Quantum property of solid hydrogen as revealed by high-resolution laser spectroscopy
Pure vibrational overtone transitions of solid parahydrogen were studied using high-resolution laser spectroscopy. Extremely narrow spectral linewidth (~20 MHz) allowed us to observe rich spectral structure that originates in subtle intermolecular interactions in the crystal. It was found that aniso...
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Hiroyuki Katsuki Mizuho Fushitani Takamasa Momose 2018-01-14T13:13:20Z 2018-01-14T13:13:20Z 2003 Quantum property of solid hydrogen as revealed by high-resolution laser spectroscopy / Hiroyuki Katsuki, Mizuho Fushitani, Takamasa Momose // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 1093-1100. — Бібліогр.: 25 назв. — англ. 0132-6414 PACS: 33.20.Ea, 63.50.+x, 67.80.-s https://nasplib.isofts.kiev.ua/handle/123456789/128935 Pure vibrational overtone transitions of solid parahydrogen were studied using high-resolution laser spectroscopy. Extremely narrow spectral linewidth (~20 MHz) allowed us to observe rich spectral structure that originates in subtle intermolecular interactions in the crystal. It was found that anisotropy of the distribution of zero-point lattice vibration of hydrogen molecules perturbs the energy levels of the vibrationally excited states significantly. Large amplitude of the zero-point lattice vibration being an intrinsic nature of quantum solids, was directly observed from the present high-resolution spectroscopy. The first observation of a pure vibrational overtone transition of solid orthodeuterium is also discussed. The work described herein was supported in part by the Grant-in Aid for Scientific Research of the Ministry of Education, Science, Culture, and Sports of Japan. The authors would like to thank Prof. H. Meyer who drew our attention to the problems of solid deuterium. Further, H. Katsuki would also like to acknowledge the support from JSPS Research Fellowships for Young Scientists. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Spectroscopy in Cryocrystals and Matrices Quantum property of solid hydrogen as revealed by high-resolution laser spectroscopy Article published earlier |
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Quantum property of solid hydrogen as revealed by high-resolution laser spectroscopy |
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Quantum property of solid hydrogen as revealed by high-resolution laser spectroscopy Hiroyuki Katsuki Mizuho Fushitani Takamasa Momose Spectroscopy in Cryocrystals and Matrices |
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Quantum property of solid hydrogen as revealed by high-resolution laser spectroscopy |
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Quantum property of solid hydrogen as revealed by high-resolution laser spectroscopy |
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Quantum property of solid hydrogen as revealed by high-resolution laser spectroscopy |
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Quantum property of solid hydrogen as revealed by high-resolution laser spectroscopy |
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quantum property of solid hydrogen as revealed by high-resolution laser spectroscopy |
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Hiroyuki Katsuki Mizuho Fushitani Takamasa Momose |
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Hiroyuki Katsuki Mizuho Fushitani Takamasa Momose |
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Spectroscopy in Cryocrystals and Matrices |
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Spectroscopy in Cryocrystals and Matrices |
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2003 |
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Физика низких температур |
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
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Article |
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Pure vibrational overtone transitions of solid parahydrogen were studied using high-resolution laser spectroscopy. Extremely narrow spectral linewidth (~20 MHz) allowed us to observe rich spectral structure that originates in subtle intermolecular interactions in the crystal. It was found that anisotropy of the distribution of zero-point lattice vibration of hydrogen molecules perturbs the energy levels of the vibrationally excited states significantly. Large amplitude of the zero-point lattice vibration being an intrinsic nature of quantum solids, was directly observed from the present high-resolution spectroscopy. The first observation of a pure vibrational overtone transition of solid orthodeuterium is also discussed.
