Single particle dynamical properties of matter studied by Neutron - PowerPoint PPT Presentation

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 VESUVIO spectrometer • Resolution improvements { VESUVIO Project • VESUVIO • • Theoretical formalism • Scientific goals • Experimental { • Deep Inelastic Neutron Scattering (DINS) Technique 20 Å -1 <q<150 Å -1 ; ħ ω >0.5 eV 4 He, 3 He, H , 4 He, 3 •Highlights: Highlights: H H 2 , D 2 He, H 2 S • 2 , D 2 , 2 S • Future

N(P) N(P) SCHEMATIC SCHEMATIC

RAL 15th April 2002 RAL 15th April 2002 Momentum distributions • Diatomic molecules: Ψ ( r 1 , r 2 ) → FT → ˜ Ψ ( p 1 , p 2 ) 2 ˜ n ( p 1 , p 2 ) = Ψ ( p 1 , p 2 ) ∫ p 2 n ( p 1 , p 2 ) n 1 ( p 1 ) = d • Mean kinetic energy (variance of n 1 ( p 1 ) ): 1 ∫ p 1 n 1 ( p 1 )p 1 < E C > 1 = 2 d 2 M 1

RAL 15th April 2002 RAL 15th April 2002 C.M. R.M. Decoupling: Ψ ( r 1 , r 2 ) = Φ ( R ) φ ( r ) R = 1 1 + r 1 − r 2 ) 2 ( r r = ( r 2 ), { N(P) for the Centre of n 1 ( p 1 ) = 8 d ∫ p n ( p ) N ( P ) mass motion, C.M. n(p) for the relative p 1 = ( P/2 + p ) motion, R.M. < E C > 1 = 1 [ ] < E C > CM + < E C > r 2

RAL 15th April 2002 RAL 15th April 2002 [ ] ⇒ − P 2 /( 4 M H k B T ) N (P ) = N exp • C.M. 2 = 4 ⇒ σ P 3 M H < E C > CM ----------------------------------------------------- φ ( r ) = 1 r u v , j ( r ) Υ j , m j ( ˆ r ) ⇒ u v , j ( r ) → describing vibrations → radial Υ j , m j ( ˆ r ) → angular wave function 2  ∞  1 ∫   < n ( p ) > ˆ p = n v , j ( p ) = rJ j ( pr / h ) u v , j ( r ) dr • R.M. 2 π 2 h 3     o

Vesuvio Project Vesuvio VESUVIO tank & filter chamber • Resolution improvements n(p) lineshapes • Theoretical formalism • Science: -n(p), ψ (r) ,<E K > in molecular systems -Quantum effects in fluids and solids -Single particle dynamics in amorphous materials, polymers, catalysts and metal hydrides.

RAL 15th April 2002 RAL 15th April 2002 Deep Inelastic Neutron Scattering on VESUVIO High q: 15 A -1 < q < 200 A -1 • Incoherent approximation Incoherent approximation • → If q>> 2 π /d σ i σ : 2 σ ′ σ d k d Ω d ω = S i ( q , ω ) 4 π k where: ∑ ∑ 2 S i ( q , ω ) = < F exp( i q ⋅ r ) I > p I I F δ ( h ω + E I − E F )

RAL 15th April 2002 RAL 15th April 2002 At high ω : ħ ω > 0.5 eV • Impulse approximation Impulse approximation (IA) (short time expansion) • t recoil energy r (t) = r (o) + q M ↓ 2 q − h q ⋅ p 2 ( h ω − h ∑ i ( q , ω ) = p I < I δ I > S IA ) 2 M M I   h ω − ( p + h q ) 2 − h p 2 i ( q , ω ) = ∫   d p n ( p ) δ IA S     2 M 2 M ↑ n(p) of the initial state = ( p + h q ) 2 p 2 E I = → E F 2 M 2 M   h 2 q 2 M   y = h ω − • West scaling   2 q   h 2M

RAL 15th April 2002 RAL 15th April 2002 IA F ( y , q ) = h q IA ( y ) = n z ( y ) S i ( q , ω ) → F q →∞ M ∞ ∞ where: ∫ ∫ n z ( p z ) = n ( p ) dp x dp y −∞ −∞ example: Molecular f luid (decoupling) if N ∏ Ψ = Φ ( R 1 ,..., R N ) φ i ( r i ) i = 1 S(q, ω ) = S CM (q, ω ) ⊗ S r (q, ω ) then F(y, q) = F CM (y,q) ⊗ F r (y, q)

Molecular Systems Molecular Systems RAL 15th April 2002 RAL 15th April 2002 Two regimes for IA 1) Incident neutron energy < < Minimum internal excitation energy of the single molecule F CM (y,q) -----> response to roto-translational motion of • F CM (y,q) • single molecule (MARI, VESUVIO) ♦ N(p) F CM (y,q)--- ---> F > F CM (y) N(p)--- ---> <E > <E K > CM F CM (y,q) CM (y) K > CM q---> ∞ 2) Incident neutron energy > > Internal excitation energy of the single molecule F r (y,q) -----> response to internal vibrational dynamics • F r (y,q) • (y) ♦ n F r (y,q)--- ---> F > F r n ato (p) ---- ----> <E > <E K > r of molecule F r (y,q) r (y) ato (p) K > r q---> ∞ ⊗ F (y,q) ⊗ ---> F(y,q) = F > F(y,q) = F CM F r (y,q) --- CM (y,q) r (y,q) On VESUVIO ♦ n 1 ( p 1 ) ---> > ---

Chopper Instrument Chopper Instrument N(p) measurements CHOPPER CHOPPER DAE DAE Detector 2 Θ Detector SAMPLE SAMPLE M M eVS/VESUVIO eVS/VESUVIO n 1 ( p 1 ) measurements FOIL FOIL DAE DAE Detector Detector 2 Θ SAMPLE SAMPLE M M

