β Scribed by Lali Chatterjee
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A b s t r a c t . The Energy levels of a muonic atom, taking electron screening into account are determined by directly solving the Dirac Equation in a screened Coulomb potential of the ALLIS-MORSE type. The non-relativistic limit of the result agrees with the values obtained by solving the Schrodinger Equation for a muon in such a potential. The deviation from the Coulomb case is of the form 3 exp (-xZm/m,), where x w 2 to 7 for the lSlje state and is thus small if values of a, are taken from the tables of ALLIS and MORSE. However these values, fitted t o electron-scattering experiments may not be relevant for muonic atoms so that experimental determination of al for muonic atoms is requirqd. If a, should be smaller, the perturbation of the Coulomb levels would be greater, especially for the outer shells, and one could vary the parameter a, to fit the results with experiments.
I n h a l t s u b e r s i c h t . Die Energieniveaus der Muon-Atome werden direkt durch Gsen der Dirac-Gleichungen mit abgeschirmtem Potential vom ALLIS-MORSE-% berbcbnet. I m nicht-relativistischen Fall stimmen die erhaltenen Werte mit den entsprechenden Losungen der Schrodigergleichung uberein. Die Abweichungen vom Coulombfall sind im lSl,z-Zustand von der Form 3 exp (-xZzm/nz,), worin x w 2-7, und sind damit klein, wenn die a,-Werte den Tabellen von ALLIS und MORSE entsprechen. Jedoch sind diese an die Elektronenstreuversuche angepalten Werte moglicherweise nicht fiir Muon-Atome malgebend, so dal3 eine experimentelle Bestimmung von a, speziell fur Muon-Atome erforderlich ist. Wenn a, kleiner sein sollte, niirde die Storung der Coulomb-Niveaud, insbesondere der iiuleren Schalen, groler sein, und man konnte den Parameter al den Versuchsergebnissen anpassen.
π SIMILAR VOLUMES
Energy levels of muonic atom states with highrprincipal quantum number are examined. A Thomas-Fermi type treatment is used in all but the lightest atoms to take account of the effects of electron shielding. Transition energies of the muon are compared to electron binding energies, and implications f
Energies and radiative lifetimes are caIcuIated for all bound and quasibound Ievels of the positive muon molecuIar ion He/J,+, together with the tunneling predissociation lifetimes of its quasibound levels. The radiative lifetimes obtained are much longer than the positive muon decay lifetime, so sp
Programming language: FORTRAN IV High speed store required: 55000 words. No of bits in a word: 60 Is the program overlaid? Yes No. of magnetic tapes required: 4 may be used for input data, intermediate storage and to store the results What other peripherals are used? Disk (in lieu of tapes); Extende