Gravitational-Wave Stochastic Background Detection with Resonant-Mass Detectors

In this paper we discuss how the standard optimal Wiener filter theory can be applied, within a linear approximation, to the detection of an isotropic stochastic gravitational-wave background with two or more detectors. We apply then the method to the AURIGA-NAUTILUS pair of ultra low temperature bar detectors, near to operate in coincidence in Italy, obtaining an estimate for the sensitivity to the background spectral density of $\simeq 10^{-49}
Hz^{-1}$,thatconvertstoanenergydensityperunitlogarithmicfrequencyof$\simeq 8\times10^{-5}\times\rho_c$with$\rho_c\simeq1.9 \times 10^{-26}
kg/m^3$ the closure density of the Universe. We also show that by adding the VIRGO interferometric detector under construction in Italy to the array, and by properly re- orienting the detectors, one can reach a sensitivity of $\simeq 6 \times10^{-5}\times\rho_c$. We then calculate that the pair formed by VIRGO and one large mass spherical detector properly located in one of the nearby available sites in Italy can reah a sensitivity of $\simeq 2\times10^{-5}\times \rho_c$ while a pair of such spherical detectors at the same sites of AURIGA and NAUTILUS can achieve sensitivities of $\simeq 2\times {10}^{-6}{\rho }_c$.