RAL 15th April 2002 RAL 15th April 2002 DINS in 4 He

RAL 15th April 2002 RAL 15th April 2002 DINS in 3 He

RAL 15th April 2002 RAL 15th April 2002 DINS in p-H 2 <E K > 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 DINS from p-H 2 and o-D 2 • Experiments • Exact and WKB U(r) Quanto-mechanical calculations of DINS |F > spectra from p-H 2 and o-H 2 (Morse potential) |I > r

RAL 15th April 2002 RAL 15th April 2002 WKB in p-H 2 Calculated F(y, q), T=17 K f or three values of θ : 36 0 (red line); 50 0 (green line); 65 0 (blue line); F I A (y), (dark green line)

RAL 15th April 2002 RAL 15th April 2002 DINS in H 2 S

INFM team: publications within VESUVIO project INFM team: publications within VESUVIO project DINS theoretical formalism DINS theoretical formalism DINS in molecular systems (H2S, H2O) DINS in molecular systems (H2S, H2O) J. M.F.Gunn, C.Andreani, J.Mayers, "A new "A new C. Andreani et al. JCP 114 114 387 (2001) 387 (2001) J. M.F.Gunn, C.Andreani, J.Mayers, C. Andreani et al. JCP approach to impulsive neutron scattering” approach to impulsive neutron scattering” C. Andreani et al. JCP 115 115 1 (2001) 1 (2001) C. Andreani et al. JCP Journal of Physics C Journal of Physics C 19 19, L835 (1986) , L835 (1986) DINS in Quantum systems DINS in Quantum systems 4 He : 4 He : J.Mayers et al. PR B 39 39, 2022 (1989) , 2022 (1989) J.Mayers et al. PR B - C. Andreani et al. PR B C. Andreani et al. PR B 50 50 12744 (1994) 12744 (1994) - C.Andreani et al. PL A 171 171, 76 (1992) , 76 (1992) C.Andreani et al. PL A - - J. Mayers et al. JP C J. Mayers et al. JP C 9 9 1 1- -11 (1997) 11 (1997) C. Andreani et al. PR B 51 51, 8854 (1995) , 8854 (1995) C. Andreani et al. PR B - D. Colognesi et al. EL - D. Colognesi et al. EL 50 50 202 (2000) 202 (2000) C. Andreani et al. PR B 54 54, 6255 (1996) , 6255 (1996) C. Andreani et al. PR B H 2 and D 2 : H 2 and D 2 : C. Andreani et al. JP C 10 C. Andreani et al. JP C 10, 7091 (1998) , 7091 (1998) – – C. Andreani e al. C. Andreani e al. Physica B , Physica B , 234 234 334 (1997) 334 (1997) C. Andreani et al. PR B C. Andreani et al. PR B 60 60 10008 (1999) 10008 (1999) – – C. Andreani et al. C. Andreani et al. Physica B , Physica B , 234 234 329 (1997) 329 (1997) C. Andreani et al JPC C. Andreani et al JPC 12 12 A139 (2000) A139 (2000) – 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) – Instrumental work Instrumental work – C. Andreani et al. PR B C. Andreani et al. PR B 60 60 10008 (1999) 10008 (1999) – C.Andreani et al. NIM A276 C.Andreani et al. NIM A276, 297 (1989) , 297 (1989) – C. Andreani et al. NN, C. Andreani et al. NN, 11 11 n. 1, 21, (2000) n. 1, 21, (2000) – C.Andreani et al. Momentum Distrib. 333 (1989) C.Andreani et al. Momentum Distrib. 333 (1989) 3 3 He : He : C.Andreani et al. Momentum Distrib. 355 (1989 ) C.Andreani et al. Momentum Distrib. 355 (1989 ) – R. Senesi et al. R. Senesi et al. PRL – PRL 86 86 4584 (2001) 4584 (2001) R. Senesi et al. Physica B 276 276- -278 278 200 (2000) 200 (2000) R. Senesi et al. Physica B – R. R. Senesi JLTP 126 126 57 57- -62 (2002) 62 (2002) JLTP – Senesi e e t t a a l l . .

VESUVIO VESUVIO e.VERDI e.VERDI

RAL 15th April 2002 RAL 15th April 2002 e.VERDI e.VERDI 139 La foil) final neutron energy E f =72 eV ( final energy E f = 6.7 eV ( 238 U foil) 5 30 2.500 28 2.000 4 26 180.0 1.500 Energy Transfer (eV) 24 160.0 Energy Transfer (eV) 1.000 22 140.0 3 0.5000 120.0 20 Scattering angles (deg) 100.0 18 2 Scattering angles (deg) 16 14 1 12 10 120 140 160 180 200 2 4 6 8 10 -1 ) Q(Å -1 ) Q(Å VESUVIO VESUVIO e.VERDI e.VERDI

Science on VESUVIO & e.VERDI VESUVIO e.VERDI • Hydrogen bonded molecular systems • Atomic and molecular quantum systems • Amorphous materials, Polymers, Catalysts, Metal hydrides • Electronic transitions (intermultiplet transitions in rare-earths, interband electronic transitions in semiconductors, itinerant ferromagnets)

RAL 15th April 2002 RAL 15th April 2002 INS and DINS neutron spectroscopy with e.VERDI INS and DINS neutron spectroscopy with e.VERDI Interband Electron Transitions 100 Exchanged energy (eV) 10 Stoner Excitations 1 e.VERDI Physics 0.1 Atomic recoil 0.01 1E-3 Crystal field transitions 1E-4 0 5 10 15 20 80 120 160 200 -1 ) Q (Å