Nucleon transfer in heavy ion reactions

An analytical formula is derived for the amplitude for transfer of a nucleon in quasi-elasticreactions between heavy ions. The derivation takes advantage of the semiclassical conditionsfound in peripheral collisions between heavy ions. The relative motion of the two nucleiis treated classically and the transfer amplitude is calculated by a perturbation method.Under the approximation of small overlap between the nuclear potentials, the semiclassicalamplitude is reduced to a surface integral. This can be calculated analytically by usingHankel function forms for the bound-state wavefunctions and by approximating the actualorbit by a constant velocity orbit tangential to it at the distance of closest approach.These approximations seem reasonable in strong absorption conditions. Corrections to theformula of the amplitude are evaluated. The analytical form of the amplitude exhibits anexponential behaviour as a function of the distance of closest approach. The decay constantof the exponential is given explicitly and it is found to be an important parameterof the reaction. Kinematical conditions for maximum transfer are derived which relate theincident energy to the reaction Q-value. The physical interpretation of the amplitude isdiscussed. In the case of proton transfer, the effect of Coulomb potential results in a shiftof the binding energy of the proton. With this prescription we still obtain the same formof the transfer amplitude for both neutrons and protons. The formula for the semiclassicaltranfer amplitude is used to calculate angular distributions within a simplified formalismderived from the distorted wave Born approximation (DWBA). The reactions consideredare 208Pb(16O,l50)209Pb, 26Mg(11B,10B) 27Mg and 34S(32 S, 33S)33S for neutron transferand 208Pb(16O, 15N)209Bi for proton transfer. It is found that the shapes of the presentangular distributions agree with full DWBA calculations but the magnitude of the formerdepends on whether the distance of closest approach is that of the initial channel, thefinalchannel or some average of the two. Conditions for the selective population of definitestates are discussed in relation to the reaction Q-value, energy and initial and final statesinvolved. It is found that an inversion of the selectivity with respect to the spins of theinitial and final state occurs when the energy of relative motion at distance of closest approach equals the reaction Q-value. An approximate formula for the angle-integrated crosssection has also been derived.