Question

is captured 5.) A deuteron d has spin 1, whereas a " has spin 0 and negative parity. If a r on a d from a p-wave orbit, so that "+d 2n, (1) (n is a noutron) show that the two neutrons must be in a spin-singlet state.

Answer 1

We have given T +d 2n we can also write it as - I + d nt n Permion Fermion Important Note - If system has two identical fermeons then, total = antisymmetric Total exchange symmetry = (-1) L+S + (-1) - L+S = even - Also we know tatal angular momentum of deutron is at Now we see the total angular momentum. of reactants and producs, then total equate both be g. - Jp angulae momenten) of Reactanti I- + Total angular momentum of Products n + l d = 4+ - In- - I +Š. 1 to n. Shaž SE & J = 1 + 5 where 50 - 5h + 5n - 1 + (Sp = '0, 1) & Jp = J R = 0, 1, 2 & T = Jp - SP 2 Jp = Jy + Ja s + I > JR = 0, 1, 2

Post I ute get Loo up = 1 4 = 2 (Sp-o, Sp = 0 (Sp= 0 Jp = o) Jp =)) Jo =2) when for Lp = 18 1 1 (Sp = 1, Ipo lp=0, 1, 2, (Sp-1, Joel i Lp = 6, 2,3 l Sp=1, Jpo 2) - 2000 Oonala .. possible values of Lo, we get are 0, 1, 2, 3 using the concept of conservation of parity d at I- n tn Parity: even odd even even conserving Parity Pd Por- (-1) 4 = P P HLP (+1)(-1) (-1)" - (H1) (+1) File - [ 46 = even 2 only possible valuu o o o o o 2 using important note, from o 18+ Sp = even for identical fermis .e. Lp + Sp = even , when Sp = 0 o to = even 2 + 0 = even A when Sp = 1 = Lp + Sp z odd. 0 + 1 = odd 2 +3 - odd. This means two neutrons must be in spin. single state