Nitrogen lasers: Optical devices of variable gain coefficient

A N₂-laser system, consists of an oscillator and an amplifier of different electrode lengths, ranged from 5 to 31 cm, operating under the optimized gas pressures conditions and 14 kV input voltage, was used to measure small signal gain, g₀, and saturation energy density, E_s. It was found that g₀-parameter follows a profile of the type m + n/l_AMP, where l_AMP is the effective electrode length of the laser amplifier, and (m, n) are some constants. So, by reducing the active length a gain value as high as ∼1.2 cm⁻¹ for l_AMP = 5 cm was obtained. The proposed function, with a rather good approximation, can be used to explain almost all the reported g₀-values of laser systems with moderate current densities. For explaining more details of the reported gain coefficients, the g₀l_AMP-parameter was introduced, where it was realized that with a good approximation a Gaussian profile is a suitable function for explaining the reported g₀l_AMP-products. Furthermore, we found that at a constant input voltage the saturation energy density and output energy density, E_out, regardless of the type of N₂-lasers and their operational conditions, are linearly correlated. Based on this observation, and by operating the system at different input voltages, the functional dependence of the measured E_s/E_out-values with respect to the operational voltages is introduced. Details of our present observations, along with the previously reported g₀, and E_s-measurements are presented graphically, or tabulated. The results are giving some interesting features of TE/TEA N₂-lasers for lasers g₀, E_s predictions which are valuable for laser designs and also for further theoretical investigations.     

A two dimensional theoretical model for describing gain coefficient in N2-lasers and the model validity for CVL and excimer lasers

Based on our previously reported measurements on the gain-value in a N₂- laser and numerical calculations, we introduce a method to obtain an analytical expression for the small signal gain, g₀, where the dependency of g₀ on the laser geometrical configuration, including electrodes length and gap separation, is demonstrated. For this study one- and two-dimensional approaches for the photon density have been applied independently to determine gain-parameter, where for explaining the observed dependency of the gain-parameter on the laser electrodes separation, d_AMP, which was found experimentally and explained by an empirical expression of the type g₀ = r + q/d_AMP, with r and q some constants, realization of introducing an extra dimension along the gap separation was unavoidable. For the electrodes length, l_AMP, we have already shown that an empirical equation of the type g₀ = m + n/l_AMP, with m and n some constants, is consistent with the measurements corresponding to N₂-lasers. With this realization, it is proved that the gain-parameter in N₂-lasers can be written as g₀^{above threshold} = m″ + g_0z(γ_L^z, z) + g_0y(γ_L^y, y), where it consists of two independent gain-values along the electrodes length (z) and gap separation (y) with the corresponding power losses given by γ_L^z and γ_L^y. m″ is a very small quantity showing that laser is operating slightly above the threshold. The results of this calculation are consistent with our recent measurements and also other reported N₂-laser gain values measured under moderate current density conditions. To check the validity of the model for other types of lasers, the reported gain-values for copper vapor lasers of different laser tube radii, R_AMP, and tube lengths, l_AMP, have been examined using the one-dimensional model of either g₀(R_AMP) or g₀(l_AMP) and the consistency with the observed measurements was found to be quite satisfactory. The model was also found to be valid for the excimer lasers of different types, different gas mixtures and pressures at a constant input operational voltage. Due to limited numbers of the reported experimental measurements, for the graphs preparation of g₀(l_AMP) in excimer lasers we used the observed data at V₀ = 30 kV and also some variations of the input voltages in the range of ΔV ≅ 20 kV have been adopted. The results for both cases were found to be consistent with the proposed one-dimensional model.     

