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We analyze particular two-photon processes as possible means to exploreelectronic quadrupole states in free small deformed atomic clusters. Theanalysis is done in the time-dependent local density approximation (TDLDA). Itis shown that the direct two-photon population (DTP) and off-resonantstimulated Raman (ORSR) scattering can be effectively used for excitation ofthe quadrupole states in high-frequency (quadrupole plasmon) and low-frequency(infrared) regions, respectively. In ORSR, isolated dipole particle-hole statesas well as the tail of the dipole plasmon can serve as an intermediate state. Asimultaneous study of low- and high-frequency quadrupoles, combining DTP andORSR, is most effective. Femtosecond pulses with intensities $I = 2\cdot10^{10} - 2\cdot 10^{11} W/cm^2$ and pulse durations $T = 200 - 500$ fs arefound to be optimal. Since the low-lying quadrupole states are dominated by onesingle electron-hole pair, their energies, being combined with thephotoelectron data for hole states, allow to get the electron spectrum abovethe Fermi level and thus greatly extend our knowledge on the single particlespectra of clusters. Besides, the developed schemes allow to estimate thelifetime of the quadrupole states.Comment: 18 pages, 7 figure

Exploration of electronic quadrupole states in atomic clusters by two-photon processes