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Single particle dynamical properties of matter studied by Neutron Spectroscopy at the eV energies: VESUVIO VESUVIO Project Carla Andreani RAL 15th April 2002 RAL 15th April 2002 Summary n(p) and <E K > Basic formula for DINS on

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Single particle dynamical properties of matter studied by Neutron Spectroscopy at the eV energies: VESUVIO VESUVIO Project

Carla Andreani

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Summary

  • n(p) and <EK>
  • Basic formula for DINS on VESUVIO spectrometer
  • VESUVIO

VESUVIO Project

  • Experimental

Technique

  • Highlights:

Highlights: H H2

2, D

, D2

2,

, 4

4He,

He, 3

3He, H

He, H2

2S

S

  • Future

RAL 15th April 2002 RAL 15th April 2002

  • Deep Inelastic Neutron Scattering (DINS)

20 Å-1<q<150 Å-1; ħω>0.5 eV

  • Resolution improvements
  • Theoretical formalism
  • Scientific goals

{

{

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N(P) N(P) SCHEMATIC SCHEMATIC

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Momentum distributions

  • Diatomic molecules:
  • Mean kinetic energy (variance of n1(p1)):

Ψ(r1 ,r2 ) → FT → ˜ Ψ (p1,p2 ) n(p1 ,p2) = ˜ Ψ (p1,p2 )

2

n1 (p1) = d

∫ p 2 n(p1, p2)

< EC >1= 1 2M1 d

∫ p 1 n1(p1 )p1

2

RAL 15th April 2002 RAL 15th April 2002

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SLIDE 5

N(P) for the Centre of mass motion, C.M. n(p) for the relative motion, R.M.

RAL 15th April 2002 RAL 15th April 2002

n1(p1 ) = 8 d

∫ p n(p)N(P)

p1 = (P/2 + p) < EC >1= 1 2 < EC >CM + < EC > r

[ ]

{

Ψ(r1,r

2) = Φ(R)φ(r)

R = 1 2 (r

1 + r 2),

r = (r

1 − r2)

Decoupling:

C.M. R.M.

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SLIDE 6
  • C.M.
  • R.M.

N (P ) = N exp − P 2 /( 4 M H k B T )

[ ]⇒

⇒ σ P

2 = 4

3 M H < E C > CM

φ (r) = 1 r uv, j(r )Υj, m j ( ˆ r ) ⇒ uv, j(r ) → describing vibrations → radial Υj, m j ( ˆ r ) → angular wave function

<n(p ) >ˆ

p =nv,j(p) =

1 2π2h3 rJj(pr/h)

  • ∞

∫

uv, j(r) dr        

2

RAL 15th April 2002 RAL 15th April 2002

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SLIDE 7

Vesuvio Vesuvio Project

  • Resolution improvements

n(p) lineshapes

  • Theoretical formalism
  • Science:
  • n(p), ψ(r) ,<EK>

in molecular systems

  • Quantum effects in fluids and

solids

  • Single particle dynamics in

amorphous materials, polymers, catalysts and metal hydrides.

VESUVIO tank & filter chamber

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SLIDE 8

Deep Inelastic Neutron Scattering

  • n VESUVIO

High q: 15 A-1 < q < 200 A-1

  • Incoherent approximation

Incoherent approximation If q>> 2π/d σi σ : where:

→

d

2σ

dΩ dω = ′ k k σ 4π Si (q,ω )

Si(q,ω ) = pI

F

∑

I

∑

< F exp(iq ⋅ r) I >

2

δ (hω + EI − EF )

RAL 15th April 2002 RAL 15th April 2002

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SLIDE 9

At high ω: ħ ω > 0.5 eV

  • Impulse approximation

Impulse approximation (IA) (short time expansion) recoil energy n(p) of the initial state

  • West scaling

S IA

i (q , ω ) =

p I < I δ ( h ω − h

2 q 2

2 M − h q ⋅ p M ) I >

I

∑

S

IA i (q , ω ) = ∫

d p n ( p ) δ h ω − ( p + h q ) 2 2 M − h p 2 2 M        

r (t) = r (o) + q t M

↑

↓

E I = p 2 2 M → E F = ( p + h q ) 2 2 M

y = M h

2 q

h ω − h 2 q

2

2M        

RAL 15th April 2002 RAL 15th April 2002

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SLIDE 10

where:

example: Molecular f luid (decoupling) if then

nz( pz) = dp x

−∞ ∞

∫

dp y

−∞ ∞

∫

n(p)

Ψ = Φ (R 1 ,..., R N ) φ i

i = 1 N

∏

(ri )

S(q,ω ) = SCM (q, ω ) ⊗ Sr(q,ω ) F(y, q) = F

CM (y,q) ⊗ F r(y, q)

F( y, q) = h q M S i(q, ω ) → F

IA ( y) = n z ( y)

q →∞

RAL 15th April 2002 RAL 15th April 2002

IA

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Molecular Systems Molecular Systems Two regimes for IA

