16432578
Dust as a standard of space and time in canonical quantum gravity.
The coupling of the metric to an incoherent dust introduces into spacetime a privileged dynamical reference frame and time foliation. The comoving coordinates of the dust particles and the proper time along the dust worldlines become canonical coordinates in the phase space of the system. The Hamiltonian constraint can be resolved with respect to the momentum that is canonically conjugate to the dust time. Formal imposition of the resolved constraint as an operator restriction on the quantum states yields a functional Schr\"odinger equation. The ensuing Hamiltonian density has an extraordinary feature: it depends only on the geometric variables, not on the dust coordinates or time. This has three important consequences. First, the functional Schr\"odinger equation can be solved by separating the dust time from the geometric variables. Second, disregarding the standard factor-ordering difficulties, the Hamiltonian densities strongly commute and therefore can be simultaneously defined by spectral analysis. Third, the standard constraint system of vacuum gravity is cast into a form in which it generates a true Lie algebra. The particles of dust introduce into space a privileged system of coordinates that allows the supermomentum constraint to be solved explicitly. The Schr\"odinger equation yields a formally conserved inner product that can be written in terms of either the instantaneous state functionals or the solutions of constraints. Gravitational observables admit a similar dual representation. Examples of observables are given, though neither the intrinsic metric nor the extrinsic curvature are observables. This comes as close as one can reasonably expect to a satisfactory phenomenological quantization scheme that is free of most of the problems of time.
15583656
Black hole pair creation and the entropy factor.
It is shown that in the instanton approximation the rate of creation of black holes is always enhanced by a factor of the exponential of the black hole entropy relative to the rate of creation of compact matter distributions (stars). This result holds for any generally covariant theory of gravitational and matter fields that can be expressed in Hamiltonian form. It generalizes the result obtained previously for the pair creation of magnetically charged black holes by a magnetic field in Einstein--Maxwell theory. The particular example of pair creation of electrically charged black holes by an electric field in Einstein--Maxwell theory is discussed in detail.
10814443
Black hole entropy and the Hamiltonian formulation of diffeomorphism invariant theories.
Path integral methods are used to derive a general expression for the entropy of a black hole in a diffeomorphism invariant theory. The result, which depends on the variational derivative of the Lagrangian with respect to the Riemann tensor, agrees with the result obtained from Noether charge methods by Iyer and Wald. The method used here is based on the direct expression of the density of states as a path integral (the microcanonical functional integral). The analysis makes crucial use of the Hamiltonian form of the action. An algorithm for placing the action of a diffeomorphism invariant theory in Hamiltonian form is presented. Other path integral approaches to the derivation of black hole entropy include the Hilbert action surface term method and the conical deficit angle method. The relationships between these path integral methods are presented. \textcopyright{} 1995 The American Physical Society.
13491513
Shell-model analysis of high-resolution data for elastic and inelastic electron scattering on 19F.
A comprehensive theoretical and experimental investigation of electron scattering on /sup 19/F is presented. Theoretical procedures for calculating the various components of electron scattering form factors from multiparticle shell-model wave functions are summarized. These procedures are used to compare shell-model predictions with data from electron scattering on /sup 19/F. For the positive-parity states of /sup 19/F we use 1s0d shell-model wave functions obtained with a new ''universal'' Hamiltonian and for the negative-parity states we use 0p-1s0d shell-model wave functions based on the cross-shell Hamiltonian of Millener and Kurath. The comparisons are made with measured longitudinal and transverse form factors for momentum transfers up to 2.4 fm/sup -1/ which are extracted from experimental data obtained with electron energies from 78 to 340 MeV, and angles of 45/sup 0/, 90/sup 0/, and 160/sup 0/. The energy resolution was 25--50 keV and most of the known levels below 8 MeV in excitation were resolved and compared with theory.
12038680
Strangeness condensation and cooling of neutron stars.