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0132-6414 |
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https://nasplib.isofts.kiev.ua/handle/123456789/128935 |
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Quantum property of solid hydrogen as revealed by high-resolution laser spectroscopy / Hiroyuki Katsuki, Mizuho Fushitani, Takamasa Momose // Физика низких температур. — 2003. — Т. 29, № 9-10. — С. 1093-1100. — Бібліогр.: 25 назв. — англ. |
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AT hiroyukikatsuki quantumpropertyofsolidhydrogenasrevealedbyhighresolutionlaserspectroscopy AT mizuhofushitani quantumpropertyofsolidhydrogenasrevealedbyhighresolutionlaserspectroscopy AT takamasamomose quantumpropertyofsolidhydrogenasrevealedbyhighresolutionlaserspectroscopy |
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2025-11-26T22:53:25Z |
| last_indexed |
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1850779142640893952 |
| fulltext |
Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10, p. 1093–1100
Quantum property of solid hydrogen as revealed by
high-resolution laser spectroscopy
Hiroyuki Katsuki1, Mizuho Fushitani2, and Takamasa Momose
Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
E-mail: momose@kuchem.kyoto-u.ac.jp
Pure vibrational overtone transitions of solid parahydrogen were studied using high-resolution
laser spectroscopy. Extremely narrow spectral linewidth (�20 MHz) allowed us to observe rich
spectral structure that originates in subtle intermolecular interactions in the crystal. It was found
that anisotropy of the distribution of zero-point lattice vibration of hydrogen molecules perturbs
the energy levels of the vibrationally excited states significantly. Large amplitude of the
zero-point lattice vibration being an intrinsic nature of quantum solids, was directly observed from
the present high-resolution spectroscopy. The first observation of a pure vibrational overtone tran-
sition of solid orthodeuterium is also discussed.
PACS: 33.20.Ea, 63.50.+x, 67.80.–s
1. Introduction
Optical linewidths of the condensed phase are, in
general, two or three orders of magnitude broader
than that in the gas phase. The broadness of the
linewidths wipes out most spectral information that
might give us detailed information on intermolecular
interactions and other properties of condensed phases.
However, an exception to this generalization was re-
cently found for solid hydrogen crystals [1–3]. Opti-
cal transitions of hydrogen crystals in the infrared
spectral region are, surprisingly, as narrow as 4 MHz
(= 0.00013 cm–1) [4]. The exceptional sharpness of
the optical transitions of hydrogen crystals allows us
to observe fine spectral structures originating in sub-
tle interactions in the condensed phase, which pro-
vides a new methodology to investigate properties of
the condensed phase from a microscopic point of view.
Solid hydrogen has been attracting attention not
only because it is the simplest and most fundamental
molecular crystal [5,6] but also because it is a quan-
tum crystal [7]. Since hydrogen molecules have vibra-
tional and rotational degrees of freedom, studies of
solid hydrogen will shed light on different aspects of
quantum crystals that can never be obtained from
studies of solid He.
One of the important properties of quantum crys-
tals is the large amplitude of zero-point lattice vibra-
tion. Due to the small mass of a hydrogen molecule in
addition to the weak intermolecular interaction be-
tween hydrogen molecules, the mean amplitude of the
zero-point lattice vibration of solid hydrogen crystal
extends approximately 20 % of the intermolecular dis-
tance. The delocalization of the wavefunction of hy-
drogen molecules in the lattice must affect most prop-
erties of the crystal. However, observation of such a
quantum effect is difficult and few experimental ob-
servations directly related to the quantum effect have
been reported so far. High-resolution spectroscopy,
then, offers a promising technique to observe the
quantum effect directly, because the optical spectra
give us greatly detailed microscopic information.
Here, we discuss on the quantum feature of solid
hydrogen revealed by high-resolution spectroscopy of
pure vibrational overtone transitions. We have ob-
served and analyzed the Q2(0) (v � �2 0, J � �0 0)
and Q3(0) (v � �3 0, J � �0 0) absorption transi-
tions of solid parahydrogen induced by an impurity
orthohydrogen molecule. Since the transitions we
have studied are induced by intermolecular interac-
tions, which are a function of the distance between
© Hiroyuki Katsuki, Mizuho Fushitani, and Takamasa Momose, 2003
1 Present address: Physical Chemistry Institute, University of Zurich, Switzerland
2 Present address: Institute für Experimentalphysik, Freie Universität Berlin, Germany
molecules, the transition frequencies contain informa-
tion on the effect of the large amplitude of zero-point
lattice vibration. Here, we focus on the quantum
property of solid hydrogen obtained form the analysis
of the optical spectral structure.
In addition to the Qn(0) transitions of solid
parahydrogen, the first observation of the high-resolu-
tion spectrum of the Q2(0) transition of solid
orthodeuterium is also discussed.
