Gamow-Teller transitions from 24Mg and its impact on the electron capture rates in the O + Ne + Mg cores of stars

Electron captures on nuclei play an important role in the collapse of stellar core in the stages leading to a type-II supernova. Recent observations of subluminous Type II-P supernovae (e.g. 2005cs, 2003gd, 1999br) were able to rekindle the interest in 8 - 10 which develop O+Ne+Mg cores. We used the proton-neutron quasiparticle random phase approximation (pn-QRPA) theory to calculate the B(GT) strength for 24Mg \rightarrow 24Na and its associated electron capture rates for incorporation in simulation calculations. The calculated rates, in this letter, have differences with the earlier reported shell model and Fuller, Fowler, Newman (hereafter F2N) rates. We compared Gamow-Teller strength distribution functions and found fairly good agreement with experiment and shell model. However, the GT centroid and the total GT strength, which are useful in the calculation of electron capture rates in the core of massive pre-supernova stars, lead to the enhancement of our rate up to a factor of four compared to the shell model rates at high temperatures and densities.

💡 Research Summary

The paper investigates the Gamow‑Teller (GT) transition strength for the reaction 24Mg → 24Na and the resulting electron‑capture rates under conditions relevant to the O+Ne+Mg cores of 8–10 M⊙ stars approaching core collapse. Electron captures on nuclei are a key driver of the deleptonization and entropy reduction that precede a Type‑II supernova, and the rate of capture is highly sensitive to the distribution, centroid, and total strength of GT + transitions (proton → neutron). Earlier compilations, notably the Fuller‑Fowler‑Newman (F²N) tables and shell‑model calculations (e.g., Oda et al., Takahara et al.), either relied on sparse experimental data or assumed a fixed log ft = 5.0 for unknown transitions. These approximations can underestimate the capture rates, especially at the high densities (ρ ≈ 10¹¹ g cm⁻³) and temperatures (T ≈ 10⁹–10¹⁰ K) encountered just before bounce.

To improve upon these limitations, the authors employ the proton‑neutron quasiparticle random‑phase approximation (pn‑QRPA). Single‑particle energies and wave functions are generated with the Nilsson model, incorporating nuclear deformation. The residual interactions are treated in both particle‑hole (ph) and particle‑particle (pp) channels, with coupling constants χ = 0.001 MeV and κ = 0.05 MeV for 24Mg. A large model space (7 ħω) is used, covering 136 excited states of 24Mg up to ~40 MeV and, for each parent state, 100 daughter states in 24Na. Experimental level information is substituted whenever the calculated excitation energy lies within 0.5 MeV of a known level; missing states are added, and mirror/inverse transitions are accounted for. A standard quenching factor of 0.77 is applied to the GT matrix elements.

The resulting GT strength distribution shows a prominent peak at 0.97 MeV in the daughter nucleus, consistent with (p,n), (d,²He) and (³He,t) measurements. The total B(GT) summed up to 7 MeV is 2.65, lying between the shell‑model value (≈ 2.1) and the experimentally extracted value (≈ 1.36). The Ikeda sum rule is satisfied, confirming the internal consistency of the calculation.

Electron‑capture rates λₑ are computed using the standard β‑decay formalism λ = (ln 2) · f · B(GT)/ft, where the phase‑space integral f₍ᵢⱼ₎ is evaluated for each transition at the relevant temperature and density. At low densities (ρ ≤ 10⁷ g cm⁻³) and temperatures (T ≤ 10⁸ K) the QRPA rates agree well with shell‑model results. However, as the core contracts to ρ ≈ 10¹¹ g cm⁻³, the QRPA rates become significantly larger—by factors of 3.7 to 4 at T ≈ 10⁹ K—because the total GT strength in the QRPA calculation exceeds that of the shell model. This enhancement is independent of the detailed distribution of strength; at such high electron Fermi energies the capture rate is governed primarily by the integrated GT strength. The authors also note that they do not invoke Brink’s hypothesis, which is often used in large‑scale shell‑model rate tables, thereby preserving the temperature dependence of the strength distribution.

When compared with the classic F²N rates, the QRPA rates are higher in the low‑density regime (where F²N’s fixed log ft = 5.0 underestimates the strength) and comparable or modestly higher at the highest densities, again reflecting the larger total GT strength.

Astrophysically, the enhanced electron‑capture rates imply a more rapid reduction of the electron fraction Yₑ and a lower entropy in the O+Ne+Mg core during the final stages of stellar evolution. Recent simulations (e.g., Kitaura et al. 2006) that employed the older Takahara/Oda shell‑model rates found only delayed explosions, partly because the reduced capture slowed the collapse and kept the shock radius large. Incorporating the QRPA rates could lead to a smaller Yₑ, a more compact core, and potentially a stronger bounce shock, thereby affecting the likelihood of prompt versus delayed explosions. Moreover, the altered Yₑ and entropy trajectories would influence nucleosynthesis pathways, including low‑entropy r‑process scenarios that have been proposed for such progenitors.

In summary, the paper provides a comprehensive QRPA‑based calculation of GT strength and electron‑capture rates for 24Mg, demonstrates significant differences from previous shell‑model and F²N rates at supernova‑relevant conditions, and highlights the importance of updating weak‑interaction rate libraries in stellar evolution and core‑collapse supernova models.