Advanced search
Publication Cover
Molecular Physics
An International Journal at the Interface Between Chemistry and Physics
Volume 77, 1992 - Issue 2
Submit an article Journal homepage
155
Views
101
CrossRef citations to date
0
Altmetric
Original Articles

Exchange-coulomb potential energy curves for He-He, and related physical properties

Ronald A. Aziz Department of Physics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada
,
M.J. Slaman Department of Physics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada
,
A. Koide Department of Chemistry, University of Western Ontario, London, Ontario, N6A 5B7, Canada; Japan Science Institute, IBM, Japan, Ltd., 5-19, Sanban-cho, Chiyoda-ku, Tokyo, 102, Japan
,
A.R. Allnatt Department of Chemistry, University of Western Ontario, London, Ontario, N6A 5B7, Canada
&
William J. Meath Department of Chemistry, University of Western Ontario, London, Ontario, N6A 5B7, Canada
Pages 321-337 | Received 03 Dec 1991, Accepted 18 Feb 1992, Published online: 22 Aug 2006

Citations (101)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (7)

Henri Piel & Michael Chrysos. (2020) From Lippmann-Schwinger formulations to a general formula for absolute asymptotic scattering phase functions and shifts: a unified framework for potentials of any range. Molecular Physics 118:1.
Read now
Henri Piel & Michael Chrysos. (2018) A shortcut to quantum-mechanical absolute scattering phase-shift computations in van der Waals systems. Molecular Physics 116:18, pages 2364-2373.
Read now
ASHOK K. DHAM. (1996) Multi-property predictions from recent He-CO potential energy surfaces and related comments on the nature of heteronuclear-rare gas interactions. Molecular Physics 88:2, pages 339-353.
Read now
RichardJ. Wheatley. (1996) The solvation of sodium ions in water clusters: intermolecular potentials for Na+-H2O and H2O-H2O. Molecular Physics 87:5, pages 1083-1116.
Read now
RichardJ. Wheatley. (1995) First-order Coulomb interaction energies for atoms and diatomic molecules. Molecular Physics 86:3, pages 443-465.
Read now
RichardJ. Wheatley & WilliamJ. Meath. (1993) Dispersion energy damping functions, and their relative scale with interatomic separation, for (H, He, Li)-(H, He, Li) interactions. Molecular Physics 80:1, pages 25-54.
Read now
RichardJ. Wheatley & WilliamJ. Meath. (1993) On the relationship between first-order exchange and Coulomb interaction energies for closed shell atoms and molecules. Molecular Physics 79:2, pages 253-275.
Read now

Articles from other publishers (94)

Henri Godfrin & Eckhard Krotscheck. 2024. Encyclopedia of Condensed Matter Physics. Encyclopedia of Condensed Matter Physics 946 958 .
Lorenz Kranabetter, Henrik H. Kristensen, Areg Ghazaryan, Constant A. Schouder, Adam S. Chatterley, Paul Janssen, Frank Jensen, Robert E. Zillich, Mikhail Lemeshko & Henrik Stapelfeldt. (2023) Nonadiabatic Laser-Induced Alignment Dynamics of Molecules on a Surface. Physical Review Letters 131:5.
Crossref
Massimo Boninsegni. (2023) The Solid Phase of 4He: A Monte Carlo Simulation Study. Entropy 25:8, pages 1114.
Crossref
Jeonghwan Ahn & Yongkyung Kwon. (2023) Vacancy-induced supersolidity of the second layer on a biphenylene carbon sheet . Physical Review B 107:9.
Crossref
Benjamin J. Sutherland, William H. D. Moore & David E. Manolopoulos. (2021) Nuclear quantum effects in thermal conductivity from centroid molecular dynamics. The Journal of Chemical Physics 154:17.
Crossref
Jeonghwan Ahn, Tyler Volkoff, Jae-Sung Kim & Yongkyung Kwon. (2020) Two-dimensional superfluidity in clusters intercalated into graphite . Physical Review B 102:14.
Crossref
Takaaki Miyazaki & Toshiyuki Takayanagi. (2019) Ionization dynamics of Ne-doped helium clusters at low temperature: Ring-polymer molecular dynamics simulations including electronically nonadiabatic transitions. Computational and Theoretical Chemistry 1163, pages 112537.
