The Response of a ³He Fermi Liquid Droplet to Vibronic Excitation of an Embedded Glyoxal Molecule

Abstract

The zero-phonon line (ZPL) and the sideband in the vibronic spectrum of a single glyoxal molecule inside a (3)He droplet are analyzed within the framework of the Lax formalism. The new theory takes full account of the coupling of the molecule to the single particle-hole (PH) and collective excitations of the doped Fermionic droplet. The effect on the coupling of the wavevector dependence of the effective (3)He mass and the large local density of the first (3)He shell, resulting from the interaction with the chromophore, are also included in the theory. By fitting of a coupling parameter and the phase factor between the PH and collective response functions, the shape and relative intensity of the observed ZPL and its slowly decreasing multiexcitation sideband are well-reproduced. The new theory is consistent with the previous explanation of the surprisingly sharp phonon line superimposed on the sideband in terms of the dense first (3)He shell, which acts as a Helmholtz resonator for the zero sound of the droplet.

Raman scattering signatures of the unusual vibronic interaction of molecules in liquid helium-3

“…Fermi excitations have been observed in the absorption spectrum of doped helium-3 droplets, as shown experimentally in [1] and interpreted theoretically in [1,6,7]. It was found that Fermi excitations essentially affect the spectrum in the vicinity of the zero-phonon line (ZPL) by causing: (i) the disappearance of the dip (existing for helium-4 droplets) between the zero-phonon line and the phonon tail; (ii) a 0.5 cm À1 broadening and strong asymmetry of the line.…”

“…Such dependence can then be derived from their orthogonality conditions [12]. The procedure has been illustrated in two previous papers [1,7]. A salient point is that the dependence of the matrix elements on the radial momentum transfer q can be conveniently transformed into an approximate dependence on the energy transfer E. The approximation is actually the matching at the cross-over energy E co ¼ 2m k 2 F =ðm F Ã Þ 2 between the low-energy limit, where Q ( k F , and the high-energy limit, where Q ffi ð2mEÞ 1=2 and Q ) k F , with k F the Fermi wave vector and m F ⁄ the 3 He atom effective mass [7].…”

“…The potential-potential correlation function of Fermi quasi-particles and quasi-holes takes the comparatively simple form [7] …”

“…(21) with their temperature-dependent expressions, to explicitly obtain the particle-hole response function u PH ðEÞ as [7] u PH ðEÞ ¼ a1ðEÞ…”

“…The actual behavior of u PH ðEÞ at zero temperature and at T = 0.15 K, the latter corresponding to the actual experimental droplet temperature [1,7], is shown in Fig. 1 …”