- #1
Demon117
- 165
- 1
Hello all, I am having trouble understanding how this works. In Krane there arises a discussion on total angular momentum I of the deuteron. While it is true it has three components, namely the individual spins of the neutron and proton, but also the orbital angular momentum l of the nucleons as they move about their common center of mass. This total angular momentum can be denoted by
[itex]I=s_{p} + s_{n} + l[/itex]
He continues on to talk about the different ways to couple these contributions and states there are only four possibilities. I can see the first two possibilities for total angular momentum I=1, but the other two make no sense. These are the possibilities:
(1) [itex]s_{n}[/itex] and [itex]s_{p}[/itex] are parallel with [itex]l=0[/itex]
(2) [itex]s_{n}[/itex] and [itex]s_{p}[/itex] are antiparallel with [itex]l=1[/itex]
(3) [itex]s_{n}[/itex] and [itex]s_{p}[/itex] are parallel with [itex]l=1[/itex]
(4) [itex]s_{n}[/itex] and [itex]s_{p}[/itex] are parallel with [itex]l=2[/itex]
One can see why (1) and (2) hold by inspection but (3) and (4) make my brain hurt. Perhaps I am just not seeing the correct orientation. Any suggestions?
[itex]I=s_{p} + s_{n} + l[/itex]
He continues on to talk about the different ways to couple these contributions and states there are only four possibilities. I can see the first two possibilities for total angular momentum I=1, but the other two make no sense. These are the possibilities:
(1) [itex]s_{n}[/itex] and [itex]s_{p}[/itex] are parallel with [itex]l=0[/itex]
(2) [itex]s_{n}[/itex] and [itex]s_{p}[/itex] are antiparallel with [itex]l=1[/itex]
(3) [itex]s_{n}[/itex] and [itex]s_{p}[/itex] are parallel with [itex]l=1[/itex]
(4) [itex]s_{n}[/itex] and [itex]s_{p}[/itex] are parallel with [itex]l=2[/itex]
One can see why (1) and (2) hold by inspection but (3) and (4) make my brain hurt. Perhaps I am just not seeing the correct orientation. Any suggestions?
Last edited: