Theoretical estimates of supernova-neutrino cross sections for the stable even-even lead isotopes: Charged-current reactions

A detailed study of the charged-current supernova electron neutrino and electron antineutrino scattering off the stable even-mass lead isotopes $A=204$, 206, and 208 is reported in this work. The proton-neutron quasiparticle random-phase approximation (pnQRPA) is adopted to construct the nuclear final and initial states. Three different Skyrme interactions are tested for their isospin and spin-isospin properties and then applied to produce (anti)neutrino-nucleus scattering cross sections for (anti)neutrino energies below 80 MeV. Realistic estimates of the nuclear responses to supernova (anti)neutrinos are computed by folding the computed cross sections with a two-parameter Fermi-Dirac distribution of the electron (anti)neutrino energies. The computed cross sections are compared with earlier calculations and the analyses are extended to take into account the effects coming from the neutrino oscillations.

Figure 1

Cumulative ${\beta }^{-}$ (a) and ${\beta }^{+}$ (b) strengths for Gamow-Teller transitions from ${}^{208}\mathrm{Pb}$ to states in ${}^{208}\mathrm{Bi}$ and ${}^{208}\mathrm{Tl}$ computed using the three interactions. Flanders 1989 refers to Ref. [39].

Figure 2

Comparison of the computed total CC neutrino cross sections as functions of the energy of the incoming neutrino for ${}^{208}\mathrm{Pb}$. The upper panel (a) is a magnification of the low-energy region of the lower panel (b). In this figure Lazauskas 2007 refers to Ref. [25] and Kolbe 2001 refers to Ref. [24]

Figure 3

Comparison of the computed total CC antineutrino cross sections as functions of the energy of the incoming antineutrino for ${}^{208}\mathrm{Pb}$. The upper panel (a) is a magnification of the low-energy region of the lower panel (b). Lazauskas 2007: Ref. [25].

Figure 4

Cumulative sums of the averaged cross section for the neutrino (a) and antineutrino (b) scattering off ${}^{208}\mathrm{Pb}$ computed using the three considerd Skyrme interactions. The (anti)neutrino parameters are $(T,\alpha )=(4,3)$. The pairing strength is $G_n$.

Figure 5

Comparison between our averaged cross sections and those of Kolbe 2001, i.e., Ref. [24], for the charged-current neutrino (a) and antineutrino (b) scattering off ${}^{208}\mathrm{Pb}$.

Figure 6

Contributions of the various multipole channels to the averaged cross sections of the antineutrino (a) and neutrino (b) scattering off ${}^{208}\mathrm{Pb}$. The folding parameters in these plots are $(T,\alpha )=(4,3)$ and the pairing strength is $G_n$.

Figure 7

Contributions from the final nuclear states to the normalized averaged differential cross sections for the neutrino [panels (a)–(c)] and antineutrino [panels (d)–(f)] scattering off lead isotopes for the SkX interaction. The (anti)neutrino parameters are $T=4$ and $\alpha =3$, and the pairing strength is $G_n$.

Figure 8

Computed averaged neutrino-scattering cross sections for the different lead isotopes [panels (a)-(c)] without neutrino oscillations (${\nu }_e$) and with neutrino oscillations for the normal hierarchy (${\nu }_{\mathrm{ex}}^{\mathrm{NH}}$) and inverted hierarchy (${\nu }_{\mathrm{ex}}^{\mathrm{IH}}$). Results corresponding to the supernova model (I) of Table 13 for the three adopted Skyrme interactions are shown by vertical bars..

Figure 9

The same as Fig. 8 for the computed averaged antineutrino-scattering cross sections.