Solution of the Dirac Equation for Strong External Fields

Abstract

emission was assumed, and a universal 1-nsec lifetime was taken to allow us to estimate the fraction of the metastable emitters which decayed within the distance viewed by our X-ray detector. We thus have clear and direct experimental evidence that both two-and three-e,lectron chlorine systems a r e produced which have lifetimes in the nanosecond region and which de-excite at least partially by KCY X-ray emission. We further find that an appreciable fraction (about 60%) of our metastable X-ray emitters belong to systems of more than three electrons. The number of X rays detected from these systems is large because of the charge-state equilibrium at 45 MeV, in spite of the small probability per emerging ion for their production. The appropriate experiment to detect these species directly in a coincidence experiment is in preparation.The identification of the charge states of these X-ray emitters in no way settles the question of their identity. Sellin et al. ' have attributed their metastable Auger-electron emitters to quartet states in three-electron systems whose autoion-X-ray energy with that expected from a two-o r three-electron chlorine system, even though more than half of the associated chlorine ions appear to survive with four o r more electrons, leads us to suspect that the states Seen here may be better attributed to metastable two-electron systems which a r e accompanied by further electrons residing in shells of very high principal quantum number. Such a system would have to owe its metastability against Auger processes at least in part to the poor overlap of the wave function of the outer-shell electron with that of the inner shells, and to slow radiative progression from outer to inner shells by soft photon emission. Experimental observation of the radiation which should accompany such a progression and deduction of the overall excitation states of the outer shells of foil-excited ions would clearly be of importance in helping such an hypothesis to emerge from the speculation stage.ization is inhibited by spin selection rules. They seconds and thus a r e probably not the states we %. L. House, Astrophys. J., Suppl. Ser. E, 21 observe. The consistency of the measured K f f (1969). Solution of the Dirac Equation for Strong External Fields*Berndt ~Ü l l e r , Heinrich Peitz, Johann Rafelski, and Walter Greiner The 1s bound state of superheavy atoms and molecules reaches a binding energy of -2 m c 2 a t 2% 169. It is shown that the K shell is still localized in r space even beyond this critical proton number and that it has a width r (several keV large) which is a positron escape width for ionized K shells. The Suggestion is made that this effect can be observed in the collision of very heavy ions (superheavy molecules) during the collision. The discrete energy eigenvalues for an electron nucleus; the energy eigenvalues a r e then given by bound to a nucleus, which a r e obtained from the the well-known Sommerfeld fine-structure formuDirac equation, lie between moc2 and -moc2, la. In this case th...

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“…Special attention for the existence of critical electric fields and the possible condition for electron- Greiner [7]. They analyzed the specific pair creation process of an electron-positron pair around both a point-like and extended bare nucleus by direct integration of Dirac equation.…”

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