Hole Decay Research Articles

Quantum gravitational collapse of a scalar field and the wave function of black hole decay.

We develop a quantum description of spherically symmetric gravitational collapse of a massless scalar field. The canonical quantization procedure is applied to a minisuperspace model in which the four-metric and scalar field variables are restricted to a self-similar functional form. Our main purpose is to propose a mechanism of black hole decay in terms of a time evolution of the wave function defined on the minisuperspace. For the self-similar classical dynamics there exists a one-parameter family of solutions for the Einstein-scalar equations, and the Hamiltonian turns out to play the role of the critical parameter which separates the supercritical solution corresponding to a black hole formation from the subcritical one corresponding to a wave reflection to infinity. We derive a set of the eigenfunctions of the quantum Hamiltonian operator, which is interpreted to be the quantum version of the supercritical and subcritical solutions. One of the metric components is also treated as a quantum operator which does not commute with the Hamiltonian operator. The expansion of the eigenfunction of the metric operator in terms of the Hamiltonian eigenfunctions motivates us to introduce the superposition principle and the time-dependent Schr\odinger equation which lead to the uncertainty of the Hamiltonian eigenvalue. Then we study the time evolution of the initial black hole state, which is chosen to be one of the supercritical Hamiltonian eigenstates. We arrive at the conclusion that the time evolution toward black hole decay is essentially due to the breakdown of orthogonality of the Hamiltonian eigenfunctions: The quantum black hole behaves like a wave packet written by a superposition of the various subcritical states. The localized structure of the black hole wave packet begins to spread as each subcritical state evolves with time according to the Schr\odinger equation. We can estimate the decay time and find the final behavior of the wave function describing an outgoing flux of scalar waves observable at future null infinity.

Selectively excited core-to-core fluorescence of potassium halides.

Core-to-core fluorescence transitions from resonantly excited K 2${\mathit{p}}^{\mathrm{\ensuremath{-}}1}$3d states in KF and KI have been measured and specific interaction energies of the final 3${\mathit{s}}^{\mathrm{\ensuremath{-}}1}$3d configuration were determined. Delocalization of the excited electron in the 2${\mathit{p}}^{\mathrm{\ensuremath{-}}1}$3d states was observed to compete with the core hole decay. Furthermore, evidence for an influence of the chemical surrounding on potassium properties such as the 3s core hole lifetime, the 3s3d exchange splitting, and the configuration interaction of the 3s core hole state was found.

The dynamics of core hole excitation and decay in adsorbed and condensed molecules on solid surfaces

In isolated molecules, the decay of neutral and ionic core-excited species leads to distinctly different decay electron spectra which are usually termed autoionization and Auger spectra, respectively. If a molecule is coupled to a substrate in an adsorbate state, or to other surrounding species in a condensed phase, this coupling can modify or, in the extreme, eliminate this difference; also, satellite structure can be influenced. This results from charge and/or energy transfer between the target molecule and its surroundings before the decay event, and can therefore be used to obtain information about such processes on time scales on the order of the core hole life time or shorter. Additional information can be derived from the registration of fragmentation of the molecule as a consequence of the primary excitation and/or the final states of decay. In this case, a third time scale, that of motion of atoms or groups of atoms, comes into play which in extreme cases can compete with those of hole decay and electronic coupling to the surroundings. Such coupling to nuclear motion is also at work in the interference of the electronic evolution with vibrational motion in the molecule which can be investigated with sufficient resolution in the primary excitation. Again, the change induced here into the behavior of the free molecule by the presence of a coupled medium (substrate or condensate) can be used to extract information on the relative time scales. At present much of this information is of a qualitative nature; adequate theories would be very helpful for more detailed understanding.

