Mass selective nuclear momentum distribution measurements: H, D, Li - PowerPoint PPT Presentation

Mass selective nuclear momentum distribution measurements: H, D, Li and beyond

Nuclear momentum distribution in LiH and LiD Motivation: • Testing the Validity of the Born- Oppenheimer Approximation in NCS; • Benchmarking ab initio results from CASTEP PW-DFT calculation; • Testing whether nuclear momentum distribution can be measured for lithium nuclei with accuracy beyond the mean kinetic energy.

Validity of the Born-Oppenheimer Approximation in NCS Collisonally-induced non-adiabatic electronic excitation owing to ultra-short (i.e. attosecond) timescale of the NCS process. M τ = The value of the Watson scattering time: q σ  q q Gives us estimate of the energy scale involved. − τ 16 q  10 s When the time becomes, τ q  /  6.5 eV we obtain which is of the order of the separation of electronic levels.

Validity of the Born-Oppenheimer Approximation in NCS Two different mechanisms responsible for electronic excitation: • the centre of mass recoil (CMR) effect; • the non-adiabatic coupling (NAC) between the electrons and the nuclei

Validity of the Born-Oppenheimer Approximation in NCS Adiabatic approximation to molecular systems reveals that it is insufficient for describing the electronic excitation ( ) 2 ( ) ( ) ( ) = Ψ Ψ Ψ = Φ i q R  m m P E ; E e ; R r , X R r R ; t q f i i f n n n Using the orthogonality condition for the electronic wavefunctions, we get: = ∫ 2 ( ) ( ) ( ) ⋅ δ m i q R m P E ; E d X R R e X ' R t q n m ' ' nm n n ' nn ' We therefore find that the adiabatic approximation does not allow for other than CMR type of electronic excitation

Validity of the Born-Oppenheimer Approximation in NCS ( ) Ψ q Represents a wave-packet composed of plane waves with R , t ω , a distribution of momenta around q and moving with recoil velocity. The energy spread of the average wavepacket:   σ 2 2    2 2  4  q q ∆ = = E      Ψ τ 3 2 M 2 M q    q

Validity of the Born-Oppenheimer Approximation in NCS ( ) 2 ( ) 2 ( ) ω = α ω + β ω S q , S q , S q , q 1 q 2 ∆ ∆ 2 2 E E 2 2 2 2  q  q ( ) ( ) Ψ Ψ ω ω − + + S q , and S q , are centred at and E q q 1 2 2 M 2 M E E For high q, the scattering function splits in two distributions, S1 (main) and S2 (secondary), separated by ∆ 2 E Ψ + 2 E q E

Validity of the Born-Oppenheimer Approximation in NCS Expansion in the 1 σ g and 2 σ g basis

Testing the Validity of the Born-Oppenheimer Approximation in NCS by measuring nuclear momentum distributions in LiH and LiD Comparison with ab initio predictions: LiH electronic band structure of ca. 2.99 eV at the Gamma point. PW-DFT GGA PBE 750 eV

Testing the Validity of the Born-Oppenheimer Approximation in NCS by measuring nuclear momentum distributions in LiH and LiD Comparison with ab initio predictions: PW-DFT GGA PBE VDOS and PVDOS for H and Li in LiH 750 eV

Testing the Validity of the Born-Oppenheimer Approximation in NCS by measuring nuclear momentum distributions in LiH and LiD Comparison with ab initio predictions: PW-DFT GGA PBE VDOS and PVDOS for D and Li in LiD 750 eV

Testing the Validity of the Born-Oppenheimer Approximation in NCS by measuring nuclear momentum distributions in LiH and LiD Comparison with ab initio predictions: momentum distributions Previous experiments Theory

Testing the Validity of the Born-Oppenheimer Approximation in NCS by measuring nuclear momentum distributions in LiH and LiD Comparison with ab initio predictions: momentum distributions Theory Values calculated from Experimental σ values using: On the basis of the above, the work estimates an upper conservative bound of 2-3 % for the effects of non-adiabatic dynamics on the second moment and Laplacian of the atomic momentum distributions in this benchmark system.

