Reduction of neutrino - nucleon scattering rate by nucleon - nucleon collisions

The collapse-driven supernova is supposed to be an outcome of gravitational collapse of a massive star ∼ 8M at the end of its evolution. Although more than 60 years have passed since the original idea by Baade and Zwicky [1,2], and the detection of neutrinos from SN1987A [3,4] confirmed that our scenario is correct on the whole, we have not yet figured out how this phenomenon occurs. These days many researchers of the supernova consider that neutrinos diffusing out of the proto neutron star play a crucial role in heating the material behind the shock wave and expelling the outer layer of the star [5,6]. It turned out, however, that this mechanism is quite sensitive to the neutrino luminosity [7,8]. In fact, Janka and Müller [8] showed by numerical simulations that only about 20% of increase in neutrino luminosity could lead to a successful explosion of a model which otherwise failed to explode. Hence mechanisms to boost the neutrino luminosity have been quested. Although many authors have been devoted in the study of convection in the core and it has been shown that the convection does help neutrinos heat matter, it is still controversial if the convection alone is sufficient for successful explosion or not [8–12]. It is also found that the sophistication of the numerical treatment of neutrino transport could increase the neutrino luminosity although the quantitative assessment of the difference it makes in the realistic context remains to be done [13–15]. On the other hand, our knowledge of the neutrino reaction rates in the hot dense medium is rather poor. In fact, even in the most elaborate simulations of supernovae it has been assumed that the reactions of neutrinos with nucleons are the same as in vacuum and the effect of surrounding matter is ignored [16–19]. However, the wavelength of a 30MeV neutrino, for example, is longer than the mean separation of nucleons for the density ∼ 10g/cm, and the time scale corresponding to the same energy is roughly of the same order as the mean free time of nucleon between collisions. Hence we have to study the spatial and temporal correlations of the matter, and it could be possible that the many body effects change the opacity for neutrinos considerably and we get the desired enhancement of neutrino luminosity and/or energy. In fact, efforts to find a possible modification of rates of neutrino reactions with nucleons have been made by several authors [20–31]. In these studies neutrino nucleon scatterings are one of the targets, since it is one of the major sources of opacity for neutrinos. Reddy et al. [29,30] pointed out that taking a correct effective mass of nucleon into account changes the scattering rate in the high density regime ∼ ρ0 which is the saturation density. Horowitz et al. [22], Burrows et al. [27,28], Reddy et al. [29,30] and Yamada et al. [31] discussed the correlation effects due to the particle hole excitation using a random phase approximation (RPA). In these studies the nucleons were assumed to be quasi-particles with the vanishing width of the spectral functions. On the other hand, Raffelt and his collaborators [24–26] claimed that the neutrino scattering rate could be also reduced by losing the temporal correlations of the spins of nucleon, thus broadening the width of the structure function due to collisions of the nucleon with other nucleons surrounding it (see also [23]). This is a counter part for scattering of the so-called Landau-Pomeranchuk-Migdal effect [32–34] for the bremsstrahlung. It was also pointed out that this