✍ Scribed by Archibald W Hendry
No coin nor oath required. For personal study only.
Starting with a set of harmonic oscillator wavefunctions, we calculate partial decay rates of excited A* and N* states into a nucleon with single pion emission.
Good agreement with values estimated from data is obtained for N < 6, thus indicating that the simple quark model is reasonable over a much wider range than expected. The calculated decay rates of the even higher states depend more sensitively on the finer details of the nucleon wavefunction.
In the last 10 or so years, it has become clear that the harmonic oscillator quark model [l-3] provides a reasonably satisfactory picture of baryon resonances with masses up to about 2 GeV. These baryons lie within the ground state level (N = 0) and the first two excited levels (N= 1,2) of the h.o. quark model scheme. In particular, by incorporating a one-gluon-like effective potential between quarks to bring about mass splittings and state mixing, Isgur et al. [4,5] have shown that it is possible to obtain exceptionally good agreement between calculated and observed values for the masses of the baryons and their partial decay rates to the ground state nucleon.
More recently, evidence has been found [6,7] for the existence of quite a number of highly excited d* and N* baryon resonances in the 2 to 4 GeV mass region. In the N ,< 2 levels of the quark scheme, the highest spin attainable is 7/2, corresponding to the F,, and F,, states of the pion-nucleon system. These new resonances, however, have spins that go up much further, through 21/2. Presumably they belong to the more highly excited levels of the three-quark system. Also estimated for the new resonances are their elasticities which, together with their total widths, provide some measure of the resonance partial widths r,, for decay into a final state nucleon plus pion.
The spectrum for the three-quark system has already been worked out in some detail by Horgan [2], Dalitz and Reinders [8], and we show in Fig. 1 (taken from these references) the many configurations that occur for N< 10. Here the circles, squares, and triangles correspond respectively to symmetric, mixed-symmetry, and antisymmetric combinations of three quarks, and L is the total quark orbital angular 65
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