Basil Aleisteir Crowley - Academia.edu (original) (raw)

Papers by Basil Aleisteir Crowley

Journal of Physics G: Nuclear Physics, 1978

A general description of eikonal theory is given in the form of a self-consistent and exact forma... more A general description of eikonal theory is given in the form of a self-consistent and exact formalism involving an effective Hamiltonian. Such a Hamiltonian may be used as an approximation in the treatment of high-energy potential scattering. The approach is similar to those of Sugar and Blankenbecler (1969) and of Osborn (1970), but with an important difference which involves making the correct distinction between the wavevector which is the free parameter of the theory and that which is associated with the eigenvalue of the Hamiltonian. The result is a more precise statement of the unitarity and reciprocity theorems and obviates the need for the 'Glauber rotation anzatz' if the free parameter is chosen so as to restore true energy conservation to an elastic s-matrix element. Furthermore the resulting wavefunctions are more suitable for use in distorted-wave theories than the more usual ones.

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2011

Using numerical simulations, we investigate the equilibrium dynamics of a single component fluid ... more Using numerical simulations, we investigate the equilibrium dynamics of a single component fluid with Yukawa interaction potential. We show that, for a wide range of densities and temperatures, the dynamics of the system are in striking agreement with a simple model of generalized hydrodynamics. Since the Yukawa potential can describe the ion-ion interactions in a plasma, our results have significant applicability for both analyzing and interpreting the results of x-ray scattering data from high power lasers and fourth generation light sources.

Scientific Reports, 2012

Creating non-equilibrium states of matter with highly unequal electron and lattice temperatures (... more Creating non-equilibrium states of matter with highly unequal electron and lattice temperatures (T ele ?T ion) allows unsurpassed insight into the dynamic coupling between electrons and ions through time-resolved energy relaxation measurements. Recent studies on low-temperature laser-heated graphite suggest a complex energy exchange when compared to other materials. To avoid problems related to surface preparation, crystal quality and poor understanding of the energy deposition and transport mechanisms, we apply a different energy deposition mechanism, via laser-accelerated protons, to isochorically and non-radiatively heat macroscopic graphite samples up to temperatures close to the melting threshold. Using time-resolved x ray diffraction, we show clear evidence of a very small electron-ion energy transfer, yielding approximately three times longer relaxation times than previously reported. This is indicative of the existence of an energy transfer bottleneck in non-equilibrium warm dense matter.

Physical Review Letters, 2012

The Fermi-degenerate plasma conditions created in liquid deuterium by a laserablation-driven shoc... more The Fermi-degenerate plasma conditions created in liquid deuterium by a laserablation-driven shock wave were probed with noncollective, spectrally resolved, inelastic x-ray Thomson scattering (XRTS) employing Cl Ly α line emission at 2.96 keV. These first XRTS measurements of the microscopic properties of shocked deuterium show an inferred spatially-averaged electron temperature of 8±5 eV, an electron density of 2.2 (±0.5) × 10 23 cm-3 and an ionization of 0.8 (-0.25, +0.15). Two-dimensional measurements, the x-ray scattering experimental platform offers the considerable advantage of probing off-Hugoniot states. This experimental result is a significant step toward achieving accurate measurements of all thermodynamic variables needed to provide stringent tests of EOS models, which would require at least three thermodynamic variables like pressure, mass density, and temperature.

Physical Review E, 2013

The equation of state of light elements is essential to understand the structure of Jovian planet... more The equation of state of light elements is essential to understand the structure of Jovian planets and inertial confinement fusion research. The Omega laser was used to drive a planar shock wave in the cryogenically cooled deuterium, creating warm dense matter conditions. X-ray scattering was used to determine the spectrum near the boundary of the collective and noncollective scattering regimes using a narrow band x-ray source in backscattering geometry. Our scattering spectra are thus sensitive to the individual electron motion as well as the collective plasma behavior and provide a measurement of the electron density, temperature, and ionization state. Our data are consistent with velocity-interferometry measurements previously taken on the same shocked deuterium conditions and presented by K. Falk et al. [High Energy Density Phys. 8, 76 (2012)]. This work presents a comparison of the two diagnostic systems and offers a detailed discussion of challenges encountered.