Testing the Validity of the Born-Oppenheimer Approximation in NCS by measuring nuclear momentum distributions in LiH and LiD Idea: compare GCs in two isoelectric systems, e. g. LiH and LiD M ( ) ( ) ( ) = +   J y J y J y ( ) ( )   ω ω S q , and S q , 1 2 q 1 2   2 2 2 2 2 σ 2 M  q 4  q  ∆ ∆ 2 2 E E 2 2 2 2  q  q = ω − + y E   Ψ Ψ − + + are centred at and E 1 gap q q 2  q 2 M 3 2 M 2 M   2 M 2 M E E   2 2 2 2 2 σ 2 M  q 4  q  = ω − − − y E E   2 gap gap 2  q 2 M 3 2 M 2 M   H in LiH D in LiD 60 400 y y y1 (main) y1 (main) 350 y2 (secondary) y2 (secondary) 40 300 250 20 200 y [inv. A] y [inv. A] 0 150 100 -20 50 0 -40 -50 -60 -100 0 100 200 300 400 500 600 0 100 200 300 400 500 600 TOF [us] TOF [us]

Testing the Validity of the Born-Oppenheimer Approximation in NCS by measuring nuclear momentum distributions in LiH and LiD Idea: compare GCs in two isoelectric systems, e. g. LiH and LiD LiH Theory TOF spectrum simulation 0.35 θ = 50 o ; t 0 = 0 µ s; L 0 = 10.7 m; L 1 = 0.7 m; E 1 = 4908 meV; E Lor = 24 meV; E Gauss = 73 meV; 0.3 1 1 0.25 arb. units 0.2 0.15 0.1 0.05 Simulation @ 300K 0 50 100 150 200 250 300 350 400 450 500 550 600 Scattering angle 50 degrees TOF [us] LiD Band gap = 3 eV TOF spectrum simulation Excitation probability 5% 0.12 θ = 50 o ; t 0 = 0 µ s; L 0 = 10.7 m; L 1 = 0.7 m; M E 1 = 4908 meV; E Lor = 24 meV; E Gauss ( ) ( ) ( ) = 73 meV; = +   1 1 J y J y J y 0.1   1 2 q 0.08 arb. units   2 2 2 2 2 σ 2 M  q 4  q  0.06 = ω − + y E   1 gap 2  q 2 M 3 2 M 2 M   0.04   2 2 2 2 2 σ 2 M  q 4  q  0.02 = ω − − − y E E   2 gap gap 2  q 2 M 3 2 M 2 M   0 50 100 150 200 250 300 350 400 450 500 550 600 TOF [us]

Testing the Validity of the Born-Oppenheimer Approximation in NCS by measuring nuclear momentum distributions in LiH and LiD where and L = (H,D) for forward scattering or L = Li for backscattering. Furthermore, with M = Li in forward scattering and M = Al in both forward and backscattering.

Ockham’s razor: Forwad scattering

Ockham’s razor: Backward scattering

Model no 4 (forward scattering): LiH LiD

Model no 4 (backscattering): LiH LiD

Testing the Validity of the Born-Oppenheimer Approximation in NCS by measuring nuclear momentum distributions in LiH and LiD Sums of normalised data and fits: LiH LiD Ockham's razor: Gaussian Approximation (GA) provides a satisfactory description of NMDs in LiH and LiD. Possible higher-order effects are sufficiently small such that their overall influence on the estimation of second moments for H, D, and Li is practically negligible in both LiH and LiD.

Going beyond lithium: simultaneous NMDs of H, C and O in the squaric acid across the paraelectric phase transition h-SA in the paraelectric phase is characterised by an equal sharing of protons across adjacent oxygen atoms on the a-c plane, a situation where nuclear quantum effects (e.g., tunnelling through barriers) would be expected to dominate.

Going beyond lithium: simultaneous NMDs of H, C and O in the squaric acid across the paraelectric phase transition Backscattering data @ 300K Forward scattering data @ 300K

Going beyond lithium: simultaneous NMDs of H, C and O in the squaric acid across the paraelectric phase transition width of proton momentum distributio width of oxygen momentum distributio width of carbon 16.0 15.5 -1 ) 15.0 width of proton momentum distributio (A 14.5 14.0 13.5 13.0 12.5 12.0 11.5 11.0 4.80 4.75 4.70 4.65 4.60 4.55 4.50 0 100 200 300 400 500 temperature (K)

Heavy atom nuclear momentum distributions from Gamma resonances

CsHSO4 @ 10K, Detector 135 0.7 0.6 0.5 0.4 0.3 C[t] 0.2 0.1 0.0 -0.1 0 10000 20000 30000 40000 50000 C(E0) = A L(E0, dE0/dE1 dE1_lor) ⊗ G_th(E0, dE0/dE1 dE1_gauss) ⊗ G_x(E0,dE0/dx dx) Despite different values of lifetime widths at 5.5 and 22.5 eV the Doppler widths are equal within one st dev. They are: 471.9 meV (FWHM) = 200.4 (st dev) @ 5.5 eV 466.9 meV (FWHM) = 198.3 meV (st dev) @22.5 eV

How to account for a resonance peak? dx = v0 h/w L n n γ Θ n n Cs Cs Cs