An Interlude — Question 10

Question 10

Neutral antimatter can be distinguished by internal additive numbers

A neutron has charge 0, baryon number +1 and spin 1/2. Its antiparticle has baryon number -1. Consider two proposed final states from a neutron-antineutron pair at rest: (A) two neutral mesons with B=0 each; (B) two neutrons. Both proposals conserve charge.

1. Check baryon number for both proposals.

2. If each initial rest energy is 940 MeV and each final meson rest energy is 300 MeV, find each meson kinetic energy for channel A, assuming it occurs.

Question 10 - Solution

Neutral antimatter can be distinguished by internal additive numbers

(a) Method and calculation

$$\boxed{B_i=1-1=0,\quad B_A=0+0=0,\quad B_B=1+1=2}.$$$$\boxed{A:\text{ not excluded by baryon number};\quad B:\text{ excluded if }B\text{ is conserved}}.$$

(b) Interpretation and further calculation

$$\mathbf p_1=-\mathbf p_2,\ m_1=m_2\Rightarrow\boxed{E_1=E_2=940\,\mathrm{MeV}}.$$$$\boxed{K_1=K_2=940-300=640\,\mathrm{MeV}}.$$

Physical check

Equal electric charge does not make neutron and antineutron identical. Passing charge, baryon-number and energy tests does not prove a nonzero reaction amplitude.