Effect of target deformation in superheavy nuclei synthesis

Effects of target and projectile deformation on the shell corrections are calculated within the deformed two-center shell model. The relations for deformed two center oscillator potential, V(r)(ρ, z), which assures equipotentiality on the surface of the two intersected nuclei reads are given. The two center oscillator potential for fusion like shapes follows the changes of the two spheroidal partner deformations. The total Hamiltonian of the system is: H = - ℎ2/2m0Δ + V(r)(ρ, z) + VΩs + VΩ2, where VΩs and VΩ2V s are the spin-orbit and the squared angular momentum interaction potentials. The spin-orbit operator is calculated as usual using creation and annihilation components. In this way the angular momentum dependent operators are also shape-dependent. Details of calculation and matrix element formulae are given elsewhere. The superheavy synthesis reaction U+48Ca → 112 has been analyzed for different isotopes of uranium spanning continuously the spheroidal target deformation. The level schemes and the shell effects for protons Eshell(p) and total Eshell are drawn. Differences are apparent at higher energy levels. Until the last part of the overlapping almost no difference exists within the proton shell correction. Divergence in the curve behaviour appears at the end of the fusion process. The two branches in Eshell correspond to the two proton level scheme deformations of Z=112 (where the ratio of spheroid semiaxes is χ = 0.89 and χ = 1). The total shell correction Eshell follows the same behaviour slightly lowering the 232U reaction shell correction in the first part of the process. Shell correction values less than those corresponding to sphere suggest a more deformed ground state for 112 isotopes than those taken into account here. (author)