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Deduction of the quantum unmbers of low-lying states of the (e+e+e-e-) system from symmetry consideration
The feature of the low-lying spectrum and a complete set of quantum numbers
of the (e+e+e-e-) system have been deduced based on symmetry consideration. The
existence of a low odd-parity L=1 excited state with the spins of the two
electrons coupled to s1=1 and the two positrons coupled to s2=0 (or s1=0 and
s2=1) and a low even-parity L=0 excited state with s1=s2=1 have been predicted.
The discussion is generalized to 2-dimensional (e+e+e-e-) systems.Comment: 12 pages, 5 tables, no figure
A restriction of Euclid
Euclid is a well known two-player impartial combinatorial game. A position in
Euclid is a pair of positive integers and the players move alternately by
subtracting a positive integer multiple of one of the integers from the other
integer without making the result negative. The player who makes the last move
wins. There is a variation of Euclid due to Grossman in which the game stops
when the two entrees are equal. We examine a further variation that we called
M-Euclid in which the game stops when one of the entrees is a positive integer
multiple of the other. We solve the Sprague-Grundy function for M-Euclid and
compare the Sprague-Grundy functions of the three games
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