Physical Review E, 2012

We have extended the classical hydrodynamics formalism to include nonlocal quantum behavior via t... more We have extended the classical hydrodynamics formalism to include nonlocal quantum behavior via the phenomenological Bohm potential. We have then solved the quantum hydrodynamics equations to derive an expression for the dynamical structure factor, which describes the density-density correlations in the system. This formalism can be applied to high density strongly coupled electron fluids in the long wavelength domain. We show that at densities above 7 × 10 25 cm −3 there are significant differences in the dispersion relation. Future experiments at large laser facilities could provide an experimental test of the theory.

Physical Review A, 1990

A method for numerically modeling hot plasma over a wide range of densities is described. The mod... more A method for numerically modeling hot plasma over a wide range of densities is described. The model generalizes the essential aspects of the Stewart-Pyatt model to plasmas comprising mixtures of elements and extends the treatment to include the effects of electron polarization and screening. A practical numerical prescription is provided that is a straightforward generalization of the ionsphere cell model. In addition, exact closed-form expressions are given for the continuum lowering. The model also addresses the problem of the microfield, i.e. , the plasma-potential Auctuations that perturb the upper electronic states, and provides a suitable framework for improved practical approaches to this.

Nuclear Fusion, 1989

Recent suggestions that nuclear fusion might be induced in ordinary matter at room temperature mo... more Recent suggestions that nuclear fusion might be induced in ordinary matter at room temperature motivated this study of the processes that influence the reaction rate in highly compressed matter. An approximate model that applies in the regime of strongly coupled plasma (Γ > 1) is developed and used to estimate the rates of the nuclear reactions: d(p, γ) He3, in hydrogen of natural isotopic composition which has implications for energy generation within the giant planets, and the dd reactions under conditions that might be or might have been obtained in the laboratory. The conclusions do not support the recent claims that this reaction occurs, at observable rates, in small electrolytic cells and suggest that compressively induced fusion of hydrogen is likely to be of importance only in large dense systems as may be encountered in astrophysics.

New Journal of Physics, 2013

This paper reviews the treatment of high-frequency Thomson scattering in the non-relativistic and... more This paper reviews the treatment of high-frequency Thomson scattering in the non-relativistic and near-relativistic regimes with the primary purpose of understanding the nature of the frequency redistribution correction to the differential cross-section. This correction is generally represented by a factor involving the ratio ω α /ω β of the scattered (α) to primary (β) frequencies of the radiation. In some formulae given in the literature, the ratio appears squared, in others it does not. In Compton scattering, the frequency change is generally understood to be due to the recoil of the particle as a result of energy and momentum conservation in the photon-electron system. In this case, the Klein-Nishina formula gives the redistribution factor as ω α /ω β 2. In the case of scattering by a many-particle system, however, the frequency and momentum changes are no longer directly interdependent but depend also upon the properties of the medium, which are encoded in the dynamic structure factor. We show that the redistribution factor explicit in the quantum cross-section (that seen by a photon) is ω α /ω β , which is not squared. Formulae for the many-body cross-section given in the literature, in which the factor is squared, can often be attributed to a different (classical) definition of the cross-section, though not all authors are explicit about which definition they are using. What is shown not to be true is that the structure factor simply gives the ratio of the many-electron to one-electron differential cross-sections, as is sometimes supposed. Mixing up the cross-section definitions can lead to errors when describing x-ray scattering. We illustrate the nature of the discrepancy by deriving the energy-integrated angular 3 Author to whom any correspondence should be addressed. Content from this work may be used under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Journal of Quantitative Spectroscopy and Radiative Transfer, 2006

ABSTRACT

Journal of Quantitative Spectroscopy and Radiative Transfer, 2006

Experiments have been performed, using the HELEN laser, to measure absorption spectra in the temp... more Experiments have been performed, using the HELEN laser, to measure absorption spectra in the temperature range 20–60eV and density range 0.5–3g/cm3. K-shell spectra of aluminium were studied to investigate the effect of the plasma environment on the absorption spectrum. The experiments show the effect, at high-density, of array broadening and the merging of high series lines. Comparisons of the experimental

