Frozen planet

Notwithstanding, after hydrogen, helium is also the simplest naturally available atomic species, which, in contrast to one electron atoms, exhibits the additional electron-electron interaction, as a source of electronic correlations. Hence, helium is one of the simplest systems where electronic correlations can be studied. Direct manifestations of electronic correlations have been found, e.g., in doubly excited states of helium localized along highly asymmetric, though very stable, frozen planet configurations (FPC) (K. Richter et.al., 1990), or scarred by... 

In the present contribution, we will study the quantum signatures of the FPC and the ASC. In section 2 we briefly sketch our theoretical approach, in section 3 we review the most important aspects of the classical FPC and ASC, and study the implications thereof for the quantum spectrum. In section 4 we consider the quantum aspects of the driven frozen planet configuration. We conclude in section 5. 

If this argument holds true, already the frozen planet configurations of planar helium should exhibit enhanced autoionization rates as compared to the ID case. In figure 2 (right) we therefore compare the decay rates of our 2D frozen planet states with the earlier ID and 3D results. Clearly, the 2D rates are of the same order of magnitude as the 3D rates,... 

Another well-defined configuration of the classical three body Coulomb problem with unambiguous quantum correspondence is the collinear antisymmetric stretch configuration, where the electrons are located on opposite sides of the nucleus. In contrast to the frozen planet orbit, the antisymmetric stretch is unstable in the axial direction (G.S. Ezra et.al., 1991 P. Schlagheck et.al., 2003), with the two electrons colliding with the nucleus in a perfectly alternating way (Fig. 3 (left)). Hence, already the one dimensional treatment accounts for the dominant classical decay channel of this configuration. As for the frozen planet, there are doubly excited states of helium associated to the periodic orbit of the ASC as illustrated in Fig. 3 (left). 

For the driven atom, we developed an accurate approach without any adjustable parameter, and with no other approximation than the confinement of the accessible configuration space to two dimensions. This method was successfully applied for the study of the near resonantly driven frozen planet configuration. Floquet states were found that are well localized in the associated phase space and propagate along near-... 

Camus et a/.34 explained their observations by a picture which has sometimes been called the frozen planet model. Qualitatively, the relatively slowly moving outer electron produces a quasi-static field at the inner electron given by l/rc2, and this field leads to the Stark effect in Ba+. The field allows the transitions to the n >n0Z and ,f 0 states and leads to shifts of the ionic energies. The presence of the njpn0f and n in0t resonances in the spectrum of Fig. 23.12 is quite evident. Camus et al. compared the shifts to those calculated in a fashion similar to a Bom-Oppenheimer calculation. With the outer electron frozen in place at ra they calculated the Ba+ energies, W,(rQ), and wavefunctions. They then added the energy W0(r0) to the normal screened coulomb potential seen by the outer electron. This procedure leads to a phase shift in the outer electron wavefunction... 

The frozen planet model is simple and physically appealing. In addition, it is clearly related to the treatment based on + and - states originally given by Cooper et al.2 The most convincing demonstrations of the legitimacy of the frozen... 

The frozen planet model also agrees with classical calculations of Richter and Wintgen,39 who find a classically stable state in which both electrons are on the same side of the atom in orbits which exhibit pronounced angular correlation, even though the orbital radii of the two electrons are very different. 

Especially in the highly excited semiclassical regime the quantum properties and dynamics of atomic and molecular systems are most naturally discussed within the framework of chaos. Not only does chaos theory help to characterize spectra and wave functions, it also makes specific predictions about the existence of new quantum dynamical regimes and hitherto unknown exotic states. Examples are the discovery of frozen planet states in the helium atom by Richter and Wintgen (1990a) and... 

Ice has been found at the poles new measurements of Mars southern polar region indicate the presence of extensive frozen water. The polar region contains enough frozen water to cover the whole planet with a layer of liquid approximately 36 ft deep. A joint NASA-Italian Space Agency instrument on the European Space Agency s Mars Express spacecraft provided these data (NASA press release, 15 March 2007). It must be assumed that volcanic exhalations contained large amounts of water. 

J In outer space, frozen water, or ice, has been found on the moon, on planets— particularly Mercury, Mars, Neptune, and Pluto—and in comets and clouds between stars in our galaxy. Recent explorations of Mars indicate that there may be liquid water underground on Mars.This means there could be microorganisms living there ... 