High resolution studies of the electronic decay of core holes in molecules: there is no threshold at the “XPS threshold”

Using high resolution excitation with synchrotron radiation we have studied the electronic decay of core hole excited states in CO 2 as the excitation energy is varied across the threshold for the core electron photoemission. All throughout this energy region the core hole decay spectra develop continuously and there is no threshold behavior observed in these spectra. These experimental observations are in agreement with recent theoretical work treating the excitation of core electrons continuously across the ionization threshold.

KLL resonant Auger electron emission from silicon compounds in solid phase

The resonant Auger electron emissions from solid silicon compounds with different relaxation properties (Si, SiC, SiO 2) have been studied using synchrotron radiation. We found that the energy of the SiKL 2,3L 2,3 Auger electrons from SiO 2 is split into two peaks, i.e. normal and resonant Auger peaks, when the photon energy is close to the Si 1s → 3p resonance. Such energy splits of the Auger peaks are not observed in Si and SiC, because the core holes are well screened and the charge is delocalized before the core hole decay happens. It was also found that the energy of the resonant Auger peak of SiO2 increases almost in proportion to the photon energy. This gradual energy gain is interpreted as the broad band width of unoccupied valence orbitals of solid Si02 compared to isolated atoms and molecules in gas phase.

Coherent excitation of vibrational wave functions observed in core hole decay spectra of O 2, N 2 and CO

High resolution studies of the electron emission generated in the decay of neutral core to bound state excitations in small molecules, reflect the dynamics of the time evolution of the coherently excited vibronic wavefunctions in the core excited states. This coherent excitation gives rise to interference effects observed in the electronic decay processes. Since the lifetime of the core excited states in O 2, N 2 and CO is only a few fs, the study of these interference phenomena offers a stringent test of the quantum mechanical description of the time evolution of the excited states. Here we demonstrate that the resulting interference effects are not only observed when the lifetime broadening of the core excited state approaches the vibrational spacing but also for systems where the vibrational levels are clearly resolved in the excitation spectrum.

The σ* absorption peak at the oxygen 1s edge of O2: Exchange splitting, ultrafast dissociation, and atomiclike Auger spectra

The x-ray absorption spectrum of solid O2 at the O 1s absorption edge is analyzed, using its polarization dependence and the Auger de-excitation spectra. Rydberg states are quenched in the solid, and the exchange splitting of the 1s ionization threshold (1.1 eV) can be observed. Below the ionization threshold, core electrons can be excited into unoccupied antibonding π* and σ* orbitals. We conclude from the relative intensities and from the polarization dependence, that the exchange splitting of the σ* final state is small (<1 eV). This is confirmed by LDA calculations of core-excited states. The calculated σ* potential surfaces are repulsive, which explains the large width of this absorption peak. Because of ultrafast dissociation (∼5 fs), core hole decay is likely to occur at large interatomic distances. Auger spectra at the σ* absorption of O2 do indeed show peaks that would be expected for free core-excited oxygen atoms.

Photodissociation of SF6 near the F 1s absorption edge

Core-excited fragmentation of SF6 is analyzed by using monochromatic synchrotron radiation and time-of-flight mass spectroscopy. Excitation of fluorine K and sulfur L levels yields highly dissociated and multiply charged ions such as SF2+, S2+, and S3+ that are not seen with valence level excitation. Excitation of sulfur L levels is found to be more dissociative than that of fluorine K levels in the sense that more atomic ions and more multiply charged sulfur ions are produced. In addition to the above results, the generation mechanism for these ions is discussed by considering the multistep Auger cascade decay of core holes.

Correlation of preexisting diamagnetic defect centers with induced paramagnetic defect centers by ultraviolet or vacuum-ultraviolet photons in high-purity silica glasses.