Crossref
Hsuan Hao Fan & Eckhard Krotscheck. (2019) Variational and Parquet-diagram theory for strongly correlated normal and superfluid systems. Physics Reports 823, pages 1-59.
Crossref
Jeonghwan Ahn, Mujin You, Gwangyoung Lee, Tyler Volkoff & Yongkyung Kwon. (2019) Symmetry-changing commensurate-incommensurate solid transition in the monolayer on 6,6,12-graphyne . Physical Review B 99:2.
Crossref
Kento Suzuki, Takaaki Miyazaki, Toshiyuki Takayanagi & Motoyuki Shiga. (2018) Nuclear quantum effects in the direct ionization process of pure helium clusters: path-integral and ring-polymer molecular dynamics simulations on the diatomics-in-molecule potential energy surfaces. Physical Chemistry Chemical Physics 20:41, pages 26489-26499.
Crossref
Eiki Ozama, Sadia Adachi, Toshiyuki Takayanagi & Motoyuki Shiga. (2018) Quantum Simulation Verifies the Stability of an 18-Coordinated Actinium-Helium Complex. Chemistry - A European Journal 24:48, pages 12716-12721.
Crossref
Sungjin Park & Yongkyung Kwon. (2018) 4He adsorption on a single C40 molecule: Path integral Monte Carlo study. Journal of the Korean Physical Society 72:1, pages 95-100.
Crossref
Haruna Imaoka & Kenichi Kinugawa. (2017) Transport coefficients of normal liquid helium-4 calculated by path integral centroid molecular dynamics simulation. Chemical Physics Letters 671, pages 174-181.
Crossref
Yusuke Seki, Toshiyuki Takayanagi & Motoyuki Shiga. (2017) Photoexcited Ag ejection from a low-temperature He cluster: a simulation study by nonadiabatic Ehrenfest ring-polymer molecular dynamics. Physical Chemistry Chemical Physics 19:21, pages 13798-13806.
Crossref
Haohua Wen & C.H. Woo. (2016) Quantum statistical vibrational entropy and enthalpy of formation of helium-vacancy complex in BCC W. Journal of Nuclear Materials 482, pages 99-104.
Crossref
Tyler Volkoff, Yongkyung Kwon & K. Birgitta Whaley. (2016) Path integral Monte Carlo simulation of global and local superfluidity in liquid reservoirs separated by nanoscale apertures . Physical Review B 94:14.
Crossref
Jeonghwan Ahn, Hoonkyung Lee & Yongkyung Kwon. (2016) Prediction of stable and metastable commensurate solid phases for on graphite . Physical Review B 93:6.
Crossref
Robert E. Zillich. (2015) Combination of the pair density approximation and the Takahashi–Imada approximation for path integral Monte Carlo simulations. Journal of Computational Physics 301, pages 111-118.
Crossref
Sungjin Park, Byeongjoon Kim & Yongkyung Kwon. (2015) Anisotropic superfluidity of 4He on a C36 fullerene molecule. The Journal of Chemical Physics 143:10.
Crossref
Jeonghwan Ahn, Sungjin Park, Hoonkyung Lee & Yongkyung Kwon. (2015) Interlayer correlation between two monolayers adsorbed on both sides of -graphyne . Physical Review B 92:3.
Crossref
Yongkyung Kwon. (2015) Van der Waals correlation between two 4He monolayers on the opposite sides of graphene. Journal of the Korean Physical Society 66:12, pages 1856-1861.
Crossref
Patrick J. Kelleher, Christopher J. Johnson, Joseph A. Fournier, Mark A. Johnson & Anne B. McCoy. (2015) Persistence of Dual Free Internal Rotation in NH 4 + (H 2 O)·He n =0–3 Ion–Molecule Complexes: Expanding the Case for Quantum Delocalization in He Tagging . The Journal of Physical Chemistry A 119:18, pages 4170-4176.
Crossref
Jeonghwan Ahn, Hoonkyung Lee & Yongkyung Kwon. (2014) Commensurate-incommensurate solid transition in the monolayer on -graphyne . Physical Review B 90:7.
Crossref
Sungjin Park & Yongkyung Kwon. (2014) adsorption on a -plated molecular surface: The formation of helium buckyballs . Physical Review E 89:4.
