Occupation Number Density Research Articles

Effects of mean-field and pairing correlations on the Bogoliubov quasiparticle resonance

The quasiparticle resonances are investigated by examining three kinds of quasiparticle spectra, i.e., the density of quasiparticle states, the occupation number density, and the pair number density in the continuum Skyrme Hartree-Fock-Bogoliubov theory with the Greens function method.Taking the weakly bound nucleus $^{66}$Ca as an example, the quasiparticle resonant energies and widths extracted from these three kinds of quasiparticle spectra are compared.For the narrow resonances, the extracted resonant energy and the width are consistent with each other. However, it is difficult to use the density of quasiparticle states to identify the broad resonances due to the background of nonresonant continuum.By switching off the pairing potential and/or the Hartree-Fock (HF) potential respectively in the calculation of these quasiparticle spectra, the roles of HF mean-field and pairing correlations in the quasiparticle resonances are demonstrated clearly. It turns out that all the quasiparticle resonances corresponding to the deeply bound, weakly bound and positive-energy single-particle resonant states, are mainly contributed by the HF potential.The pairing potential helps to slightly increase the resonant energy and the width. However, the pairing potential is important to make the nucleons occupy the low-lying nonresonant continuum states near the threshold and take part in the pairing correlations here, especially for the partial waves with small angular momentum $\ell$.

How the Electronic Structure in URu2Si2 Changes with Temperature: A High-Resolution Compton Scattering Study

We have measured directional Compton profiles on the (001) plane in URu2Si2 single crystal at several temperatures. Two-dimensional electron occupation number densities (2D-EONDs) were obtained fro...

Counting states and the Hadron Resonance Gas: Does X(3872) count?

We analyze how the renowned X(3872), a weakly bound state right below the DD¯⁎ threshold, should effectively be included in a hadronic representation of the QCD partition function. This can be decided by analyzing the DD¯⁎ scattering phase-shifts in the JPC=1++ channel and their contribution to the level density in the continuum from which the abundance in a hot medium can be determined. We show that in a purely molecular picture the bound state contribution cancels the continuum providing a vanishing occupation number density at finite temperature and the X(3872) does not count below the Quark-Gluon Plasma crossover happening at T∼150 MeV. In contrast, within a coupled-channels approach, for a non vanishing cc¯ content the cancellation does not occur due to the onset of the X(3940) which effectively counts as an elementary particle for temperatures above T≳250 MeV. Thus, a direct inclusion of the X(3872) in the Hadron Resonance Gas is not justified. We also estimate the role of this cancellation in X(3872) production in heavy-ion collision experiments in terms of the corresponding pT distribution due to a finite energy resolution.

First principles investigation of binary intermetallics in Mg–Al–Ca–Sn alloy: Stability, electronic structures, elastic properties and thermodynamic properties

The structural stability, electronic structures, elastic properties and thermodynamic properties of the main binary phases Mg17Al12, Al2Ca, Mg2Sn and Mg2Ca in Mg–Al–Ca–Sn alloy were determined from the first-principles calculation. The calculated lattice parameters are in good agreement with the experimental and literature values. The calculated heats of formation and cohesive energies show that Al2Ca has the strongest alloying ability and structural stability. The densities of states (DOS), Mulliken electron occupation number, metallicity and charge density difference of these compounds are given. The elastic constants of Mg17Al12, Al2Ca, Mg2Sn and Mg2Ca phases are calculated, and the bulk moduli, shear moduli, elastic moduli and Poisson ratio are derived. The calculations of thermodynamic properties show that the Gibbs free energies of Al2Ca and Mg2Sn are lower than that of Mg17Al12, which indicates that Al2Ca and Mg2Sn are more stable than Mg17Al12 phase. Hence, the heat resistance of Mg–Al-based alloys can be improved by adding Ca and Sn additions.