2. Qn(0) transitions of solid hydrogen
The Qn(0) (v n� � 0, J � �0 0) transitions of H2
and D2 become optically active when these molecules
are placed under an electric field. Due to the
polarizability � of hydrogen molecules, an electric
field E induces a dipole moment � �� E on the hydro-
gen molecule, which interacts with radiation to cause
the Qn(0) transitions [2,8,9].
The Qn(0) transitions we have studied here are
those induced by the electric field of the averaged
quadrupole moment of an impurity J = 1 hydrogen
molecule in the crystal. Upon the Qn(0) transitions,
the inducer J = 1 hydrogen also changes its value of
the quantum number M which is the projection of the
rotational angular momentum J. Thus, the Qn(0)
transitions we have observed are simultaneous transi-
tions which should be written as Qn(0) + Q0(1) [8].
Vibrons produced by the transitions are almost local-
ized near the inducer J = 1 hydrogen molecule, con-
trary to the cases of the Raman [2] and Condon [9]
transitions.
The crystal structure of solid parahydrogen and
solid orthodeuterium is known to be hexagonal close
packed. There are two types of the nearest-neighbor
pair between two hydrogen molecules in a crystal of
the hexagonal close packed structure. One is the
in-plane (IP) pair and the other is the out-of-plane
(OP) pair. Figure 1 depicts the 12 nearest neighbor
molecules of a J = 1 hydrogen molecule in a crystal of
the hexagonal close packed structure. Six hydrogen
molecules reside on the hexagonal plane, while three
hydrogen molecules are above and three molecules are
below the plane. The IP pair is a pair between two hy-
drogen molecules in the same hexagonal plane
(Fig. 1(a)), and the OP pair is a pair between two hy-
drogen molecules in a different plane next to each
other (Fig. 1 (b)). Since the environment around the
pair is different between IP and OP pairs, we treat
these pairs separately in the following discussion.
The Q1(0), Q2(0), and Q3(0) transitions have been
observed at 4,153, 8,070 [10,11], and 11,758 cm–1
[12], respectively. We have studied the Q2(0) and
Q3(0) transitions with higher spectral resolution than
previous works to find new, fine splittings of the
spectra [13,14]. It was concluded that these fine
splittings we have observed contain important infor-
mation on the quantum property of solid hydrogen.
3. Intermolecular interactions in quantum
crystals
Before going into details about the experimental
results, we will discuss the quantum effect on
intermolecular interactions. The effect of the large
amplitude of zero-point lattice vibration in solid hy-
drogen has to be taken into account when interaction
between hydrogen molecules is considered. Inclusion
of the effect of the zero-point vibration is often re-
ferred to as the «renormalization problem», and it has
been discussed by Luryi and van Kranendonk in the
case of hydrogen crystals [15].
Here we consider intermolecular interaction be-
tween J = 0 hydrogen and J = 1 hydrogen molecules.
When the two molecules are fixed at a distance of R0,
the anisotropic interaction between these two mole-
cules is well described as [6,13]
V R B R C( , ) ( ) ( ),0 1 0 0 20 1� �� , (1)
where �1 is the orientation of the J = 1 hydrogen mo-
lecule with respect to the axis between two molecules
(hereon, the pair-axis). The symbol Cl,m (�) ex-
presses the Racah spherical harmonics, which are re-
lated to the standard spherical harmonics Yl m, ( )� as
C l Yl m l m, ,( ) ( ) ( )� � �� �4 2 1 . The coefficient B0 in
Eq. (1) is a function of R0. The expression in Eq. (1)
1094 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10
Hiroyuki Katsuki, Mizuho Fushitani, and Takamasa Momose
Fig. 1. A J = 1 hydrogen molecule (displayed as ellipses)
and its twelve nearest neighbor hydrogen molecules in a
crystal of the hexagonal close packed structure. (a)
In-plane (IP) pair configurations. (b) Out-of-plane (OP)
pair configurations. Molecules in the same basal plane are
connected by solid lines. The IP and OP pairs are repre-
sented by a bold broken line. The crystal-fixed-axis
(XYZ) and the pair-axis (xyz) are also shown. The crys-
tal c axis is the same as the Z axis.
is applicable only to the case when two molecules are
rigidly fixed at a distance of R0.
