Production cross section and decay study of ${}^{243}\mathrm{Es}$ and ${}^{249}\mathrm{Md}$

In the study of the odd-$Z$, even-$N$ nuclei ${}^{243}\mathrm{Es}$ and ${}^{249}\mathrm{Md}$, performed at the University of Jyväskylä, the fusion-evaporation reactions ${}^{197}\mathrm{Au}({}^{48}\mathrm{Ca},2n){}^{243}\mathrm{Es}$ and ${}^{203}\mathrm{Tl}({}^{48}\mathrm{Ca},2n){}^{249}\mathrm{Md}$ have been used for the first time. Fusion-evaporation residues were selected and detected using a gas-filled separator coupled with its focal-plane spectrometer. For ${}^{243}\mathrm{Es}$, the recoil decay correlation analysis yielded a half-life of $24\pm 3\mathrm{s}$ and a maximum production cross section of $37\pm 10\mathrm{nb}$. In the same way, a half-life of $26\pm 1\mathrm{s}$, an $\alpha$-branching ratio of $75\pm 5\%$, and a maximum production cross section of $300\pm 80\mathrm{nb}$ were determined for ${}^{249}\mathrm{Md}$. The decay properties of ${}^{245}\mathrm{Es}$, the daughter of ${}^{249}\mathrm{Md}$, were also measured: an $\alpha$-branching ratio of $54\pm 7\%$ and a half-life of $65\pm 6\mathrm{s}$. Experimental cross sections were compared to the results of calculations performed using the kewpie2 statistical fusion-evaporation code.

Figure 1

$\alpha$-particle energy spectrum of ${}^{243}\mathrm{Es}$ measured in the DSSD resulting from recoil-$\alpha$ correlations using a maximum search time of 268 s.

Figure 2

Time distribution of $\alpha$ decays with respect to the ${}^{243}\mathrm{Es}$ fusion-evaporation residue implantation. The inset shows the same data as a function of $ln\left(\mathrm{\Delta }T\right)$ with $\mathrm{\Delta }T$ expressed in milliseconds. It should be noted that the range is different for the two spectra: 350 s for the main panel and 135 h for the inset. The fit using a two-component decay curve (real and random) is shown with a solid line.

Figure 3

$\alpha$-particle energy spectra of ${}^{249}\mathrm{Md},{}^{249}\mathrm{Fm}$ and ${}^{245}\mathrm{Es}$ resulting from (a) recoil-$\alpha$ and (b), (c) recoil-$\alpha \text{−}\alpha$ correlations using a maximum search time of 10 min.

Figure 4

$\alpha$-decay time distribution on a logarithmic scale (from $\sim 7\mathrm{ms}$ to $\sim 20\min$) as a function of the decay energy.

Figure 5

Time distribution of $\alpha$ decays with respect to the ${}^{249}\mathrm{Md}$ fusion-evaporation residue implantation. The inset shows the same data as a function of $ln\left(\mathrm{\Delta }T\right)$ with $\mathrm{\Delta }T$ expressed in milliseconds. It should be noted that the range is different for the two spectra: 300 s for the main panel and 18.2 h for the inset. The fit using a one-component decay curve is shown with a solid line.

Figure 6

Time distribution of the $\alpha$ decay of ${}^{245}\mathrm{Es}$ with respect to the ${}^{249}\mathrm{Md}$ $\alpha$ decay. The inset shows the same data as a function of $ln\left(\mathrm{\Delta }T\right)$ with $\mathrm{\Delta }T$ expressed in seconds. It should be noted that the range is different for the two spectra: 600 s for the main panel and 2.25 h for the inset. The fit using a one-component decay curve is shown with a solid line.

Figure 7

Systematics of the fusion-evaporation cross sections in the $2n$ channel as a function of $Z$ of the residual nucleus. The filled red squares correspond to reactions induced by a ${}^{48}\mathrm{Ca}$ beam, whereas the blue circles correspond to those using other beams. The new ${}^{243}\mathrm{Es}$ and ${}^{249}\mathrm{Md}$ measurements are denoted by empty square symbols. The mass number $A$ of the residual nucleus is given to the right of each symbol. Data are taken from Refs. [28] (${}^{238,240,241}\mathrm{Cf}$), [29] (${}^{244}\mathrm{Cf}$), this paper (${}^{243}\mathrm{Es},{}^{249}\mathrm{Md}$), [30] (${}^{244,246}\mathrm{Fm}$), [31] (${}^{250}\mathrm{Fm}$), [32] (${}^{251}\mathrm{Md}$), [33] (${}^{250}\mathrm{No}$), [34] (${}^{252,253}\mathrm{No}$), [14] (${}^{254}\mathrm{No},{}^{255}\mathrm{Lr}$), [35] (${}^{256}\mathrm{Rf}$), [20] (${}^{257}\mathrm{Db}$), [36] (${}^{259}\mathrm{Sg}$), [21] (${}^{260}\mathrm{Sg}$), [37] (${}^{261}\mathrm{Bh}$), [38] (${}^{264}\mathrm{Hs}$).

Figure 8

Comparison between the experimental production cross sections for (a) ${}^{243}\mathrm{Es}$ obtained in the present paper and the calculations of the $1n,2n$, and $3n$ cross sections performed with the kewpie2 code using the default parameters (macroscopic part described by the Thomas-Fermi parametrization as proposed by Myers-Świątecki [39] and the microscopic part based on the FRDM shell corrections [40]). (b) The same for ${}^{249}\mathrm{Md}$.

Figure 9

Comparison between the experimental production cross sections for ${}^{243}\mathrm{Es}$ extracted in the present paper and the calculations performed with the kewpie2 code considering either an adjustment of +500 keV of the barrier heights or an adjustment of the reduced friction parameter to $\beta =6\times {10}^{21}{\mathrm{s}}^{-1}$.