Dispersion sum rules for the amplitudes of radiative transitions in quarkonium

A dispersion approach is suggested, based on the asymptotic freedom in QCD and on analyticity, which leads to sum rules for the amplitudes of radiative transitions in quarkonium $\text{(}\text{c}\text{c}\text{,}\text{b}\text{b}\text{, …)}$ and allows one to estimate these amplitudes in a model-independent way. As an example such sum rules are derived for the ${}^3\text{P}{}_0\text{?}{}^3\text{S}{}_1$ and ${}^3\text{S}{}_1\text{?}{}^1\text{S}{}_0$ transitions. For charmonium they agree with the available data and with the predictions of nonrelativistic models.     

Self-broadening and shift of Doppler-free two-photon lines of Rb

The self-broadening and shift rates of 14 two-photon lines of the $\text{5}{}^2\text{S}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{?n}{}^2\text{D}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext><mtext>,</mtext><mtext>5</mtext><mtext>2</mtext>}}$ series and 8 lines of the $\text{5}{}^2\text{S}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{?n}{}^2\text{S}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ series of Rb were measured using thermionic detector and the technique of Doppler-free two-photon spectroscopy. The dependence of the broadening and shift of the lines on the principal quantum number is discussed and compared with experimental data for the Rb principal series lines and recent theoretical estimates.     

New measurements of the n2P12,32 energy levels of Cs(I)

The energies of the $\text{n}{}^2\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(7 ≤ n ≤ 13)}$ and $\text{n}{}^2\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{(7 ≤ n ≤ 27)}$ levels of CsI have been redetermined photographically from high resolution absorption measurements of the principal series lines $\text{6}{}^2\text{S}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? n}{}^2\text{P}{}_{\mathrm{<mtext>J</mtext>}}$X. The new data disagree significantly [ ≈0.13 cm^-1] with the values given in the NBS-Tables of Moore¹ which are taken from a paper by Kratz.² By means of an extended Ritz-formula, the ionization energy of CsI was found to be 31406.46±0.03 cm^-1, which is, within the limit of uncertainty, in agreement with the data of Kleiman,³ Eriksson et al.,⁴ Bockasten,⁵ and Eriksson and Wenåker.⁶     

Broadening and oscillator strengths of Cs quadrupole lines

The oscillator strengths of the first 14 quadrupole lines of $\text{Cs}\text{(6}{}^2\text{S}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{→5?11}{}^2\text{D}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext><mtext>,</mtext><mtext>3</mtext><mtext>2</mtext>}}\text{)}$ were measured in absorption using a high resolution spectrometer. In addition to this, the broadening of the$\text{6}{}^2\text{S}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{→5}{}^2\text{D}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ and $\text{6}{}^2\text{S}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{→5}{}^2\text{D}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ lines was investigated. Taking into account not only the impact region of the lines but also the quasi-static wings, the integrated absorption of the lines increases overproportionally to the practicle density. It was established that the electron transitions which form the quasi-static wings of the lines(molecular electron transitions) have higher transition probabilities than the corresponding impact broadened lines. A rough estimate of the molecular oscillator strengths is given.     

Low temperature optical study of Gadolinium molybdate and influence of an external magnetic field

We describe the optical absorption spectrum of a single crystal of Gadolinium Molybdata (GMO) at the temperature of liquid helium. We observe a set of sharp lines in the near ultra violet region; we clasify the lines into three groups A, B, and C. We study the positions of the lines as functions of the orientation of the crystal relative to the polarization of the incident light and we investigate the Zeeman effect on the lines of the groups A and B. We suggest that the observed lines of all three groups are due to transitions between the ground ${}^8\text{S}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ state and the excited ${}^6\text{P}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$, ${}^6\text{P}{}_{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$ and ${}^6\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ states of the Gd³⁺ ion in the crystal.     

Chemical diffusion in nonstoichiometric chromium sulfide,Cr2+yS3

Using the re-equilibration kinetic method the chemical diffusion coefficient in nonstoichiometric chromium sesquisulfide, Cr_2+yS₃, has been determined as a function of temperature (1073–1373 K) and sulphur vapour pressure (10?10⁴ Pa). It has been found that this coefficient is independent of sulphur pressure and can be described by the following empirical equation: $\text{D}\text{?}\text{Cr}{}_{\mathrm{2+y}}\text{S}{}_3\text{=50.86}\text{exp(-39070 cal/mole/}\text{RT)}\text{(cm}{}^2\text{s}{}^{\mathrm{?1)}}$. It has been shown that the mobility of the point defects inCr_2+yS₃ is independent of their concentration and that the self-diffusion coefficient of chromium in this sulfide has the following function of temperature and sulphur pressure: . (cm²s^?1).     

