A Class of Charged Relativistic Superdense Star Models

In this article we obtain a new class of well behaved charged solutions by using particular forms of the metric potential g ₄₄ and electric intensity, which involves a parameter K. The metric describing the superdense stars joins smoothly with the Reissner-Nordstrom metric at the pressure free boundary. This class of solutions describes well behaved charged fluid balls. The class of solutions gives range of parameter K (0.13≤K≤1.9999) for which the solution is well behaved hence, suitable for modeling of super dense star. The interior of the stars possess there energy density, pressure, pressure-density ratio and velocity of sound to be monotonically decreasing towards the pressure free interface. In view of the surface density 2×10¹⁴ gm/cm³, the maximum mass of the charged fluid balls and corresponding radius are 0.4711M _Θ and 7.0122 km. The red shift at the centre and boundary are found to be 0.1640 and 0.1100 respectively.     

A Class of Well Behaved Charged Analogues of Schwarzchild’s Interior Solution

A class of well behaved charged analogues of Schwarzchild’s interior solution has been obtained using a particular electric intensity. The solutions of this class are utilized to depict a superdense star model with surface density 2×10¹⁴ g cm⁻³. The solution obtained is new and the pressure (p), density (c ² ρ), velocity of sound and (p/(c ² ρ)) are monotonically decreasing towards the pressure free interface. Moreover the adiabatic constant is found to be more than (4/3) which is necessary for stability under radial perturbation. Also the electric intensity increases monotonically towards the surface. The well behaved model has the maximum mass M=1.740793M _Θ , Radius 12.130308 km. The redshift at the center and on the surface is given by z ₀=0.384261 and z _a =0.292489. Out of the models of superdense star obtained couple of models represent Vela Pulsar for (i) α ²=1.03, b=0.33, , Radius=10.8566 km, M=1.18331M _Θ , I=0.642601×10⁴⁵, (ii) α ²=1.1, b=0.3, , Radius=11.197533 km, M=1.311438M _Θ , I=0.774508×10⁴⁵. All the solutions mentioned above are reducible to Schwarzchild interior solution in the absence of charge.     

Submillimetric cyclotron resonance linewidths and electron relaxation time in copper

For the first time submillimetric microwaves (λ<1 mm) are used to observe Azbel' Kaner cyclotron resonance in metals. The very high frequency used (typicallyF≅400 GHz) gives a large value ofωτ (typically 500) and therefore very sharp peaks. The fundamental resonance fieldH _c=m ^* cω/e is rather high (typically 200 KG), so subharmonicsH _c/n can be observed at many values ofH in the field region 0–27 KG. If relatively few electrons participate in the resonance and ifω _cτ≧50 (ω _c=eH/m ^* c,τ relaxation time) thenChambers has shown that the line shapes are independent of relaxation time while the fractional linewidthΔH/H varies as l/ωτ. For the belly orbit in pure copper the conditions of Chambers' theory are satisfied forH≧20 KG parallel to [111] axis.m ^* is a minimum andτ=1.8×10⁻¹⁰ s.     

Local Semicircle Law at the Spectral Edge for Gaussian <Emphasis Type="Italic">β</Emphasis>-Ensembles

We study the local semicircle law for Gaussian β-ensembles at the edge of the spectrum. We prove that at the almost optimal level of n^-2/3+e{n^{-2/3+\epsilon}}, the local semicircle law holds for all β ≥ 1 at the edge. The proof of the main theorem relies on the calculation of the moments of the tridiagonal model of Gaussian β-ensembles up to the p _n -moment, where p_n = O(n^2/3-e){p_n = O(n^{2/3-\epsilon})}. The result is analogous to the result of Sinai and Soshnikov (Funct Anal Appl 32(2), 1998) for Wigner matrices, but the combinatorics involved in the calculations are different.     

Logarithmic temperature dependence of the conductivity of the two-dimensional metal

We report on the first observation and studies of a weak delocalizing logarithmic temperature dependence of the conductivity, which causes the conductivity of the 2D metal to increase as T decreases down to 16 mK. The prefactor of the logarithmic dependence is found to decrease gradually with density, to vanish at a critical density n _c , 2∼2×10¹² cm⁻², and then to have the opposite sign at n>n _c ,2. The second critical density sets the upper limit on the existence region of the 2D metal, whereas the conductivity at the critical point, G _c ,2∼120e ²/h, sets an upper (low-temperature) limit on its conductivity. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 6, 497–501 (25 September 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Zero bias anomaly in the density of states of low-dimensional metals

