$\beta$ decay of nuclei around ${}^{90}$Se: Search for signatures of a $N=56$ subshell closure relevant to the $r$ process

Background: Nuclear structure plays a significant role on the rapid neutron capture process ($r$ process) since shapes evolve with the emergence of shells and subshells. There was some indication in neighboring nuclei that we might find examples of a new $N=56$ subshell, which may give rise to a doubly magic ${}_{34}^{90}$Se${}_{56}$ nucleus.

Purpose: $\beta$-decay half-lives of nuclei around ${}^{90}$Se have been measured to determine if this nucleus has in fact a doubly magic character.

Method: The fragmentation of a ${}^{136}$Xe beam at the National Superconducting Cyclotron Laboratory at Michigan State University was used to create a cocktail of nuclei in the $A=90$ region.

Results: We have measured the half-lives of 22 nuclei near the $r$-process path in the $A=90$ region. The half-lives of ${}^{88}$As and ${}^{90}$Se have been measured for the first time. The values were compared with theoretical predictions in the search for nuclear-deformation signatures of a $N=56$ subshell, and its possible role in the emergence of a potential doubly magic ${}^{90}$Se. The impact of such hypothesis on the synthesis of heavy nuclei, particularly in the production of Sr, Y, and Zr elements was investigated with a weak $r$-process network.

Conclusions: The new half-lives agree with results obtained from a standard global QRPA model used in $r$-process calculations, indicating that ${}^{90}$Se has a quadrupole shape incompatible with a closed $N=56$ subshell in this region. The impact of the measured ${}^{90}$Se half-life in comparison with a former theoretical predication associated with a spherical half-life on the weak $r$ process is shown to be strong.

Figure 1

Particle-identification (PID) spectrum. The ToF of the transmitted nuclei is shown versus their energy-loss $\Delta E$ in the first Si PIN detector at the experiment station. (See text for details.)

Figure 2

Measured total-kinetic-energy (TKE) distributions for Sr isotopes, including fully stripped, hydrogen-like, and helium-like ions (38${}^{+}$, 37${}^{+}$, and 36${}^{+}$, respectively). (a), (b), and (c) correspond to all nuclei detected with the first Si-stack detector (PIN 1); (d), (e), and (f) depict nuclei that were implanted in the most downstream Si-stack detector (PIN 4); (g), (h), and (i) represent nuclei that were implanted in the doubly sided Si detector (DSSD); and (j), (k), and (l) correspond to all nuclei that punched through the (DSSD) and were implanted in the single-sided Si detector (SSSD).

Figure 3

$\beta$-decay half-lives obtained in this work from the maximum likelihood method for the As, Se, Br, Kr, Rb, Sr, and Y isotopes (filled circles), compared with results from previous experiments [29] (open circles); the latter were shifted slightly in $A$ for visual clarity.

Figure 4

A comparison of the $r$-process abundaces resulting from a simulation using the new measured half-life of ${}^{90}$Se (solid red line) and the value calculated with Möller's QRPA model for a spherical ${}^{90}$Se (blue dashed line). (a) Outputs of both simulations shown against the scaled solar abundances (green thin line) [38]. (b) Relative difference between the two calculated abundance patterns. The $r$-process simulation uses constant temperature conditions with $T=1.43\times {10}^9$ K and initial neutron density of $N_n=5.0\times {10}^{22}$/cm${}^3$. All three curves are normalized to each other at $A=80$.

Figure 5

$\beta$-decay half-lives obtained from the maximum likelihood method for As (a) and Se (b) isotopes (filled dots), compared with results from calculations by Möller et al. QRPA97 [40] (solid black line) and QRPA03 [43] (dashed red line), both of which use the nuclear deformation parameters from FRDM [44]. The dotted blue line corresponds to QRPAsph, which was calculated assuming spherical nuclear shapes. The half-lives measured in previous experiments [29] are shown by open circles. (See text for details.)