In solid hydrogen, however, zero-point motion of
intermolecular vibration is considerably large so that
the «instantaneous» position of a molecule displaced
from its equilibrium position needs to be explicitly
taken into account. According to Luryi and van
Kranendonk [15], Eq. (1) should be modified for
quantum crystal as
~( , ) ~ ( ) ( ) ~ ( )[ ( ), ,V R B R C B R C0 1 0 0 20 1 2 0 22 1� � �� � �
�C2 2 1,– ( )]� , (2)
where the intermolecular interaction potential is ex-
panded in terms of the R0. The coefficients ~B0 and ~B2
are the function of the R0 only. The first term of the
right-hand side of Eq. (2) has the same orientational
dependence as the right-hand side of Eq. (1). But
since the effect of zero-point vibration is renorma-
lized, the tilde is used for the coefficient in Eq. (2) in
order to distinguish it from the coefficient in Eq. (1).
The second term of the right-hand side of Eq. (2)
originates in the anisotropy of the distribution of the
zero-point vibration. More explicitly, when the in-
stantaneous position of the hydrogen molecule relative
to the lattice point is described by the u, the coeffi-
cient ~ ( )B R2 0 in Eq. (2) is approximately related to
the coefficient B R0 0( ) in Eq. (1) as
~ ( ) ( )B R B R2 0 0 0
6
4
� , (3)
where is the nonaxiality parameter defined as
�
1
0
2
2 2
R
u ux y . (4)
The Cartesian components ux and uy of the instanta-
neous vector u are those for the pair-axis as shown in
Fig. 1.
The physical origin of the second term of the
right-hand side of Eq. (2) may become more clear,
when we look at the problem from the group theoreti-
cal point of view. When the distribution is axially
symmetric with respect to the pair-axis, the interac-
tion potential should be described by only the first
term of the right-hand side of Eq. (2), because the po-
tential has to be totally symmetric with respect to any
symmetry operation along the pair-axis that belongs
to the C v� point group. However, the distribution
may not necessarily be axially symmetric. For exam-
ple, in the case of the IP pair shown in Fig. 1 (a), the
distribution of zero-point vibration could be deformed
towards the hexagonal plane or elongated toward the
c axis. Then the potential has to be totally symmetric
with respect to any symmetry operation that belongs
to the C2v point group. It is also true for the OP pair
that the potential has to be totally symmetric in C2v.
When we construct symmetry adapted functions of
linear combinations of the Racah spherical harmonics
up to the second rank, the totally symmetric functions
among them (besides C00, ( )� ) in the C2v point group
are found to be C20, ( )� and C C22 2 2, ,( ) ( )� ��
, the
latter being the second term of the right-hand side of
Eq. (2). Thus, the second term originates in the
nonaxiality of the distribution of zero-point vibration
relative to the pair-axis. Although both parameters ~B0
and ~B2 contain information on the renormalized ef-
fect, it should be emphasized that the parameter ~B2
contains only the pure quantum effect of the solid.
Each hydrogen molecule in solid hydrogen is under
the potential which is approximated as a sum of the
pair intermolecular interaction from all the surround-
ing hydrogen molecules. We call this potential the
«crystal field potential». For the analysis of the spec-
tra of the Qn(0) transitions, we only need to consider
the interaction potential between an impurity J = 1
hydrogen molecule and surrounding parahydrogen
molecules [13]. In addition, since the quantum effect
shown in Eq. (2) significantly contributes only to the
nearest-neighbor pairs but not to distant pairs,
Eq. (2) is used for the interaction between nearest
neighbor pairs, while Eq. (1) is used for further dis-
tant pairs in the present analysis.
