Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Canadian Journal of Physics

Spin-polarized hydrogen, deuterium, and tritium: I. Ground-state energy calculated by a lowest order constrained-variation method

Magne Haugen, Erlend Østgaard

Published Jan 1, 1989• 5 citations
Publisher

Abstract

The ground-state energy of spin-polarized hydrogen, deuterium, and tritium is calculated by means of a modified variational lowest order constrained-variation method, and the calculations are done for five different two-body potentials. Spin-polarized H↓ is not self-bound according to our theoretical results for the ground-state binding energy. For spin-polarized D↓, however, we obtain theoretical results for the ground-state binding energy per particle from −0.42 K at an equilibrium particle density of 0.25 σ−3 or a molar volume of 121 cm3/mol to + 0.32 K at an equilibrium particle density of 0.21 σ−3 or a molar volume of 142 cm3/mol, where σ = 3.69 Å (1 Å = 10−10 m). It is, therefore, not clear whether spin-polarized deuterium should be self-bound or not. For spin-polarized T↓, we obtain theoretical results for the ground-state binding energy per particle from −4.73 K at an equilibrium particle density of 0.41 σ−3 or a molar volume of 74 cm3/mol to −1.21 K at an equilibrium particle density of 0.28 σ−3 or a molar volume of 109 cm3/mol.

DOI
10.1139/p89-008

Related papers

The ground state properties of spin-aligned atomic hydrogen, deuterium, and tritium

Richard David Etters, John V. Dugan, Raymond W. Palmer

The bulk, ground state properties of atomic hydrogen, deuterium, and tritium systems are calculated assuming that all pair interactions occur via the 3Σ+u atomic triplet potential. The conditions required to obtain this system, including inhibition of recombination through the energetically favorable singlet interaction, are discussed. The internal energy, pressure, and compressibility are calculated over the volume range 40 cm3/mole ? V ⩽200 cm3/mole applying the Monte Carlo technique with a quantum mechanical variational wavefunction. The system studied consisted of 32 atoms in a box with periodic boundary conditions. Results show that atomic triplet hydrogen and deuterium remain gasous at 0 K; i.e., the internal energy is positive at all molar volumes considered. Under the same conditions, tritium forms a liquid with a binding energy of E0 ? −0.75 K per atom, at a volume of V ? 130 cm3/mole. The pair distribution function for these systems is also calculated. A brief discussion of the predicted superfluid behavior of 3Σ+u hydrogen and tritium is presented.

The Journal of Chemical Physics•Jan 15, 1975•76 citations

Constrained variational calculations for many-body spin-polarized atomic deuterium

B. Skjetne, Erlend Østgaard

A lowest-order constrained variational (LOCV) method, with modified conditions of healing on the two-body Jastrow wave function, is investigated in calculations for the ground-state energy levels of many-body spin-polarized atomic deuterium. Results are obtained for the , and phases, corresponding to equal occupations of one, two or three nuclear spin states. Estimates for the optimum healing conditions are obtained by comparison of LOCV results with current Monte Carlo benchmarks. The nature of the phases, i.e., quantum gas or quantum liquid, is discussed, the energy of the phase in our calculations always occurring above the gas-liquid interphase for healing conditions within a physically acceptable range.

Journal of Physics Condensed Matter•Oct 1, 1999•9 citations

Spin-polarized hydrogen and its isotopes: A rich class of quantum phases (Review Article)

I. Bešlić, Leandra Vranješ Markić, Jordi Boronat

We review the recent activity in the theoretical description of spin-polarized atomic hydrogen and its isotopes at very low temperatures. Spin-polarized hydrogen is the only system in nature that remains stable in the gas phase even in the zero temperature limit due to its small mass and weak interatomic interaction. Hydrogen and its heavier isotope tritium are bosons, the heavier mass of tritium producing a self-bound (liquid) system at zero temperature. The other isotope, deuterium, is a fermion with nuclear spin one making possible the study of three different quantum systems depending on the population of the three degenerate spin states. From the theoretical point of view, spin-polarized hydrogen is specially appealing because its interatomic potential is very accurately known making possible its precise quantum many-body study. The experimental study of atomic hydrogen has been very difficult due to its high recombination rate, but it finally led to its Bose-Einstein condensate state in 1998. Degeneracy has also been observed in thin films of hydrogen adsorbed on the 4He surface allowing for the possibility of observing the Berezinskii–Kosterlitz–Thouless superfluid transition.