We consider the effect of Coulomb interactions on the average density of states (DOS) of disordered low-dimensional metals for temperatures T and frequencies ω smaller than the inverse elastic life-time 1/τ. Using the fact that long-range Coulomb interactions in two dimensions (2d) generate ln²-singularities in the DOS ν(ω) but only ln-singularities in the conductivity σ(ω), we can re-sum the most singular contributions to the average DOS via a simple gauge-transformation. If σ(ω) > 0, then a metallic Coulomb gapν(ω) ∝ |ω|/e ⁴ appears in the DOS at T = 0 for frequencies below a certain crossover frequency Ω ₂ which depends on the value of the DC conductivity σ(0). Here, - e is the charge of the electron. Naively adopting the same procedure to calculate the DOS in quasi 1d metals, we find ν(ω) ∝ (|ω|/Ω ₁)^1/2exp(- Ω ₁/|ω|) at T = 0, where Ω ₁ is some interaction-dependent frequency scale. However, we argue that in quasi 1d the above gauge-transformation method is on less firm grounds than in 2d. We also discuss the behavior of the DOS at finite temperatures and give numerical results for the expected tunneling conductance that can be compared with experiments. Received 28 August 2001 / Received in final form 28 January 2002 Published online 9 July 2002     

The nature of binding in the ground state of the scandium dimer

For the study of the nature of binding in the Sc₂ dimer, the ground state, X⁵Σ _u ^–, was calculated by the valence multireference configuration interaction method with single and double excitations plus Davidson correction, MRCISD (+Q), at the complete basis set (CBS) limit. The employment of the C_2v symmetry group, allowed us to obtain the Sc atoms in different states at the dissociation limit. From the Mulliken population analysis and comparison with atomic energies follows that in the ground state Sc₂ dissociates on one Sc in the ground state and the other in the second excited quartet state, ⁴F _u . The spectroscopic parameters of the ground potential curve, obtained at the valence MRCISD (+Q)/CBS level, are: R _e  = 5.20 bohr, D _e  = 50.37 kcal/mol, and ω _e  = 234.5 cm^-1. The obtained value for the harmonic frequency agrees very well with the experimental one, ω _e  = 239.9 cm^-1. The dissociation energy with reference to the dissociation on two Sc in the ground states was estimated as D _e  = 9.98 kcal/mol. In contrast with many other studied transition-metal dimers, which are attributed to the van der Waals bonded molecules, the Sc₂ dimer is stabilized by the covalent bonding on the hybrid atomic orbitals.     

Negative ion effects in CO2 convection laser discharges

Negative ions are computed to be formed on a time scale and in quantities such that they may be a cause of plasma instability observed in low pressure electrical discharge convection CO₂ lasers. In a typical CO₂−N₂−He−H₂O laser mixture the principal ions are CO ₃ ⁻ , CO ₄ ⁻ and H⁻ with the total negative ion densityn ₋ given by 0.1n _e <n ₋<n _e , wheren _e is the electron density: but if the gases are re-cycled or if there is an air leak NO ₂ ⁻ and NO ₃ ⁻ are formed in significant amounts andn ₋ can become greater thann _e in a time considerably less than the gas dwell time in the electrical excitation discharge. CO is effective in reducingn ₋ in a system without re-cycling, but is ineffective in a re-cycled system with the oxides of nitrogen present.     

Low-temperature mobility of surface electrons and ripplon-phonon interaction in liquid helium

The low-temperature dc mobility of the two-dimensional electron system localized above the surface of superfluid helium is determined by the slowest stage of the longitudinal momentum transfer to the bulk liquid, namely, by the interaction between the surface and volume excitations of liquid helium, which decreases rapidly with the temperature. Thus, the temperature dependence of the low-frequency mobility is μ_dc ≈ 8.4 × 10⁻¹¹ n _e T ^−20/3 cm⁴ K^20/3/(V s), where n _e is the surface electron density. The relation T ^20/3 E_⊥⁻³ ≪ 2 × 10⁻⁷ between the pressing electric field (in kilovolts per centimeter) and temperature (in Kelvins) and the value ω ≲ 10⁸ T ⁵ K⁻⁵ s⁻¹ of the driving-field frequency have been obtained, at which the above effect can be observed. In particular, E _⊥ ≃ 1 kV/cm corresponds to T ≲ 70 mK and ω/2π ≲ 30 Hz.     