Because of the difference of the polarizability of
hydrogen molecules in different vibrational states, the
crystal field potential has to be considered separately
between the ground state and the vibrationally ex-
cited states. When all the J = 0 hydrogen molecules
are in the ground state, the crystal field potential is
found to be
V R Cc
gr ( , ) ( ),� �0 2 20�
. (5)
The coefficient
2c is called the crystal field parame-
ter. In order to derive Eq. (5), we used the relation of
C D Cm n m
n
n2 1
2
2, , ,( ) ( ) ( )� � � R � to change the axis sys-
tem from the pair-axis to the crystal-fixed axis (see
Fig. 1), where � is the orientation of the J = 1 mole-
cule relative to the crystal-fixed axis and R is the ori-
entation of the pair-axis with respect to the crys-
tal-fixed axis. The function Dn m, ( )2 R is the Wigner
rotation matrix [16]. In Eq. (5), only the term pro-
portional to C2,0(�) remains although we used Eq.
(2) for the nearest neighboring pairs. Terms other
than C2,0(�) vanish because of the symmetry of the
crystal (D3h) around the central hydrogen molecule.
When one of the parahydrogen molecules is in the
vibrationally excited state, the crystal field potential
becomes more complex than Eq. (5). We express the
Quantum property of solid hydrogen as revealed by high-resolution laser spectroscopy
Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 1095
crystal field potential of the vibrationally excited
states as a sum of the crystal field potential of the
ground state (Eq. (5)) and the correction terms due to
the excitation. When the jth hydrogen molecule is ex-
cited to its vibrationally excited state, the crystal
field potential of such expression becomes,
V R Cc
ex ( , ) ( ),� �0 2 20� �
� ��
�
��� �
~ ( ) ( ),
'
,
*B D Dm
m
j m0 0
2
2
2
0
2R
� ��
� �
�
��� �
~ [ ( ) ( )] ( ), , ,
*B D D Dm
m
j m j m2 2
2
2
2
2
2
0
2R R , (6)
where the first term of the right-hand side is the
ground state crystal field potential, and the second
and third terms express the correction due to the vi-
brational excitation. The symbol R j is the Euler an-
gle of the pair-axis between the jth hydrogen mole-
cule and the central J = 1 hydrogen molecule relative
to the crystal-fixed axis. The symbol �
~Bn (n = 0 or 2)
represents ~ ~B Bn n
ex
, where ~Bn
ex is the coefficient of
the pair interaction potential in Eq. (2) between the
vibrationally excited J = 0 hydrogen molecule and the
ground J = 1 hydrogen molecule. It should be noted
that the parameter �
~B2 related to the pure quantum
effect appears explicitly in Eq. (6). In other words,
the determination of the parameter �
~B2 corresponds
to the direct observation of the quantum effect of
solid hydrogen.
4. Experiments
Parahydrogen crystals were grown by the same
method as described previously [13,17]. Briefly, pure
parahydrogen gas prepared using a ferric oxide cata-
lyst [17] was continuously introduced in an optical
cell kept at about 8 K to grow transparent crystals.
The cell was made of copper with both ends sealed
with BaF2 windows with indium gaskets. The size of
the cell was 5 cm long and 2 cm in diameter. The con-
centration of orthohydrogen in the crystal was esti-
mated to be less than 0.01 %. In order to observe the
Q3(0) transition, which is about two orders of magni-
tude weaker than the Q2(0) transition, the concentra-
tion of orthohydrogen was increased up to 0.1 %.
Orthodeuterium crystals were prepared using a
method similar to the one described above [18]. The
conversion of paradeuterium to orthodeuterium was
carried out with the ferric oxide catalyst kept at 18 K.
The crystals were grown at 10.5 K as well. The con-
centration of paradeuterium was estimated to be
around 0.25 %.
The high-resolution spectra of the Q2(0) transi-
tions of both parahydrogen and orthodeuterium crys-
tals were observed using a difference frequency laser
system developed in our laboratory [19]. The Q3(0)
transition was observed using a ring type Ti:sapphire
laser. The spectral purity of both laser systems was
better than a few MHz (= 10–4 cm–1). The tone burst
modulation technique was used for sensitive detection
[20,21]. All the measurements were done at 4.8 K.
5. Q2(0) and Q3(0) transitions of solid
parahydrogen
5.1. Observed spectra
Figure 2 shows the observed spectra of the Q2(0)
and the Q3(0) transitions of solid parahydrogen.
