Impact of complex many-body correlations on electron capture in thermally excited nuclei around ${}^{78}\mathrm{Ni}$

We link complex many-body correlations, which play a decisive role in the structural properties of atomic nuclei, to the electron capture occurring during star evolution. The recently developed finite-temperature response theory, taking into account the coupling between single-nucleon and collective degrees of freedom, is applied to spin-isospin transitions, which dominate the electron capture rates. Calculations are performed for ${}^{78}\mathrm{Ni}$ and for the surrounding even-even nuclei associated with a high-sensitivity region of the nuclear chart in the context of core-collapse supernova simulations. The obtained electron capture rates are compared to those of a simpler thermal quasiparticle random phase approximation (TQRPA), which is standardly used in such computations. The comparison indicates that correlations beyond TQRPA lead to significantly higher electron capture rates under the typical thermodynamical conditions.

Figure 1

Evolution of the Gamow-Teller ${\mathrm{GT}}_{+}$ spectrum in ${}^{78}\mathrm{Ni}$ with temperature within FT-pnRRPA and FT-pnRTBA.

Figure 2

Evolution of the Gamow-Teller ${\mathrm{GT}}_{+}$ spectrum in ${}^{76}\mathrm{Ni}$ with temperature. The legends “FT-pnR(Q)RPA” and “FT-pnR(Q)TBA” denote calculations with the superfluid pairing at $T=0$ and without it at $T\ge 1\mathrm{MeV}$, when the BCS superfluidity vanishes. The upper panel shows a comparison of the approaches with (FT-pnRQRPA, FT-pnRQTBA, solid curves) and without (FT-pnRRPA, FT-pnRTBA, dashed curves) superfluid pairing at $T=0$.

Figure 3

Same as in Fig. 2, but for ${}^{80}\mathrm{Ni}$.

Figure 4

Same as in Fig. 2, but for ${}^{76}\mathrm{Fe}$.

Figure 5

Same as in Fig. 2, but for ${}^{80}\mathrm{Zn}$.

Figure 6

Electron capture rate as a function of temperature for neutron-rich even-even nuclei around ${}^{78}\mathrm{Ni}$ at $\lg \left(\rho Y_e\right)=9$.

Figure 7

Same as in Fig. 6, but at $\lg \left(\rho Y_e\right)=11$.

Figure 8

Electron capture rate as a function of electron density for neutron-rich even-even nuclei around ${}^{78}\mathrm{Ni}$ at $T=1.5\mathrm{MeV}$.

Figure 9

(Left panel) Gamow-Teller ${\mathrm{GT}}_{+}$ transitions in ${}^{78}\mathrm{Ni}$ computed within pnRRPA (blue curve) and beyond it taking into account the PVC mechanisms: without (pnRTBA, red curve) and with ($\mathrm{pnRTBA}+{\mathrm{GSC}}_{\text{PVC}}$, light green curve) ground-state correlations induced by PVC. (Right panel) Electron capture rate at $T=1\mathrm{MeV}$ as a function of electron density for ${}^{78}\mathrm{Ni}$ within the respective approximations (temperature dependence of the ${\mathrm{GT}}_{+}$ strength functions is neglected).