Low Temperature Physics•Oct 1, 2013•9 citations

Stability limits of mixed spin-polarised tritium clusters

I Bešlić, Leandra Vranješ Markić, Jordi Boronat

We present variational and diffusion Monte Carlo studies of pure and mixed spin-polarised tritium clusters. Our results for pure clusters, consisting of only tritium atoms T↓, are in good agreement with previous calculations. We show that mixed clusters, consisting of up to 60 T↓ atoms and one spin-polarized deuterium D↓ atom are stable. On the other hand, we verified that tritium clusters of up to N = 60 atoms do not bind even one H↓ atom; the ground-state energy of the considered mixed T↓-H↓ clusters is within the errorbars equal to or higher than the energy of the pure tritium cluster. In addition to the energy, we present results of the structure of the clusters, which has been determined using unbiased estimators. For larger N , a D↓ atom forms an Andreev state on the surface of a tritium cluster core. The H↓ atoms stay further away from the center of the cluster than the D↓ atoms and slowly increase their separation as the simulation proceeds, indicating instability.

Journal of Physics Conference Series•Feb 1, 2009•4 citations

Ground-state phases of polarized deuterium species

Robert M. Panoff, J. W. Clark

Microscopic prediction of the ground-state phase of electron-spin-aligned bulk atomic deuterium (D\ensuremath{\downarrow}) is attempted, based on the variational Monte Carlo method. The accurate pair potential of Kolos and Wolniewicz is assumed, and three versions of D\ensuremath{\downarrow} are considered, which, respectively, involve one, two, and three equally occupied nuclear spin states. The most definitive results on the zero-temperature equations of state of these systems are obtained with optimized ground-state trial wave functions incorporating Jastrow pair correlations, triplet correlations, and momentum-dependent backflow effects. The species D${\ensuremath{\downarrow}}_{3}$ is bound already at the pure Jastrow level, while the energy expectation value of D${\ensuremath{\downarrow}}_{2}$ dips below zero upon supplementing the Jastrow description by triplets and momentum-dependent backflow. The variational energy of D${\ensuremath{\downarrow}}_{1}$ remains positive under all current refinements of the ground-state trial function. We conclude that the systems D${\ensuremath{\downarrow}}_{3}$ and D${\ensuremath{\downarrow}}_{2}$, if they could be manufactured and stabilized at relevant densities, would be Fermi liquids at sufficiently low temperature; on the other hand, it is likely that D${\ensuremath{\downarrow}}_{1}$ would remain gaseous down to absolute zero.

Physical review. B, Condensed matter•Oct 1, 1987•20 citations

Ground state of small mixed helium and spin-polarized tritium clusters: A quantum Monte Carlo study

Petar Stipanović, Leandra Vranješ Markić, Jordi Boronat +1 more

We report results for the ground-state energy and structural properties of small (4)He-T↓ clusters consisting of up to four T↓ and eight (4)He atoms. These results have been obtained using very well-known (4)He-(4)He and T↓- T↓ interaction potentials and several models for the (4)He- T↓ interatomic potential. All the calculations have been performed with variational and diffusion Monte Carlo methods. It takes at least three atoms to form a mixed bound state. In particular, for small clusters the binding energies are significantly affected by the precise form of the (4)He- T↓ interatomic potential but the stability limits remain unchanged. The only exception is the (4)He(2)T↓ trimer whose stability in the case of the weakest (4)He- T↓ interaction potential is uncertain while it seems stable for other potentials. The mixed trimer (4)He(T↓)(2), a candidate for the Borromean state, is not bound. All other studied clusters are stable. Some of the weakest bound clusters can be classified as quantum halo as a consequence of having high probability of being in a classically forbidden region.