Panels (a) and (b) show the absorption spectra with
the polarization of light parallel to the c axis and with
the polarization perpendicular, respectively. Panels
(c) and (d) show the Q3(0) spectra with the polariza-
tion parallel and perpendicular, respectively. In both
transitions, the spectral shapes appear as a second de-
rivative type because of the tone-burst modulation
technique. The differences in the intensities of each
transition between panels (a) and (b) and between
panels (c) and (d) in Fig. 2 clearly show that each
transition has definite polarization dependence rela-
tive to the crystal-fixed axis.
The Q2(0) spectrum is roughly split into a doublet
with a spacing of 0.30 cm–1. Each component exhibits
further fine splittings; the lower frequency component
shows eight lines, while the higher displays ten. On
the other hand, the Q3(0) spectrum is roughly split
into a doublet with a spacing of 0.45 cm–1. Similar
spectral structure was also observed in the Q3(0) tran-
sition, but the number of fine splittings in each com-
ponent is smaller in the Q3(0) transitions than in
Q2(0); the lower frequency component shows four
lines, while the higher component exhibits six.
Previously, Dickson et al. [12] observed roughly
the same spectral structure in the Q3(0) transition as
shown in panels (c) and (d) of Fig. 2. Their spectrum,
however, showed a much broader linewidth than ours.
The linewidth (FWHM) of each transition shown in
Fig. 2 (c) and (d) is about 30 MHz, which is less than
one third of the width observed previously. The nar-
rower spectral linewidth is due to the lower
orthohydrogen concentration in our sample. The sharp
linewidth allowed us to resolve all the fine splittings
in the Q3(0) transition clearly.
5.2. Analysis
The theoretical framework for the analysis of the
Qn(0) transition was discussed in a previous paper
1096 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10
Hiroyuki Katsuki, Mizuho Fushitani, and Takamasa Momose
[13]. Briefly, the Hamiltonian H for the analysis con-
sists of four terms; H = Hrv + Vcrystal + Hhop +
+ VStark. The first term is the standard rotation-vibra-
tion Hamiltonian of hydrogen molecules, the second
terms is the crystal field potential, the third term is
the vibron hopping Hamiltonian, and the last term is
the Stark potential of the quadrupolar field of the cen-
tral J = 1 hydrogen.
As for the crystal field potential, Eqs. (5) and (6)
were used to describe the ground and vibrationally ex-
cited state, respectively. In addition, since there are
two different pairs in the crystal, different parameters
of both �
~B0 and �
~B2 were employed for IP and OP
pairs. These are designated as �
~B0 (IP) and �
~B2 (IP)
for the IP pair, and �
~B0 (OP) and �
~B2 (OP) for the
OP pair.
The vibron hopping Hamiltonian Hhop is respon-
sible for the delocalization of the vibrational excited
states in the crystal. In the previous paper [13] we
found that the Q2(0) spectrum could not be properly
interpreted without the vibron hopping effect. The
hopping frequency is designated as �. On the other
hand, the hopping in the v = 3 vibrationally excited
state is estimated to be negligibly small.
The Stark field potential VStark arises from the elec-
tric field of the J = 1 hydrogen molecule. A quantita-
tive discussion of the Stark energy is given in Ref. 13.
The observed transition frequencies were fitted em-
ploying the standard least-squares fitting method with
the use of a total of six parameters,
2c, �
~B0 (IP), �
~B0
(OP), �
~B2 (IP), �
~B2 (OP), and �. The fitting calcu-
lation was performed separately for the Q2(0) and
Q3(0) transitions. The best fitted parameters are
listed in Table.
Table
Crystal field parameters and vibron hopping frequency of
the Q2(0) and Q3(0) transitions (in cm–1)
Parameter Q
2
(0) Q
3
(0)
2c
–0.0116(2) –0.0112(2)
�
~B0 (IP) –0.5278(5) –0.7879(4)
�
~B0 (OP) –0.5287(5) –0.7880(3)
�
~B2 (IP) –0.0045(2) –0.0069(3)
�
~B2 (OP) 0.0149(3) 0.0236(2)
� –0.0038(1) 0.0
5.3. Crystal field potential
Although the parameters for the Q2(0) and Q3(0)
transitions were calculated separately, the agreement
of the crystal field parameter
2c between these two
transitions is noteworthy. The parameter gives the
crystal field splitting of
�
1 21 0 0 6� � �
� �
E M E M c( ) ( ) . (7)
for an orthohydrogen molecule in pure parahydrogen
crystal.
