Neutrino-pair emission from hot nuclei during stellar collapse

We present shell-model calculations showing that residual interaction-induced configuration mixing enhances the rate of neutral current de-excitation of thermally excited nuclei into neutrino-antineutrino pairs. Though our calculations reinforce the conclusions of previous studies that this process is the dominant source of neutrino pairs near the onset of neutrino trapping during stellar collapse, our shell-model result has the effect of increasing the energy of these pairs, possibly altering their role in entropy transport in supernovae.

Figure 1

Neutral current neutrino pair emission from an excited nucleus $A^{*}$.

Figure 2

Thermally populated nuclear state with excitation energy $E_i$ de-excites via virtual $Z^0$ emission to a final state with excitation energy $E_f$.

Figure 3

Neutrino-pair emission transition strength for ${}^{28}$Si (averaged over 12 initial states), ${}^{47}$Ti (two initial states), and ${}^{56}$Fe (three initial states) at 27.6 MeV initial excitation shown as functions of the difference between initial excitation energy $E_i$ and final excitation energy $E_f$.

Figure 4

Energy loss by neutrino-pair emission per nucleon for ${}^{28}$Si, ${}^{47}$Ti, and ${}^{56}$Fe shown as functions of excitation energy.

Figure 5

Energy loss by neutrino-pair emission per nucleon for ${}^{28}$Si, ${}^{47}$Ti, and ${}^{56}$Fe shown as functions of temperature. The “rescaled” line shows the ${}^{28}$Si result with the temperature scaled by a factor of ${\left(\frac{28}{56}\right)}^{1/2}$, allowing the ${}^{28}$Si and ${}^{56}$Fe results to be compared directly, as in Fig. 4.

Figure 6

Both panels: lower line corresponds to 20 MeV excitation, middle line is 30 MeV, and upper line is 40 MeV. Bottom: Transition strengths for ${}^{28}$Si as functions of transition energy. Top: Energy emission rates per nucleon via neutrino pairs for ${}^{28}$Si as functions of transition energy.

Figure 7

${}^{28}$Si strength and neutrino pair energy emission rate at 30 MeV excitation computed with spin-orbit splitting in the nuclear Hamiltonian set to zero. The strong central peak, lack of wings, and concomitant drastic reduction in neutrino production confirm the role of spin-orbit splitting and spin-flip transitions in producing the high rates computed in our more realistic models.

Figure 8

${}^{56}$Fe at $T=2$ MeV computed using an independent single particle model similar to that used in Fuller and Meyer (1991) [1]. Top: Transition strength. Bottom: Neutrino-pair energy emission rate per nucleon.

Figure 9

Computed density of states as a function of excitation energy for ${}^{28}$Si. Upper line: negative-parity states. Lower line: positive-parity states.

Figure 10

Energy per baryon per second emitted in neutrino pairs as a function of temperature. (a) ${}^{28}$Si as computed in this paper. (b) ${}^{56}$Fe from Fuller and Meyer independent single-particle shell-model calculation [1]. (c) ${}^{56}$Fe from Fuller and Meyer analytic approximation [1]. (d) ${}^{56}$Fe from Kolb and Mazurek [2]. (e) Electron bremsstrahlung into neutrino pairs for ${\rho }_{12}=1$ from Dicus et al. [23]. (f) Nucleon bremsstrahlung into neutrino pairs at nuclear matter density from Friman and Maxwell [53].