ESRF Single Particle Dynamics in Quantum Systems ( 4 He and 3 He) - PowerPoint PPT Presentation

ESRF Single Particle Dynamics in Quantum Systems ( 4 He and 3 He) W.G. Stirling ESRF/University of Liverpool

ESRF Collaborators H.R. Glyde R.T. Azuah P.E. Sokol K.H. Andersen The eVS/VESUVIO team The Liverpool team The ISIS team

ESRF Summary • 4 He: n 0 , n(k), FSE, <E K > • 3 He: n(k), <E K > • 4 He in Vycor: n 0 , n(k), <E K > • MARI and eVS

ESRF Measurement of n(k) and <KE> via recoil scattering Final-state effects (FSE)

ESRF • To allow for FSE Essence of Glyde-Azuah method J IA . R FSE (Q) = J(Q) • Requires wide range of Q and ω (hence MARI) • Model for n(k) • Allows separate identification of n(k) = An 0 + A * n * (k) n(k) and FSE by fitting to S(Q, ω ) or J(Q,y) • J IA (y) = ∫ kn(k)dk, longitudinal BE condensate k>o states momentum distribution above c’densate • y = M( ω - ω R )/ ħ Q • Parameters describing n(p) and R FSE separated by dependence • ħω R = ( ħ Q) 2 / 2M on Q

ESRF Glyde et al, PRB62, 14337, 2000 Azuah et al, PRB56, 14620, 1997 • 4 He • 15 < Q(Å -1 ) < 29 • T=0.5 – 3.5K • Both SF and NF phases • MARI • J(Q,y), n 0 (T), n(k), R(Q,y)

ESRF Parameters at 1.6K n 0 (%) α 2 (Å -2 ) etc → n(k) β 3 Q(Å -4 ) etc → R(Q)

ESRF n 0 (T) n omentum distribution n(k), M g Sosnick et al (IPNS) 1.6K and 2.3K

ESRF Mayers, Andreani, Colognesi, JPCM, 9,10639,1997 • 4 He • 90 < Q(Å -1 ) < 150 • T = 1.3 – 2.5K • Both SF and NF phases • eVS • Analysers: Au → 130 meV FWHM U → 63 meV FWHM • <E K >, J(y), n 0 1.4K and 2.5K (Au)

ESRF VESUVI O VESUVI O

ESRF !" eVS !" o Sosnick et al (IPNS) ! Path integral MC

ESRF Azuah et al, JLTP, 101, 951, 1995 • 3 He • 9 < Q(Å -1 ) < 20 • T = 1.4K • MARI • <E K >, n(k), R(Q,y)

ESRF • Model n(k) Fermi system • Data cannot distinguish between Fermi and dimerized distribution • KE=10.4K (theory 12-13K)

ESRF Senesi et al, PRL 86, 4584, 2001 • 3 He (dense liquid, hcp, bcc) • 90 < Q(Å -1 ) < 140 • T = 2K isotherm • eVS • <E K >

ESRF • KE as fn of mol vol - n • Monte Carlo - o • SC Phonon – ………… • need for better allowance for anharmonic effects

ESRF Azuah, Glyde, Fåk, Scherm to be published • 4 He in Vycor glass • 24 < Q(Å -1 ) < 29 • T = 0.5 – 2.25K • Both SF and NF phases • MARI • J(Q,y), n 0 (T), n(k), R(Q,y) 4 He in Vycor (30% porosity) • Results are similar to bulk

ESRF The Future : what will VESUVIO bring to these studies? • Improved resolution • Improved sensitivity • Improved signal/noise