PPT Slide

?-matching

Heavy-Ion induced nucleon transfer reactions - 2

David M. Brink, Phys. Lett. B40 (1972) 37

N. Anyas-Weiss et al., Physics Reports, 12 (1974) 201

projectile

target

Linear momentum in y-direction (relative motion), before and after:

k-matching: Dk = k 0 – ?1 / R1 – ?2 / R2 ? 0 ; Dk ? 2p/R

Angular momentum projected in the z-direction (perpendicular):

Qeff = Q – (Z1f Z2f – Z1i Z2i ) e2 / R

DL ? = ( ?2 – ?1 ) ? + ½ mv (R1 - R2) + R Qeff / v ;

And finally, there is a simple requirement that ? 1 + l 1 = even and ? 2 + l 2 = even

Initial y1 = u1(r1) Y?1,l 1 (q1,f1)

Final y2 = u2(r2) Y?2,l 2 (q2,f2)

and the main contribution to the

transfer is at the reaction plane:

? q 1 = q 2 = p / 2

But Y ? l (p /2, f ) = 0 unless

? + l = even

excitation energy

Prob (Ex)

Matching probability for given Dl transfer