Polarization-dependent gain and saturation energy density in a TE N2-laser amplifier

The polarization-dependent gain, g₀, and saturation energy density, E_s, in a TE N₂-laser amplifier were measured, using an oscillator-amplifier laser system for different amplifier electrode gap separations, d_AMP, of 7, 9 and 4 mm and gas pressure of p = 77, 60, and 165 Torr, respectively. It was realized that for the amplifier with the gap separation of 7 and 9 mm, where the pd_AMP-value has its optimum-value of 54 Torr cm, the gain-coefficient for the input beam with the polarization parallel to the discharge electrodes (P-polarized beam) is slightly higher than the case when the beam polarization is perpendicular to the discharge electrodes (S-polarized beam). In this case, the depolarization ratio for d_AMP = 7 mm is the range of ∼0.998 to ∼0.962 as the input voltage increases from 12 to 15.5 kV, having a minimum of 0.937 around 14 kV. For the E_s-parameter, the reversed order is true. Also, it was found that the saturation energy densities for three states of polarization are linearly related to the output energy densities, having different slopes of 0.11, 0.14, and 0.17 for R (randomly), P- and S-polarization, respectively. The present measurement supports qualitatively the prediction of polarization-inhomogeneity model for the stimulated emission cross-section, showing that randomly oriented dipoles exhibit slightly larger gain on the direction of the electric field.     

Semi-empirical analysis of magnetic moments of single-particle (or-hole) states around the 208Pb core

Magnetic moments of single-particle (or-hole) states around the ²⁰⁸Pb core were fitted by three state-independent parameters δg_l^(p), δg_l⁽ⁿ⁾ and α, where α is a parameter that is connected closely with δg_S and g_p. The analysis was performed under the assumptions that (i) the state-dependence of radial integral I((nl)²(n'l')²) involved in δg_s and g_p is calculated by the harmonic-oscillator potential, and (ii) δg_s is taken as being equal to ?4g_p, as expected from the δ-force type core polarization. An excellent fit was obtained when δg_l^(p) = 0.10(2), δg_l⁽ⁿ⁾ = ?0.05(1) and α = 1.2(1), which show that the main contributor to δg_s is the M1 core polarization and δg_l⁽ⁿ⁾ is certainly smaller than 0. B(M1)'s for allowed transitions calculated with the use of the same parameters as above are smaller than the observed B(M1)'s whereas α = 1.01(1) explains well the observed B(M1)'s.     

Some physical properties of Ternary germanium bismuth telluride (GeBi4Te7) semiconducting crystals

High purity crystals of GeBi₄Te₇ have been prepared, and values of the electrical conductivity, thermoelectric power, Hall constant and of the i.r. reflectivity in the plasma oscillation region have been obtained. To interpret the results a simple three-valley model of the constant energy surfaces is proposed. Values of the dielectric constant (?_g = 35), high frequency index of refraction (n_λ→0 = 5.9), the character of scattering of the free carriers, the Fermi level (E_F = 0.16eV), the mean relaxation time of the free carriers (〈τ〉) = 5.79 × 10^?15sec), the free electron concentration (N = 1.63 × 10²⁰cm^?3), the conductivity effective mass $\text{(m}{}^1{}_{\mathrm{c}}\text{= 0.27)}$ and m₁ = m₃ = 0.51 m₃, m₂ = 0.18 m₀ have been calculated.     

Multichanel localization and magnetic impurities

The behaviour of an electron in N-coupled conducting chains of the length L is studied in the presence of magnetic impurities. The electron flow can be expanded in an orthonormal set of 2N channels. Each channel has its own transmission coefficient T_n(L). Spontaneous breaking of the symmetry between channels results in 2N different exponential dependences T_n(L) ～ exp (—L/l¹_n) where l¹_n is a localization length in the nth channel. Low frequency kinetic behaviour depends on the channel with the maximum localization length l¹₀.     

Thermodynamic and structural properties of liquids modelled by ‘2-Lennard-Jones centres’ pair potentials

Molecular dynamics calculations have been carried out for model liquid systems of N (=108 or 256) molecules interacting through two Lennard-Jones (12–6) centres coinciding with the positions of the atomic masses (the ‘atom-atom’ pair potential). The objectives were (a) to study the dependence of the properties on the molecular anisotropy defined by the reduced distance l*=l/σ between the centres in the range 0·5–0·8; and (b) to compare the computed quantities with those of real liquids (F₂, Cl₂, Br₂, CO₂). This paper deals with thermodynamic and structural features. Time-dependent correlations will be treated in a future communication.

In the liquid region not too far from the triple point the energy and pressure isochores are well represented by straight lines, the slopes of which increase with density and anisotropy. Thermodynamically consistent expressions for the energy and pressure as functions of density and temperature have been obtained for each system.