arXiv:1012.3262•The Journal of Chemical Physics•Feb 2, 2011•16 citations
The ground-state energy of spin-polarized hydrogen, deuterium, and tritium is calculated by means of a modified variational lowest order constrained-variation method, and the calculations are done for five different two-body potentials. Spin-polarized H↓ is not self-bound according to our theoretical results for the ground-state binding energy. For spin-polarized D↓, however, we obtain theoretical results for the ground-state binding energy per particle from −0.42 K at an equilibrium particle density of 0.25 σ−3 or a molar volume of 121 cm3/mol to + 0.32 K at an equilibrium particle density of 0.21 σ−3 or a molar volume of 142 cm3/mol, where σ = 3.69 Å (1 Å = 10−10 m). It is, therefore, not clear whether spin-polarized deuterium should be self-bound or not. For spin-polarized T↓, we obtain theoretical results for the ground-state binding energy per particle from −4.73 K at an equilibrium particle density of 0.41 σ−3 or a molar volume of 74 cm3/mol to −1.21 K at an equilibrium particle density of 0.28 σ−3 or a molar volume of 109 cm3/mol.
The bulk, ground state properties of atomic hydrogen, deuterium, and tritium systems are calculated assuming that all pair interactions occur via the 3Σ+u atomic triplet potential. The conditions required to obtain this system, including inhibition of recombination through the energetically favorable singlet interaction, are discussed. The internal energy, pressure, and compressibility are calculated over the volume range 40 cm3/mole ? V ⩽200 cm3/mole applying the Monte Carlo technique with a quantum mechanical variational wavefunction. The system studied consisted of 32 atoms in a box with periodic boundary conditions. Results show that atomic triplet hydrogen and deuterium remain gasous at 0 K; i.e., the internal energy is positive at all molar volumes considered. Under the same conditions, tritium forms a liquid with a binding energy of E0 ? −0.75 K per atom, at a volume of V ? 130 cm3/mole. The pair distribution function for these systems is also calculated. A brief discussion of the predicted superfluid behavior of 3Σ+u hydrogen and tritium is presented.
A lowest-order constrained variational (LOCV) method, with modified conditions of healing on the two-body Jastrow wave function, is investigated in calculations for the ground-state energy levels of many-body spin-polarized atomic deuterium. Results are obtained for the , and phases, corresponding to equal occupations of one, two or three nuclear spin states. Estimates for the optimum healing conditions are obtained by comparison of LOCV results with current Monte Carlo benchmarks. The nature of the phases, i.e., quantum gas or quantum liquid, is discussed, the energy of the phase in our calculations always occurring above the gas-liquid interphase for healing conditions within a physically acceptable range.
We review the recent activity in the theoretical description of spin-polarized atomic hydrogen and its isotopes at very low temperatures. Spin-polarized hydrogen is the only system in nature that remains stable in the gas phase even in the zero temperature limit due to its small mass and weak interatomic interaction. Hydrogen and its heavier isotope tritium are bosons, the heavier mass of tritium producing a self-bound (liquid) system at zero temperature. The other isotope, deuterium, is a fermion with nuclear spin one making possible the study of three different quantum systems depending on the population of the three degenerate spin states. From the theoretical point of view, spin-polarized hydrogen is specially appealing because its interatomic potential is very accurately known making possible its precise quantum many-body study. The experimental study of atomic hydrogen has been very difficult due to its high recombination rate, but it finally led to its Bose-Einstein condensate state in 1998. Degeneracy has also been observed in thin films of hydrogen adsorbed on the 4He surface allowing for the possibility of observing the Berezinskii–Kosterlitz–Thouless superfluid transition.
We present variational and diffusion Monte Carlo studies of pure and mixed spin-polarised tritium clusters. Our results for pure clusters, consisting of only tritium atoms T↓, are in good agreement with previous calculations. We show that mixed clusters, consisting of up to 60 T↓ atoms and one spin-polarized deuterium D↓ atom are stable. On the other hand, we verified that tritium clusters of up to N = 60 atoms do not bind even one H↓ atom; the ground-state energy of the considered mixed T↓-H↓ clusters is within the errorbars equal to or higher than the energy of the pure tritium cluster. In addition to the energy, we present results of the structure of the clusters, which has been determined using unbiased estimators. For larger N , a D↓ atom forms an Andreev state on the surface of a tritium cluster core. The H↓ atoms stay further away from the center of the cluster than the D↓ atoms and slowly increase their separation as the simulation proceeds, indicating instability.
Microscopic prediction of the ground-state phase of electron-spin-aligned bulk atomic deuterium (D\ensuremath{\downarrow}) is attempted, based on the variational Monte Carlo method. The accurate pair potential of Kolos and Wolniewicz is assumed, and three versions of D\ensuremath{\downarrow} are considered, which, respectively, involve one, two, and three equally occupied nuclear spin states. The most definitive results on the zero-temperature equations of state of these systems are obtained with optimized ground-state trial wave functions incorporating Jastrow pair correlations, triplet correlations, and momentum-dependent backflow effects. The species D${\ensuremath{\downarrow}}_{3}$ is bound already at the pure Jastrow level, while the energy expectation value of D${\ensuremath{\downarrow}}_{2}$ dips below zero upon supplementing the Jastrow description by triplets and momentum-dependent backflow. The variational energy of D${\ensuremath{\downarrow}}_{1}$ remains positive under all current refinements of the ground-state trial function. We conclude that the systems D${\ensuremath{\downarrow}}_{3}$ and D${\ensuremath{\downarrow}}_{2}$, if they could be manufactured and stabilized at relevant densities, would be Fermi liquids at sufficiently low temperature; on the other hand, it is likely that D${\ensuremath{\downarrow}}_{1}$ would remain gaseous down to absolute zero.
We report results for the ground-state energy and structural properties of small (4)He-T↓ clusters consisting of up to four T↓ and eight (4)He atoms. These results have been obtained using very well-known (4)He-(4)He and T↓- T↓ interaction potentials and several models for the (4)He- T↓ interatomic potential. All the calculations have been performed with variational and diffusion Monte Carlo methods. It takes at least three atoms to form a mixed bound state. In particular, for small clusters the binding energies are significantly affected by the precise form of the (4)He- T↓ interatomic potential but the stability limits remain unchanged. The only exception is the (4)He(2)T↓ trimer whose stability in the case of the weakest (4)He- T↓ interaction potential is uncertain while it seems stable for other potentials. The mixed trimer (4)He(T↓)(2), a candidate for the Borromean state, is not bound. All other studied clusters are stable. Some of the weakest bound clusters can be classified as quantum halo as a consequence of having high probability of being in a classically forbidden region.