Measurement of the H(n=2) density matrix for 20–100-keV collisions of H+ on He

Density matrices are experimentally determined which describe H(n=2) atoms produced in electron-transfer collisions between 20-100-keV protons and helium. The density matrix contains the electron-transfer cross sections σ2s, σ2p0, and σ2p+/-1, as well as the real and imaginary parts of the s0p0 coherence. Experimentally, a monoenergetic proton beam traverses a helium gas cell producing hydrogen atoms H(n) via electron transfer. Within the gas cell an electric field is applied either axial or transverse to the proton beam. The Stokes parameters describing the intensity and linear polarization of Lyman-α radiation (122 nm) emitted by H(n=2) atoms are determined as a function of applied electric-field strength. The density-matrix elements are determined from a linear least-squares fit of the Stokes parameters to the set of five fitting functions which represent the contributions from individual density-matrix elements. The density-matrix results are self-consistent. Separate determinations using axial or transverse electric fields agree with each other. The general results indicate σ2s>σ2p0>σ2p+/-1 between 20 and 100 keV. The electric dipole moment z has a value near zero at 20 keV rising to a maximum of about 1.3 a.u. near 40 keV and remaining nearly constant through 100 keV. The z,s moment has a maximum of about 0.5 a.u. at 25 keV, passing through zero near 70 keV. These results compare favorably with available experimental results and are qualitatively predicted by present theoretical models. Comparison with previous H(n=3) results indicates that the Runge-Lenz vector z is larger for n=3 than for n=2 and that z,s has the same values for both n

Measurement of the H(n=2) density matrix for 20–100-keV collisions of H+ on He

Density matrices are experimentally determined which describe H(n=2) atoms produced in electron-transfer collisions between 20-100-keV protons and helium. The density matrix contains the electron-transfer cross sections σ2s, σ2p0, and σ2p+/-1, as well as the real and imaginary parts of the s0p0 coherence. Experimentally, a monoenergetic proton beam traverses a helium gas cell producing hydrogen atoms H(n) via electron transfer. Within the gas cell an electric field is applied either axial or transverse to the proton beam. The Stokes parameters describing the intensity and linear polarization of Lyman-α radiation (122 nm) emitted by H(n=2) atoms are determined as a function of applied electric-field strength. The density-matrix elements are determined from a linear least-squares fit of the Stokes parameters to the set of five fitting functions which represent the contributions from individual density-matrix elements. The density-matrix results are self-consistent. Separate determinations using axial or transverse electric fields agree with each other. The general results indicate σ2s>σ2p0>σ2p+/-1 between 20 and 100 keV. The electric dipole moment z has a value near zero at 20 keV rising to a maximum of about 1.3 a.u. near 40 keV and remaining nearly constant through 100 keV. The z,s moment has a maximum of about 0.5 a.u. at 25 keV, passing through zero near 70 keV. These results compare favorably with available experimental results and are qualitatively predicted by present theoretical models. Comparison with previous H(n=3) results indicates that the Runge-Lenz vector z is larger for n=3 than for n=2 and that z,s has the same values for both n

Experimental determination of the H(n=3) density matrix for 80-keV H+ on He

The density matrix is determined for H(n=3) atoms produced in axially symmetric electron-transfer collisions of 80-keV protons on helium. In the experiment axial or transverse electric fields with respect to the proton beam are applied to the collision region. The intensity and polarization of Balmer-α radiation emitted by the H(n=3) atoms are measured as a function of the strength of the external electric field. Detailed analysis of the measured optical signals, taking into account the time evolution of the H(n=3) atoms in the applied electric field, makes it possible to extract the complete density matrix of the H(n=3) atoms at the moment of their formation, averaged over all impact parameters. Significant improvements in the experimental technique and in the data analysis associated with the fit of the density matrix to the optical signals have eliminated systematic effects that were present in our previous work [Phys. Rev. A 33, 276 (1986)]. The improvements in the apparatus are as follows: application of electric fields using electrodes with a simple geometry for the axial and transverse orientations that allows accurate calculation of the spatial variation of the electric field inside the collision chamber; use of high-quality optical elements and a rotatable, single-unit design for the polarimeter; automated gas handling for background subtraction; and full computer control of the electric fields, polarimeter, gas handling, and data acquisition. The analysis incorporates the following improvements: hyperfine structure of the H(n=3) manifold; cascade from the H(n=4) manifold; nonuniform detection efficiency over the viewing region; and modeling of the nonuniform electric fields, the nonuniform gas density, and the exponential decrease of the proton beam current in the gas cell due to electron transfer. With these improvements the results from axial electric field measurements are in good agreement with results obtained independently from transverse electric fields. Moreover, the extracted density-matrix elements are found to be within their physically meaningful bounds. The major results from 80-keV collisions are that the H(n=3) density matrix has an average coherence of 81%±1%, an electric dipole moment of 3.50±0.09 a.u., and a first-order moment of the electron current density distribution 〈(L×A)z,s〉 of -0.13±0.02 a.u. Results from a recent calculation show qualitative agreement with the experiment

