Unified approach to structure factors and neutrino processes in nucleon matter

Abstract

We present a unified approach to neutrino processes in nucleon matter based on Landau's theory of Fermi liquids that includes one-and two-quasiparticle-quasihole pair states as well as mean-field effects. We show how rates of neutrino processes involving two nucleons may be calculated in terms of the collision integral in the Landau transport equation for quasiparticles. Using a relaxation time approximation, we solve the transport equation for density and spin-density fluctuations and derive a general form for the response functions. We apply our approach to neutral-current processes in neutron matter, where the spin response function is crucial for calculations of neutrino elastic and inelastic scattering, neutrino-pair bremsstrahlung and absorption from strongly-interacting nucleons. We calculate the relaxation rates using modern nuclear interactions and including many-body contributions, and find that rates of neutrino processes are reduced compared with estimates based on the one-pion exchange interaction, which is used in current simulations of core-collapse supernovae.PACS numbers: 97.60. Bw, 26.50.+x, 95.30.Cq, I. INTRODUCTIONNeutrino emission, absorption and scattering processes in nucleon matter play a crucial role for the physics of stellar collapse, supernova explosions and neutron stars [1,2]. Since the leptons in these processes interact weakly, the neutrino rates can be expressed compactly in terms of the response of nuclear matter to axial and vector probes. In many situations, the axial response is the more important, and in this paper we concentrate on this case, which for a system of nonrelativistic nucleons amounts to the spin or spin-isospin response. These responses have been calculated by a number of groups [3,4,5,6,7] allowing for single nucleon quasiparticle-quasihole pair states. 1 However, this is insufficient for rates of neutrino processes involving two nucleons, such as neutrino-pair bremsstrahlung and absorption, and modified Urca reactions, in which two particle-hole pair states are necessary. The possible importance of two particle-hole pair states for neutrino inelastic scattering, in particular for energy exchange and the formation of the neutrino spectra, has been emphasized by Raffelt et al. [8,9,10]. Bounds on the magnitude of the two particle-hole pair weight have been investigated in Ref. [11] and it has been shown how the two-pair response is directly related to the collision term in Landau's transport equation for quasiparticles [12].Noncentral contributions to nuclear interactions, such as tensor forces from pion exchanges and spin-orbit forces, are essential for the two particle-hole pair response, as is clear from calculations of neutrino-pair bremsstrahlung and the modified Urca processes [13] and from general considerations based on conservation laws [11]. Neutrino-pair bremsstrahlung and absorption change the number of neutrinos and are key for equilibrating muon and tau neutrino number densities in supernovae. The standard rates for bremsstrahlung are based on the...

Medium modification of the charged-current neutrino opacity and its implications

“…6) by a Lorentzian with a width Γ = 1/τ . Here, as before z = (q 0 +μ)/T and ∆ǫ p+q = ǫ p+q −ǫ p .The Lorentzian form is obtained in the relaxation time approximation discussed in [7], and is valid when |q 0 |τ ≫ 1.…”

“…This naturally leads to collisional broadening allowing the response to access multi-particle kinematics and alters both the overall shape and magnitude of the response function [5,7]. Here, as a first step, we adapt the general structure of the response function from [7] to show that two-particle excitations play an important role in the charged current process. We include a finite τ through the following ansatz for the imaginary part of the polar-ization function…”

“…At temperatures encountered in PNS cooling, energy-momentum restrictions do not forbid the single-particle interactions, but they do strongly frustrate them due to final state blocking. The excitation of two particle states in neutral current reactions has been included in a unified approach described in [7] and incorporated into the total response function by introducing a finite quasi-particle lifetime τ . This naturally leads to collisional broadening allowing the response to access multi-particle kinematics and alters both the overall shape and magnitude of the response function [5,7].…”

“…The excitation of two particle states in neutral current reactions has been included in a unified approach described in [7] and incorporated into the total response function by introducing a finite quasi-particle lifetime τ . This naturally leads to collisional broadening allowing the response to access multi-particle kinematics and alters both the overall shape and magnitude of the response function [5,7]. Here, as a first step, we adapt the general structure of the response function from [7] to show that two-particle excitations play an important role in the charged current process.…”

“…Matter degeneracy, strong and electromagnetic correlations, and multi-particle excitations have all been shown to be important, especially at supra-nuclear densities [e.g. [1][2][3][4][5][6][7][8][9]. Supernova and protoneutron star (PNS) simulations that employ some subset of these improvements to the free gas neutrino interaction rates have found that these corrections play a role in shaping the temporal and spectral aspects of neutrino emission [4,[10][11][12].…”