Determination of the value and sign of �1 has been
attracting much attention because it may explain the
anomalous behavior of the specific heat of solid
parahydrogen [6,22]. The most accurate value of �1 so
far reported is 0.0071 cm–1 by Dickson et al. [12].
Our experimental results support their value. Since
our spectral resolution was much better than the pre-
vious experiment [12], our parameter must be more
Quantum property of solid hydrogen as revealed by high-resolution laser spectroscopy
Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10 1097
cm
8070.220 8070.240 8070.540 8070.560
–1
–1Wavenumber,
Wavenumber,
( )d
11785.380 .395 .850 11758.875
cm
( )b
( )a
( )c
Fig. 2. (a) and (b): The Q2(0) transition of solid
parahydrogen. The polarization of light is parallel (a) and
perpendicular (b), respectively. (c) and (d): The Q3(0)
transition of solid parahydrogen. The polarization of light
is parallel (c) and perpendicular (d), respectively. The
spectral shapes appear as a second derivative type because
of the tone-burst modulation technique.
accurate than theirs. From our observations we con-
clude that the M = � 1 level is above the M = 0 level
and the separation is (0.00696 � 0.00012) cm–1 =
= (10.01 � 0.17) mK.
5.4. Quantum effect
As discussed above, the parameter �
~B2 originates in
the pure quantum effect. Although the absolute values
of the �
~B2 determined are small, they play a signifi-
cant contribution to the energy levels of the
vibrationally excited states. In order to observe the ef-
fect of the parameter �
~B2 in detail, we also performed
the fitting calculation without the parameter �
~B2.
Figure 3 compares the calculated results with the ob-
served spectrum. Panel (a) shows the calculated fre-
quencies of the Q3(0) transition using only three pa-
rameters
2c, �
~B0 (IP), and �
~B0 (OP) for the fitting,
while panel (b) shows the frequencies calculated
using all of the five parameters
2c, �
~B0 (IP), �
~B0
(OP), �
~B2 (IP), and �
~B2 (OP). (The vibron hopping
frequency � was fixed at zero.) Panel (c) shows the
observed spectrum. It is clear from panels (a) and (b)
compared to panel (c) that the inclusion of the param-
eter �
~B2 is essential for the quantitative analysis of
the observed spectrum. In other words, the quantum
effect is directly observed in the Qn(0) spectrum.
From Table, we see significant difference of the pa-
rameter �
~B2 between the IP and OP pairs. This diffe-
rence must be related to the difference of nonaxiality
parameter in Eq. (4). It has been discussed by Luryi
and van Kranendonk [15] that the nonaxiality parame-
ters for the IP pair ( (IP)) and the OP pair ( (OP))
are related and expressed as ( ) ( )IP OP �
1 3. From
the analysis of our spectrum, we obtained the ratio of
| ~ ( ) ~ ( ) | .� �B B2 2 0 30IP OP � . Since our ratio is not the
ratio ~ ( ) ~ ( )B B2 2IP OP of the ground state, but the ra-
tio of the difference of the parameter ~B2 between the
vibrationally excited state and the ground state, our
ratio of | ~ ( ) ~ ( ) | .� �B B2 2 0 30IP OP � can not be com-
pared directly with the ratio of ( ) ( ) .IP OP �
1 3
But the similarity is worth noting.
The parameter �
~B0 contains more complicated quan-
tum effect than the parameter �
~B2 [13], and we do not
discuss this here. We just mention that the parameter
�
~B0 is found to be very close between the IP pairs and
OP pairs. More detailed discussion on the parameters
shown in Table is given in a separate paper [14].
6. Q2(0) transition of solid orthodeuterium
It has been shown that there are remarkable differ-
ences in the behaviors of solid H2 and solid D2 [5].
Some of the differences have come to be well under-
stood — such as slower ortho-para conversion in solid
D2 than in solid H2, and slower quantum diffusion in
solid D2. But there are still some puzzling differences
between them. For example, the fact that impurity
J = 1 pairs show sharp NMR lines in solid H2, but not
in solid D2 is yet to be understood [23,24].
