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Nuclear Urca processes play important roles in the cooling of stars. Electron-capture and $\beta$- decay rates of the nuclear pairs, $^{25}$Mg-$^{25}$Na and $^{23}$Na-$^{23}$Ne, were evaluated by the shell model, and successfully applied to the cooling of O-Ne-Mg cores of stars with M$_{\odot}$ [1]. The Urca processes were shown to induce the cooling of neutron star (NS) crusts [2], where the weak rates were evaluated using the QRPA. The shell model was used to evaluate the weak rates of the $^{31}$Al-$^{31}$Mg pair [3-5], which is important for the cooling of NS crusts.
Recently, an indication of the possible existence of nuclear Urca processes in the NS ocean was obtained from the observation of superburst MAXI J1752-457 [6]. Here, we evaluate the weak rates of Urca pairs in the $sd$- and $pf$-shells, relevant to the cooling of the NS ocean [2,7] by the shell model in stellar environments, including screening effects. The nuclear pairs with $A$ =25 and 23 in the $sd$-shell are evaluated with the USDB [8], while those in the $pf$-shell, $^{57}$Mn-$^{57}$Cr, $^{63}$Ni$^{\ast}$-$^{63}$Co, $^{57}$Fe$^{\ast}$-$^{57}$Mn, $^{55}$Mn-$^{55}$Cr, $^{65}$Cu-$^{65}$Ni, $^{49}$Ti-$^{49}$Sc, and $^{67}$Cu-$^{67}$Ni, are evaluated with the GXPF1J [9]. Experimental B(GT) and energies are used as far as they are available.
The cooling strengths, L$_{34}$, [4,5,7] are evaluated by taking into account the calculated and experimental rates and energies, effective Q values obtained with the inclusion of the screening effects, and Coulomb distortion corrections. While dominant contributions to L$_{34}$ come from transitions between the ground states, when the g.s. to g.s. transition is forbidden, the contribution from the transition from (to) excited states becomes important. L$_{34}$ values increase with temperature due to contributions from transitions involving excited states. When there are forbidden transitions between low-lying states with low excitation energies, L$_{34}$ decreases. Compared to the estimates in Ref. [7], the L$_{34}$ values are found to be enhanced by a few to several times. A comparison of the L$_{34}$ values for the $^{25}$Mg-$^{25}$Na pair is also made to those in Ref. [5]. An evaluation of L$_{34}$ for the nuclear pairs in the $pfg$-shell, $^{69}$Zn-$^{69}$Cu, $^{73}$Ga-$^{73}$Zn, $^{79}$As-$^{79}$Ge, $^{81}$Se-$^{81}$As, and $^{81}$Br-$^{81}$Se, is now under way.
[1] H. Toki, T. Suzuki, K. Nomoto, S. Jones, and R. Hirschi. PRC 88, 015806 (2013);
T. Suzuki, H. Toki, and K. Nomoto, Astrophys. J. 817, 163 (2016).
[2] H. Schatz et al., Nature 505, 62 (2014).
[3] T. Suzuki and N. Shimizu, Frontiers in Physics 12, 1434598 (2024).
[4] S. Sharma, P. C. Srivastava, and T. Suzuki, Phys. Rev. C 112, 015806 (2025).
[5] L. J. Wang et al., Phys. Rev. Lett. 127, 172702 (2021).
[6] H. Huang, A. Dohi, A. Aoyama, T. Takeda, and N. Nishimura, arXiv:2602.19018 (2026).
[7] A. Deibel, Z. Meisel, H. Schatz, E. F. Brown, and A. Cumming, Astrophys. J. 831, 13 (2016).
[8] W. A. Richter, S. S. Mkhize and B. A. Brown, Phys. Rev. C 78, 064302 (2008).
[9] M. Honma, T. Otsuka, T. Mizusaki, M. Hjorth-Jensen, and B. A. Brown, J. Phys.: Conf. Ser. 20, 7 (2005); M. Honma et al., Phys. Rev. C 65, 061301(R) (2002); 69, 034335 (2004).
| Category | Theory |
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