With Lennard-Jones parameters adjusted so as to secure the best overall fit, the agreement between experimental and computed thermodynamic properties is very satisfactory for F₂ (l*=0·505), quite good for Cl₂ and Br₂ (l*=0·608–0·63), but rather poor for CO₂ (l*=0·793). The ‘interatomic distances’ are close to the experimental values.

The static structural correlations are discussed in terms of the pair-correlation functions (pcf) g _A(r*) for the separation between ‘atoms’, the first few functions g_ll'm (R*) which arise from the expansion of the g(R*, θ₁, θ₂, φ₁₂) in spherical harmonics, and the pcf's for certain special near-neighbour configurations. The computed atom-atom structure factor is compared with the experimental data for liquid Br₂.

Mean square forces and torques have been evaluated and are related to some experimental results.     

Threshold conditions and bound states for locally periodic delta potentials

We present a systematic study of the conditions for the generation of threshold energy eigen states and also the energy spectrum generated by two types of locally periodic delta potentials each having the same strength λV and separation distance parameter a: (a) sum of N attractive potentials and (b) sum of pairs of attractive and repulsive potentials. Using the dimensionless parameter g = λV a in case (a) the values of g = g _n , n = 1, 2, …, N at which threshold energy bound state gets generated are shown to be the roots of Nth order polynomial D ₁(N, g) in g. We present an algebraic recursive procedure to evaluate the polynomial D ₁(N, g) for any given N. This method obviates the need for the tedious mathematical analysis described in our earlier work to generate D ₁(N, g). A similar study is presented for case (b). Using the properties of D ₁(N, g) we establish that in case (a) the critical minimum value of g which guarantees the generation of the maximum possible number of bound states is g = 4. The corresponding result for case (b) is g = 2. A typical set of numerical results showing the pattern of variation of g _n as a function of n and several interesting features of the energy spectrum for different values of g and N are also described.     

Neutron induced reaction cross-section of115In around 14 MeV

A systematic investigation was carried out on¹¹⁵In to determine the contribution of different reactions to the total non-elastic cross-section in the 13.43 and 14.84 MeV incident neutron energy range. All the major components ofσ _NE were measured with exception of theσ ^g(n, n′) cross section. An analytical expression is recommended to estimate theσ _NE data as a function of mass number at E_n=14.1 MeV. By the knowledge ofσ _NE, the energy dependence ofσ ^g(n, n′) could be deduced. The isomeric cross section ratios both for (n, 2n) and (n, n′) processes were also determined in the given energy range. The present experiment proves the dependence ofσ ^m/(σ ^g+σ ^m) ratio on the spin value (I _m) of the isomeric state in the (n, 2n) reaction. Excitation functions of the (n, 2n), (n, n′) (n, p) and (n∶ p, α) reactions calculated by STAPRE code show good agreement with the experimental results.     

Free energies of the spherical model of a spin glass

Free energies g(m, m_s) and f(m, q) of the spherical spin glass (SG) model due to Kosterlitz et al. are calculated explicitly as functions of the uniform magnetization m, and SG order parameter m_s and the Edwards-Anderson order parameter q. It is shown that g(0, m_s) and f(0, q) below the transition temperature T_g are constant in the ranges 0 ≦ m_s ≦ m_s⁰ and 0 ≦ q ≦ q₀ respectively, where $\text{q}{}_0\text{= (1 -?}\text{T}\text{T}{}_{\mathrm{g}}\text{) = m}{}^2{}_{\mathrm{s}}{}^0$. The proper equilibrium values of m_s( = m_s⁰) and q( d=q₀) are then fixed from the inspection of their behaviors under infinitesimal uniform field proproportional to N^-a($\text{a ≧ 0}$).     

