Production cross sections of elements near theN=126shell inCa48-induced reactions withGd154,Tb159,Dy162, andHo165targets

Abstract

Excitation functions for shell-stabilized evaporation residues produced in $^{48}\mathrm{Ca}$-induced reactions with $^{154}\mathrm{Gd},^{159}\mathrm{Tb},^{162}\mathrm{Dy}$, and $^{165}\mathrm{Ho}$ targets have been measured in experiments performed at the Cyclotron Institute at Texas A University. The examined energy range predominantly covers the $3n$ and $4n$ evaporation channels with higher cross sections measured for the $4n$ products. The ${\ensuremath{\sigma}}_{4n}$ are nearly invariant within experimental uncertainty in reactions with $^{159}\mathrm{Tb},^{162}\mathrm{Dy}$, and $^{165}\mathrm{Ho}$ with the maxima at 12.6 \ifmmode\pm\else\textpm\fi{} 1.9, 12.6 \ifmmode\pm\else\textpm\fi{} 1.7, and 9.4 \ifmmode\pm\else\textpm\fi{} 1.3 mb, respectively. For the reaction with $^{154}\mathrm{Gd}$, the maximum is slightly lower at 4.0 \ifmmode\pm\else\textpm\fi{} 0.6 mb. A simple model to describe the measured production cross sections was employed. Capture was estimated by using the ``diffused barrier formula'' from the ``fusion by diffusion'' model proposed by \ifmmode \acute{S}\else \'{S}\fi{}wi\k{a}tecki et al. [Phys. Rev. C 71, 014602 (2005)]. The fusion probability was estimated by using a phenomenological expression presented by Siwek-Wilczy\ifmmode \acute{n}\else \'{n}\fi{}ska et al. [Int. J. Mod. Phys. E 17, 12 (2008)]. The survival probability was calculated according to the formula of Vandenbosch and Huizenga [Nuclear Fission (Academic, New York, 1973)], derived from transition-state theory. The best agreement is reached between calculation and experiment upon inclusion of collective effects in the calculation of the survival probability, shown previously to be important for production of weakly deformed nuclei. This, in turn, challenges the expectation that strong shell stabilization benefits the production cross section. The present data are compared with earlier studies on production of neutron-deficient nuclei in Ca-induced reactions with lanthanide targets.