Studying multi-nucleon transfer reaction in a recoil mass spectrometer

We present simulation of a recoil mass spectrometer for measurement of multi-nucleon transfer reactions, based on Monte Carlo techniques. Target-like ions are generated event by event and transported to the focal plane of the spectrometer by the method of transfer matrices. Measured focal plane spectra for the elastic and six transfer channels of the reaction ^28 Si+ ^94 Zr are reproduced at two projectile energies near the Coulomb barrier. Excellent reproduction is achieved even with first-order ion-optical calculations, indicating not so significant role of higher order aberrations in conventional recoil separators with smaller acceptance. This is in striking contrast with the large acceptance magnetic separators used for studying transfer reactions, for which complex trajectory reconstruction algorithms involving higher order aberrations are essential. Transmission efficiency of the spectrometer, calculated by the reported code, is crucial to convert measured transfer probabilities to differential and integral transfer cross sections for each channel. We show effectiveness of the proposed methodology by extracting differential elastic scattering cross sections from measured yields for the reaction ^28 Si+ ^94 Zr. Besides being useful for other recoil mass spectrometers, our methodology can be employed for measurement of quasi-elastic reaction cross sections in velocity filters and gas-filled separators.