Nucleosynthesis of ${}^{92}\text{Nb}$ and the relevance of the low-lying isomer at 135.5 keV

Background: Because of its half-life of about 35 million years, ${}^{92}\text{Nb}$ is considered as a chronometer for nucleosynthesis events prior to the birth of our sun. The abundance of ${}^{92}\text{Nb}$ in the early solar system can be derived from meteoritic data. It has to be compared to theoretical estimates for the production of ${}^{92}\text{Nb}$ to determine the time between the last nucleosynthesis event before the formation of the early solar system.

Purpose: The influence of a low-lying short-lived isomer on the nucleosynthesis of ${}^{92}\text{Nb}$ is analyzed. The thermal coupling between the ground state and the isomer via so-called intermediate states affects the production and survival of ${}^{92}\text{Nb}$.

Method: The properties of the lowest intermediate state in ${}^{92}\text{Nb}$ are known from experiment. From the lifetime of the intermediate state and from its decay branchings, the transition rate from the ground state to the isomer and the effective half-life of ${}^{92}\text{Nb}$ are calculated as functions of the temperature.

Results: The coupling between the ground state and the isomer is strong. This leads to thermalization of ground state and isomer in the nucleosynthesis of ${}^{92}\text{Nb}$ in any explosive production scenario and almost 100% survival of ${}^{92}\text{Nb}$ in its ground state. However, the strong coupling leads to a temperature-dependent effective half-life of ${}^{92}\text{Nb}$ which makes the ${}^{92}\text{Nb}$ survival very sensitive to temperatures as low as about 8 keV, thus turning ${}^{92}\text{Nb}$ at least partly into a thermometer.

Conclusions: The low-lying isomer in ${}^{92}\text{Nb}$ does not affect the production of ${}^{92}\text{Nb}$ in explosive scenarios. In retrospect this validates all previous studies where the isomer was not taken into account. However, the dramatic reduction of the effective half-life at temperatures below 10 keV may affect the survival of ${}^{92}\text{Nb}$ after its synthesis in supernovae, which are the most likely astrophysical sites for the nucleosynthesis of ${}^{92}\text{Nb}$.

Figure 1

Partial level scheme of ${}^{92}\text{Nb}$ (approximately to scale; from Ref. [1]). The IMS with $J^{\pi }=4^{+}$ at $E^{*}=480.3\text{keV}$ is marked by a bold horizontal line. Primary decays from the IMS are shown with full arrows; secondary $\gamma$ rays are shown with dashed arrows. Except for the ground state, the spin assignments are only tentative but very probable, according to a comment in Ref. [1]. Therefore, the parentheses in the tentative ${\left(J\right)}^{\pi }$ assignments are omitted in this work. The influence of $J^{\pi }$ assignments on the results of this work is restricted to statistical weights and thus remains limited when compared to the dominating Boltzmann factors.

Figure 2

Stellar transition rate ${\lambda }^{*}$ for the transition from the $7^{+}$ ground state to the $2^{+}$ isomer via the $4^{+}$ IMS in ${}^{92}\text{Nb}$. The horizontal line at ${\lambda }^{*}=1.0/\mathrm{s}$ marks the typical time scale of supernova explosions.

Figure 3

Effective half-life $t_{1/2}^{\mathrm{eff}}$ of ${}^{92}\text{Nb}$ as a function of temperature. The inset shows the dramatic decrease of the effective half-life around $kT\approx 8\text{keV}$ and the nuclear uncertainties of a 20% increased or decreased coupling (dashed lines). An upper limit from ${\beta }^{+}$ decay (without electron capture) is shown as dotted line. The dash-dotted line represents an intermediate plasma density of $n_e=5\times {10}^{26}/{\mathrm{cm}}^3$. For further discussion, see text.