Non-analyticity of the entropy and Nernst's law in random spin systems

It is shown explicitly for a soluble model that a random spin system can have an entropy which is non-analytic at (H = 0, T = 0), with $\text{(}\text{?S}\text{?H}\text{)}{}_{\mathrm{H=0}}$ and/or $\text{(}\text{?}{}^2\text{S}\text{?H}{}^2\text{)}{}_{\mathrm{H=0}}$non-vanishing in the T → 0 limit, while nevertheless Nernst's law is satisfied.     

Radiative decay of the 2 3Po0 level of beryllium-like ions

A Z-expansion technique is used to estimate the radiative rate for the $\text{2}{}^3\text{P}{}^{\mathrm{<mtext>o</mtext>}}{}_0\text{?2}{}^1\text{S}{}_0$ transition in berryllium-like ions. It is concluded that the transition rate is so slow as to be unobservable.     

Ultraviolet absorption spectra of Zn2 and Cd2 in solid argon and krypton at 10 K

Zinc and cadmium atoms have been condensed with argon and krypton at 10 K. The most intense absorption is due to the ${}^1\text{P}{}_1\text{←}{}^1\text{S}{}_0$ atomic transition, and a weak band is due to the ${}^3\text{P}{}_1\text{←}{}^1\text{S}{}_0$ atomic absorption. Structured absorptions at 252 and 254 nm in solid argon and krypton with vibrational spacings of 140-120 cm^?1 are due to the ${}^1\text{Σ}{}_{\mathrm{u}}{}^{\mathrm{+}}\text{←}{}^1\text{Σ}{}_{\mathrm{g}}{}^{\mathrm{+}}$ transition of Zn₂. Similar 273 and 277 nm absorptions with 110-90 cm^?1 vibrational spacings are due to Cd₂ in solid argon and krypton, respectively.     

Temperature and thickness dependence of low temperature transport in amorphous silicon thin films: A comparison to amorphous germanium

The temperature and thickness dependence of the low temperature electrical transport of amorphous silicon thin films measured in-situ in ultra-high vacuum are presented. As for a-Ge there is an extended range of $\text{ln ? ∝ T}{}^{\mathrm{<mtext>?1</mtext><mtext>4</mtext>}}$ for thick films with $\text{ln ? ∝ S}{}_2\text{T}{}^{\mathrm{<mtext>?1</mtext><mtext>3</mtext>}}$ for thin films with $\text{S}{}_2\text{∝ d}{}^{\mathrm{<mtext>?1</mtext><mtext>3</mtext>}}$ as expected from a variable range tunneling mechanism.     

Heavy quarkonia and asymptotic freedom

We use semiclassical methods to discuss the scaling behaviour of quarkonium level splittings up to $\text{M(}\text{Q}\text{Q}\text{) = 200}\text{GeV}$. Special emphasis is laid on the effects of asymptotic freedom which are found to be essential for $\text{M(}\text{Q}\text{Q}\text{) ? 30}\text{GeV}$. The bound t$\text{t}$ system will almost look like the ? system except that $\text{R = ΔM (}{}^3\text{P}{}_2\text{?}{}^3\text{P}{}_1\text{)/ΔM(}{}^3\text{P}{}_1\text{?}{}^3\text{P}{}_0\text{)}$ is larger than 0.8. In the ? system R will already be close to 0.8.     

Precise measurement of electronic gJ value of helium,gJ(4He,23S1)

We report the measurement of $\text{g}{}_{\mathrm{J}}\text{(}{}^4\text{He,2}{}^3\text{S}{}_1\text{)}\text{g}{}_{\mathrm{J}}\text{(}{}^{85}\text{Rb}\text{,5}{}^2\text{S}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$ by the atomic beam magnetic reson ance method using separated oscillating fields, and hence the determination $\text{g}{}_{\mathrm{J}}\text{(}{}^4\text{He,2}{}^3\text{S}{}_1\text{)}\text{g}{}_{\mathrm{J}}\text{(H,1}{}^2\text{S}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}\text{? 1? (23.19±0.07) × 10}{}^{\mathrm{?6}}$, which agrees with theory and with other less precise recent measurements.     

Neutral mesons with heavy quarks and mixing angles in the six-quark model

In the framework of the six-quark model, based on the gauge group SU(2)_L × U(1) we have obtained expressions for the amplitudes of $\text{K}{}^0\text{?}\text{K}{}^0\text{,}\text{D}{}^0\text{?}\text{D}{}^0\text{,}\text{B}{}^0\text{?}\text{B}\text{B}{}_{\mathrm{S}}{}^0\text{?}\text{B}{}_{\mathrm{S}}{}^0\text{,}\text{T}{}^0\text{?}\text{T}{}^0\text{and}\text{T}{}_{\mathrm{c}}{}^0\text{?}\text{T}{}_{\mathrm{C}}{}^0$ transitions at final 4-momenta of external lines Feynman box diagrams. We have estimated the correctness of using the approximation of extremely small 4-,omenta of valence quarks, composing K⁰-like mesons. The constraints for the parameters of the unitary matrix of weak charged currents have been found at arbitrary value of the t-quark mass. Estimates of numerical values for the mixing parameters and for the parameters of CP violation for neutral systems similar to $\text{K}{}^0\text{?}\text{K}{}^0$ are given.     

