PPT Slide

?-matching

Heavy-Ion induced nucleon transfer reactions

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

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

projectile

target

IDEA: for the transferred nucleon, we match the initial and final values

of the linear momentum and of the angular momentum

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

pi = mv – ??1 / R1 pf = ??2 / R2 Dp = pf – pi ? 0

Set Dp=0 within accuracy of Uncertainty Principle Dp ? ?/Dy ; Dy?R/2

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

Angular momentum projected in the z-direction (perpendicular to relative motion) is given by

Linit = L(relative motion) i + ?1 ? = mv R + ?1 ? and Lfinal = L(relative) f + ?2 ?

DL ? = Lfinal – Linit = ( ?2 – ?1 ) ? + d (mv R ) where each of m, v and R changes

DL ? = ( ?2 – ?1 ) ? + ½ mv (R1 - R2) + R Qeff / v ; Qeff = Q – (Z1f Z2f – Z1i Z2i ) e2 / R

Q-value Coulomb-corrected for

nucleon rearrangement

Set DL = 0 precisely, in principle (in practice, classical treatment of Erel ? allow DL ? 2)

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