Journal of Quantitative Spectroscopy and Radiative Transfer, 2001

This paper describes the CASSANDRA LDA average-atom model for dense plasmas and liquid metals. Re... more This paper describes the CASSANDRA LDA average-atom model for dense plasmas and liquid metals. Recent equation-of-state and opacity calculations are described by way of illustration. Crown Copyright

Journal of Physics A: Mathematical and General, 1978

The author considers the short wavelength (semi-classical) limits of the s-matrix for elastic sca... more The author considers the short wavelength (semi-classical) limits of the s-matrix for elastic scattering, and the distorted wave Born approximation (DWBA) t-matrix for a direct reaction, and derive some interesting and useful formulae. One result takes the form of an integral representation of the elastic s-matrix which resembles the Poisson sum representation of the exact elastic s-matrix. The main result of this paper is a new approximate expression for the DWBA t-matrix in which the main effects of the distorting potentials are described in terms of average elastic phase shifts. This approximation is applicable in various forms to the treatment of a wide range of direct nuclear and atomic reactions. It possesses a number of attractive and useful features offering some practical advantages over the original quantal expression. In particular the formulae are easy to evaluate and are amenable to detailed interpretation and further analytical approximation. Conditions for their validity are stated and demonstrate their wide range of applicability. More detailed discussion is given of application to peripheral reactions and to Coulomb excitation.

Journal of Physics A: Mathematical and General, 1980

A semiclassical theory based upon the oscillatory integral representation of the quantal wavefunc... more A semiclassical theory based upon the oscillatory integral representation of the quantal wavefunction is applied to the one-dimensional Schrodinger equations describing motion in linear and parabolic potentials. For more general one and two turning point problems, the oscillatory integral approach would seem to be equivalent to the method of uniform approximation using linear or parabolic comparison functions. The technique yields both continuum and discrete solutions for the parabolic potential-the former corresponding to scattering states (barrier problem) and the latter to resonances or bound states (harmonic oscillator). Oscillatory integral type solutions are globally valid not only in coordinate space but also in parameter space. This enables the general parabolic connection formula relating the asymptotic wavefunction in different parts of the complex coordinate plane to be derived.

Journal of Physics A: Mathematical and General, 1980

Journal of Physics A: Mathematical and General, 1979

Accurate numerical calculations performed for the linear, quartic and square-well potentials (V(X... more Accurate numerical calculations performed for the linear, quartic and square-well potentials (V(X)=A mod Xnu mod , nu =1,4, infinity ) fail to confirm the recent claim by Turschner to have found an exact closed-form formula for the eigenvalues of the Hamiltonian H(P,X)=P2+A mod Xnu mod for any nu >0. The formula is found to be an approximation (except for nu =2). However, for the lowest eigenvalues of the potentials considered, it is found to be significantly more accurate than the simple WKB approximation based upon the Bohr-Sommerfeld integral.

Journal of Physics: Conference Series, 2010

Measurement of the dynamic properties of hydrogen and helium under extreme pressures is a key to ... more Measurement of the dynamic properties of hydrogen and helium under extreme pressures is a key to understanding the physics of planetary interiors. The inelastic scattering signal from statically compressed hydrogen inside diamond anvil cells at 2.8 GPa and 6.4 GPa was measured at the Diamond Light Source synchrotron facility in the UK. The first direct measurement of the local field correction to the Coulomb interactions in degenerate plasmas was obtained from spectral shifts in the scattering data and compared to predictions by the Utsumi-Ichimaru theory for degenerate electron liquids.

