Kinetic energy and momentum distribution spectroscopy with eV - - PowerPoint PPT Presentation

Kinetic energy and momentum distribution spectroscopy with eV neutrons

Roberto Senesi Roma, 6 –5-2004

Microscopic dynamics of quantum fluids within the e.VERDI Project at ISIS

Why and

Distribution functions

are key quantities for the microscopic description of condensed systems

Radial distribution

function: microscopic

• ccupation probability

in r-space

Momentum distribution

function: microscopic

• ccupation probability

in p-space

KE ( ) n p

Contain information

• n the average

instantaneous dynamics

They do not give

direct information on collective and single-particle excitations but reflect the properties

• f many-body

condensed systems

and

KE ( ) n p

Quantum statistical mechanics: no general results

and

are always greater (broader) than the classical values, because of:

zero-point motion

[x,p]=i Heisemberg principle

Bogoliubov inequality

interacting systems density dependence

Ad hoc descriptions

• f for Bosons,

fermions etc.

Wigner-Kirkwood

perturbative approach limited to almost-classical systems (Landau book), such as liquid and solid Ne.

KE ( ) n p

• ( )

n p

Systems studied:

Atomic electrons

(Du Mond -1929)

Nucleons in nuclei,

etc (ref. West scaling variable)

Neutron matter Nucleons Degenerate

ultracold atomic gases

Liquid Helium-s ,

Mixtures, Quantum solids

Molecular systems

velocity distribution of a cloud of rubidium atoms at (a) just before the appearance of the Bose-Einstein condensate, (b) just after the appearance of the condensate and (c) after further evaporation left a sample of nearly pure condensate

and spectroscopy of quantum fluids and solids: Deep Inelastic Scattering of eV Neutrons

KE ( ) n p

• High energy -high momentum

neutron scattering VESUVIO spectrometer at ISIS

The atom’s velocity before scattering event can be measured!

2

2

i

q E v q M ∆ = + ⋅

• Scattering in the Impulse

Approximation: when a He atom recoils freely

Longitudinal Compton Profile Analysis

The analysis and

interpretation of the lineshape of the recoil peak give access to and

Desiderata:

The spectrometer response must be (much) narrower than n(p)!

KE ( ) n p

• pen problems

Quantitative description of

Density and Temperature dependence :

Dependence on the state of

aggregation: liquid-solid discontinuity

“Fermiology”: does

liquid 3He have a fermionic lineshape? 3 ( , ) 2

B

KE k T f T ρ = +

• pen problems-continued

Kinetic energy reduction in

interacting quantum systems!

Breakup of the density-

dependence in liquid helium mixtures?

16 18 20 22 24 26 5 10 15 20 25 <T>3(n) [K] Atomic density n [nm

• 3]

• pen problems-continued

Does helium in narrow

channels (xerogels, nanotubes, etc) show axial confinement?

Supersolid He in VYCOR

ZSM-5 zeolite. The cavity and channel structure seen by Argon atoms.

• pen problems-continued

Kinetic energy in strong quantum solids

3He 4He

Research activity on Quantum Fluids within the e.VERDI project

Kinetic energy of

helium in xerogel

Kinetic energy of

solid 3He

Kinetic energy of

helium mixtures across the liquid- solid boundary

Kinetic energy of

He-Ne mixtures

Accurate momentum

distribution of 3He

Research activity on Quantum Fluids within the e.VERDI project

• Resolution improvements

have been accomplished within VESUVIO project by fine analysis of neutron energy after scattering event

High quality data with improved resolution

Research activity on Quantum Fluids within the e.VERDI project

Energy Selector (resonant foil)+ Velocity Selector (veto on transit time)

Resolution narrowing with respect to VESUVIO