Possible effects of strangeness condensation, which has been estimated to occur in dense neutron matter at densities of 2.3--3.0 times nuclear matter density, are calculated with special reference to the cooling of the neutron star probably formed in SN1987A. Although the center of the neutron star will cool much faster in the presence of strangeness condensation than through conventional mechanisms, down to Tapprox.2 x 10/sup 8/ K at the present time, the heat conductivity of the neutron star is such that it will take at least a few tens of years for effects of this drop in temperature to reach the surface of the neutron star and be observable.
29372740
Strength functions and spreading widths of simple shell model configurations.
The exact solution of the many-body problem in the framework of the nuclear shell model with a realistic residual Hamiltonian makes it possible to study the fragmentation of simple configurations as a function of excitation energy and interaction strength. The analysis is performed for 839 states with quantum numbers {ital J}{sup {pi}}{ital T}=0{sup +}0 in a system of 12 valence particles within the {ital sd} shell. Our statistics allow us to establish the generic shape of the strength function in the region of strong mixing. For the realistic interaction, the strength function is close to Gaussian in the central part and has exponential wings. The spreading width is larger than predicted by the standard golden rule. At the artificially suppressed interaction strength, we recover the Breit-Wigner shape and the golden rule for the spreading width. The transition between these regimes agrees with theoretical considerations based on the idea of chaotic dynamics. {copyright} {ital 1996 The American Physical Society.}
7469645
Proton capture reaction rates in the rp process.
Detailed shell-model calculations have been performed to study the structure of excited states in neutron deficient {ital T}=1, {ital T}=3/2, and {ital T}=2 nuclei in the mass range {ital A}=23--43. Excitation energies, single-particle spectroscopic factors, as well as {gamma}-transition strengths were computed. On the basis of these results new reaction rates were calculated for proton capture on the {ital T}=1/2 nucleus {sup 35}Ar, on the odd-odd {ital T}=1 nuclei {sup 24}Al and {sup 32}Cl, on the even-even {ital T}=1 nuclei {sup 26}Si, {sup 30}S, {sup 34}Ar, and {sup 42}Ti and the {ital T}=3/2 nuclei {sup 23}Al, {sup 27}P, {sup 31}Cl, and {sup 35}K. The new reaction rates are compared with the results of statistical model calculations as well as with previous estimates. The consequences of these new rates for the reaction flow and the {ital rp} process nucleosynthesis at different stellar temperature and density conditions will be discussed.
31262338
Mass systematics for A=29-44 nuclei: The deformed A~32 region.
Further evidence for the presence of an anomaly in binding energies for the island of inversion'' centered at {ital Z}=11, {ital N}=21 is obtained by comparison of shell-model calculations to experiment. The calculations were done with a shell-model interaction that is applicable to nuclei with active valence nucleons in both the (1{ital s},0{ital d}) and (0{ital f},1{ital p}) major shells. This interaction is described in detail as are its predictions for binding energies and energy spectra of {ital Z}=8--20, {ital N}=18--25 nuclei. These calculations provide the background for the exploration of the island of inversion.'' The extent of the island'' and the magnitude of the anomaly is explored by calculating the binding energies of 2{h bar}{omega} excitations of neutrons from the (1{ital s},0{ital d}) shell to the (0{ital f},1{ital p}) shell relative to the 0{h bar}{omega} ground state. The reason why mixed (0+2){h bar}{omega} calculations are not considered reliable is addressed. Truncation schemes and a weak-coupling approximation are used to extend the range of the calculations. It is found that for {ital Z}=10--12, {ital N}=20--22 (and possibly {ital N}{gt}22) nuclei the lowest 2{h bar}{omega} state is more bound than the 0{h bar}{omega} ground state. The role of odd {ital n}more » {ital n}{h bar}{omega} excitations is considered and it is found that the 1{h bar}{omega} ground state always lies below that of 3{h bar}{omega}, and for {ital N}=19, 21, and 23, the lowest 1{h bar}{omega} state is in close competition with 2{h bar}{omega} for the lowest binding energy. Collectivity is considered via {ital E}2 observables and energy spectra for the 2{h bar}{omega} ground-state bands. The reason for the existence of the island'' is discussed.« less