1) Incident neutron energy < < Minimum internal excitation energy of the single molecule

  • F

FCM

CM(y,q)

(y,q) -----> response to roto-translational motion of

single molecule (MARI, VESUVIO)

F FCM

CM(y,q)

(y,q)---

  • --> F

> FCM

CM(y)

(y) ♦ N(p) N(p)---

  • --> <E

> <EK

K>

>CM

CM

2) Incident neutron energy > > Internal excitation energy of the single molecule

  • F

Fr

r(y,q)

(y,q) -----> response to internal vibrational dynamics

  • f moleculeF

Fr

r(y,q)

(y,q)---

  • --> F

> Fr

r(y)

(y) ♦ n nato

ato(p)

(p) ----

  • ---> <E

> <EK

K>

>r

r

On VESUVIO

  • --> F(y,q) = F

> F(y,q) = FCM

CM(y,q)

(y,q) ⊗ ⊗ F Fr

r(y,q)

(y,q)

  • -->

> ♦ n1(p1)

RAL 15th April 2002 RAL 15th April 2002

q---> ∞ q---> ∞

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SLIDE 12

DAE DAE

FOIL FOIL SAMPLE SAMPLE M M

2Θ

Detector Detector

eVS/VESUVIO eVS/VESUVIO

n1(p1) measurements

DAE DAE

CHOPPER CHOPPER SAMPLE SAMPLE M M

2Θ Detector

Detector

Chopper Instrument Chopper Instrument N(p) measurements

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SLIDE 13

DINS in 4He

RAL 15th April 2002 RAL 15th April 2002

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DINS in 3He

RAL 15th April 2002 RAL 15th April 2002

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DINS in p-H2

<EK>TRAS vs T ! ρ ρ = 22. 41 nm- 3 " ρ = 10. 45 nm

  • 3

# Langel et al.

* PIMC

  • -

classical model

__

harmonic model

RAL 15th April 2002 RAL 15th April 2002

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DINS from p-H2 and o-D2

RAL 15th April 2002 RAL 15th April 2002

U(r) r |I > |F >

  • Experiments
  • Exact and WKB

Quanto-mechanical calculations of DINS spectra from p-H2 and o-H2 (Morse potential)

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WKB in p-H2

Calculated F(y, q), T=17 K f or three values of θ: 360 (red line); 500 (green line); 650 (blue line); FI A(y), (dark green line)

RAL 15th April 2002 RAL 15th April 2002

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DINS in H2S

RAL 15th April 2002 RAL 15th April 2002

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INFM team: publications within VESUVIO project INFM team: publications within VESUVIO project

DINS theoretical formalism DINS theoretical formalism

  • J. M.F.Gunn, C.Andreani, J.Mayers,
  • J. M.F.Gunn, C.Andreani, J.Mayers, "A new

"A new approach to impulsive neutron scattering” approach to impulsive neutron scattering” Journal of Physics C Journal of Physics C 19 19, L835 (1986) , L835 (1986) J.Mayers et al. PR B J.Mayers et al. PR B 39 39, 2022 (1989) , 2022 (1989) C.Andreani et al. PL A C.Andreani et al. PL A 171 171, 76 (1992) , 76 (1992)

  • C. Andreani et al. PR B
  • C. Andreani et al. PR B 51

51, 8854 (1995) , 8854 (1995)

  • C. Andreani et al. PR B
  • C. Andreani et al. PR B 54

54, 6255 (1996) , 6255 (1996)

  • C. Andreani et al. JP C
  • C. Andreani et al. JP C 10

10, 7091 (1998) , 7091 (1998)

  • C. Andreani et al. PR B
  • C. Andreani et al. PR B 60

60 10008 (1999) 10008 (1999)

  • C. Andreani et al JPC
  • C. Andreani et al JPC 12

12 A139 (2000) A139 (2000)

Instrumental work Instrumental work

C.Andreani et al. NIM C.Andreani et al. NIM A276 A276, 297 (1989) , 297 (1989) C.Andreani et al. Momentum Distrib. 333 (1989) C.Andreani et al. Momentum Distrib. 333 (1989) C.Andreani et al. Momentum Distrib. 355 (1989 C.Andreani et al. Momentum Distrib. 355 (1989) )

  • R. Senesi et al. Physica B
  • R. Senesi et al. Physica B 276

276-

  • 278

278 200 (2000) 200 (2000)

DINS in molecular systems (H2S, H2O) DINS in molecular systems (H2S, H2O)

  • C. Andreani et al. JCP
  • C. Andreani et al. JCP 114

114 387 (2001) 387 (2001)

  • C. Andreani et al. JCP
  • C. Andreani et al. JCP 115

115 1 (2001) 1 (2001)

DINS in Quantum systems DINS in Quantum systems

4 4He :

He :

  • C. Andreani et al. PR B
  • C. Andreani et al. PR B 50

50 12744 (1994) 12744 (1994)

  • J. Mayers et al. JP C
  • J. Mayers et al. JP C 9

9 1 1-

  • 11 (1997)

11 (1997)

  • D. Colognesi et al. EL
  • D. Colognesi et al. EL 50

50 202 (2000) 202 (2000)

H H2

2 and D

and D2

2 :

: – – C. Andreani e al.