Crossref
JOHN W. CLARK. (2013) MEMORIAL TRIBUTE TO MANFRED L. RISTIG (1935–2011). International Journal of Modern Physics B 27:29, pages 1347003.
Crossref
Yongkyung Kwon, Hyeondeok Shin & Hoonkyung Lee. (2013) Mott-insulator to commensurate-solid transition in a He layer on -graphyne . Physical Review B 88:20.
Crossref
Byeongjoon Kim & Yongkyung Kwon. (2012) Structural and Superfluid Properties of the 4He Monolayer on a C28 Molecule. Journal of Low Temperature Physics 171:5-6, pages 599-605.
Crossref
Yongkyung Kwon & David M. Ceperley. (2012) He adsorption on a single graphene sheet: Path-integral Monte Carlo study . Physical Review B 85:22.
Crossref
Piotr Kowalczyk, Piotr A. Gauden, Artur P. Terzyk, Sylwester Furmaniak & Katsumi Kaneko. (2011) Cryogenic Helium Adsorbed in Zeolite Rho: Inside Localization Controlled Self-Diffusion of Confined Quantum Particles. The Journal of Physical Chemistry C 115:37, pages 18105-18110.
Crossref
Jian Liu, Berni J. Alder & William H. Miller. (2011) A semiclassical study of the thermal conductivity of low temperature liquids. The Journal of Chemical Physics 135:11, pages 114105.
Crossref
Orly Kletenik-Edelman, David R. Reichman & Eran Rabani. (2011) On the mode-coupling treatment of collective density fluctuations for quantum liquids: Para -hydrogen and normal liquid helium . The Journal of Chemical Physics 134:4.
Crossref
K. A. GERNOTH & M. L. RISTIG. (2012) RENORMALIZED BOSONS AND FERMIONS. International Journal of Modern Physics B 24:25n26, pages 4979-4992.
Crossref
M. L. Ristig & K. A. Gernoth. (2009) Statistical Properties of Strongly Correlated Quantum Liquids. Foundations of Physics 40:9-10, pages 1253-1262.
Crossref
Orly Kletenik-Edelman, Eran Rabani & David R. Reichman. (2010) Analytic continuation average spectrum method for transport in quantum liquids. Chemical Physics 370:1-3, pages 132-136.
Crossref
Ashok K. Dham, George C. McBane, Frederick R. W. McCourt & William J. Meath. (2010) An exchange-Coulomb model potential energy surface for the Ne–CO interaction. II. Molecular beam scattering and bulk gas phenomena in Ne–CO mixtures. The Journal of Chemical Physics 132:2.
Crossref
K. A. GERNOTH & M. L. RISTIG. (2012) FLUID HELIUM-4 IN THERMAL EQUILIBRIUM. International Journal of Modern Physics B 23:20n21, pages 4096-4108.
Crossref
K. A. GERNOTH. (2012) QUASICLASSICAL FOURIER PATH INTEGRAL QUANTUM CORRECTION TERMS TO THE KINETIC ENERGY OF INTERACTING QUANTUM MANY-BODY SYSTEMS. International Journal of Modern Physics B 23:20n21, pages 3979-3991.
Crossref
Piotr Kowalczyk, Piotr A. Gauden, Artur P. Terzyk & Sylwester Furmaniak. (2009) Frequency-Dependent Diffusion Constant of Quantum Fluids from Path Integral Monte Carlo and Tikhonov’s Regularizing Functional. Journal of Chemical Theory and Computation 5:8, pages 1990-1996.
Crossref
Ashok K. Dham, Frederick R. W. McCourt & William J. Meath. (2009) An exchange-Coulomb model potential energy surface for the Ne–CO interaction. I. Calculation of Ne–CO van der Waals spectra. The Journal of Chemical Physics 130:24.
Crossref
Piotr Kowalczyk, Lorenzo Brualla, Piotr A. Gauden & Artur P. Terzyk. (2009) Static and thermodynamic properties of low-density supercritical 4He—breakdown of the Feynman–Hibbs approximation. Physical Chemistry Chemical Physics 11:40, pages 9182.