Relation between spectroscopic constants with limited Dunham coefficients

Statement of Kaur and Mahajan [1] about the definition of Δ used by Chandra [2] is not correct. Even if we take Δ = μω _e ² r _e ² /2D_e, the relation between Δ and G(=8ω_ex_e/B_e) is obtained as Δ = 4.21452856G, provided the vibrational energy of a diatomic molecule is expressed in terms of limited Dunham coefficients, Y₁₀, Y₂₀, Y₀₁ and Y₁₁. This relation is still different from that of Kaur and Mahajan [3]     

On the phase boundaries of the integer quantum Hall effect. Part II

It has been shown that the observation of the transitions between the dielectric phase and the integer-quantum-Hall-effect phases with the quantized Hall conductivity σ _xy ^q ≥ 3e ²/h announced in a number of works is unjustified. In these works, the crossing points of the magnetic-field dependence of the diagonal resistivity ρ _xx at different temperatures T and ω_cτ = 1 have been misidentified as the critical points of the phase transitions. In fact, these crossing points are due to the sign change of the derivative dρ _xx /dT owing to the quantum corrections to the conductivity. Here, ω_c = eB/m is the cyclotron frequency, τ is the transport relaxation time, and m is the effective electron mass.     

Length of the Instability Intervals for Hill's Equation

The length of instability intervals is investigated for the Hill equation y′′+ω(ω− 2∈p(x)y = 0, where p(x) has an infinite Fourier series of coefficients c _n. For any small ∈ it is shown that these lengths are completely characterized by the c _n's.     

Comment on: “Universal relation between spectroscopic constants”

Kaur and Mahajan [1] have claimed to derive a universal relation InG = 1.91578(±0.09727) + 0.97111(±0.03809) In Δ between the Sutherland parameter Δ(=ω _er _e ² /2D_e) and the dimensionless parameterG(= 8ω _ex_e/B_e) for the ground as well as excited electronic states of diatomic molecules. Validity of this relation is checked and we find that the relation is not correct. Next, we checked the validity of the relation Δ = 2.2r_e for the alkali group diatomic molecules. This relation is also found not to be correct.     

Wei Hua’s four-parameter potential: Comments and computation of molecular constants αe and εeXe

The value of adjustable parameterC in the four-parameter potentialU(r) =D _e [(1 - exp[-b(r -r _e)])/(1 -C exp[-b(r -r _e)])]² has been expressed in terms of molecular parameters and its significance has been brought out. The potential so constructed, withC derived from the molecular parameters, has been applied to ten electronic states in addition to the states studied by Wei Hua. Average mean deviation for these 25 states has been found to be 3.47 as compared to 6.93, 6.95 and 9.72 obtained from Levine, Varshni and Morse potentials, respectively. Also Dunham’s method has been used to express rotation-vibration interaction constant (α_e) and anharmonicity constant (ω_ex_e) in terms ofC and other molecular constants. These relations have been employed to determine these quantities for 37 electronic states. For α_e, the average mean deviation is 7.2% compared to 19.7% for Lippincott’s potential which is known to be the best to predict these values. Average mean deviation for (ω_ex_e) turns out to be 17.4% which is almost the same as found from Lippincott’s potential function.     

Ponderomotive acceleration of electrons by a whistler pulse

A Gaussian whistler pulse is shown to cause ponderomotive acceleration of electrons in a plasma when the peak whistler amplitude exceeds a threshold value and the whistler frequency is greater than half the cyclotron frequency, ω>ω _c /2. The threshold amplitude decreases with the ratio of plasma frequency to electron cyclotron frequency, ω _p /ω _c . However, above the threshold amplitude, the acceleration energy decreases with ω _p /ω _c . The electrons gain velocities about twice the group velocity of the whistler.     

Spin-orbit coupling in the ground and low-lying excited states of HF<Superscript>+</Superscript> and HF<Superscript>-</Superscript>

Electronic structure and spectroscopic properties B _e, ω_e, ω_e x _e, α_e, T _e of ground state and the low-lying excited states of HF⁺ and HF^- molecular ions were investigated within scalar relativistic multireference configuration interaction with single and double excitations framework using the GAMESS-US program package. All potential energy curves (PECs) were calculated using the relativistic complete active space self-consistent field/spin-orbit multi-configuration quasi-degenerate perturbation theory (CASSCF/SO-MCQDPT). The curves are all fitted to the analytical potential energy function (APEF), from which accurate spectroscopic constants are derived. The spin-orbit splitting was also been studied, the split value of X²P^{2}{\rm \Pi} state of HF⁺ is determined to be 288.38 cm^-1. The calculated properties are in good agreement with the available experimental value. Spectroscopic constants of the ground states of HF^- that have never been observed in experiment are obtained. These curves provide an interpretation of the known experimental observations on this system and suggest a number of further experiments which possible provide a critical test of this data.     

