Infrared-radio frequency double resonance observations of pure rotational Q-branch transitions of methane

The $\text{F}{}_2{}^{\mathrm{(2)}}\text{← F}{}_1{}^{\mathrm{(2)}}$ and $\text{F}{}_2{}^{\mathrm{(2)}}\text{← F}{}_1{}^{\mathrm{(1)}}$ transitions of the J = 7 levels of the ground state of CH₄ have been observed by infrared-radio frequency double resonance using the 3.39 μ HeNe laser line. The transition frequencies are 423.02 ± 0.02 MHz and 1246.55 ± 0.02 MHz, respectively. Using these frequencies and the splitting of the E and F₂ levels of the J = 2 state calculated from the molecular beam magnetic resonance spectra of Ozier, the centrifugal distortion constants are derived to be D_t = 132933 ± 10 Hz, H_4t = ? 16.65 ± 0.2 Hz, and H_6t = 10 ± 1 Hz. The J = 15 E⁽¹⁾ → E⁽²⁾ microwave transition is predicted as 14150 ± 9 MHz.     

Noncoplanar correlation spectra from the 2H(p, 2p)n reaction at Einc = 44.9 MeV

The differential cross section $\text{d}{}^3\text{σ/}\text{d}\text{Ω}{}_3\text{d}\text{Ω}{}_4\text{d}\text{E}{}_3$ for the ²H(p, 2p)n reaction at E_inc = 44.9 MeV is measured in noncoplanar geometry. The Amado model in general gives a good fit to the absolute cross section. The dependence of the cross section on the momentum of the undetected particle Q₅, on the scattering angle θ₃₄, as well as on the angle of the undetected particle is investigated.     

Intermittent incommensurate chaos

Near the onset of intermittent chaos from quasiperiodic motion lying on an attracting 2D torus with rotation number ρ=ω₂/ω₁=(√5?1)/2, the power spectrum of the cartesian coordinate of the intersection point on the Poincaré section is studied. The Poincaré section is distorted from the ellipse near the onset of chaos. Then a sequence of spectral lines are excited at frequencies $\text{Ω}{}_{\mathrm{i}}\text{= ρ}{}^{\mathrm{i}}\text{Ω}{}_2\text{, (i=1,2,…)}$. Their intensities are found to obey the power law $\text{Ω}{}^4{}_{\mathrm{i}}\text{or}\text{Ω}{}^2{}_{\mathrm{i}}\text{for}\text{i ? 1}$ according as the Poincaré section has a sharp wrinkle or not. A similar spectrum is obtained also in the chaotic regime ε > 0. The mean value of time intervals of quasiperiodic states between two consecutive bursts and the square root of their variance are found to be inversely proportional to ε near the onset point g3 = 0.     

On the asymptotic behaviour of the mass operator near the Fermi energy

By taking due account of momentum conservation, it is shown that, when ω is near the Fermi energy ω_F, the imaginary part of the mass operator $\text{M(}\text{k}\text{, ω)}$ for an infinite Fermi system behaves like (ω ? ω_F)^p(k) where the exponent p(k) ? 2 depends on the interval in which $\text{|}\text{k}\text{|}$ is lying. In particular, the commonly asserted quadratic behaviour (ω ? ω_F² is shown to be true only for $\text{|}\text{k}\text{| ? 3k}{}_{\mathrm{<mtext>F</mtext>}}$. It is explicity assumed that the Fermi system admits a perturbative type treatment.     

Inclusive pion distributions in e+e− annihilation from sum rules and duality

The threshold behaviour of pion production presented in our earlier work is successfully compared with the new SPEAR data. By using duality and sum rules we derive F_T^(π+)(x) ≈ F_L^(π+)(x) ≈ F_T^(π0)(x) ? F_L^(π0)(x) for x near 1. An accompanying results is $\text{σ}{}_{\mathrm{<mtext>\pi </mtext><mtext>A</mtext>}}{}_2\text{(s) ≈ 2σ}{}_{\mathrm{\pi \omega }}\text{(s) ≈ 4σ}{}_{\mathrm{\pi \pi }}\text{(s) ≈ 9(m}{}_{\mathrm{?}}{}^2\text{/s)}{}^3\text{σ}{}_{\mathrm{<mtext>\mu </mtext><mtext>\mu </mtext>}}$ for large s.     