Crossref
Haruki Motegi, Akira Kakizaki, Toshiyuki Takayanagi, Yuriko Taketsugu, Tetsuya Taketsugu & Motoyuki Shiga. (2008) Path-integral molecular dynamics simulations of BeO embedded in helium clusters: Formation of the stable HeBeO complex. Chemical Physics 354:1-3, pages 38-43.
Crossref
K. A. GERNOTH, M. SERHAN & M. L. RISTIG. (2012) STRONGLY CORRELATED BOSONS AT NONZERO TEMPERATURES. International Journal of Modern Physics B 22:25n26, pages 4315-4326.
Crossref
K. A. Gernoth, M. Serhan & M. L. Ristig. (2008) Quantum structure of normal-liquid and supercritical . Physical Review B 78:5.
Crossref
Alexander B. Pacheco, Brian Thorndyke, Andrés Reyes & David A. Micha. (2007) Quantum dynamics of an excited alkali atom in a noble gas cluster: Lithium attached to a helium cluster. The Journal of Chemical Physics 127:24.
Crossref
Ashok K. Dham, Frederick R. W. McCourt & Alan S. Dickinson. (2007) Accuracy of recent potential energy surfaces for the He–N2 interaction. I. Virial and bulk transport coefficients. The Journal of Chemical Physics 127:5.
Crossref
K. A. GERNOTH, MANFRED L. RISTIG & THOMAS LINDENAU. (2012) QUANTUM BOLTZMANN LIQUIDS. International Journal of Modern Physics B 21:13n14, pages 2157-2168.
Crossref
KEOLA WIERSCHEM & EFSTRATIOS MANOUSAKIS. (2012) MONOLAYER CHARGED QUANTUM FILMS: A QUANTUM SIMULATION STUDY. International Journal of Modern Physics B 20:19, pages 2667-2676.
Crossref
Ashok K. Dham, William J. Meath, Jason W. Jechow & Frederick R. W. McCourt. (2006) New exchange-Coulomb N2–Ar potential-energy surface and its comparison with other recent N2–Ar potential-energy surfaces. The Journal of Chemical Physics 124:3.
Crossref
Eran Rabani, Goran Krilov, David R. Reichman & B. J. Berne. (2005) Transport properties of normal liquid helium: Comparison of various methodologies. The Journal of Chemical Physics 123:18.
Crossref
TOSHIYUKI TAKAYANAGI, MOTOYUKI SHIGA & TETSUYA TAKETSUGU. (2011) DEVELOPMENT OF A THREE-DIMENSIONAL AB INITIO POTENTIAL ENERGY SURFACE FOR THE He – Cl 2 (X) SYSTEM AND ITS APPLICATION TO SOLVATION STRUCTURES IN THE He n Cl 2 CLUSTERS . Journal of Theoretical and Computational Chemistry 04:01, pages 197-207.
Crossref
Hua Wei, Robert J. Le Roy, Richard Wheatley & William J. Meath. (2005) A reliable new three-dimensional potential energy surface for H2–Kr. The Journal of Chemical Physics 122:8.
Crossref
Klaus A. Gernoth. (2003) Crystallographic point and space group symmetries in the one-and two-body density of crystals and generalized Patterson functions: Fourier path integral Monte Carlo case studies of novel high-temperature/high-pressure 4 He quantum crystals . Zeitschrift für Kristallographie - Crystalline Materials 218:10, pages 651-674.
Crossref
Toshiyuki Takayanagi & Motoyuki Shiga. (2003) Photodissociation of Cl2 in helium clusters: an application of hybrid method of quantum wavepacket dynamics and path integral centroid molecular dynamics. Chemical Physics Letters 372:1-2, pages 90-96.
Crossref
J. H. Dymond, K. N. Marsh & R. C. Wilhoit. 2003. Virial Coefficients of Mixtures. Virial Coefficients of Mixtures 1 12 .
Toshiyuki Takayanagi & Motoyuki Shiga. (2002) Path integral molecular dynamics combined with discrete-variable-representation approach: the effect of solvation structures on vibrational spectra of Cl2 in helium clusters. Chemical Physics Letters 362:5-6, pages 504-510.
Crossref
Tim Gollisch & Christof Wetterich. (2002) Equation of state for helium-4 from microphysics. Physical Review B 65:13.