High Energy Density Physics, 2007

A systematic study has been carried out on the changes in the L-shell absorption structure of nio... more A systematic study has been carried out on the changes in the L-shell absorption structure of niobium as a result of changing the population of the n=3 shell from full to having vacancies in the 3d level. The niobium spectra were measured in the 2–3keV frequency range, which spanned the 2p-nd transitions where 3≤n≤11. In addition to the detailed structure in these arrays the data also show 2s-4p and 2p-4s transitions and the bound-free L edge. The frequencies and widths of transition arrays, transmission between arrays, and the absorption due to the bound-free edge, can be seen in the data. The sample conditions were found from a combination of two-dimensional radiation-hydrodynamics calculations using the AWE NYM code and flux measurements using X-ray diodes, measurements of 1s-2p absorption spectra in aluminium and mixed aluminium/niobium samples. The electron temperature error, inferred from the modelling, is ±2eV, with a density error of 30%. The data were recorded over the temperature range from ∼28 to 45eV and show marked changes in the spectra over this range.The data were compared to spectra predicted by the AWE CASSANDRA [B.J.B. Crowley, J.W.O. Harris, J. Quant. Spectrosc. Radiat. Transfer 71 (2000) p. 257] opacity code. The calculated spectra were able to reproduce the measurements reasonably well. However, there are some differences in line positions that cannot be accounted for by gradients and there are differences in the array structure in the prediction and the measurements, with additional structure predicted but not seen in the measurements. There is also lower transmission on the blue side of the 2p-3d transition arrays compared to prediction.

High Energy Density Physics, 2010

Cassandra is an AWE opacity code used to model plasmas in local thermal equilibrium: there is a d... more Cassandra is an AWE opacity code used to model plasmas in local thermal equilibrium: there is a desire to expand its use to calculating plasma equations of state. Cassandra's self-consistent field calculation (scf) uses the local density approximation for bounds states and has a free electron contribution based upon the Thomas-Fermi model [B.J.B. Crowley et al., J. Quant. Spectro. Radiat. Trans. 71, 257(2001)]. Whilst this is applicable for very high temperature or low density plasmas; in hot and dense matter the effect of ionization will lead to discontinuities in the effective ionisation, Z⋆. The electron contribution to hydrostatic pressure is associated with Z⋆, thus these discontinuities produce unphysical jumps in the resulting calculated material pressure.We describe a procedure to mitigate the effect by calculating the free electron wave functions within the generalized ion-cell model [B.J.B. Crowley et al., Phys. Rev. A 41, 2179(1990)], and thus explicitly calculate free-electron resonances.

Journal of Physics G: Nuclear Physics, 1978

A general description of eikonal theory is given in the form of a self-consistent and exact forma... more A general description of eikonal theory is given in the form of a self-consistent and exact formalism involving an effective Hamiltonian. Such a Hamiltonian may be used as an approximation in the treatment of high-energy potential scattering. The approach is similar to those of Sugar and Blankenbecler (1969) and of Osborn (1970), but with an important difference which involves making the correct distinction between the wavevector which is the free parameter of the theory and that which is associated with the eigenvalue of the Hamiltonian. The result is a more precise statement of the unitarity and reciprocity theorems and obviates the need for the 'Glauber rotation anzatz' if the free parameter is chosen so as to restore true energy conservation to an elastic s-matrix element. Furthermore the resulting wavefunctions are more suitable for use in distorted-wave theories than the more usual ones.

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2011

Using numerical simulations, we investigate the equilibrium dynamics of a single component fluid ... more Using numerical simulations, we investigate the equilibrium dynamics of a single component fluid with Yukawa interaction potential. We show that, for a wide range of densities and temperatures, the dynamics of the system are in striking agreement with a simple model of generalized hydrodynamics. Since the Yukawa potential can describe the ion-ion interactions in a plasma, our results have significant applicability for both analyzing and interpreting the results of x-ray scattering data from high power lasers and fourth generation light sources.

Scientific Reports, 2012

Creating non-equilibrium states of matter with highly unequal electron and lattice temperatures (... more Creating non-equilibrium states of matter with highly unequal electron and lattice temperatures (T ele ?T ion) allows unsurpassed insight into the dynamic coupling between electrons and ions through time-resolved energy relaxation measurements. Recent studies on low-temperature laser-heated graphite suggest a complex energy exchange when compared to other materials. To avoid problems related to surface preparation, crystal quality and poor understanding of the energy deposition and transport mechanisms, we apply a different energy deposition mechanism, via laser-accelerated protons, to isochorically and non-radiatively heat macroscopic graphite samples up to temperatures close to the melting threshold. Using time-resolved x ray diffraction, we show clear evidence of a very small electron-ion energy transfer, yielding approximately three times longer relaxation times than previously reported. This is indicative of the existence of an energy transfer bottleneck in non-equilibrium warm dense matter.

