A deuteron d is a nucleus with charge +1, composed of a proton (p) and a neutron (n). The deuteron has spin 1 and parity +. A negative pion π−, with charge −1 and spin 0, can be bound to the deuteron...

A deuteron d is a nucleus with charge +1, composed of a proton (p) and a neutron (n). The deuteron has spin 1 and parity +. A negative pion π−, with charge −1 and spin 0, can be bound to the deuteron to form a sort of “deuterium atom”. Let us suppose that this system is formed in the lowest Bohr orbit.

(a) Compute the ratio between the Bohr radius of this system and the standard Bohr radius, and compute the binding energy of the system. Some masses needed for the computation are listed below, in MeV/c²:

(b) The bound system described above decays with the reaction π− + d → n + n. Both angular momentum and parity are conserved in the decay. Discuss if one can determine the intrinsic parity of the π− from these data.

(c)) Compute the angular distribution of neutrons in the final state, knowing that in the initial state Jz = 0.

(d)) Explain why the hydrogen atom does not decay via a somewhat analogous process, e− + p → n+ν, where ν is the (electron) neutrino.