Well Behaved Charged Generalization of Buchdahl’s Fluid Spheres

In the present article, we have obtained a class of well behaved charged analogues of Buchdahl (Phys. Rev. 116:1027–1034, 1959) neutral perfect fluid solution, which reduces to its neutral counter part in the absence of charge. The solutions so obtained are utilized to depict the super-dense stars models such as models for neutron stars and strange star. It is observed that the models are well behaved for restricted range of the parameter K (1<K≤1.64). Over all the maximum mass and corresponding radius is 2.4495M _Θ and 16.7289 respectively and moment of inertia . Also the pulsars character of the super-dense stars so obtained and has been analyzed with the help of moment of inertia. The analysis of the models reveals both vela and crab pulsars.     

Mode transition in magnetic pole enhanced inductively coupled argon plasmas

The electrical probe (Langmuir probe) diagnostics of different plasma parameters and operation regimes (E/H modes) of magnetic pole enhanced, inductively coupled (MaPE-ICP) argon plasmas are investigated. It is shown that uniform, high density (n _e ∼ 10¹² cm^-3) and low electron temperature (T _e ∼ 1.5 eV) plasma can be produced in low pressure argon discharges at a low power (100 W). It is found that an MaPE-ICP reactor operates in two different modes; capacitive (E mode) and inductive (H mode). No density jump or hysteresis are reported between these modes. The effect of pressure on transition power, where the mode changes from E to H mode at 20 sccm gas flow rate are studied and it is found that for all pressures tested (∼7.5 mTorr to 75 mTorr) the transition power remains same. In the inductive mode, the above plasma parameters show a smooth variation with increasing filling gas pressure at fixed power. The intensity of the emission line at 750.4 nm due to 2p ₁ → 1s ₂ (Paschen’s notation) transition, closely follows the variation of n _e with RF power and filling gas pressure. Measured electron energy probability function (EEPF) shows that electron occupation mostly changes in the high-energy tail, which enlightens close similarity of the 750.4 nm argon line to electron number density (n _e ). The behaviour of the electron energy probability function (EEPF) with regard to pressure and RF power in two operational modes is presented.     

Black holes with metric and fields of the same form

We present two rotating black hole solutions with axion ξ, dilaton f{\phi} and two U(1) vector fields. Starting from a non-rotating metric with three arbitrary parameters, which we have found previously, and applying the “Newman–Janis complex coordinate trick” we get a rotating metric g _μν with four arbitrary parameters namely the mass M, the rotation parameter a and the charges electric Q _E and magnetic Q _M . Then we find a solution of the equations of motion having this g _μν as metric. Our solution is asymptotically flat and has angular momentum J = M a, gyromagnetic ratio g = 2, two horizons, the singularities of the solution of Kerr, axion and dilaton singular only when r = a cos θ = 0 etc. By applying to our solution the S-duality transformation we get a new solution, whose axion, dilaton and vector fields have one more parameter. The metrics, the vector fields and the quantity l = x+ie^-2f{\lambda=\xi+ie^{-2\phi}} of our solutions and the solution of: Sen for Q _E , Sen for Q _E and Q _M , Kerr–Newman for Q _E and Q _M , Kerr, Reference Kyriakopoulos [Class. Quantum Grav. 23:7591, 2006, Eqs. (54–57)], Shapere, Trivedi and Wilczek, Gibbons–Maeda–Garfinkle–Horowitz–Strominger, Reissner–Nordstr?m, Schwarzschild are the same function of a, and two functions ρ ² = r(r + b) + a ² cos² θ and Δ = r(r + b) − 2Mr + a ² + c, of a, b and two functions for each vector field, and of a, b and d respectively, where a, b, c and d are constants. From our solutions several known solutions can be obtained for certain values of their parameters. It is shown that our two solutions satisfy the weak the dominant and the strong energy conditions outside and on the outer horizon and that all solutions with a metric of our form, whose parameters satisfy some relations satisfy also these energy conditions outside and on the outer horizon. This happens to all solutions given in the “Appendix”. Mass formulae for our solutions and for all solutions which are mentioned in the paper are given. One mass formula for each solution is of Smarr’s type and another a differential mass formula. Many solutions with metric, vector fields and λ of the same functional form, which include most physically interesting and well known solutions, are listed in an “Appendix”.