A is captured at rest by a deuteron from the atomic orbital ( ) of the atom

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Particle Physics & Quantum Fields · Symmetry, groups and the quark model

Symmetry and Flavour, Ch Parity, charge conjugation and time reversal as operators, and the CPT theorem

Problem

\pi^-

is captured at rest by a deuteron from the

1s

atomic orbital (

L=0

) of the

\pi^-d

atom, giving

\pi^-d\to nn

about three quarters of the time. The deuteron has

J^P=1^+

, the pion has spin

0

, and each neutron has intrinsic parity

P(n)=+1

. ((a)) Give the total angular momentum

J

of the atomic state just before capture. ((b)) List the two-neutron spectroscopic states

^{2S+1}L_J

with this value of

J

, for

S=0

and

S=1

and

L=0,1,2

. ((c)) Eliminate the states forbidden by the Pauli principle for two identical neutrons (which requires

L+S

even), and identify the single surviving state. ((d)) Use that surviving state to determine

P(\pi^-)