Electron-spin-resonance (ESR) and vacuum-ultraviolet (vuv) absorption measurements were performed on a series of high-purity silica glasses exposed to 6.4-eV photons, 7.9-eV photons from excimer lasers, and to \ensuremath{\gamma} rays. The concentration of defect centers varies from ${10}^{14}$ to ${10}^{16}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ depending on the method of material fabrication and photon energy of the irradiating lasers. Variation of the defect species with both the incident-photon energy and manufacturing condition is observed by ESR measurements. E' centers (\ifmmode^\circ\else\textdegree\fi{}Si\ensuremath{\cdot}) are observed in all types of silicas. Nonbridging-oxygen hole centers (NBOHC's \ifmmode^\circ\else\textdegree\fi{}Si-O\ensuremath{\cdot}) in high-OH silica ([OH]\ensuremath{\approxeq}1000 ppm) and peroxy radicals (PR's, \ifmmode^\circ\else\textdegree\fi{}Si-O-O\ensuremath{\cdot}) in oxygen-surplus silica ([OH]1 ppm) are observed, only when the samples are exposed to 7.9 eV photons. The defect centers observed in \ensuremath{\gamma}-irradiated silica are qualitatively in agreement with those in 7.9 eV laser-irradiated silica. The variation of defect species with manufacturing methods indicates that the observed paramagnetic centers are created from preexisting defects. Concentration of the defects induced by either 6.4 or 7.9 eV laser photons is proportional to the square of the pulse energy, indicating that two-photon absorption process dominates in the defect formation. The defect formation process can be understood in terms of the creation of an electron-hole (e-h) pair by two-photon excitation and the subsequent hole trapping or decay of an e-h pair at the site of preexisting defects. Dependence of the induced-defect species on incident-photon energy can be explained by the variation in the energy level of preexisting defects or in the defect formation energy. Results of vuv-absorption measurements reveal the conversion of diamagnetic precursor defects (e.g., \ifmmode^\circ\else\textdegree\fi{}Si-Si\ifmmode^\circ\else\textdegree\fi{}, \ifmmode^\circ\else\textdegree\fi{}Si-O-O-Si\ifmmode^\circ\else\textdegree\fi{}, and \ifmmode^\circ\else\textdegree\fi{}Si-OH) introduced during the manufacturing process, into paramagnetic defect centers, the E' centers, NBOHC's, and PR's.

Determination of the exchange splitting of the shape resonance of O2 using the core hole decay spectrum as a "fingerprint."

We have determined the exchange splitting of the 1${\mathrm{\ensuremath{\sigma}}}_{\mathit{g}}^{\mathrm{\ensuremath{-}}1}$3${\mathrm{\ensuremath{\sigma}}}_{\mathit{u}}$ shape resonance excitation of gas phase ${\mathrm{O}}_{2}$, which cannot unambiguously be identified using conventional absorption spectroscopy. By identifying the electronic decay spectrum of the shape resonance excitation we could separately monitor the decay of the ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{*}}$ shape resonance and the Rydberg states. Using this fingerprint method we measured the pure core to 3${\mathrm{\ensuremath{\sigma}}}_{\mathit{u}}$ bound state absorption spectrum in partial secondary electron yield spectroscopy.

Persistent infrared hole burning spectroscopy of NH3D+ doped in [(NH4)x,Rb1−x]2SO4 mixed crystals

[(NH4)x,Rb1−x]2SO4 mixed crystals (0.16≤x≤1) were doped with NH3D+. Four of the eight N–D stretching bands of the NH3D+ ion gradually disappear with increasing Rb+ ion concentration while the widths of the N–D stretching bands increase, indicating that Rb+ ions first substitute NH4+ ions only in one type of crystal site, and that addition of Rb+ ions introduces glasslike disorder into the (NH4)2SO4-type crystalline structure. Infrared hole burning has been demonstrated in the broadened N–D stretching band of NH3D+ ion using a combination of a diode laser and a Fourier-transform infrared spectrometer. The initial hole width decreases proportionally with the center frequency of the hole at all Rb+ ion concentrations and agrees with the measurements of the [(NH4)x,K1−x]2SO4 mixed crystals. The similar proportionality, long known for many hydrogen-bonded systems in solution, suggests that the widths observed in solution are homogeneous. A longer irradiation time (≳10 min), however, leads to a wider spectral hole. Measured hole decay rates decrease with decrease of the center frequency of the hole, showing that the rotational tunneling barrier increases with the strength of the hydrogen bond. The change of the rotational tunneling barrier with Rb+ ion concentration is also observed as a change of the hole decay rate (more than tenfold in the experimental range). On the other hand, the hole burning quantum efficiency shows little change with the Rb+ ion concentration, or temperature. The observed steady holeburning quantum efficiency supports the infrared hole burning mechanism proposed in our previous study: The configurational change of the hole burning must occur in the excited vibrational state.