Brane Big-Bang Brought by Bulk Bubble

We propose an alternative inflationary universe scenario in the context of Randall-Sundrum braneworld cosmology. In this new scenario the existence of extra-dimension(s) plays an essential role. First, the brane universe is initially in the inflationary phase driven by the effective cosmological constant induced by small mismatch between the vacuum energy in the 5-dimensional bulk and the brane tension. This mismatch arises since the bulk is initially in a false vacuum. Then, the false vacuum decay occurs, nucleating a true vacuum bubble with negative energy inside the bulk. The nucleated bubble expands in the bulk and consequently hits the brane, bringing a hot big-bang brane universe of the Randall-Sundrum type. Here, the termination of the inflationary phase is due to the change of the bulk vacuum energy. The bubble kinetic energy heats up the universe. As a simple realization, we propose a model, in which we assume an interaction between the brane and the bubble. We derive the constraints on the model parameters taking into account the following requirements: solving the flatness problem, no force which prohibits the bubble from colliding with the brane, sufficiently high reheating temperature for the standard nucleosynthesis to work, and the recovery of Newton's law up to 1mm. We find that a fine tuning is needed in order to satisfy the first and the second requirements simultaneously, although, the other constraints are satisfied in a wide range of the model parameters.Comment: 20pages, 5figures, some references added, the previous manuscript has been largely improve

Evidence for Rigid Triaxial Deformation in Ge 76 from a Model-Independent Analysis

An extensive, model-independent analysis of the nature of triaxial deformation in Ge76, a candidate for neutrinoless double-beta (0νββ) decay, was carried out following multistep Coulomb excitation. Shape parameters deduced on the basis of a rotational-invariant sum-rule analysis provided considerable insight into the underlying collectivity of the ground-state and γ bands. Both sequences were determined to be characterized by the same β and γ deformation parameter values. In addition, compelling evidence for low-spin, rigid triaxial deformation in Ge76 was obtained for the first time from the analysis of the statistical fluctuations of the quadrupole asymmetry deduced from the measured E2 matrix elements. These newly determined shape parameters are important input and constraints for calculations aimed at providing, with suitable accuracy, the nuclear matrix elements relevant to 0νββ

Inflation and Braneworlds: Degeneracies and Consistencies

Scalar and tensor perturbations arising in an inflationary braneworld scenario driven by a single scalar field are considered, where the bulk on either side of the brane corresponds to Anti-de Sitter spaces with different cosmological constants. A consistency relation between the two spectra is derived and found to have an identical form to that arising in standard single-field inflation based on conventional Einstein gravity. The dS/CFT correspondence may provide further insight into the origin of this degeneracy. Possible ways of lifting such a degeneracy are discussed.Comment: 10 page