关于B0→π－l+ν l衰变过程分支比的计算

通过构造适当的关联函数,计算B→π跃迁形状因子f⁺_Bπ(q²),f _{Bπ(q²)和标量形状因子f⁰(q²),从而就能研究轻子质量对B⁰→π ^{关键词： B介子半轻衰变 形状因子 分支比}}     

Behavioral studies of gain and saturation energy density in a N2 laser with corona preionization

By the use of an oscillator-amplifier (OSC-AMP) TE N₂ laser system, both operating with corona preionizers, the laser parameters (small-signal gain g ₀ and saturation energy density E _s) have been measured at different N₂ gas pressure and for different states of the AMP preionizer. The details of our measurements are presented. In addition, the effect of He buffer gas on the laser parameters has also been investigated; it was found that both laser parameters remain almost constant up to 150 Torr of He gas pressure, indicating that He mainly affects the discharge uniformity. Finally, with the variation of the N₂ laser gain values in the literature, we found that the g ₀-N₂-laser parameter depends strongly on the length of the laser channel. Based on the most recent measurements, a graph showing this dependency is introduced.     

A class of solvable reaction-diffusion processes on a Cayley tree

Considering the most general one-species reaction-diffusion processes on a Cayley tree, it has been shown that there exist two integrable models. In the first model, the reactions are the various creation processes, i.e. °°→•°, °°→•• and °•→••, and in the second model, only the diffusion process •°→°• exists. For the first model, the probabilities P_l(m;t), of finding m particles on the lth shell of the Cayley tree, have been found exactly, and for the second model, the functions P_l(1;t) have been calculated. It has been shown that these are the only integrable models if one restricts consideration to the L+1-shell probabilities P(m₀,m₁,…,m_L;t).     

Multielectron ionization of atoms by fast ions: An approximation by normalized exponentials

Multielectron ionization of neutral atoms by fast positive ions is considered in terms of the independent particle model. A relatively simple technique for calculating the multielectron ionization probabilities and cross sections through the impact parameter is suggested in which one-electron ionization probabilities are represented as normalized exponentials p _nl(b) = p _nl(b) = p _nl(0)exp(?α_nl b), where b is the impact parameter and n and l are quantum numbers of the target atomic shell. Exponent α_nl is determined from the Born one-electron ionization cross section for target atoms, and preexponential p _nl(0) (the ionization probability at a zero impact parameter) is found from a geometrical model. This technique provides the normalization condition p _nl(b) ≤ 1 irrespective of the velocity and charge of striking ions and makes it possible to calculate the one-, two-, and three-electron ionization cross sections, which, when added up, make a major contribution to the total cross section, up to a factor of 2. The results of our computations are compared with experimental data and analytical results of other authors.     

Wirkungsquerschnitte und Isomerenverhältnis für die Reaktionen89Y(α, 3n)90g Nb und89Y(α, 3n)90m Nb

Absolute cross-sections and isomeric cross-section ratios have been measured for the reactions⁸⁹Y(α, 3n)^{90g, 90m} Nb. The energy of the α-particles was varied between 34 and 54 MeV. The experimental isomeric ratios are compared with statistical-model calculations.     

Anomalies in the orbital magnetism of neutrons in the 190,192Pt nuclei

For the ^190,192Pt nuclei, the g factors of the ν9/2^?[505]?ν11/2⁺[615] 10^? isomeric states populated in the relevant (α, 2n) reactions are measured by the method of an integrated disturbed angular distribution in an external magnetic field. From these measurements, it follows that the g factors are 0.009(8) and 0.010(6) for ¹⁹⁰Pt and ¹⁹²Pt, respectively. From the above g factors, it is found that the anomalous g _l factor of the neutron is δg _l(n)=?0.017(6).     

An effective lagrangian for multiphoton processes and a non-linear Born-Infeld lagrangian

An effective lagrangian for multiphoton processes (of Euler-Heisenberg type) is computed for an electromagnetic field interacting with massive scalar, fermion and vector particles. It is found that if the charges g_I, masses m_I and numbers N_I of massive particles satisfy the “supersymmetric” conditions, N_Sm_S⁴+3N_Vm_V⁴?2N_Fm_F⁴=0 and g_I²/m_I⁴ is I-independent, where I=S, F, V stands for scalars, fermions and vectors respectively, then not only quartic divergences (poles at n=0 in dimensional regularization) proportional to constant terms cancel out but also maximally helicity changing interaction terms vanish in the effective lagrangian. A possibility to relate a non-linear Born-Infeld lagrangian to the effective lagrangian is examined.