Stefano Atzeni and JÜrgen Meyer-Ter-Vehn
- Published in print:
- 2004
- Published Online:
- January 2008
- ISBN:
- 9780198562641
- eISBN:
- 9780191714030
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198562641.003.0011
- Subject:
- Physics, Nuclear and Plasma Physics
Targets for inertial fusion are driven by external beams. Energy deposition of high-power laser and ion beams is considered for cold and hot dense matter. Collisional and resonance absorption of ...
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Targets for inertial fusion are driven by external beams. Energy deposition of high-power laser and ion beams is considered for cold and hot dense matter. Collisional and resonance absorption of laser light is discussed as well as parametric instabilities driven by the ponderomotive force. Ion beam energy loss is treated in terms of binary collisions and within dielectric theory, and results are presented for cold and heated materials. Stopping of charged fusion products is also discussed. Stopping powers of heavy ion beams depend on the effective ion charge in the process of slowing-down, and cases of equilibrium as well as non-equilibrium charge states are discussed. Experiments on heavy ion stopping in dense plasma are reviewed.Less
Targets for inertial fusion are driven by external beams. Energy deposition of high-power laser and ion beams is considered for cold and hot dense matter. Collisional and resonance absorption of laser light is discussed as well as parametric instabilities driven by the ponderomotive force. Ion beam energy loss is treated in terms of binary collisions and within dielectric theory, and results are presented for cold and heated materials. Stopping of charged fusion products is also discussed. Stopping powers of heavy ion beams depend on the effective ion charge in the process of slowing-down, and cases of equilibrium as well as non-equilibrium charge states are discussed. Experiments on heavy ion stopping in dense plasma are reviewed.
Arne Haaland
- Published in print:
- 2008
- Published Online:
- May 2008
- ISBN:
- 9780199235353
- eISBN:
- 9780191715594
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199235353.003.0003
- Subject:
- Physics, Condensed Matter Physics / Materials
The ground-state energy of a poly-electron atom in Group 1, 2, 12, or 18 is completely determined by its electron configuration. Due to the spin of the unpaired electron in a Group 1 atom, the ground ...
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The ground-state energy of a poly-electron atom in Group 1, 2, 12, or 18 is completely determined by its electron configuration. Due to the spin of the unpaired electron in a Group 1 atom, the ground state is doubly degenerate, but the atoms in Groups 2, 12, and 18 have non-degenerate ground states. The lowest energy configurations of the atoms in Groups 13-17, on the other hand, give rise to several non-degenerate states. This chapter defines configuration-averaged energies and ionization energies, and shows how the latter may be used to define a set of useful electronegativity constants. The variation of configuration-averaged ionization energies and atomic bonding radii across the Periodic Table is explored. Electron affinities and atomic polarizabilities are briefly described. Net atomic charges are defined and how they may be estimated by quantum chemical calculations is shown.Less
The ground-state energy of a poly-electron atom in Group 1, 2, 12, or 18 is completely determined by its electron configuration. Due to the spin of the unpaired electron in a Group 1 atom, the ground state is doubly degenerate, but the atoms in Groups 2, 12, and 18 have non-degenerate ground states. The lowest energy configurations of the atoms in Groups 13-17, on the other hand, give rise to several non-degenerate states. This chapter defines configuration-averaged energies and ionization energies, and shows how the latter may be used to define a set of useful electronegativity constants. The variation of configuration-averaged ionization energies and atomic bonding radii across the Periodic Table is explored. Electron affinities and atomic polarizabilities are briefly described. Net atomic charges are defined and how they may be estimated by quantum chemical calculations is shown.
Helmut Hofmann
- Published in print:
- 2008
- Published Online:
- September 2008
- ISBN:
- 9780198504016
- eISBN:
- 9780191708480
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198504016.003.0014
- Subject:
- Physics, Nuclear and Plasma Physics
This chapter discusses giant dipole excitations as the prime example for nuclear modes of isovector nature. Absorption and radiation of the classical dipole are described exploiting the benefits of ...