Physical Review Letters, 2012

The Fermi-degenerate plasma conditions created in liquid deuterium by a laserablation-driven shoc... more The Fermi-degenerate plasma conditions created in liquid deuterium by a laserablation-driven shock wave were probed with noncollective, spectrally resolved, inelastic x-ray Thomson scattering (XRTS) employing Cl Ly α line emission at 2.96 keV. These first XRTS measurements of the microscopic properties of shocked deuterium show an inferred spatially-averaged electron temperature of 8±5 eV, an electron density of 2.2 (±0.5) × 10 23 cm-3 and an ionization of 0.8 (-0.25, +0.15). Two-dimensional measurements, the x-ray scattering experimental platform offers the considerable advantage of probing off-Hugoniot states. This experimental result is a significant step toward achieving accurate measurements of all thermodynamic variables needed to provide stringent tests of EOS models, which would require at least three thermodynamic variables like pressure, mass density, and temperature.

Physical Review E, 2013

The equation of state of light elements is essential to understand the structure of Jovian planet... more The equation of state of light elements is essential to understand the structure of Jovian planets and inertial confinement fusion research. The Omega laser was used to drive a planar shock wave in the cryogenically cooled deuterium, creating warm dense matter conditions. X-ray scattering was used to determine the spectrum near the boundary of the collective and noncollective scattering regimes using a narrow band x-ray source in backscattering geometry. Our scattering spectra are thus sensitive to the individual electron motion as well as the collective plasma behavior and provide a measurement of the electron density, temperature, and ionization state. Our data are consistent with velocity-interferometry measurements previously taken on the same shocked deuterium conditions and presented by K. Falk et al. [High Energy Density Phys. 8, 76 (2012)]. This work presents a comparison of the two diagnostic systems and offers a detailed discussion of challenges encountered.

Physical Review E, 2012

We have extended the classical hydrodynamics formalism to include nonlocal quantum behavior via t... more We have extended the classical hydrodynamics formalism to include nonlocal quantum behavior via the phenomenological Bohm potential. We have then solved the quantum hydrodynamics equations to derive an expression for the dynamical structure factor, which describes the density-density correlations in the system. This formalism can be applied to high density strongly coupled electron fluids in the long wavelength domain. We show that at densities above 7 × 10 25 cm −3 there are significant differences in the dispersion relation. Future experiments at large laser facilities could provide an experimental test of the theory.

Physical Review A, 1990

A method for numerically modeling hot plasma over a wide range of densities is described. The mod... more A method for numerically modeling hot plasma over a wide range of densities is described. The model generalizes the essential aspects of the Stewart-Pyatt model to plasmas comprising mixtures of elements and extends the treatment to include the effects of electron polarization and screening. A practical numerical prescription is provided that is a straightforward generalization of the ionsphere cell model. In addition, exact closed-form expressions are given for the continuum lowering. The model also addresses the problem of the microfield, i.e. , the plasma-potential Auctuations that perturb the upper electronic states, and provides a suitable framework for improved practical approaches to this.

Nuclear Fusion, 1989

Recent suggestions that nuclear fusion might be induced in ordinary matter at room temperature mo... more Recent suggestions that nuclear fusion might be induced in ordinary matter at room temperature motivated this study of the processes that influence the reaction rate in highly compressed matter. An approximate model that applies in the regime of strongly coupled plasma (Γ > 1) is developed and used to estimate the rates of the nuclear reactions: d(p, γ) He3, in hydrogen of natural isotopic composition which has implications for energy generation within the giant planets, and the dd reactions under conditions that might be or might have been obtained in the laboratory. The conclusions do not support the recent claims that this reaction occurs, at observable rates, in small electrolytic cells and suggest that compressively induced fusion of hydrogen is likely to be of importance only in large dense systems as may be encountered in astrophysics.

