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

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

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

Collaborators

Summary

• 4He: n0, n(k), FSE, <EK>
• 3He: n(k), <EK>
• 4He in Vycor: n0, n(k), <EK>
• MARI and eVS

ESRF

ESRF

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

Essence of Glyde-Azuah method

• Requires wide range of Q and ω

(hence MARI)

• Allows separate identification of

n(k) and FSE by fitting to S(Q, ω)

• r J(Q,y)
• JIA(y) = ∫kn(k)dk, longitudinal

momentum distribution

• y = M(ω - ωR)/ħQ
• ħωR = (ħQ)2 / 2M

ESRF

• To allow for FSE

JIA . RFSE(Q) = J(Q)

• Model for n(k)

n(k) = An0 + A*n*(k) BE condensate k>o states above c’densate

• Parameters describing n(p) and

RFSE separated by dependence

• n Q

ESRF

Glyde et al, PRB62, 14337, 2000 Azuah et al, PRB56, 14620, 1997

• 4He
• 15 < Q(Å-1) < 29
• T=0.5 – 3.5K
• Both SF and NF phases
• MARI
• J(Q,y), n0(T), n(k), R(Q,y)

ESRF

Parameters at 1.6K n0 (%) α2(Å-2) etc → n(k) β3Q(Å-4) etc → R(Q)

ESRF

n0(T) n

M

• mentum distribution n(k),

g Sosnick et al (IPNS) 1.6K and 2.3K

ESRF

Mayers, Andreani, Colognesi, JPCM, 9,10639,1997

• 4He
• 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

• <EK>, J(y), n0

1.4K and 2.5K (Au)

VESUVI O VESUVI O

ESRF

ESRF

!" !" eVS

• Sosnick et

al (IPNS) ! Path integral MC

ESRF

Azuah et al, JLTP, 101, 951, 1995

• 3He
• 9 < Q(Å-1) < 20
• T = 1.4K
• MARI
• <EK>, 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

• 3He (dense liquid, hcp, bcc)
• 90 < Q(Å-1) < 140
• T = 2K isotherm
• eVS
• <EK>

ESRF

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

for anharmonic effects

ESRF

4He in Vycor (30% porosity)

Azuah, Glyde, Fåk, Scherm to be published

• 4He in Vycor glass
• 24 < Q(Å-1) < 29
• T = 0.5 – 2.25K
• Both SF and NF phases
• MARI
• J(Q,y), n0(T), n(k), R(Q,y)
• Results are similar to bulk

ESRF The Future: what will

VESUVIO bring to these studies?

• Improved resolution
• Improved sensitivity
• Improved signal/noise