Crossref
Keiko Shinoda, Shinichi Miura & Susumu Okazaki. (2001) A generalized Ornstein–Zernike integral equation study of atomic impurities in quantum fluids. The Journal of Chemical Physics 115:9, pages 4161-4168.
Crossref
Klaus A. Gernoth. (2001) Analytical and Numerical (Monte Carlo) Studies of Point and Space Group Symmetry-Breaking in the Liquid–Solid Phase Transition. Annals of Physics 291:2, pages 202-266.
Crossref
Keiko Shinoda, Shinichi Miura & Susumu Okazaki. (2001) A molecular approach to quantum fluids based on a generalized Ornstein–Zernike integral equation. The Journal of Chemical Physics 114:17, pages 7497-7505.
Crossref
Keiko Shinoda, Shinichi Miura & Susumu Okazaki. (2001) Isotope effect on the structure of quantum fluid: a generalized Ornstein–Zernike analysis. Chemical Physics Letters 337:4-6, pages 306-312.
Crossref
Kenichi Kinugawa, Hidemi Nagao & Koji Ohta. (2001) A path integral centroid molecular dynamics method for Bose and Fermi statistics. Journal of Molecular Liquids 90:1-3, pages 11-20.
Crossref
Akira Nakayama & Koichi Yamashita. (2001) Path integral Monte Carlo study on the structure and absorption spectra of alkali atoms (Li, Na, K) attached to superfluid helium clusters. The Journal of Chemical Physics 114:2, pages 780-791.
Crossref
Klaus A. Gernoth. (2000) Explorations of the Microstructure of Crystalline Quantum Many-Body Systems. Annals of Physics 285:1, pages 61-137.
Crossref
M. E. Pierce & E. Manousakis. (2000) Role of substrate corrugation in helium monolayer solidification. Physical Review B 62:8, pages 5228-5237.
Crossref
Leszek Szybisz. (2000) Wetting of potassium surfaces by superfluid A study using variational properties of the chemical potential . Physical Review B 62:6, pages 3986-3996.
Crossref
Akira Nakayama & Koichi Yamashita. (2000) Theoretical study on the structure of Na+-doped helium clusters: Path integral Monte Carlo calculations. The Journal of Chemical Physics 112:24, pages 10966-10975.
Crossref
M. E. Pierce & E. Manousakis. (1999) Monolayer Solid Clusters on Graphite . Physical Review Letters 83:25, pages 5314-5317.
Crossref
Shuji Ogata. (1999) Path-Integral Monte Carlo Simulations for Excitation Spectra of Cs in Superfluid He. Journal of the Physical Society of Japan 68:7, pages 2153-2156.
Crossref
Kenichi Kinugawa, Hidemi Nagao & Koji Ohta. (1999) Path integral centroid molecular dynamics method for Bose and Fermi statistics: formalism and simulation. Chemical Physics Letters 307:3-4, pages 187-197.
Crossref
Shinichi Miura, Susumu Okazaki & Kenichi Kinugawa. (1999) A path integral centroid molecular dynamics study of nonsuperfluid liquid helium-4. The Journal of Chemical Physics 110:9, pages 4523-4532.
Crossref
Marlon Pierce & Efstratios Manousakis. (1999) Path-integral Monte Carlo simulation of the second layer of adsorbed on graphite . Physical Review B 59:5, pages 3802-3814.
Crossref
P. A. Whitlock, G. V. Chester & B. Krishnamachari. (1998) Monte Carlo simulation of a helium film on graphite. Physical Review B 58:13, pages 8704-8715.
Crossref
Marlon Pierce & Efstratios Manousakis. (1998) Phase Diagram of Second Layer of Adsorbed on Graphite . Physical Review Letters 81:1, pages 156-159.
Crossref
R. T. Azuah, W. G. Stirling, H. R. Glyde, M. Boninsegni, P. E. Sokol & S. M. Bennington. (1997) Condensate and final-state effects in superfluid . Physical Review B 56:22, pages 14620-14630.
Crossref
S Moroni & M Boninsegni. (1997) Bose condensate and structure of isotopic liquid-helium mixtures. Europhysics Letters (EPL) 40:3, pages 287-292.
Crossref
Massimo Boninsegni & Saverio Moroni. (1997) Microscopic Calculation of Superfluidity and Kinetic Energies in Isotopic Liquid Helium Mixtures. Physical Review Letters 78:9, pages 1727-1730.
