ISIS Poster Template

1
Neutron scattering studies of quantum fluids
hydrogen
U. Bafile(a), M. Celli(a), D. Colognesi(a), F.
Formisano(b), E. Guarini(c), R. Magli(c,d), M.
Zoppi(a) www.ifac.cnr.it/idrogeno
bafile_at_ifac.cnr.it (a) Istituto di Fisica
Applicata Nello Carrara, Consiglio Nazionale
delle Ricerche, Italy (b) Istituto Nazionale per
la Fisica della Materia, Operative Group in
Grenoble, France (c) Istituto Nazionale per la
Fisica della Materia, Unità di Firenze, Italy (d)
Dipartimento di Chimica, Biochimica e
Biotecnologie per la Medicina, Università di
Milano, Italy
www.ifac.cnr.it www.infm.it
The microscopic structure of liquid hydrogen is a
still open problem 1, because x-ray and neutron
spectroscopy are of difficult application to such
a system, a much harder case than deuterium,
already solved a decade ago 2.
Experimental data The diffraction pattern of
saturated liquid parahydrogen was measured with
the D4C diffractometer of ILL, Grenoble Sample
data temperature
T  17.1 K pressure
p  29.9 bar
molecular number density n  22.95
nm-3 concentration of para
species gt 0.9995 (by
using a catalyst in the sample container)
References 1 F.J. Bermejo, K. Kinugawa, C.
Cabrillo, S.M. Bennington, B. Fåk, M.T.
Fernández-Díaz, P. Verkerk, J. Dawidowski, and R.
Fernández-Perea, Phys. Rev. Lett. 84, 5359
(1998) A. Cunsolo, G. Pratesi, D. Colognesi. R.
Verbeni, M. Sampoli, F. Sette, G. Ruocco, R.
Senesi, M.H. Krisch, and M. Nardone, J. Low Temp.
Phys. 129, 117 (2002). 2 M. Zoppi, U. Bafile,
R. Magli, and A.K. Soper, Phys. Rev E 48, 1000
(1993) E. Guarini, F. Barocchi, R. Magli, U.
Bafile, and M.-C. Bellissent-Funel, J. Phys.
Condens. Matter 7, 5777 (1995) M. Zoppi, U.
Bafile, E. Guarini, F. Barocchi, R. Magli, and M.
Neumann, Phys. Rev. Lett. 75, 1779 (1995). 3
J.A. Young and J.U. Koppel, Phys. Rev A 135, 603
(1964) M. Zoppi, Physica B 183, 235 (1993) E.
Guarini, J. Phys. Condens. Matter 15, R775
(2003). 4 M. Celli, D. Colognesi. and M. Zoppi,
Eur. Phys. J. B 14, 239 (2000). 5 M. Zoppi, U.
Bafile, M. Celli, G.J. Cuello, F. Formisano, E.
Guarini, R. Magli, and M. Neumann, J. Phys.
Condens. Matter 15, S107 (2003) M. Zoppi, M.
Neumann, and M. Celli, Phys. Rev B 65, 092204
(2002). 6 M. Celli, D. Colognesi, M. Zoppi,
Eur. Phys. J. B. 14, 239 (2000). 7 M. Zoppi, D.
Colognesi, M. Celli, Eur. Phys. J. B. 23, 171
(2001). 8 M. Zoppi, D. Colognesi, M. Celli,
Europhys. Lett. 53, 34 (2001) M. Celli, D.
Colognesi, M. Zoppi, Phys. Rev. E 66, 021202
(2002)
Results The determination of the static
structure of liquid hydrogen is demonstrated to
be a feasible, though difficult, task. Reliable
data can be obtained by the joint use of neutron
diffraction and quantum-mechanical simulation
5.
Models and calculations The single-molecule
scattering can be exactly calculated by modelling
the hydrogen molecules as freely rotating
harmonic oscillators 3, taking into account the
density and temperature dependence of the
centre-of-mass kinetic energy of a quantum system
4. Wavelength-dependent detector efficiency,
attenuation, and the influence of the finite size
of sample, container, and detectors, can all be
taken into proper account.
The microscopic dynamics of condensed
hydrogen The physical problem is the study of the
single particle dynamics in condensed quantum
systems. From the high-energy, high-wavevector
region of hydrogen spectrum (E gt 100 meV, Q gt 80
nm-1) one can obtain information on the momentum
distribution and the density-dependent mean
kinetic energy ltEkgt of the particle. From the
low-energy region one can extract information on
the Fourier transform of the velocity
autocorrelation function (liquid) and on the
phonon density of states (solid).
Experimental spectrum
Experimental data The incoherent scattering
function of liquid and solid para-hydrogen was
measured using inelastic neutron scattering by
the TOSCA spectrometer at the pulsed neutron
source ISIS (UK). Sample data- pH2 at low
pressure and at seven temperatures (12 lt T/K lt
21) 6 and - along the isotherm T  19.3 K,
crossing the melting transition, with pressure 17
bar to 636 bar 7.
Models and calculations The scattering cross
section is obtained in the hypothesis of the
translational motion of the molecular center of
mass uncoupled from the molecular internal
motion. The internal dynamics is described by
means of a quantum free rotating harmonic
oscillator model 3. The self dynamics of the
molecular center of mass requires different
models according to the energy and wavevector
range investigated.
High-Q region results As expected, a strong
density dependence of the center of mass mean
kinetic energy, characteristic of a quantum
systems, is evident and the comparison with the
simulation is excellent 6,7.
Low-Q region results The agreement between the
experimental self dynamic structure factor of the
molecular center of mass with a quantum
simulation is impressive 8.