{\mathrm{hu}}\text{=465}\text{nm}\text{, g}{}_{\mathrm{\parallel }}\text{=1.996±0.002, g}{}_{\mathrm{\perp }}\text{=1.993±0.002; F(}\text{F}{}^{\mathrm{?}}\text{): λ}{}_{\mathrm{\parallel }}\text{=410}\text{nm}\text{, λ}{}_{\mathrm{\perp }}\text{=}\text{345}\text{nm}\text{363}\text{nm}\text{, g}{}_{\mathrm{\parallel }}\text{=1.997±0.001, g}{}_{\mathrm{\perp }}\text{=1.993+0.001. (∥}\text{and}\text{⊥}$ refer to the light polarization or the magnetic field direction with respect to the fourfold axis of the crystal).This attribution disagrees with that proposed by Nicklaus and Fischer, but accounts for the values of the energy levels of F(F^?) and F(C1^?) in BaClF and SrClF calculated by S. Lefrant and A.H. Harker.     

19.

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.     

20.

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

     

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

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.     

Local field theory of the dual string

We develop a (classical) local field theory which contains as a special solution the (classical) dual string recently discussed by Goddard, Goldstone, Rebbi and Thorn. The basic field is a gauge field F_μν(x), and the Lagrangian is given by $\text{(}\text{?1}\text{2α'}\text{)√F}{}^2$. We treat the case of closed strings (corresponding to the Shapiro-Virasoro model) where F_μν can be expressed in terms of potentials A_μ. Quantization of F_μν is briefly discussed, but a more thorough discussion is postponed.     

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.     

Electronic spectrum of 1,5-naphthyridine: Vapor spectra

Analyses of the vapor spectra of 1,5-naphthyridine-d₀ and -d₆ are presented. The spectra are characterized by two principal origins, one the true electronic origin, magnetic dipole allowed, ${}^1\text{B}{}_{\mathrm{g}}\text{←}{}^1\text{A}{}_{\mathrm{g}}$, 27 598.5 cm^?1 (-d₆ 27 676.9), and the other a vibronic origin, electricd-dipole allowed, corresponding to the activity of a low-frequency vibration 6a_u, 183 cm^?1 (-d₆ 163). Extensive sequence structure is evident and the relative intensities of the sequence bands associated with the two origins provide the strongest argument for their assignments. The absence of 6a_u as a major source of intensity in the hot bands is in agreement with vibronic coupling calculations which propose that in absorption intensity “flows” to the lower-frequency vibrations.     

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.     

Optical absorption and ESR study of F centres in BaClF and SrClF crystals

Magnetic and optical properties of two types of F centres, calledF(F^?) and F (Cl^?), created in BaClF and SrClF tetragonal crystals are described. The experimerttal position of the absorption bands and the [g] principal values of each centre are the following at 78K. In BaClF, $\text{F(}\text{Cl}{}^{\mathrm{?}}\text{): λ}{}_{\mathrm{}}\text{=438}\text{nm}\text{, λ}{}_{\mathrm{\perp }}\text{=550}\text{nm}\text{, g}{}_{\mathrm{\parallel }}\text{=1.9690 ± 0.0003, g}{}_{\mathrm{\perp }}\text{=1.9798±0.0003; F(}\text{F}{}^{\mathrm{?}}\text{): λ}{}_{\mathrm{\parallel }}\text{=532}\text{nm}\text{, λ}{}_{\mathrm{\perp }}\text{=}\text{430}\text{nm}\text{446}\text{nm}\text{, g}{}_{\mathrm{\parallel }}\text{=1.9836 ± 0.0003, g}{}_{\mathrm{\perp }}\text{=1.9695±0.0003.}\text{In SrCIF}\text{, F(}\text{Cl}{}^{\mathrm{?}}\text{): γ}{}_{\mathrm{\parallel }}\text{=380}\text{nm}\text{, λ}{}_{\mathrm{hu}}\text{=465}\text{nm}\text{, g}{}_{\mathrm{\parallel }}\text{=1.996±0.002, g}{}_{\mathrm{\perp }}\text{=1.993±0.002; F(}\text{F}{}^{\mathrm{?}}\text{): λ}{}_{\mathrm{\parallel }}\text{=410}\text{nm}\text{, λ}{}_{\mathrm{\perp }}\text{=}\text{345}\text{nm}\text{363}\text{nm}\text{, g}{}_{\mathrm{\parallel }}\text{=1.997±0.001, g}{}_{\mathrm{\perp }}\text{=1.993+0.001. (∥}\text{and}\text{⊥}$ refer to the light polarization or the magnetic field direction with respect to the fourfold axis of the crystal).This attribution disagrees with that proposed by Nicklaus and Fischer, but accounts for the values of the energy levels of F(F^?) and F(C1^?) in BaClF and SrClF calculated by S. Lefrant and A.H. Harker.     

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.