Since the high-resolution spectroscopic technique is
a powerful method for investigating properties of solid
hydrogen from a macroscopic point of view, applica-
tion of the technique to solid orthodeuterium is worth
trying. As a first step of such research, we observed
the high-resolution spectrum of the Q2(0) transition
of solid orthodeuterium for the first time.
Figure 4 shows the observed Q2(0) transition of
solid orthodeuterium. Tone-burst modulation tech-
nique was employed herein. A doublet with a spacing
of 0.27 cm–1 was observed. The doublet corresponds to
the doublet with a spacing of 0.30 cm–1 of the Q2(0)
transition of solid parahydrogen shown in Fig. 2 (a)
and (b). The linewidth of the doublet in Fig. 4 is
about 300 MHz (= 0.01 cm–1). We could not resolve
any further splitting in each component as is seen in
Fig. 2, contrary to the case of the Q2(0) transition of
solid parahydrogen. The broad linewidth is mostly due
to a higher J = 1 concentration in solid orthodeu-
terium (0.25 %) than in solid parahydrogen (0.01 %).
1098 Fizika Nizkikh Temperatur, 2003, v. 29, Nos. 9/10
Hiroyuki Katsuki, Mizuho Fushitani, and Takamasa Momose
–1
11785.380 .395 .850 11758.875
cmWavenumber,
( )b
( )a
( )c
Fig. 3. (a) Calculated Q3(0) transition frequencies with-
out using the quantum parameter �B2 for the fitting. The
best fitted parameters are
2c = –0.0238 cm–1, �
~
B0 (IP) =
= –0.7980 cm–1, and �
~
B0 (OP) = –0.7858 cm–1. The bold
lines show the perpendicular transitions, while the thin
lines show parallel transitions. (b) Calculated frequencies
with the use of all of the five parameters. The parameters
are give in Table. (c) Observed Q3(0) spectrum (same as
Fig. 2 (d)).
The doublet originates in the splitting between
M = 0 and M = � 1 in the v = 2 excited state. From the
spacing of 0.27 cm–1, we estimate the crystal field pa-
rameter �B0 to be 0.45 cm–1 for solid orthodeuterium
[4]. The ratio of �B0between solid D2 and solid H2 for
the Q2(0) transition � �B B0 0
2 2D H is roughly 0.85.
Since the intermolecular interaction between hydro-
gen molecules originates in the dispersion interaction,
the coefficient B0 in Eq. (2) is, as a first order approxi-
mation, roughly proportional to � �J J v R
� �1 0
6
, /
where � J�1 is the anisotropic polarizability of the J = 1
hydrogen molecule, � J n�0, is the isotropic polari-
zability of J = 0 hydrogen molecule in the v = n vibra-
tional state, and R is the distance between two mole-
cules. By referring to the theoretically calculated
polarizabilities [25], the ratio � �B B0 0
2 2D H is calcu-
lated to be around 0.9, which is in good agreement
with the observed value of 0.85.
Since no further splitting is observed in each com-
ponent of the doublet, we conclude that the ground
state crystal field splitting �1 of solid orthodeuterium
is less than the width; that is, 0.01 cm–1. In order to
determine the crystal field parameter accurately as in
the case of solid parahydrogen, we need to reduce the
concentration of paradeuterium in our crystal. Such
work is now underway.
7. Conclusion
In this paper, we discussed the quantum property
of solid hydrogen which is obtainable from high-reso-
lution spectroscopy of the rotation-vibration transi-
tions of hydrogen molecules. It was demonstrated that
the large amplitude of zero-point lattice vibration
modifies the energy levels of the vibrational excited
states significantly, which were clearly observed using
high-resolution spectroscopy. Further studies with
this high-resolution technique will give us more infor-
mation on the nature of quantum solids, which are
otherwise difficult to obtain.
Acknowledgments
The work described herein was supported in part by
the Grant-in Aid for Scientific Research of the Minis-
try of Education, Science, Culture, and Sports of Ja-
pan. The authors would like to thank Prof. H. Meyer
who drew our attention to the problems of solid deute-
rium. Further, H. Katsuki would also like to acknow-
ledge the support from JSPS Research Fellowships for
Young Scientists.
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