Concerning gas losses, we must subtract gas transformed into stars and the matter imprisoned in stellar corpses. The latter occur in three forms white dwarfs, neutron stars and black holes. We must also include matter going into planets and aborted stars (brown dwarfs), forever frozen and permanently withdrawn from the (nuclear) chemical evolution of the Galaxy. 

In this chapter we will consider the cosmochemistry of ice-bearing planetesimals. We will focus first on comets, because more is known about their chemistry than of the compositions of objects still in the Kuiper belt and Oort cloud. We will then explore asteroids whose ices melted long ago, and we will briefly consider some larger icy bodies, now represented by satellites of the giant planets. The importance of ice-bearing planetesimals to cosmochemistry stems from their primitive compositions, which have remained largely unchanged because of hibernation in a frozen state. 

The fact that water molecules are usually held to each other by hydrogen bonds is responsible for the success of our planet and of life-forms themselves. Hydrogen bonding in water is the reason that frozen water is less dense than liquid water. Not only does ice float, but more importantly, floating ice permits water below the surface in ponds and lakes to remain in a liquid state during the winter and therefore allows for the continuity of life in these waters. On a more aesthetic note, hydrogen bonding is responsible for the six-sided nature of snowflakes. 

Many specific properties of water are cited to make the case that water is an ideal biosolvent uniquely suited to support life Frozen water floats. Water is an excellent solvent for salts. Water is liquid over a broad range of temperature. Indeed, the concept of a habitable zone, a region around a star where life is presumed to be possible, largely posits a region in which a planet s surface or subsurface might support liquid water. One such planet in a habitable zone could export life to other suitable environments via meteoroids. 

If the iron and stony-iron meteorites came from fully differentiated asteroids, how did these asteroids heat to the point of partial melting and how did the metal segregate from the silicates Unlike large planets, where potential energy release triggers core formation, small asteroids require an additional heat source. The heat source(s) for asteroidal melting produced a wide range of products, from unmetamorphosed chondrites to fully molten asteroids, as well as partially melted asteroids. Samples from these latter asteroids provide us with a rare opportunity to observe core formation—frozen in place. 

More than any other planet. Mars has captured our attention and fueled our speculations. Much of this interest relates to the possibility of martian hfe, as championed by Percival Lowell in the last century and subsequently in scientihc papers and science fiction. Lowell s argument for life on Mars was based partly on geochemistry, in that his assessment of the planet s hospitable climate was dependent on the identification of H2O ice rather than frozen CO2 in the polar caps. Although this reasoning was refuted by Alfred Wallace in 1907, widespread belief in extant... 

Atmospheric carbon dioxide is the source of Mars s polar ice caps. Atmospheres act like giant insulators for planets, preventing heat from radiating away to space. Mars s thin atmosphere holds very little heat—a blazing summer day on Mars might get up to the freezing point of water 32 E (0 C), but at night the temperature plummets well back below 0 E (18 C). At the poles, temperatures drop well below -lOO E (-73 C), sufficiently cold for the carbon dioxide in the atmosphere to freeze. Mars s polar ice caps consist of frozen carbon dioxide with an underlayer of ice. 

Many scientists theorize that Mars s atmosphere thinned, and, as the planet cooled, the water boiled array. Some of the water may still remain c i the planet, permanently frozen in the ice caps or in the soil. Much of it was probably lost when the Sun s ultraviolet radiatim dissociated the water molecules into their hydrogen and oxygen atoms. 

Water is the most abundant substance in the human body and the most common substance on Earth, covering approximately 12% of the surface of this planet. All the water found in and on Earth s surface and in the atmosphere is collectively referred to as the hydrosphere. More than 97% of this surface water is located in the oceans. Another 2.1% is frozen in glaciers and polar ice caps. That leaves a meager 0.6% available as liquid freshwater. 

The Solar System is not stable, neither is our planet. Both are chaotic, in which luck may allow a certain degree of stasis. Thus orbital collisions occur until there are few bodies left, and interactions become so infrequent that the large planets seem to have attained stability in orbit. On a planet, geochemistry and heat production sort themselves out until the structure of the planet and its tectonic behaviour seem stable. But neither orbits nor tectonics are truly stable. Catastrophic events can and will occur that can upset the system. Planets collide. The Earth has precipitated a core, probably frozen a magma ocean, and will eventually freeze and be still. To stabilize the surface of a planet such that life can exist for 4Ga surely needs restorative feedbacks, and perhaps luck also. 

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