In Section 6.2.4 we used (6.36) to derive the masses of the Πand Σ baryons in

In Section 6.2.4 we used (6.36) to derive the masses of the Λ and Σ^ˆ—baryons in Table 6.9. Derive the mass formulas for the remaining baryons listed in this table.

²⁵These analyses also determine the mean square radii 

of the various states, where the wavefunctions are determined by the solutions of the Schr¨odinger equation for successful potentials like (6.66) and (6.67). The resulting values of r₀ for the various states shown in Figure 6.10 span just the range (6.68) in which the potential is well-determined.

Figure 6.10

Transcribed Image Text:

Table 6.9 Baryon masses (in GeV/c²) in the approximation (6.36) compared with experimental values. These have been obtained using m = 0.362 GeV/², m, = 0.539 GeV/c² and b= 0.0256 (GeV/c²)³. Particle Mass Prediction Experiment 3b Зт 0.94 0.939 4m2 36 2m + ms 1.12 1.116 4m2 Σ 2m + m, + 4 1.193 1.18 тm, т т + 2m, + 4 1.32 1.318 тm, т 36 Зт + 4m? 1.23 1.232 ь 2m + ms 2 Σ 1.38 1.385 m2 тm, т + 2m, + 1.53 1.533 т? тт 36 Зт, + 4m? Ω 1.68 1.673 [1] in /- p? Ieb(r)/° d°r ri = 72