  • C. Andreani e al. Physica B ,

Physica B , 234 234 334 (1997) 334 (1997) – – C. Andreani et al.

  • C. Andreani et al. Physica B ,

Physica B , 234 234 329 (1997) 329 (1997) – – C.Andreani et al. C.Andreani et al. EL EL 37 37 329 (1997) 329 (1997) – – C. Andreani et al. JP C

  • C. Andreani et al. JP C 10

10, 7091 (1998) , 7091 (1998) – – C. Andreani et al. PR B

  • C. Andreani et al. PR B 60

60 10008 (1999) 10008 (1999) – – C. Andreani et al. NN,

  • C. Andreani et al. NN, 11

11 n. 1, 21, (2000)

  • n. 1, 21, (2000)

3 3He :

He :

– – R. Senesi et al.

  • R. Senesi et al. PRL

PRL 86 86 4584 (2001) 4584 (2001) – – R.

  • R. Senesi

e t a l . Senesi e t a l . JLTP JLTP 126 126 57 57-

  • 62 (2002)

62 (2002)

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VESUVIO VESUVIO e.VERDI e.VERDI

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e.VERDI e.VERDI

1 2 3 4 5 2 4 6 8 10

final neutron energy Ef=72 eV (

139La foil)

Scattering angles (deg)

Q(Å

  • 1)

Energy Transfer (eV)

0.5000 1.000 1.500 2.000 2.500

10 12 14 16 18 20 22 24 26 28 30 120 140 160 180 200

Scattering angles (deg)

Energy Transfer (eV) Q(Å

  • 1)

100.0 120.0 140.0 160.0 180.0

RAL 15th April 2002 RAL 15th April 2002

VESUVIO VESUVIO e.VERDI e.VERDI

final energy Ef= 6.7 eV (238U foil)

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Science on VESUVIO VESUVIO &

  • Hydrogen bonded molecular systems
  • Atomic and molecular quantum systems
  • Amorphous materials, Polymers,

Catalysts, Metal hydrides

e.VERDI e.VERDI

  • Electronic transitions (intermultiplet

transitions in rare-earths, interband electronic transitions in semiconductors, itinerant ferromagnets)

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INS and DINS neutron spectroscopy with e.VERDI INS and DINS neutron spectroscopy with e.VERDI

5 10 15 20 80 120 160 200 1E-4 1E-3 0.01 0.1 1 10 100

e.VERDI Physics

Interband Electron Transitions Stoner Excitations

Crystal field transitions

Atomic recoil

Exchanged energy (eV) Q (Å

  • 1)

RAL 15th April 2002 RAL 15th April 2002

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e.VERDI e.VERDI schematic layout

schematic layout

RAL 15th April 2002 RAL 15th April 2002

DINS at DINS at ω ω ω ω >1 >1 eV eV, , q q < 10 Å < 10 Å-

  • 1

1 at 1°<2

at 1°<2θ θ<5° <5° I n c i d e n t b e a m I n c i d e n t b e a m VLAD detector bank VLAD detector bank

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SLIDE 25

n n’ n n’

γ

n’ X

Neutron Detector Gamma Detector

RAL 15th April 2002 RAL 15th April 2002

VESUVIO VESUVIO as Resonance

Filter Spectrometer

VESUVIO VESUVIO as Resonance

Detector Spectrometer

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SLIDE 26

DAE

FOIL FOIL SAMPLE SAMPLE MODERATOR MODERATOR

2Θ

L0

L1

Detector Detector

Li Li-

  • glass

glass Neutron Detector Neutron Detector

γ γ γ γ detector detector n n’ n n’ γ n’ X

Neutron Detector Gamma Detector

RAL 15th April 2002 RAL 15th April 2002

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VESUVIO team VESUVIO team

  • J. Tomkinson I SI S, Proj. Coordinator
  • C. Andreani Tor Vergata Univ. , I NFM
  • Z. A. Bowden I SI S
  • D. Colognesi CNR
  • A. Fielding Liverpool University
  • E. Degiorgi I NFM, Tor Vergata Univ.
  • J. Mayers I SI S
  • M. Nardone L’Aquila Univ. , I NFM
  • E. Pace Tor Vergata Univ. , I NFN
  • M. Praitano RMP, Mech. Eng. Acilia
  • N. J. Rhodes I SI S
  • E. M. Schooneveld I SI S
  • R. Senesi I NFM, Tor Vergata Univ.
  • W. G. Stirling Liverpool Univ.
  • C. Uden I SI S

VESUVIO tank & filter chamber RAL 15th April 2002 RAL 15th April 2002