New Journal of Physics, 2013

This paper reviews the treatment of high-frequency Thomson scattering in the non-relativistic and... more This paper reviews the treatment of high-frequency Thomson scattering in the non-relativistic and near-relativistic regimes with the primary purpose of understanding the nature of the frequency redistribution correction to the differential cross-section. This correction is generally represented by a factor involving the ratio ω α /ω β of the scattered (α) to primary (β) frequencies of the radiation. In some formulae given in the literature, the ratio appears squared, in others it does not. In Compton scattering, the frequency change is generally understood to be due to the recoil of the particle as a result of energy and momentum conservation in the photon-electron system. In this case, the Klein-Nishina formula gives the redistribution factor as ω α /ω β 2. In the case of scattering by a many-particle system, however, the frequency and momentum changes are no longer directly interdependent but depend also upon the properties of the medium, which are encoded in the dynamic structure factor. We show that the redistribution factor explicit in the quantum cross-section (that seen by a photon) is ω α /ω β , which is not squared. Formulae for the many-body cross-section given in the literature, in which the factor is squared, can often be attributed to a different (classical) definition of the cross-section, though not all authors are explicit about which definition they are using. What is shown not to be true is that the structure factor simply gives the ratio of the many-electron to one-electron differential cross-sections, as is sometimes supposed. Mixing up the cross-section definitions can lead to errors when describing x-ray scattering. We illustrate the nature of the discrepancy by deriving the energy-integrated angular 3 Author to whom any correspondence should be addressed. Content from this work may be used under the terms of the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Journal of Quantitative Spectroscopy and Radiative Transfer, 2006

ABSTRACT

Journal of Quantitative Spectroscopy and Radiative Transfer, 2006

Experiments have been performed, using the HELEN laser, to measure absorption spectra in the temp... more Experiments have been performed, using the HELEN laser, to measure absorption spectra in the temperature range 20–60eV and density range 0.5–3g/cm3. K-shell spectra of aluminium were studied to investigate the effect of the plasma environment on the absorption spectrum. The experiments show the effect, at high-density, of array broadening and the merging of high series lines. Comparisons of the experimental

Journal of Quantitative Spectroscopy and Radiative Transfer, 2001

This paper describes the CASSANDRA LDA average-atom model for dense plasmas and liquid metals. Re... more This paper describes the CASSANDRA LDA average-atom model for dense plasmas and liquid metals. Recent equation-of-state and opacity calculations are described by way of illustration. Crown Copyright

Journal of Physics A: Mathematical and General, 1978

The author considers the short wavelength (semi-classical) limits of the s-matrix for elastic sca... more The author considers the short wavelength (semi-classical) limits of the s-matrix for elastic scattering, and the distorted wave Born approximation (DWBA) t-matrix for a direct reaction, and derive some interesting and useful formulae. One result takes the form of an integral representation of the elastic s-matrix which resembles the Poisson sum representation of the exact elastic s-matrix. The main result of this paper is a new approximate expression for the DWBA t-matrix in which the main effects of the distorting potentials are described in terms of average elastic phase shifts. This approximation is applicable in various forms to the treatment of a wide range of direct nuclear and atomic reactions. It possesses a number of attractive and useful features offering some practical advantages over the original quantal expression. In particular the formulae are easy to evaluate and are amenable to detailed interpretation and further analytical approximation. Conditions for their validity are stated and demonstrate their wide range of applicability. More detailed discussion is given of application to peripheral reactions and to Coulomb excitation.

Journal of Physics A: Mathematical and General, 1980

A semiclassical theory based upon the oscillatory integral representation of the quantal wavefunc... more A semiclassical theory based upon the oscillatory integral representation of the quantal wavefunction is applied to the one-dimensional Schrodinger equations describing motion in linear and parabolic potentials. For more general one and two turning point problems, the oscillatory integral approach would seem to be equivalent to the method of uniform approximation using linear or parabolic comparison functions. The technique yields both continuum and discrete solutions for the parabolic potential-the former corresponding to scattering states (barrier problem) and the latter to resonances or bound states (harmonic oscillator). Oscillatory integral type solutions are globally valid not only in coordinate space but also in parameter space. This enables the general parabolic connection formula relating the asymptotic wavefunction in different parts of the complex coordinate plane to be derived.