Lepton mixing and neutrino oscillations

The present article is a review of phenomena connected with neutrino oscillations. Mixing of two neutrinos (Majorana as well as Dirac) with masses m₁ and m₂ is considered in detail. It is shown that the hypothesis of lepton mixing is not in contradiction with the existing data if |m₁²?m₂²| ? 1 (eV)². Possible experiments designed to reveal neutrino oscillations at reactor, meson factory and high energy accelerator facilities are considered. In such experiments oscillation might be found if $\text{|m}{}_1{}^2\text{?m}{}_2{}^2\text{| ? 0.01}\text{(eV)}{}^2$. The possibilities of searching for oscillations by experiments on cosmic ray neutrinos and especially on solar neutrinos are discussed in detail. The last experiments have an incredible high sensitivity from the point of view of testing the lepton mixing hypothesis (oscillation effects might be observable if $\text{|m}{}_1{}^2\text{?m}{}_2{}^2\text{| ? 10}{}^{\mathrm{?12}}\text{(eV)}{}^2$). The “solar neutrino puzzle” is also discussed from the point of view of lepton mixing. Neutrino oscillations are considered then in the case where in nature there exist N ? 2 neutrino types.In conclusion the case of heavy lepton mixing is considered. It is shown that in a concrete scheme with right-handed currents, the probabilities of such processes as μ → eγ, μ → 3e etc. can be close to existing experimental upper limits, provided the heavy lepton masses are of an order of a few GeV, whereas the probabilities of the above processes are entirely negligible if only neutrinos are mixed.     

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.     

Paзлoжeниe пo 1Z для чapтpи-фoкoвcкoй и кoppeляциoннoй энepгии, peлятивиcтcкич пoпpaвoк, дипoльнoгo мaтpичнoгo элeмeнтa

Energies and dipole matrix elements have been calculated for He, Li, Be, B, C, N, O, F, and Ne-like ions (configurations 1s²2sⁿ¹2pⁿ²?1s²2s^n1?12pⁿ²⁺¹). The Hartree-Fock energy, the correlation energy, and relativistic corrections were taken into account. Relativistic corrections were obtained by computing the entire quantity H_B. Numerical results are presented for energies of the terms in the form

$\text{E=E}{}_0\text{Z}{}^2\text{+ ΔE}{}_1\text{Z + ΔE}{}_2\text{+}\text{1}\text{Z}\text{ΔE}{}_3\text{+}\text{α}{}^2\text{4}\text{(E}{}_0{}^{\mathrm{p}}\text{Z}{}^4\text{+ ΔE}{}_1{}^{\mathrm{p}}\text{Z}{}^3\text{)}$

, and for the fine structure of the terms in the form

$\text{〈1s}{}^2\text{2s}{}^{\mathrm{n1}}\text{2p}{}^{\mathrm{n2}}\text{LSJ|H}{}_{\mathrm{Б}}\text{|1s}{}^2\text{2s}{}^{\mathrm{n1\prime }}\text{2p}{}^{\mathrm{n2\prime }}\text{L′S′J〉=(?1)}{}^{\mathrm{L+S\prime +J}}\text{LSJ}\text{S′L′1}\text{×}\text{α}{}^2\text{4}\text{(Z?A)}{}^3\text{[E}{}^{\mathrm{(0)}}\text{(Z ? B)+}\text{E}{}_{\mathrm{c0}}\text{]+(?1)}{}^{\mathrm{L\; +\; S\prime \; +\; J}}\text{LSJ}\text{S′L′2}\text{α}{}^2\text{4}\text{(Z?A)}{}^3\text{E}{}_{\mathrm{cc}}$

. Dipole matrix elements are required for calculation of oscillator strengths or transition probabilities. For the dipole matrix elements, two terms of the expansion in $\text{1}\text{Z}$ have been obtained. Numerical results are presented in the form P(a, a′) = (a/Z)[1 + (τ/Z)].     

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 $\text{D(Λ}{}_1{}^{\mathrm{+}}\text{,}{}^5\text{E}{}_{\mathrm{g}}\text{) = 0.03}$.     

Nuclear magnetic moment of the 9.7 h 12− isomer 196mAu

The magnetic hyperfine splitting v_M=|gμ_NB_HF/h| of ^196mAu (j^π=12^?; configuration ¦(π$\text{11}\text{2}$($\text{v}\text{13}\text{2}{}^{\mathrm{+}}\text{)〉}{}_{12}{}^{\mathrm{?}}$; $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 9.7}\text{h}\text{)}$ as dilute impurity in Ni has been determined with nuclear magnetic resonance on oriented nuclei as 96.0(2) MHz. With the known hyperfine field B_HF = ?264.4(3.9) kG corrected for hyperfine anomalies the g-factor and magnetic moment of ^196mAu are deduced to be |g| = 0.476(7) and |μ| = 5.72(8) μ_N. Taking into account the known magnetic properties of $\text{π}\text{1}\text{2}{}^{\mathrm{?}}$ and $\text{v}\text{13}\text{2}{}^{\mathrm{+}}$ isomeric states in the neighbouring odd Pt, Au and Hg nuclei the structure of the 12^? state is discussed.     

