Hot fusion-evaporation cross sections of ${}^{44}\mathrm{Ca}$-induced reactions with lanthanide targets

Background: Previously reported cross sections of ${}^{45}\mathrm{Sc}$-induced reactions with lanthanide targets are much smaller than ${}^{48}\mathrm{Ca}$-induced reactions on the same targets. ${}^{44}\mathrm{Ca}$ is one proton removed from ${}^{45}\mathrm{Sc}$ and could be used to produce nuclei with a relative neutron content between those produced in the ${}^{45}\mathrm{Sc}-$ and ${}^{48}\mathrm{Ca}$-induced reactions.

Purpose: As part of a systematic investigation of fusion-evaporation reactions, cross sections of ${}^{44}\mathrm{Ca}$-induced reactions on lanthanide targets were measured. These results are compared to available data for ${}^{48}\mathrm{Ca}$- and ${}^{45}\mathrm{Sc}$-induced fusion-evaporation cross sections on the same lanthanide targets. Collectively, these data provide insight into the importance of the survival against fission of excited compound nuclei produced near spherical shell closures.

Methods: A beam of ${}^{44}\mathrm{Ca}^{6+}$ at an energy of $\approx 5\mathrm{MeV}/\mathrm{u}$ was delivered by the K500 superconducting cyclotron at the Cyclotron Institute at Texas A&M University. The desired evaporation residues were selected by the Momentum Achromat Recoil Spectrometer and identified via their characteristic $\alpha$-decay energies. Excitation functions for the ${}^{44}\mathrm{Ca}+{}^{158}\mathrm{Gd},{}^{159}\mathrm{Tb}$, and ${}^{162}\mathrm{Dy}$ reactions were measured at five or more energies each. A theoretical model was employed to study the fusion-evaporation process.

Results: The ${}^{44}\mathrm{Ca}$-induced reactions have $xn$ cross sections that are two orders of magnitude larger than ${}^{45}\mathrm{Sc}$-induced reactions but two orders of magnitude smaller than ${}^{48}\mathrm{Ca}$-induced reactions on the same targets. Proton emission competes effectively with neutron emission for the ${}^{44}\mathrm{Ca}+{}^{159}\mathrm{Tb}$ and ${}^{162}\mathrm{Dy}$ reactions. The maximum $4n$ cross sections in the ${}^{44}\mathrm{Ca}+{}^{158}\mathrm{Gd},{}^{159}\mathrm{Tb}$, and ${}^{162}\mathrm{Dy}$ reactions were $2100\pm 230,230\pm 20$, and $130\pm 20\mu \mathrm{b}$, respectively. The ${}^{44}\mathrm{Ca}+{}^{158}\mathrm{Gd}$ and ${}^{159}\mathrm{Tb}$ cross sections are in good agreement with the respective cross bombardments of ${}^{48}\mathrm{Ca}+{}^{154}\mathrm{Gd}$ and ${}^{45}\mathrm{Sc}+{}^{158}\mathrm{Gd}$ once differences in capture cross sections and compound nucleus formation probabilities are corrected for.

Conclusions: Excitation functions were measured in ${}^{44}\mathrm{Ca}$-induced reactions on lanthanide targets. Evaporation residue cross sections were two orders of magnitude larger than ${}^{45}\mathrm{Sc}$-induced reactions on the same targets due to an increase in the survival probability of the compound nucleus. However, little evidence of cross-sectional enhancement due to shell stabilization of the compound nucleus was observed.

Figure 1

MARS schematic showing the layouts of target chamber and detector chamber. The magnets labeled $Q$ and $D$ indicate quadrupole and dipole magnets, respectively, with the subscript and/or number denoting the focusing plane and downstream position of each magnet. S1 and S2 are sextupole magnets. The slits (SL2) near the beam dump define the momentum acceptance.

Figure 2

Representative $\alpha$ spectra observed in the ${}^{44}\mathrm{Ca}$-induced reactions studied in this paper. The indicated center-of-target laboratory-frame energies $E_{\mathrm{Lab}\mathrm{CoT}}$ correspond to the peak of the $4n$ excitation functions. The arrows correspond to the expected locations of the $4n$ and either $5n$ (${}^{158}\mathrm{Gd}$ target) or $p3n$ (${}^{159}\mathrm{Tb}$ and ${}^{162}\mathrm{Dy}$ targets) products.