Visual understanding of the hidden-order transition inURu2Si2by high-resolution x-ray Compton scattering

We report the change of electronic structure associated with the hidden-order (HO) transition in ${\mathrm{URu}}_{2}{\mathrm{Si}}_{2}$ through Compton scattering experiment on the (001) plane of the single crystal. The two-dimensional electron occupation number densities (EONDs) obtained at 14 and 20 K, which are the projection of Fermi volume onto the ${k}_{x}\ensuremath{-}{k}_{y}$ plane of the first Brillouin zone, clearly reflect a whole image of electronic structure in the HO and paramagnetic (PM) phases, respectively. The change in electronic structure is well described by theoretical EONDs derived from the result of a band calculation, where $\mathrm{U}\phantom{\rule{0.28em}{0ex}}5f$ electrons are treated as itinerant ones. We also evaluate the electron (hole) numbers in the HO and PM phases and, therefore, its change on the HO transition. The HO transition is deeply involved with a significant change in $5f$ electrons from partially localized to itinerant states through hybridization with conduction electrons, resulting in the reconstruction of Fermi-surface structure.

Mechanical properties and electronic structures of MgCu2, Mg2Ca and MgZn2 Laves phases by first principles calculations

Mechanical properties and electronic structure of MgCu2, Mg2Ca and MgZn2 phases were investigated by means of first principles calculations from CASTEP program based on density functional theory (DFT). The calculated lattice parameters are in good agreement with the experimental and literature values. The calculated heat of formation and cohesive energies showed that MgCu2 has the strongest alloying ability and structural stability. Elastic constants of MgCu2, Mg2Ca and MgZn2 were calculated, and the bulk moduli, shear moduli, elastic moduli and Poisson ratio were derived. The calculated results show that MgCu2, Mg2Ca and MgZn2 are all ductile phases. Among the three phases, MgCu2 has the strongest stiffness and the plasticity of MgZn2 phase is the best. Melting points of the three phases were predicted using cohesive energy and elastic constants. Density of states (DOS), Mulliken population, electron occupation number and charge density difference were discussed. Finally, Debye temperature was calculated and discussed.

First-principles calculations of structural, elastic and electronic properties of AB2 type intermetallics in Mg–Zn–Ca–Cu alloy

Electronic structure and elastic properties of MgCu2, Mg2Ca and MgZn2 phases were investigated by means of first-principles calculations from CASTEP program based on density functional theory (DFT). The calculated lattice parameters were in good agreement with the experimental and literature values. The calculated heats of formation and cohesive energies shown that MgCu2 has the strongest alloying ability and structural stability. The elastic constants of MgCu2, Mg2Ca and MgZn2 phases were calculated, the bulk moduli, shear moduli, Young's moduli and Poisson's ratio were derived. The calculated results shown that MgCu2, Mg2Ca and MgZn2 are all ductile phases. Among the three phases, MgCu2 has the strongest stiffness and the plasticity of MgZn2 phase is the best. The density of states (DOS), Mulliken electron occupation number and charge density difference of MgCu2, Mg2Ca and MgZn2 phases were discussed to analyze the mechanism of structural stability and mechanical properties.

Compton profiles and nesting of Fermi surfaces for B2-TiNi and B2-TiPd

The band structures of the shape memory alloys B2-TiNi and B2-TiPd are calculated by the full potential linearized augmented plane wave method with the local density approximation. The theoretical Compton profiles for B2-TiNi and B2-TiPd are calculated. In addition, the three-dimensional (3D) occupation number densities obtained by Lock–Crisp–West (LCW) analysis are presented for the first time. These 3D occupation number densities are in good agreement with the Compton scattering experiment for TiNi. Both shape memory alloys are based on martensitic transformation, which is caused by soft phonons. The charge-density wave is created by nesting of Fermi surfaces, which leads to phonon softening. To examine the nesting vectors quantitatively, we calculate the generalized susceptibility χ(q). χ(q) shows peaks at 0.315[110]2π/a and 0.4[111]2π/a for TiNi and at 0.275[110]2π/a and 0.395[111]2π/a for TiPd. Although the nesting vector in the [110] direction agrees with that from the phonon experiment, the nesting vector in the [111] direction differs from that in the experimental results.