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This chapter discusses giant dipole excitations as the prime example for nuclear modes of isovector nature. Absorption and radiation of the classical dipole are described exploiting the benefits of linear response theory, and cross sections for the scattering of and reactions with electromagnetic waves are derived. These formulas are adapted to the nuclear case by introducing effective charges for neutrons and protons, and by giving microscopic expressions for the response functions. The damping of giant resonances is addressed in its variation with temperature. Because of couplings to isoscalar modes which exhibit statistical fluctuations, the giant mode becomes a stochastic process itself. A critical review is given for models presented in the literature, like that for motional narrowing. Assumptions made therein on timescales are examined in the light of microscopic results presented in previous chapters.Less
This chapter discusses giant dipole excitations as the prime example for nuclear modes of isovector nature. Absorption and radiation of the classical dipole are described exploiting the benefits of linear response theory, and cross sections for the scattering of and reactions with electromagnetic waves are derived. These formulas are adapted to the nuclear case by introducing effective charges for neutrons and protons, and by giving microscopic expressions for the response functions. The damping of giant resonances is addressed in its variation with temperature. Because of couplings to isoscalar modes which exhibit statistical fluctuations, the giant mode becomes a stochastic process itself. A critical review is given for models presented in the literature, like that for motional narrowing. Assumptions made therein on timescales are examined in the light of microscopic results presented in previous chapters.
Wai-yim Ching and Paul Rulis
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199575800
- eISBN:
- 9780191740992
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199575800.003.0004
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter lists many of the common physical properties that can be easily calculated using the OLCAO method discussed in Chapter 3. The most fundamental quantities are the band structures, density ...
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This chapter lists many of the common physical properties that can be easily calculated using the OLCAO method discussed in Chapter 3. The most fundamental quantities are the band structures, density of states, interatomic bonding, effective charges, and optical excitations. Simple examples obtained by using the OLCAO method are presented here while modern practical applications of such calculations of more complex systems are described in later chapters. The details of how OLCAO is used for core-level spectroscopy are discussed separately in Chapter 11.Less
This chapter lists many of the common physical properties that can be easily calculated using the OLCAO method discussed in Chapter 3. The most fundamental quantities are the band structures, density of states, interatomic bonding, effective charges, and optical excitations. Simple examples obtained by using the OLCAO method are presented here while modern practical applications of such calculations of more complex systems are described in later chapters. The details of how OLCAO is used for core-level spectroscopy are discussed separately in Chapter 11.
Anthony Duncan and Michel Janssen
- Published in print:
- 2019
- Published Online:
- October 2019
- ISBN:
- 9780198845478
- eISBN:
- 9780191880681
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198845478.003.0006
- Subject:
- Physics, History of Physics, Theoretical, Computational, and Statistical Physics
The set of principles formulated in 1915-1918, and now collectively called the old quantum theory, were successfully applied to a number of problems in atomic and X-ray spectroscopy. The three most ...
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The set of principles formulated in 1915-1918, and now collectively called the old quantum theory, were successfully applied to a number of problems in atomic and X-ray spectroscopy. The three most notable successes are all associated with the Munich school headed by Arnold Sommerfeld. First, there was the derivation of a relativistic fine-structure formula which predicted splittings of stationary state energies for orbits of varying eccentricity at a given principal quantum number. These splittings were empirically verified by Paschen for ionized helium, and constituted the first quantitative confirmation of the special relativistic mechanics introduced by Einstein a decade earlier. The relativistic fine-structure formula was also applied successfully to the splitting of lines in the X-ray spectra of atoms of widely varying atomic number. Finally, the principles of the old quantum theory (in particular, the use of Schwarzschild quantization in combination with Hamilton-Jacobi methods of classical mechanics) were successfully applied to explain the first order splitting spectral lines in the presence of an external electric field (Stark effect).Less
The set of principles formulated in 1915-1918, and now collectively called the old quantum theory, were successfully applied to a number of problems in atomic and X-ray spectroscopy. The three most notable successes are all associated with the Munich school headed by Arnold Sommerfeld. First, there was the derivation of a relativistic fine-structure formula which predicted splittings of stationary state energies for orbits of varying eccentricity at a given principal quantum number. These splittings were empirically verified by Paschen for ionized helium, and constituted the first quantitative confirmation of the special relativistic mechanics introduced by Einstein a decade earlier. The relativistic fine-structure formula was also applied successfully to the splitting of lines in the X-ray spectra of atoms of widely varying atomic number. Finally, the principles of the old quantum theory (in particular, the use of Schwarzschild quantization in combination with Hamilton-Jacobi methods of classical mechanics) were successfully applied to explain the first order splitting spectral lines in the presence of an external electric field (Stark effect).