Figure 3

$\mathrm{EvR}-\alpha$ correlations for the short-lived $4n$ products of the ${}^{44}\mathrm{Ca}+{}^{159}\mathrm{Tb}$ and ${}^{162}\mathrm{Dy}$ reactions. Panels (a) and (b) are the lifetime distributions for ${}^{199}\mathrm{At}$ and ${}^{202}\mathrm{Rn}$, respectively. The measured half-lives were extracted from the curves using Eq. (8) in Ref. [28], and the literature values for the half-lives were taken from Ref. [29]. The correlated $\mathrm{EvR}-{\alpha }_1$ position spectra are shown in (c). The parameters of the correlation search are described in the main text. The ${\alpha }_1-{\alpha }_2$ correlation search in (d) was taken over the entire energy range shown by both axes.

Figure 4

(a) The $4n$ and (b) $p3n$ excitation functions for the ${}^{44}\mathrm{Ca}$-induced reactions reported in this paper. The symbols represent the measured data with associated error and represent the same reactions in both panels. The solid lines are theoretical calculations using the model described in Sec. 4. The experimental data are also reported in Table 3.

Figure 5

Comparison of measured $4n$ cross sections of ${}^{48}\mathrm{Ca}$-, ${}^{44}\mathrm{Ca}$-, and ${}^{45}\mathrm{Sc}$-induced reactions on lanthanide targets. The black points represent the ${}^{48}\mathrm{Ca}$-induced reactions [1], the blue points represent the ${}^{44}\mathrm{Ca}$-induced reactions (reported in this paper), and the red points represent the ${}^{45}\mathrm{Sc}$-induced reactions [3]. The shapes represent groups of reactions on the same target. The solid squares are reactions on ${}^{159}\mathrm{Tb}$, the open circles are reactions on ${}^{162}\mathrm{Dy}$, and the solid diamonds are reactions on ${}^{158}\mathrm{Gd}$. See the main text for a discussion.

Figure 6

The $4n$ EvR cross sections for the cross bombardments described in this paper. The symbols are the measured data points. The solid lines represent fusion cross sections ${\sigma }_{\mathrm{fus}}={\sigma }_{\mathrm{capt}}{P}_{\mathrm{CN}}$ and are calculated with the model described in Sec. 4. Each line is associated with the data points of the same color.

Figure 7

Maximum measured $4n$ EvR cross sections (solid symbols) as a function of the average difference in the fission barrier and the neutron separation energy during the deexcitation cascade. The ${}^{44}\mathrm{Ca}$ data are compared to the model calculations described in Sec. 4, both including (dashed line) and excluding (solid line) CELD. The model calculations for all other data are performed according to the prescription in Ref. [1]. The models are identical except for the inclusion of charged-particle emission from the CN in the present paper. The gray shaded regions indicate the effects of changing the fission barrier by $\pm 0.5\mathrm{MeV}$. All reaction systems use even-$Z$ projectiles and produce CN near the $N=126$ spherical closed shell. The ${}^{48}\mathrm{Ca}$ data are reported in Ref. [1], the ${}^{44}\mathrm{Ca}$ data are reported in this paper, the ${}^{50}\mathrm{Ti}$ and ${}^{54}\mathrm{Cr}$ data are reported in Ref. [2], the ${}^{40}\mathrm{Ar}$ data are reported in Ref. [10], and the ${}^{124}\mathrm{Sn}$ data are reported in Ref. [11]. Only upper limits were measured for the ${}^{54}\mathrm{Cr}+{}^{162}\mathrm{Dy}$ reaction, and the ${}^{40}\mathrm{Ar}+{}^{176}\mathrm{Hf}$ and ${}^{124}\mathrm{Sn}+{}^{92}\mathrm{Zr}$ reactions are two cross bombardments that provide an estimate of ${\sigma }_{\max ,4n}$ for the ${}^{54}\mathrm{Cr}$-induced reaction.