A new method is proposed to produce identical beam emittances in the transverse phase planes from a severely asymmetric beam extracted from a slow-cycling synchrotron. This is important to obtain a good beam distribution at the irradiation spot when the spot scanning method is used for the treatment in hadron therapy. The method makes use of the beam rotation effect either by a solenoid or by a rotational quadrupole section, referred to as rotator, to produce identical emittances in the two transverse phase planes. It is also helpful for the stabilization of the beam spot at the irradiation point. Simulation studies with an artificially generated beam have been carried out to prove the principle. The method is not only applicable to fixed treatment nozzles but also to rotational gantry nozzles. Both a solenoid and a section of quadrupole rotator can be used, with the former being ideal for proton gantries and the latter for fixed carbon nozzles. There is a practical limit in using room-temperature solenoid due to the high beam rigidity in the case of a carbon beam, for which a superconducting solenoid has to be used. The comparison with other methods and the practical applications of the method are also presented.

The experimental data of the 6Li(d,α)4He,7Li(p,α)4He and 6Li(p,α)3He reactions obtained by other groups are reanalyzed in this work to extract their respective astrophysical S(E) factors and the screening energies provided by different environments (LiF solid targets and molecular H2 or D2 gas targets). Different from previous authors who investigated these three reactions independently, we study them simultaneously, based on the hypothesis that the screening effects are independent of the isotopic effects and the fact that the screening effects depend on the environments. The present extracted astrophysical S(E) factors result in Sbare(0) = 20.5 ± 0.5, 0.0616 ± 0.0017 and 3.63 ± 0.13 MeV b for the 6Li(d,α)4He, 7Li(p,α)4He and 6Li(p,α)3He reactions, respectively. The screening energies are 310 ± 109 and 218 ± 38 eV for the LiF solid targets and molecular H2 or D2 gas targets, respectively. These deduced screening energies are smaller than that observed by Engstler et al, and the value of Us = 218 ± 38 eV for the molecular H2 or D2 gas targets coincides with the value of 186 eV estimated from the adiabatic limit, while the value of Us = 310 ± 109 eV for the LiF solid targets is still slightly larger than that estimated from theoretical predictions.