Bruce C. Bunker and William H. Casey
- Published in print:
- 2016
- Published Online:
- November 2020
- ISBN:
- 9780199384259
- eISBN:
- 9780197562987
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199384259.003.0009
- Subject:
- Chemistry, Inorganic Chemistry
In most undergraduate chemistry classes, students are taught to consider reactions in which cations and anions dissolved in water are depicted as isolated ions. For example, the magnesium ion is ...
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In most undergraduate chemistry classes, students are taught to consider reactions in which cations and anions dissolved in water are depicted as isolated ions. For example, the magnesium ion is depicted as Mg2+, or at best Mg2+(aq). For anions, these descriptions may be adequate (if not accurate). However, for cations, these abbreviations almost always fail to describe the critical chemical attributes of the dissolved species. A much more meaningful description of Mg2+ dissolved in water is [Mg(H2O)6]2+, because Mg2+ in water does not behave like a bare Mg2+ ion, nor do the waters coordinated to the Mg2+ behave anything like water molecules in the bulk fluid. In many respects, the [Mg(H2O)6]2+ ion acts like a dissolved molecular species. In this chapter, we discuss the simple solvation of anions and cations as a prelude to exploring more complex reactions of soluble oxide precursors called hydrolysis products. The two key classes of water–oxide reactions introduced here are acid–base and ligand exchange. First, consider how simple anions modify the structure and properties of water. As discussed in Chapter 3, water is a dynamic and highly fluxional “oxide” containing transient rings and clusters based on tetrahedral oxygen anions held together by linear hydrogen bonds. Simple halide ions can insert into this structure by occupying sites that would normally be occupied by other water molecules because they have radii (ranging from 0.13 to 0.22 nm in the series from F- to I-) that are comparable to that of the O2- ion (0.14 nm). Such substitution is clearly seen in the structures of ionic clathrate hydrates, where the anion can replace one and sometimes even two water molecules. Larger anions can also replace water molecules within clathrate hydrate cages. For example, carboxylate hydrate structures incorporate the carboxylate group within the water framework whereas the hydrophobic hydrocarbon “tails” occupy a cavity within the water framework, as in methane hydrate (see Chapter 3). Water molecules form hydrogen bonds to dissolved halide ions just as they can to other water molecules, as designated by OH-Y-.
Less
In most undergraduate chemistry classes, students are taught to consider reactions in which cations and anions dissolved in water are depicted as isolated ions. For example, the magnesium ion is depicted as Mg2+, or at best Mg2+(aq). For anions, these descriptions may be adequate (if not accurate). However, for cations, these abbreviations almost always fail to describe the critical chemical attributes of the dissolved species. A much more meaningful description of Mg2+ dissolved in water is [Mg(H2O)6]2+, because Mg2+ in water does not behave like a bare Mg2+ ion, nor do the waters coordinated to the Mg2+ behave anything like water molecules in the bulk fluid. In many respects, the [Mg(H2O)6]2+ ion acts like a dissolved molecular species. In this chapter, we discuss the simple solvation of anions and cations as a prelude to exploring more complex reactions of soluble oxide precursors called hydrolysis products. The two key classes of water–oxide reactions introduced here are acid–base and ligand exchange. First, consider how simple anions modify the structure and properties of water. As discussed in Chapter 3, water is a dynamic and highly fluxional “oxide” containing transient rings and clusters based on tetrahedral oxygen anions held together by linear hydrogen bonds. Simple halide ions can insert into this structure by occupying sites that would normally be occupied by other water molecules because they have radii (ranging from 0.13 to 0.22 nm in the series from F- to I-) that are comparable to that of the O2- ion (0.14 nm). Such substitution is clearly seen in the structures of ionic clathrate hydrates, where the anion can replace one and sometimes even two water molecules. Larger anions can also replace water molecules within clathrate hydrate cages. For example, carboxylate hydrate structures incorporate the carboxylate group within the water framework whereas the hydrophobic hydrocarbon “tails” occupy a cavity within the water framework, as in methane hydrate (see Chapter 3). Water molecules form hydrogen bonds to dissolved halide ions just as they can to other water molecules, as designated by OH-Y-.