Resonant excitation and decay of core holes in condensed layers of furan and pyrrole

Near edge x-ray absorption spectra and decay electron spectra for resonant and nonresonant excitations in the C 1s and N 1s regions have been measured for condensed furan (C4H4O) and pyrrole (C4H4NH) layers. The decay spectra after resonant excitation into the lowest unoccupied orbital (π*4) are pure autoionization spectra. The participant channels show strong resonant enhancements of the photoelectron peaks, in particular after excitation of the C 1s core electrons. Overall however, the spectra are dominated by the spectator channels. The spectator spectra resemble the normal Auger spectra shifted by spectator shifts of ≊4 eV for furan and ≊2.5 eV for pyrrole. For furan the participant spectra for excitation at the two different carbon atoms show significant differences that can be qualitatively understood in terms of a simple one-electron picture by considering the localization of the corresponding orbitals on the core hole. The decay spectra after excitation into the π*5 orbital show negligible enhancement of the participant channel, a strongly reduced spectator shift, and less-pronounced structures than at higher photon energies. The latter is attributed to a competition of spectator decay and normal Auger decay after internal photoionization into Rydberg derived bands in the condensate. For excitations into the σ*-resonances pure Auger spectra are observed, indicating that these resonances fully ionize before core decay takes place.

Effects of time evolution of coherently excited vibrations in molecular core—hole decay spectra of O 2

Lifetime vibrational interference effects modulate the line shapes observed in high-resolution studies of the decay of ultra-short-lived core—hole excited states in molecules. We have analyzed the decay of the 1σ −1 u 1π 3 g core excited state in O 2, where for the first time subsets of vibronic eigenfunctions could be selected. We demonstrate that this type of spectroscopy can be used to verify the predictions of quantum mechanical interference theory describing the time evolution of coherently excited vibrational states on the femtosecond time scale.

Spectral diffusion in organic glasses. Temperature dependence of permanent and transient holes

Spectral diffusion of the S 1←S 0 0—0 transition (Q y ) of bacteriochlorophyll a (BChl a) as guest in the glasses ethanol (EtOH), triethylamine (TEA), 2-methyltetrahydrofuran (MTHF) and diethylether at low temperature has been studied by transient and permanent hole burning with a single-mode GaAlAs diode laser at ≈ 780 nm. Transient holes decay on a time scale of about 100 ms, determined by the triplet-state lifetime of BChl a. Their widths are compared to those of permanent holes probed on a time scale of minutes; both follow a T 1.3±0.1 temperature dependence between 1.2 and 4.2 K and extrapolate to the fluorescence lifetime-limited value for T→0. The amount of spectral diffusion, derived from the difference in width of permanent and transient holes over a time span between ≈ 10 −5 and ≈10 2 s, strongly depends on the glassy host.

