Nuclear structure aspects of spin-independent WIMP scattering off xenon

Abstract

We study the structure factors for spin-independent WIMP scattering off xenon based on state-ofthe-art large-scale shell-model calculations, which are shown to yield a good spectroscopic description of all experimentally relevant isotopes. Our results are based on the leading scalar one-body currents only. At this level and for the momentum transfers relevant to direct dark matter detection, the structure factors are in very good agreement with the phenomenological Helm form factors used to give experimental limits for WIMP-nucleon cross sections. In contrast to spin-dependent WIMP scattering, the spin-independent channel, at the one-body level, is less sensitive to nuclear structure details. In addition, we explicitly show that the structure factors for inelastic scattering are suppressed by ∼ 10 −4 compared to the coherent elastic scattering response. This implies that the detection of inelastic scattering will be able to discriminate clearly between spin-independent and spin-dependent scattering. Finally, we provide fits for all calculated structure factors.

Nuclear physics insights for new-physics searches using nuclei: Neutrinolessββdecay and dark matter direct detection

“…The experimental inelastic signature is distinct from the elastic one -the nucleus γ decays to the ground state-and can be realized if the target nuclei has low-lying excited nuclear states, such as the 40 keV and 80 keV first excited states in 129 Xe and 131 Xe [51,52]. For coherent scattering, the inelastic channel is always suppressed by a factor A 2 with respect to the elastic channel [48], making it presently undetectable in practice. Therefore, the observation of an inelastic signal would clearly point out to a spin-dependent interaction.…”

“…A more rigorous estimation is the recent computation of the ββ decay of 48 Ca extending the shell model configuration space from one to two major harmonic oscillator shells -limited to 2 ω excitations-reducing the core of the shell model calculation from 40 Ca to 16 O. By doing so, many previously excluded configurations were permitted, and the dimension of the problem increases from less than 10 6 to over 10 9 .…”

“…This is because at vanishing momentum-transfer, the structure factor of the leading term is F M + = A 2 , simply counting the number of nucleons. The momentum-transfer dependence is given by the nuclear density [48]. In contrast, a careful nuclear structure calculation is needed for spindependent scattering, which is very sensitive to the nuclear spin distribution among all nucleons [49].…”

“…Green squares show interacting boson model (IBM) values [14]. Finally, black bars and circles represent the shell model (SM) results obtained by the Michigan [15] and Strasbourg-Madrid [16] groups, respectively, except for the 48 Ca black circle which shows the recent shell model calculation by the Tokyo group [17]. recent measurement [21], which would bring the shell model prediction into an overestimation of the corresponding matrix element.…”

“…For instance, the shell model and the interacting boson model only solve explicitly the nuclear many-body problem in a limited configuration space around the Fermi surface, and include the effect of the remaining configurations approximately. In order to quantify the effect of the missing correlations, a many-body perturbation theory estimate found relatively moderate increases of less than 50% for the lightest ββ decay emitters 48 Ca, 76 Ge and 82 Se, for which the estimation is easier [27,28].…”