Nuclear spin structure in dark matter search: The finite momentum transfer limit

Abstract

Spin-dependent elastic scattering of weakly interacting massive dark matter particles (WIMP) off nuclei is reviewed. All available, within different nuclear models, structure functions S(q) for finite momentum transfer (q>0) are presented. These functions describe the recoil energy dependence of the differential event rate due to the spin-dependent WIMP-nucleon interactions. This paper, together with the previous paper ``Nuclear spin structure in dark matter search: The zero momentum transfer limit'', completes our review of the nuclear spin structure calculations involved in the problem of direct dark matter search.

Figures (12)

• Figure 1: Structure functions $S^{19}_{00}$ (bottom), $S^{19}_{11}$ (middle), and $S^{19}_{01}$ (top) for $^{18}$F as a function of the recoil energy $E = u b^{-2}/ M_A$ in keV calculated by (\ref{['SF-F19-pi']}). With $v_{\max} \approx 600(700)$ km/s for the $^{18}$F target one has $E_{\max} \approx 140(190)$ keV.
• Figure 2: Spin structure functions for $^{23}$Na $S^{23}_{00}$ (middle), $S^{23}_{11}$ (bottom), and $S^{23}_{01}$ (top) versus the recoil energy. Left: $S^{23}_{ij}$ approximations from Ressell and Dean Ressell:1997kx in accordance with (\ref{['Nuclear.spin.Na-23']}). Right: $S^{23}_{ij}$ from Vergados et al. Divari:2000dc following (\ref{['SF-Na23']}). With $v_{\max} \approx 700$ km/s for $^{23}$Na target one has $E_{\max} \approx 230$ keV.
• Figure 3: Structure functions $S^{27}_{00}$ (middle), $S^{27}_{11}$ (bottom), and $S^{27}_{01}$ (top) for $^{27}$Al as a function of the recoil energy calculated by (\ref{['Nuclear.spin.AL-27']}). For $^{27}$Al and the WIMP maximal velocity of 700 km/s the maximum momentum transfer is $q_{\max} \approx 117$ MeV and $E_{\max} \approx 270$ keV.
• Figure 4: Spin structure functions $S^{29}_{00}$ (top) $S^{29}_{11}$ (middle), and $S^{29}_{01}$ (bottom) for $^{29}$Si as a function of the recoil energy. Left: results of Ressell et al. Ressell:1993qm. Right: these structure functions from Vergados et al. Divari:2000dc following equations (\ref{['SF-Si29-pi']}). With $v_{\max} \approx 700$ km/s, for $^{29}$Si target one has $E_{\max} \approx 290$ keV.
• Figure 5: $^{39}$K spin structure functions $S^{39}_{00}$ (top), $S^{39}_{11}$ (middle), and $S^{39}_{01}$ (bottom) versus the recoil energy, calculated by (\ref{['SF-39K']}) from Engel, Ressell, Towner and Ormand Engel:1995gw. With $v_{\max}=700$ km/s, for $^{39}$K one has $q_{\max} = 169$ MeV, $E_{\max} = 390$ keV.