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5.5 Results

The convergence of the hyperspherical expansion for baryons was studied in some detail in Ref. [58]. Table 5.1 shows the result of a calculation with equal masses mi = 1 and the simple power-law potential V = 1 2 ∑ rij0.1, for the ground-state energy and the correlation coefficient δ(3)(r 12). In Table 5.2, we use instead a linear potential V = 1 2 ∑ rij. The convergence is spectacular for the binding energy and slightly slower for the correlation coefficient. Similar conclusions were reached by other authors [55].

For excited states, the convergence pattern is less impressive and, in practice, one has to include more harmonics in the calculation.

Table 5.1: Ground-state energy E0 and correlation coefficient δ(3)(r 12) in the potential V = 1 2 ∑ rij0.1 with unit quark masses, as a function of the maximal grand orbital. N is the number of coupled equations.

LmaxN E0 103δ(3)(r 12)
0 1 1.88075 1.128
4 2 1.88032 1.186
6 3 1.88020 1.221
8 4 1.88019 1.232
10 5 1.88018 1.239
12 7 1.88018 1.245
14 8 1.88017 1.248
16 101.88017 1.249

Table 5.2: Energy and correlation coefficient for the ground state (n = 0) and its hyper-radial excitation (n = 1) for a linear potential V = 1 2 ∑ rij and masses mi = 1

Lmax En=0 δ(3)(r 12)n=0 En=1 δ(3)(r 12)n=1
0 3.8647 0.05504 5.3280 0.05505
4 3.8633 0.05628 5.3217 0.05597
6 3.8631 0.05680 5.3208 0.05652
8 3.8631 0.05689 5.3207 0.05664

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