Fermi surface topology of deuterium-doped vanadium: Compton scattering study

The deuteration-induced effect on the Fermi surface (FS) topology of V was investigated by the synchrotron-based Compton scattering technique with 115 keV X-rays. The three-dimensional occupation number density (OND) of α-VD 0.64 single crystal and V single crystal was reconstructed by the directional Compton profiles along 13–18 directions. The observed OND shows that the FS topology of α-VD 0.64.differs from that of V at Γ, N, and H points in the crystal momentum space, which are hole position for V. This indicates that electrons that originate from deuterium modify the upper part of the host metal d bands (3rd and 4th bands) at the Fermi level E F, and forms the metal–hydrogen bonding states with the lower part of the host metal d band (1st band).

FElectron Contribution to the Change of Electronic Structure inCeRu2Si2with Temperature: A Compton Scattering Study

High resolution Compton profiles have been measured in the single crystal of CeRu(2)Si(2) above and below the Kondo temperature to elucidate the change of the Ce-4f electron from localized to itinerant states. Two-dimensional electron occupation number densities projected on the first Brillouin zone, which are obtained after a series of analyses, clearly specify the difference between itinerant and localized states. The contribution of Ce-4f electrons to the electronic structure is discussed by contrast with a band calculation.

Photon density of states in polarization-entangled laser operation

In the context of nonlinear interaction between a classical pump field and two polarization-entangled photon modes, we derive mathematical expressions involving the photon occupation number and photon density of states in polarization-entangled laser operation at low temperature.

Coexistence of polaronic and band states in a bilayer manganite from two-dimensional reconstruction of magnetic Compton profiles

We have measured directional magnetic Compton profiles between [100] and [110] directions in a bilayer manganite at $10\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The two-dimensional spin momentum distribution of the Mn $3d$ state is reconstructed from them. The result is examined in both terms of molecular orbital and band schemes. The ${e}_{\mathrm{g}}$ type orbitals are dominated by the ${x}^{2}\ensuremath{-}{y}^{2}$ type orbital. The occupation-number density in the $k$ space obtained by the Lock-Crisp-West folding is not explained only by the band picture, and suggests that a polaronic state of ${e}_{\mathrm{g}}$ type electrons coexists in the ferromagnetic metal phase below ${T}_{\mathrm{c}}$.

Comments on reconstruction of Fermi surface from high-resolution Compton data

A few comments are made on reconstruction of three-dimensional (3D) momentum density and Fermi surface mapping from high-resolution Compton data. Equivalence of LCW-folding and Schuelke's method in converting observed momentum density to occupation number density is explicitly shown.

On dispersion relations and the statistical mechanics of Hawking radiation

We analyse the interplay between dispersion relations for the spectrum of Hawking quanta and the statistical mechanics of such a radiation. We first find the general relation between the occupation number density and the energy spectrum of Hawking quanta and then study several cases in detail. We show that both the canonical and the microcanonical picture of the evaporation lead to the same linear dispersion relation for relatively large black holes. We also compute the occupation number obtained instead by assuming that the spectrum levels out (and eventually falls to zero) for very large momenta and show that the luminosity of black holes is not appreciably affected by the modified statistics.

Electron correlation effects on Compton profiles of Cr in the GW approximation

The occupation number densities N( k)s of Cr are evaluated from a first-principle calculation of the spectral function within the GW approximation. The dielectric matrix needed for the screened potential W is calculated within the random-phase approximation. The Compton profiles (CPs) of Cr are calculated using the N( k)s. Anisotropic electron correlation effects in the directional CPs of Cr, which cannot be described within the local density approximation, are successfully reproduced by using the N( k)s.

Black hole evaporation and compact extra dimensions

We study the evaporation of black holes in space-times with extra dimensions of size L by employing the microcanonical picture of Hawking's radiation. We show that the luminosity is greatly damped when the horizon becomes smaller than L and black holes born with an initial size smaller than L are almost stable. This effect is due to the strong dependence of both the occupation number density of Hawking quanta and the greybody factor of a black hole on the dimensionality of space. Although the picture of what happens when the horizon shrinks to a size L is still incomplete, we argue that there might occur an outburst of energy which leaves a quasistable remnant.