Optical second-harmonic generation in atomic thallium vapor

We observe coherent optical second-harmonic generation in atomic thallium vapor when the fundamental is tuned to half the resonance frequency of the following transitions: $\text{6}{}^2\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? 7}{}^2\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ and $\text{6}{}^2\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? 8}{}^2\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ in the presence of a static magnetic field; and $\text{6}{}^2\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? 7}{}^2\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{, 6}{}^2\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? 8}{}^2\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$in the absence of any external field.     

42P12↔42P32 mixing in potassium induced in collisions with noble gas atoms

Cross sections for$\text{4}{}^2\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{-4}{}^2\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ mixing in potassium, induced by collisions with noble gas atoms, were determined using the methods of fluorescence spectroscopy. The experiments were carried out at an optical depth of ≤3×10^-2 in the absence of radiation trapping and at noble gas pressures in the mtorr region and yielded the cross sections $\text{Q}{}_1\text{(4}{}^2\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{→4}{}^2\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{)}$ and $\text{Q}{}_2\text{(4}{}^2\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{« 4}{}^2\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{)}$ (in units of 10^-16 cm²) respectively, as follows: for He, 26.3 and 17.8; for Ne, 6.4 and 4.4; for Ar, 16.0 and 11.2; for Kr, 24.9 and 17.7; for Xe, 44.9 and 31.7. These values supersede those reported previously by Chapman and Krause (1966).     

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 ($\text{C}{}_{\mathrm{J13?}}{}^{\mathrm{(2)}}\text{- C}{}_{\mathrm{J13+}}{}^{\mathrm{(2)}}\text{) = 0.98(9)}$.     

Nuclear magnetic resonance of 9Be atoms by charge exchange with optically pumped 9Be+ ions

NMR of free ${}^9\text{Be}\text{(I =}\text{3}\text{2}\text{)}{}^1\text{S}{}_0$ atoms is observed via resonant charge exchange with optically pumped ${}^9\text{Be}{}^{\mathrm{+}}{}^2\text{S}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ ions in He buffer gas, yielding $\text{μ(}{}^9\text{Be}\text{) = ?1.1778 (9) μ}{}_{\mathrm{<mtext>n</mtext>}}$. Applications of the method suitable for all group II elements and Yb include: precision measurements of nuclear moments, chemical shifts, hfs-anomalies, and investigation of charge exchange processes.     

Three-nucleon results for separable potentials modelled on the Reid soft-core potential

Using a solution to the inverse scattering problem we have generated phase-equivalent separable potentials in the ${}^1\text{S}{}_0$ and ${}^3\text{S}{}_1\text{?}{}^3\text{D}{}_1$ states, which have nearly the same singlet UPA form factors and deuteron parameters (E_D, P_D, Q_D, A_S and $\text{A}{}_{\mathrm{D}}\text{A}{}_{\mathrm{S}}$) as the Reid soft-core potential. We compare our results for the binding energy of the triton and the neutron-deuteron doublet scattering length with the corresponding values for the Reid soft-core potential.     

42P fine-structure mixing in potassium by collisions with N2, H2, CO,and CH4

Cross sections for $\text{4}{}^2\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{?4}{}^2\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ fine-structure mixing in potassium, induced in collisions with N₂, H₂, CO, and CH₄, were determined by methods of atomic fluorescence spectroscopy. The experiments were carried out at a temperature of 342 K, a K density of 6 × 10⁹ cm^?3 and mtorr buffer gas pressures, and yielded the following cross sections $\text{Q}{}_1\text{(4}{}^2\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{→4}{}^2\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$) and $\text{Q}{}_2\text{(4}{}^2\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{→4}{}^2\text{P}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ (in units of 10^?6 cm²): for N₂, 79 and 54; for H₂, 57 and 39; for CO, 98 and 64; for CH₄, 86 and 58. The values for N₂ and H₂ supersede those reported previously by McGillis and Krause (1968).     

Remarks on Mc Bryan's convergence proof for (α-4(cos(αϕ)−1+α2ϕ2/2))2-quantum fields

With the help of Mc Bryan's method we prove the existence of F(?)₂-fields, where $\text{F(x) ?}\text{∑}\text{n=0}\text{∞}\text{a}{}_{\mathrm{2n}}\text{x}{}^{\mathrm{2n}}$ is a power series with fast decreasing coefficients. Hypercontractive estimates show the existence of fields with a superposition of exponential or cosine functions as interaction, similar to Mc Bryan's interaction.