Gravitational collapse in quantum mechanics with relativistic kinetic energy

It is proved that the quantum mechanical Hamiltonian $\text{H = Σ}{}_{\mathrm{i=1}}{}^{\mathrm{N}}\text{(p}{}^2\text{+ m}{}^2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? κ Σ}{}_{\mathrm{i>j}}\text{|x}{}_{\mathrm{i}}\text{? x}{}_{\mathrm{j}}\text{|}{}^{\mathrm{?1}}$ for bosons (resp, fermions) is bounded from below if N ≤ c_bκ^?1 (resp. $\text{N ≤ c}{}_{\mathrm{f}}\text{κ}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$). H is unbounded from below if N ≥ c_b^lκ^?1 (resp. $\text{N ≥ c}{}_{\mathrm{f}}{}^{\mathrm{l}}\text{κ}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$). The constants c_b and c_b^l (resp. c_f and c_f^l) differ by about a factor 2 (resp. 4).     

Functional derivative δTc/δα2 (Ω)F(Ω) for weak coupling superconductors

We present approximate analytic calculation of the functional derivative $\text{δT}{}_{\mathrm{c}}\text{δα}{}^2\text{(Ω)F(Ω)}$, where T_c is the superconducting critical temperature and $\text{α}{}^2\text{(Ω)F(Ω)}$ is the electron-phonon spectral function, within the “square-well model” for the phonon mediated electron-electron interaction and weak coupling limit $\text{ω}{}_{\mathrm{D}}\text{(2πT}{}_{\mathrm{c}}\text{)? 1 (ω}{}_{\mathrm{D}}$ is the Debye energy). It is found that $\text{δT}{}_{\mathrm{c}}\text{δα}{}^2\text{(Ω)F(Ω) = (1 + λ)}{}^{-1}\text{G(Ω)}$ where λ is the familiar electron-phonon coupling parameter and $\text{G(Ω)}$ is a universal function of the reduced frequency $\text{Ω}\text{=}\text{Ω}\text{T}{}_{\mathrm{c}}$. We compare this formula with accurate numerical results for several weak coupling superconductors. The overall agreement is good     

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→∞.     

Observation of compensation effects during the thermal dissolution of aluminum oxide layers on tungsten and molybdenum 〈111〉 and on tungsten {110} in the presence of electric fields

Aluminum oxide layer dissolution was studied between 700 and 1200 K in the substrate areas of W〈111〉, Mo〈111〉, and on W{110} by means of FEM. Varying the electric field strength, F, between +45 and $\text{+105}\text{MV}\text{cm}$, two types of dissolution could be observed: dissolution by surface diffusion (low F's) and dissolution by ion desorption (high F's). It is assumed that aluminum suboxides — preferentially AlO — are involved in the dissolution processes. The preexponential factors, A_F, of an Arrhenius-Frenkel type equation were measured as a function of F. The field dependence of A_F is determined by the dissolution mechanism: (a) dissolution by diffusion: $\text{log}\text{A}{}^0{}_{\mathrm{F}}\text{=}\text{log}\text{A}{}^0{}_0\text{?}\text{ΔμF}\text{2.3k}{}^1\text{T}$ (μ  molecular dipole moment, ¹T ≡ isokinetic for W〈111〉, log A⁰₀ = ? 6.0 and ${}^1\text{T = 940}\text{K}$; for Mo〈111〉, log A⁰₀ = ? 3.1 and ${}^1\text{T = 860}\text{K}$; and (b) dissolution by ion desorption: $\text{log}\text{A}{}^{\mathrm{+}}{}_{\mathrm{F}}\text{=}\text{log}\text{A}{}^{\mathrm{+}}{}_0\text{+}\text{n}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{e}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{F}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{2.3k}{}^1\text{T}$; for A⁺₀ = ? 22 and ${}^1\text{T = 1200}\text{K}$; for W〈111〉, log A⁺₀ = ? 21 and ${}^1\text{T = 1200}\text{K}$. Using earlier proposed safeguards, isokinetic relationships (compensation effects) could be established for each of the two dissolution processes. The coordinates of the isokinetic points have the following average values: $\text{log}{}^1\text{A}{}^0{}_0\text{= 2.5}$ and ${}^1\text{T = 920}\text{K}$ for diffusion; $\text{log}{}^1\text{A}{}^{\mathrm{+}}{}_0\text{= ? 1}$ and ${}^1\text{T = 1240}\text{K}$ for ion desorption. The entropy changes (at $\text{T =}{}^1\text{T}$, zero field strength, and unit pressure) for the phase changes: solid layer → diffusion layer and solid layer → ion gas, are of the order of $\text{30}\text{cal}\text{K}$ · mol and $\text{90}\text{cal}\text{K}$ · mol, respectively. The two dissolution mechanisms can be described by the following Arrhenius-Frenkel type equations:

$\text{τ}{}^0{}_{\mathrm{F}}\text{=}{}^1\text{A}{}^0{}_0\text{exp}\text{[}\text{? (E}{}^0{}_0\text{+ ΔμF)}\text{k}{}^1\text{T}\text{]}\text{exp}\text{[(}\text{E}{}^0{}_0\text{+ ΔμF)}\text{kT}\text{]}$

for diffusion and

$\text{τ}{}^{\mathrm{+}}{}_{\mathrm{F}}\text{=}{}^1\text{A}{}^{\mathrm{+}}{}_0\text{exp}\text{[}\text{? (E}{}^{\mathrm{+}}{}_0\text{? n}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{e}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{F}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}\text{k}{}^1\text{T}\text{]}\text{exp}\text{[(}\text{E}{}^{\mathrm{+}}{}_0\text{? n}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{e}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{F}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}\text{kT}\text{]}$

for ion desorption.     

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.     

Nonexponential decay law

The decay of a nonstationary state usually starts as a quadratic function of time and ends as an inverse power law (possibly with oscillations). Between these two extremes, the familiar exponential decay law may be approximately valid. The main purpose of this paper is to find the conditions which must be satisfied by the Hamiltonian and by the initial state, for the exponential law to have a significant domain of validity. It is shown that the evolution of a nonstationary state is governed by a nonnegative function W(E), having the dimensions of an energy. Among its properties are: the energy uncertainty is given by $\text{(ΔH)}{}^2\text{= ?W(E)dE}$, and the inverse lifetime by Γ = 2πW(E₀), where E₀ is the expectation value of H. The detailed shape of W(E) defines two characteristic times between which the exponential decay law is a good approximation: roughly speaking, the smoother W(E), the larger the domain of validity of the exponential law. For instance, if W(E) is very smooth ($\text{|}\text{dW}\text{dE}\text{| ? 1}$) except for a sharp threshold at E = E_thr, the transition from quadratic to exponential decay occurs for $\text{t ?}\text{1}\text{(E}{}_0\text{? E}{}_{\mathrm{<mtext>thr</mtext>}}\text{)}$, and the transition from exponential to inverse power law when $\text{Γt ?}\text{log}\text{[}\text{(E}{}_0\text{? E}{}_{\mathrm{<mtext>thr</mtext>}}\text{)}\text{Γ}\text{]}$.     

Metal-nonmetal transition in solid argon-lanthanum mixtures

A continuous metal-nonmetal transition is observed in solid ArLa mixtures. The d.c. conductivity σ starts at a La atomic fraction c_La ? 0.15 with $\text{σ = 2 × 10}{}^{-2}\text{[Ω-cm]}{}^{-1}$ and increases exponentially with c_La until σ reaches the minimum metallic conductivity $\text{σ}{}_{\min }\text{= 300 ± 100[Ω-cm]}{}^{-1}$ at c_La ? 0.4. The temperature dependence of σ shows variable range hopping between localized states for c>_La ? 0.4 and metallic behaviour for $\text{c}{}_{\mathrm{<mtext>La</mtext>}}\text{? 0.4.}$     

Quark masses

In quark gluon theory with very small bare masses, -$\text{ψ}$$\text{M}$ψ, spontaneous breakdown of chiral symmetry generates sizable masses M_u, M_d, M_s, … We find ($\text{M}{}_{\mathrm{<mtext>u</mtext>}}\text{+ M}{}_{\mathrm{<mtext>d</mtext>}}\text{) /2 ≈ m}\text{p}\text{/ √6 ≈ 312}\text{MeV}\text{,}\text{and}\text{M}{}_{\mathrm{<mtext>s</mtext>}}\text{≈ 432}\text{MeV}$. Scalar densities have well determined non-zero vaccum expectations $\text{〈0|u}{}^{\mathrm{a}}\text{|0〉 ≡ 〈0|ψ(x) (λ}{}^{\mathrm{a}}\text{/2)ψ(x)/0〉 ≈ ?}{}_{\mathrm{\pi }}{}^2\text{M}{}^{\mathrm{a}}\text{,}\text{i.e}\text{〈0? u}{}^{\mathrm{o}}\text{/vb0〉 ≈ 8 × 10}{}^{\mathrm{?3}}\text{(}\text{GeV}\text{)}{}^3$ at an SU(3) breaking of the vacuum c′ ≡ 〈0|u⁸|〉/〈0|u^o|0〉 ≈ ? 16%