Exploring the mass surface near the rare-earth abundance peak via precision mass measurements at JYFLTRAP

The JYFLTRAP double Penning trap at the Ion Guide Isotope Separator On-Line facility has been used to measure the atomic masses of 13 neutron-rich rare-earth isotopes. Eight of the nuclides, ${}^{161}\mathrm{Pm}, {}^{163}\mathrm{Sm}, {}^{164,165}\mathrm{Eu}, {}^{167}\mathrm{Gd}$, and ${}^{165,167,168}\mathrm{Tb}$, were measured for the first time. The systematics of the mass surface has been studied via one- and two-neutron separation energies as well as neutron pairing-gap and shell-gap energies. The proton-neutron pairing strength has also been investigated. The impact of the new mass values on the astrophysical rapid neutron capture process has been studied. The calculated abundance distribution results in a better agreement with the solar abundance pattern near the top of the rare-earth abundance peak at around $A\approx 165$.

Figure 1

Experimental excitation energies of the first $2^{+}$ states (solid lines) together with the ratio of the first $4^{+}$ and $2^{+}$ states (dashed lines). The inset shows a peak in $2^{+}$ energies at $N=100$. The energies have been adopted from ENSDF [25] and [6].

Figure 2

The $r$-process impact factors $F$ of masses in the region of interest [23]. Mass measurements from this work are circled in red, while black circles indicate those from an earlier study at JYFLTRAP [26]. In total, 22 ground-state masses and two isomeric states in this region have been measured at JYFLTRAP, of which 14 go beyond the limit of known nuclei in AME16 [21]. For experimental AME16 values, the mass-excess uncertainties have been indicated.

Figure 3

Time-of-flight spectrum for ${}^{165}\mathrm{Eu}{}^{+}$ using a $25-350-25\mathrm{ms}$ (On-Off-On) Ramsey-type excitation pattern. Background shading indicates the total number of ions, where darker shading indicates more ions. The red line is a fit of the lineshape to the data points (in black).

Figure 4

Projection of cyclotron motion of ${}^{162}\mathrm{Eu}^{+}$ ions on the position-sensitive detector detector using the PI-ICR technique. Two detected ion spots correspond to the ground and isomeric state of ${}^{162}\mathrm{Eu}$. In the middle figure background shading indicates the total number of ions, where darker shading indicates more ions. Center point of the two states and the center of the precision trap are marked as red dots. Figures on the left and bottom present projections of the middle figure onto the $Y$ and $X$ axes, respectively.

Figure 5

Measured frequency ratios $r={\nu }_c\left({}^{136}\mathrm{Xe}^{+}\right)/{\nu }_c\left({}^{165}\mathrm{Tb}^{+}\right)$ for ${}^{165}\mathrm{Tb}$ (black data points) together with the weighted mean (solid red line) and its error band (dashed blue lines). The Birge ratio for ${}^{165}\mathrm{Tb}$ measurements was 1.05.

Figure 6

Comparison to AME16 mass-excess values for each measured nuclide. The results from CPT [9, 29, 30] are also shown. The values for the isomeric states were adopted from NUBASE16 [59].

Figure 7

Time-of-flight spectra for ${}^{162}\mathrm{Eu}^{+}$ from campaign I using $25–350–25\mathrm{ms}$ (on-off-on) excitation pattern (top), and from this work with a 1600 ms excitation (bottom). Fitted theoretical line shapes and ${\nu }_c$ frequencies are plotted in red.

Figure 8

Experimental neutron separation energies, $S_n$, from AME16 [21] (in black), and supplemented with the JYFLTRAP results from Ref. [26] and this work (in red). Each isotopic chain has been shifted by $0.5\mathrm{MeV}$ relative to the previous chain for clarity, with the Nd chain remaining unchanged.

Figure 9

Experimental neutron separation energies $S_n$ compared to the FRDM12 mass model. The $S_n$ values affected by the JYFLTRAP measurements of this work and Ref. [26] are shown in red and AME16 values in blue. Dashed line indicates energies from FRDM12.

Figure 10

Pairing-gap energies $D_n$ for even-$N$ (left) and odd-$N$ (right) isotopes of the studied isotopic chains based on the experimental AME16 [21] mass values (dashed lines, open symbols) and the JYFLTRAP measurements from this work and [26] (solid thick lines, full symbols). The dotted lines present $D_n$ for $Z=60$, 62 and 64 based on the average parametrization of the pairing gap energy $\mathrm{\Delta }\approx 12/\sqrt{A}$ MeV [80]. Note the different scales for even and odd $N$.

Figure 11

Differences in pairing-gap energies, $D_n$, between the experimental values taken from AME16 [21] (dashed lines, open symbols) and the JYFLTRAP measurements from this work and [26] (thick solid lines, full symbols), and the FRDM12 mass model [82] (baseline). JYFLTRAP measurements extend the AME16 trend in showing that FRDM12 consistently over-estimates the effect of pairing for neutron-rich nuclei.

Figure 12

Two-neutron separation energies, $S_{2n}$, based on the AME16 [21] experimental mass values (in black) and the JYFLTRAP mass measurements from this work and Ref. [26] (in red).

Figure 13

$D_{2n}$ values based on the AME16 [21] experimental mass values (dashed lines and open symbols) and the JYFLTRAP mass measurements from this work and Ref. [26] (thick solid lines and full symbols). No subshell at $N=100$ is apparent but two peculiar peaks appear at $N=93$ and $N=97$.

Figure 14

Experimental $D_{2n}$ values for the Tb isotopic chain, based on AME16 [21] (in blue) and the JYFLTRAP measurements from this work and Ref. [26] (in red), and comparison to various commonly used mass models, such as Duflo-Zuker (D-Z) [72], FRDM12 [22], HFB24 [71], UNEDF0 [84], WS3 [73], $\mathrm{WS}3+$ [74], WS4 [75], and $\mathrm{WS}4+$ [75]. None of these models predict the enhancement seen at $N=97$.

Figure 15

A measure of the average $p-n$ interaction of valence nucleons in odd-odd nuclei according to Eq. (9). Calculations were done using the experimental mass values from AME16 [21] (dashed lines and open symbols) and supplemented by the JYFLTRAP measurements from this work and Ref. [26] (solid lines and full symbols).

Figure 16

Odd-odd $\delta V_{pn}$ values (in MeV) for $80\le N\le 126$ and $50\le Z\le 82$ according to Eq. (9). Values affected by JYFLTRAP measurements are circled, and black lines indicate $Z_{\text{val}}=N_{\text{val}}$ (solid) and equal fractions of the $N$ and $Z$ shells filled (dashed).

Figure 17

Top: Solar $r$-process abundances $Y$ as a function of the mass number $A$ (black data points) together with the calculated abundances using the AME16 [21] and FRDM12 [82] mass-excess values (purple), and with the addition of the values from the first experimental campaign at JYFLTRAP (green) [26], and with the masses from this work (red). Middle: Change (in %) between the calculated abundances from this work and from the previous JYFLTRAP experiment [26]. Bottom: Residuals based on the mass values from this work (red) and the baseline (purple), where the bands represent the solar abundance uncertainties.