Nuclear Physics

The mass formula provided relates the mass of baryons to their isospin ( ) and hypercharge ( ) through the parameters , , and . The term indicates that the mass is related to both isospin and hypercharge. For hyperons and hyperons, their masses must be the same. This means that their corresponding values of and must be related in such a way that the mass formula gives the same result for both particles. Since and hyperons have the same mass, the relationship between and should not affect the mass in the same way for both.
- Option (B): is correct because the mass depends on the hypercharge , as seen in the formula.
- Option (C): does not depend on is also correct. The mass formula shows that the isospin term, involving , does not significantly affect the overall mass of the baryon, as it is coupled with the hypercharge term.
Thus, the correct answers are (B) and (C).

In the spin singlet state, the total spin of the system is zero, and the spin operators and for the two particles are related by: Thus, the value of is .