Measurement of the H(n=2) density matrix for 20–100-keV collisions of H+ on He

Density matrices are experimentally determined which describe H(n=2) atoms produced in electron-transfer collisions between 20-100-keV protons and helium. The density matrix contains the electron-transfer cross sections σ2s, σ2p0, and σ2p+/-1, as well as the real and imaginary parts of the s0p0 coherence. Experimentally, a monoenergetic proton beam traverses a helium gas cell producing hydrogen atoms H(n) via electron transfer. Within the gas cell an electric field is applied either axial or transverse to the proton beam. The Stokes parameters describing the intensity and linear polarization of Lyman-α radiation (122 nm) emitted by H(n=2) atoms are determined as a function of applied electric-field strength. The density-matrix elements are determined from a linear least-squares fit of the Stokes parameters to the set of five fitting functions which represent the contributions from individual density-matrix elements. The density-matrix results are self-consistent. Separate determinations using axial or transverse electric fields agree with each other. The general results indicate σ2s>σ2p0>σ2p+/-1 between 20 and 100 keV. The electric dipole moment z has a value near zero at 20 keV rising to a maximum of about 1.3 a.u. near 40 keV and remaining nearly constant through 100 keV. The z,s moment has a maximum of about 0.5 a.u. at 25 keV, passing through zero near 70 keV. These results compare favorably with available experimental results and are qualitatively predicted by present theoretical models. Comparison with previous H(n=3) results indicates that the Runge-Lenz vector z is larger for n=3 than for n=2 and that z,s has the same values for both n

Measurement of the H(n=2) density matrix for 20–100-keV collisions of H+ on He

Density matrices are experimentally determined which describe H(n=2) atoms produced in electron-transfer collisions between 20-100-keV protons and helium. The density matrix contains the electron-transfer cross sections σ2s, σ2p0, and σ2p+/-1, as well as the real and imaginary parts of the s0p0 coherence. Experimentally, a monoenergetic proton beam traverses a helium gas cell producing hydrogen atoms H(n) via electron transfer. Within the gas cell an electric field is applied either axial or transverse to the proton beam. The Stokes parameters describing the intensity and linear polarization of Lyman-α radiation (122 nm) emitted by H(n=2) atoms are determined as a function of applied electric-field strength. The density-matrix elements are determined from a linear least-squares fit of the Stokes parameters to the set of five fitting functions which represent the contributions from individual density-matrix elements. The density-matrix results are self-consistent. Separate determinations using axial or transverse electric fields agree with each other. The general results indicate σ2s>σ2p0>σ2p+/-1 between 20 and 100 keV. The electric dipole moment z has a value near zero at 20 keV rising to a maximum of about 1.3 a.u. near 40 keV and remaining nearly constant through 100 keV. The z,s moment has a maximum of about 0.5 a.u. at 25 keV, passing through zero near 70 keV. These results compare favorably with available experimental results and are qualitatively predicted by present theoretical models. Comparison with previous H(n=3) results indicates that the Runge-Lenz vector z is larger for n=3 than for n=2 and that z,s has the same values for both n

Experimentally determined density matrices for H(n=3) formed in H+-He collisions from 20 to 100 keV

Density matrices describing H(n=3) atoms produced in collisions of 20- to 100-keV protons with He atoms have been determined experimentally. In the experiment the intensity and polarization of Balmer-α radiation emitted from a He gas cell are measured as a function of the strength of an externally applied electric field. Electric fields are applied in a direction either axial to or transverse to the proton beam. Density matrices are extracted by detailed analysis of the optical data. Data are obtained for each field direction and then analyzed, separately and in combination, to yield density matrices. Satisfactory agreement is found between density matrices determined from axial and transverse electric field data except at the lowest energies studied. Some nonzero density-matrix elements are determined more accurately using axial electric fields than with transverse fields, while other elements are more accurately determined using transverse electric fields. The combined analysis using data from both field directions gives a better determination of the density matrix than the separate data sets. Results for the H(n=3) electron-transfer cross sections (relative to 3s), the electric dipole moment of the charge distribution 〈d〉z, a first-order moment of the current distribution 〈L×A〉z,s, and the average coherence Tr(σ32) are obtained. The experimental results are compared to two recent calculations using the augmented atomic orbital (AO+) theory and the continuum distorted-wave approximation with post-collision interaction theory, and to one recent experimental measurement of the diagonal density-matrix elements. Both theories show qualitative agreement with the general trends in the data. The AO+ method gives better quantitative agreement. The experimental results are displayed in graphical form as distributions of the electronic charge D(r) and of the electronic current density j(r)