Journal of Physics A: Mathematical and General, 1980

Journal of Physics A: Mathematical and General, 1979

Accurate numerical calculations performed for the linear, quartic and square-well potentials (V(X... more Accurate numerical calculations performed for the linear, quartic and square-well potentials (V(X)=A mod Xnu mod , nu =1,4, infinity ) fail to confirm the recent claim by Turschner to have found an exact closed-form formula for the eigenvalues of the Hamiltonian H(P,X)=P2+A mod Xnu mod for any nu >0. The formula is found to be an approximation (except for nu =2). However, for the lowest eigenvalues of the potentials considered, it is found to be significantly more accurate than the simple WKB approximation based upon the Bohr-Sommerfeld integral.

Journal of Physics: Conference Series, 2010

Measurement of the dynamic properties of hydrogen and helium under extreme pressures is a key to ... more Measurement of the dynamic properties of hydrogen and helium under extreme pressures is a key to understanding the physics of planetary interiors. The inelastic scattering signal from statically compressed hydrogen inside diamond anvil cells at 2.8 GPa and 6.4 GPa was measured at the Diamond Light Source synchrotron facility in the UK. The first direct measurement of the local field correction to the Coulomb interactions in degenerate plasmas was obtained from spectral shifts in the scattering data and compared to predictions by the Utsumi-Ichimaru theory for degenerate electron liquids.

High Energy Density Physics, 2007

A systematic study has been carried out on the changes in the L-shell absorption structure of nio... more A systematic study has been carried out on the changes in the L-shell absorption structure of niobium as a result of changing the population of the n=3 shell from full to having vacancies in the 3d level. The niobium spectra were measured in the 2–3keV frequency range, which spanned the 2p-nd transitions where 3≤n≤11. In addition to the detailed structure in these arrays the data also show 2s-4p and 2p-4s transitions and the bound-free L edge. The frequencies and widths of transition arrays, transmission between arrays, and the absorption due to the bound-free edge, can be seen in the data. The sample conditions were found from a combination of two-dimensional radiation-hydrodynamics calculations using the AWE NYM code and flux measurements using X-ray diodes, measurements of 1s-2p absorption spectra in aluminium and mixed aluminium/niobium samples. The electron temperature error, inferred from the modelling, is ±2eV, with a density error of 30%. The data were recorded over the temperature range from ∼28 to 45eV and show marked changes in the spectra over this range.The data were compared to spectra predicted by the AWE CASSANDRA [B.J.B. Crowley, J.W.O. Harris, J. Quant. Spectrosc. Radiat. Transfer 71 (2000) p. 257] opacity code. The calculated spectra were able to reproduce the measurements reasonably well. However, there are some differences in line positions that cannot be accounted for by gradients and there are differences in the array structure in the prediction and the measurements, with additional structure predicted but not seen in the measurements. There is also lower transmission on the blue side of the 2p-3d transition arrays compared to prediction.

High Energy Density Physics, 2010

Cassandra is an AWE opacity code used to model plasmas in local thermal equilibrium: there is a d... more Cassandra is an AWE opacity code used to model plasmas in local thermal equilibrium: there is a desire to expand its use to calculating plasma equations of state. Cassandra's self-consistent field calculation (scf) uses the local density approximation for bounds states and has a free electron contribution based upon the Thomas-Fermi model [B.J.B. Crowley et al., J. Quant. Spectro. Radiat. Trans. 71, 257(2001)]. Whilst this is applicable for very high temperature or low density plasmas; in hot and dense matter the effect of ionization will lead to discontinuities in the effective ionisation, Z⋆. The electron contribution to hydrostatic pressure is associated with Z⋆, thus these discontinuities produce unphysical jumps in the resulting calculated material pressure.We describe a procedure to mitigate the effect by calculating the free electron wave functions within the generalized ion-cell model [B.J.B. Crowley et al., Phys. Rev. A 41, 2179(1990)], and thus explicitly calculate free-electron resonances.