Persistent infrared holeburning spectroscopy of (NH4)2SO4–K2SO4 mixed crystals

Infrared holeburning has been observed from mixed crystals. NH3D+ ions were imbedded in (NH4)2SO4–K2SO4 mixed crystals, the sample irradiated at the N–D stretching frequency, and resulting spectral hole then continuously monitored by a Fourier-transform infrared (FTIR) spectrometer. The holewidth decreases proportionally to the center frequency of the hole; within the range of 2240–2300 cm−1, the width changes from 10 to 5 cm−1 at 7.5 K. A longer irradiation time (≳10 min), however, leads to a wider spectral hole and also comparatively larger antiholes. The holewidth also shows a T2 type increase with temperature over the range of 7.5–45 K. Decay of the hole (hole filling) is not exponential, indicating that there is a distribution of decay rates. The holeburning quantum efficiency remains almost unchanged with temperature. Similarly, it remains almost constant with the variation of the mole-fraction of (NH4)2SO4 in the solid solution [in the range of 5%–100% mole-fraction of (NH4)2SO4], while the hole decay rate varies more than 20-fold. The constant holeburning quantum efficiency is surprising, considering that the phonon density increases by several orders of magnitude in the experimental temperature range and that the variation of the (NH4)2SO4 concentration changes the height of the rotational barrier of the ammonium ion. Thus, the holeburning must occur by conformational change in the excited vibrational state.

The string universe. High Tc superconductor or quantum Hall conductor?

Our answer is the latter. Space-time singularities, including the initial one, are described by world-sheet topological abelian gauge theories with a Chern-Simons term. Their effective N = 2 supersymmetry provides an initial fixed point where the Bogomolny bound is saturated on the world-sheet, corresponding to an extreme Reissner-Nordstrom solution in space-time. Away from the singularity the gauge theory has world-sheet matter fields, bosons and fermions, associated with the generation of target space-time. Because the fermions are complex (cf. the quantum Hall effect) rather than real (cf. high- T c superconductors) the energetically-preferred vacuum is not parity or time-reversal invariant, and the associated renormalization group flow explains the cosmological arrow of time, as well as the decay of real or virtual black holes, with a monotonic increase in entropy.

The nature of core excited states in fullerene C60 as exhibited by the Auger line shape

This paper compares the C{sub 60} C KVV Auger line shape and {pi} band covalency to those of graphite and benzene to determine the core excited electronic states. Shakeup satellites are used to determine delocalization times of these core excited states relative to the core hole lifetime. Based on these, C {sub 60} appears to have excitations that delocalize in times that are short relative to the core hole decay.

Femtosecond relaxation of photoexcited holes in bulk gallium arsenide.

The relaxation to the top of the valence band of nonequilibrium photoexcited holes in n-type doped bulk gallium arsenide at 77 K is selectively measured by a femtosecond luminescence up-conversion technique. In the low-excitation regime, hole decay times between 560 and 330 fs are observed for fully-ionized-donor concentrations in the range 6×10 17 to 2.4×10 18 cm -3

On the evaporation of black holes in string theory

We show that, in string theory, the quantum evaporation and decay of black holes in two-dimensional target space is related to imaginary parts in higher-genus string amplitudes. These arise from the regularisation of modular infinities due to the sum over world-sheet configurations, that are known to express the instabilities of massive string states in general, and are not thermal in character. The absence of such imaginary parts in the matrix-model limit confirms that the latter constitutes the final stage of the evaporation process, at least in perturbation theory. Our arguments appear to be quite generic, related only to the summation over world-sheet surfaces, and hence should also apply to higher-dimensional target spaces.

Hole-burning in the amorphous and in the crystalline local environment of an n-hexadecane Shpol'skiĭ matrix

The dye tetra-4-tert-butyl phthalocyanine, incorporated into an n-hexadecane Shpol'skiĭ matrix, was investigated using hole-burning spectroscopy. At T = 1.5 K, a series of spectral holes was burnt into the absorption spectrum, using experimental parameters of earlier measurements on the same hole-burning dye in polymer matrices. The maximum hole-depth and, thus, the quantum yield of the photochemical reaction follows the absorption of the amorphous background, showing no significant deviation in the region of the dominant Shpol'skiĭ line. Reducing the time scale of the hole-burning detection scheme, however, revealed spectral holes in the Shpol'skiĭ line with an extrapolated width of 21 MHz. The hole decay time constant of about 40 s was verified with fluorescence measurements.