Crossref
Florent Xavier Gadea & Ivana Paidarová. (1996) Ab initio calculations for Ar2+, He2+ and He3+, of interest for the modelling of ionic rare-gas clusters. Chemical Physics 209:2-3, pages 281-290.
Crossref
Massimo Boninsegni & David M. Ceperley. (1996) Density fluctuations in liquid4He. Path integrals and maximum entropy. Journal of Low Temperature Physics 104:5-6, pages 339-357.
Crossref
Carey Bissonnette, Claudio E. Chuaqui, Kenneth G. Crowell, Robert J. Le Roy, Richard J. Wheatley & William J. Meath. (1996) A reliable new potential energy surface for H2–Ar. The Journal of Chemical Physics 105:7, pages 2639-2653.
Crossref
B. Skjetne & E. �stgaard. (1996) Liquid4He: Modified LOCV ground-state energy calculations. Journal of Low Temperature Physics 104:3-4, pages 275-291.
Crossref
Richard J. Wheatley & William J. Meath. (1996) Dispersion and induction energy damping functions, and their scale with interspecies distance, for the interaction of H− with H, He and Li atoms. Chemical Physics 203:2, pages 209-221.
Crossref
Saverio Moroni & Massimo Boninsegni. (1996) Monte Carlo study of isotopic liquid Helium mixtures. Czechoslovak Journal of Physics 46:S1, pages 303-304.
Crossref
A. R. Janzen & R. A. Aziz. (1995) Modern He–He potentials: Another look at binding energy, effective range theory, retardation, and Efimov states. The Journal of Chemical Physics 103:22, pages 9626-9630.
Crossref
Ashok K. Dham, Frederick R. W. McCourt & William J. Meath. (1995) Exchange–Coulomb model potential energy surface for the N2–Ar interaction. The Journal of Chemical Physics 103:19, pages 8477-8491.
Crossref
Jacek Komasa & Ajit J. Thakkar. (1995) Accurate Heitler-London interaction energy for He2. Journal of Molecular Structure: THEOCHEM 343, pages 43-48.
Crossref
Ashok K. Dham & William J. Meath. (1995) Exchange-Coulomb potential energy surfaces, and related physical properties, for KrN2. Chemical Physics 196:1-2, pages 125-138.
Crossref
Ashok K. Dham, A.R. Allnatt, A. Koide & William J. Meath. (1995) Representations of dispersion energy damping functions for interactions of closed shell atoms and molecules. Chemical Physics 196:1-2, pages 81-99.
Crossref
D. M. Ceperley. (1995) Path integrals in the theory of condensed helium. Reviews of Modern Physics 67:2, pages 279-355.
Crossref
Ronald A. Aziz, Alec R. Janzen & Michael R. Moldover. (1995) Ab Initio Calculations for Helium: A Standard for Transport Property Measurements . Physical Review Letters 74:9, pages 1586-1589.
Crossref
Richard J. Wheatley & John B. O. Mitchell. (2004) Gaussian multipoles in practice: Electrostatic energies for intermolecular potentials. Journal of Computational Chemistry 15:11, pages 1187-1198.
Crossref
M. Boninsegni, C. Pierleoni & D. M. Ceperley. (1994) Isotopic shift of helium melting pressure: Path integral Monte Carlo study. Physical Review Letters 72:12, pages 1854-1857.
Crossref
Richard J. Wheatley & William J. Meath. (1994) Induction and dispersion damping functions, and their relative scale with interspecies distance, for (H+, He+, Li+)-(H, He, Li) interactions. Chemical Physics 179:3, pages 341-364.
Crossref
Robert J. LeRoy, Carey Bissonnette, Thomas H. Wu, Ashok K. Dham & William J. Meath. (1994) Improved modelling of atom–molecule potential-energy surfaces: illustrative application to He–CO. Faraday Discuss. 97, pages 81-94.
Crossref
Fei Luo, Geunsik Kim, Clayton F. Giese & W. Ronald Gentry. (1993) Influence of retardation on the higher-order multipole dispersion contributions to the helium dimer potential. The Journal of Chemical Physics 99:12, pages 10084-10085.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.