Temperature influence on the valence Compton profiles of aluminum and lithium

We present temperature-dependent valence Compton profiles of single-crystalline Al and Li measured with 30 keV incident energy and $173\ifmmode^\circ\else\textdegree\fi{}$ scattering angle with momentum space resolution of 0.1 a.u. The valence profiles for both samples measured at low temperature are above the high-temperature ones at momentum ${p}_{z}\ensuremath{\approx}{p}_{F},$ the Fermi momentum, and below at ${p}_{z}=0\mathrm{a}.\mathrm{u}.,$ which corresponds to a narrowing of the valence Compton profiles with increasing temperature. This fundamental temperature dependence can be attributed to the variation of the lattice constant and thus the variation of the Fermi momentum with temperature when the experimental results are compared with jellium calculations of the valence Compton profiles utilizing a correlation corrected occupation number density. In addition the Li experiment shows a significant temperature dependence even for ${p}_{z}>{p}_{F},$ which is assigned to the diminished contribution of higher momentum components to the valence Compton profile with increasing temperature. The Li results are in good agreement with calculations using an empirical temperature-dependent local pseudopotential.

Ultra-high Resolution Compton Scattering of Li Metal: Evaluation with Respect to the Correlation Corrected Occupation Number Density

Directional Compton profiles of Li metal measured with ultra-high momentum space resolution (0.02 a.u.) were analysed in terms of their reciprocal form factors

A POSSIBLE GENERALIZATION OF THE SCHRÖDINGER EQUATION BASED ON THE GAUSS PRINCIPLE OF LEAST SQUARES

The linear Schrodinger equation is generalized into non-linear equation based on the Gauss' principle of least squares. The weight function is assigned in such a way that it might be interpreted as occupation number density of hidden particles that obey the Fermi–Dirac stastistics. It is shown that the motion of a free particle, according to the so generalized non-linear equation, is described by a well behaved nondeforming wave packet moving with a constant velocity, in contrast to the always deforming wave packet according to the linear Schrodinger equation.

Electron momentum-space densities and Fermi surface ofLi100−xMgx(0<~x<~40)alloys: Compton scattering experiment versus theory

Directional Compton profiles (CP's) of ${\mathrm{Li}}_{100\ensuremath{-}x}{\mathrm{Mg}}_{x}(0<~x<~40)$ were measured for (11)12 directions of the momentum transfer q with (0.14) 0.16 a.u. $(\mathrm{a}.\mathrm{u}.=\mathrm{a}\mathrm{t}\mathrm{o}\mathrm{m}\mathrm{i}\mathrm{c}$ units: $\ensuremath{\Elzxh}=e=m=1)$ momentum space resolution using synchrotron x rays, monochromatized to (31) 59 keV (values in brackets refer to $x=0).$ The total experimental valence electron CP's, their second derivatives, and the associated directional differences were compared with the corresponding Korringa-Kohn-Rostoker--coherent-potential-approximation--local-density-approximation (KKR--CPA--LDA) computations. Discrepancies between measurements and calculations are partly traced back to an inadequate treatment of electron correlation effects within the LDA framework. The three-dimensional (3D) valence-electron momentum density, \ensuremath{\rho}(p), as well as the 3D occupation number density $N(\mathbf{k}),$ were reconstructed from experimental data using the Fourier-Bessel method. The reconstructed \ensuremath{\rho}(p)'s exhibit evidence of higher momentum components due to 110 umklapp processes, whose variations with x are in reasonable agreement with the KKR-CPA calculations. The experimental $N(\mathbf{k})$'s provide a direct measure of the Fermi-surface anisotropy and show the presence of necks on the 110 Brillouin-zone boundaries for $x>~13$ in good accord with 2D positron annihilation experiments.