ATOMIC, MOLECULAR AND OPTICAL PHYSICS

Together with colleagues (faculty and students), I have used hyperspherical harmonics to "do" nuclear, molecular and atomic calculations: the atomic calculations seem especially promising. Our goal is to construct good, relatively simple, wave functions for atomic systems with more than 2 electrons, that yield energies with errors less than 1 part in 10,000, and do this for excited states as well as for the ground state - which is much easier to calculate. That is very important as current methods cannot be extended to more than 2 electrons, or can do so only with very great difficulties.

Colleagues and I have developed a method in which the essential parts of atomic wave functions are isolated and written in terms of 1-body and 2-body amplitudes. These can then be expanded, in a particularly economical way, in terms of a subset of a general hyperspherical basis. We obtain by this procedure wave functions which faithfully preserve 2-body correlations, while enormously simplifying calculations. Testing this method by doing calculations for helium and H-minus (2 electron systems) we obtained very good results.

The challenge is now to calculate binding energies for 3 and 4-electron systems (Lithium and Beryllium), and demonstrate the worth of our method for more than 2 electrons. This is what we have started to do.

STATISTICAL MECHANICS

One of my longstanding interests has been to demonstrate and implement a beautiful relationship between Statistical Mechanics and Scattering theory. It allows us to calculate traces in statistical mechanics, just from binding energies and asymptotic quantities (large distance properties of the few body wave functions) such as few body S-matrices. The goal is to calculate cluster coefficients (and therefore also coefficients arising from density expansions of thermodynamical quantities), which at the present time we can do classically, but are still only learning to do quantum mechanically.

I have pioneered in trying to obtain the few body S-matrix by using Hyperspherical methods (going to a "higher dimensional" coordinate system well suited to describe wave functions of 3 and more particles) and Adiabatic bases. Besides our use of the S-matrix in the statistical mechanics context, its calculation gives us results interesting in other areas, such as atomic and molecular physics, since it involves looking at such phenomena as elastic and inelastic scattering rearrangements and break-up. Though many results have been obtained (3-body clusters at very low temperatures, semi-classical limits, hyperspherical harmonics, model S-matrix calculations...), by my collaborators and me, great challenges remain!

Mu Decay with Nonconvervation of Parity - S. Larsen, E. Lubkin and M. Tausner. Phys. Rev. 107, 856 (1957).

Quantum-Mechanical Calculation of the Third Virial Coefficient of He⁴ - S. Y. Larsen. Phys. Rev. 130, 1426 (1963).

Three-Body Bound State in He⁴ - J. M. Blatt, J. N. Lyness and S. Y. Larsen. Phys. Rev. 131, 2131-3132 (1963).

On the Behaviour of the Compressibility Along the Critical Iso\-therm - S. Larsen and J. M. H. Levelt Sengers. Advances in Thermophysical Properties of Extreme Temperatures and Pressures, A.S.M.E., 74 (1965).

On the Validity of the Lorentz-Lorenz Equation Near the Critical Point - S. Larsen, R. Mountain, and R. Zwanzig. J. Chem. Phys. 42, 2187 (l965).

Thermodynamics of the Rigid Rotor at High Temperature - J. Kilpatrick, Y. Fukuda and S. Larsen. J. Chem. Phys. 43, 430 (1965).

Suppression at High Temperature of Effects Due to Statistics in the Second Virial Coefficient of a Real Gas - S. Larsen, J. Kilpatrick, E. Lieb and H. Jordan. Phys. Rev. 140, A129 (1965).

On the Quantum Mechanical Pair Correlation Function of He⁴ Gas at Low Temperatures - S. Larsen, K. Witte and J. Kilpatrick. J. Chem. Phys. 44, 213 (1966).

Exchange and Direct Second Virial Coefficients for Hard Spheres - M. Boyd, S. Larsen and J. Kilpatrick. J. Chem. Phys. 45, 499 (1966).

Quantum Mechanical Calculations of the Second Virial Coefficients for Hydrogen - M.E. Boyd and S. Y. Larsen. NBS Technical No. 412 (1967).

Note on the Pair-Correlation Function of Hard Spheres - S.Y. Larsen. Published in the Proceedings of the I.U.P.A.P. Conference on Statistical Mechanics and Thermodynamics, Copenhagen, July 1967, W. A. Benjamin, Inc.

Second Virial Coefficients of He$^4$ in the Temperature Range from 2 to 20 K - Journal of Research, N.B.S. A - Physics and Chemistry - M.E. Boyd, S.Y. Larsen and H. Plumb, 72A 155 (1968).

On the Quantum Mechanical Pair - Correlation Function of Hard Spheres - S.Y. Larsen. J. Chem. Phys. 48, 1701 (1968).

Quantum Mechanical Second Virial Coefficient of a Lennard Jones Gas. Helium - M. E. Boyd and S. Y. Larsen and J. E. Kilpatrick. J. Chem. Phys. 50, 4034 (1969).

Bound States in Noble Gas Molecules - S. Larsen, J. Kilpatrick, H. DeWitt. UCRL preprint 71981, Sept. 17, 1969.

Equilibrium Critical Phenomena in Fluids and Mixtures: A Comprehensive Bibliography with Key-word Descriptors - Stella Michaels, Melville S.Green and Sigurd Y. Larsen. National Bureau of Standards Special Publication 327, June 1970.

The Quantum-Mechanical Third Virial Coefficient and Three Body Phase Shifts - Sigurd Y. Larsen and P. Leonardo Mascheroni. Phys. Rev. A2, 1018 (1970).

First Q.M. Correction to the Classical Viscosity Cross Section of Hard Spheres - M.E. Boyd and S. Y. Larsen. Phys. Rev. A4, 1155 (1971).

The Quantum Mechanical Second Virial Coefficient for Anisotropic Interactions: Hydrogen Molecule-Helium Atom - S. Y. Larsen and J. D. Poll. Can. J. Phys. 52, 1914 (1974).

Is there a Helium Molecule? - C. Poulat, S. Y. Larsen and O. Navaro. Mol. Phys. 30, 645 (1975).

Quantum Mechanical Correction to Transport Cross Sections for Hard Spheres - J. G. Solomon and S. Y. Larsen. Thermal Conductivity 14 (1976), Plenum Press, New York.

Relative Density of States and the Second Virial Coefficient of the Hard Sphere Gas - R. Kayser, J. E. Kilpatrick and S. Y. Larsen. Mol. Phys. 33, 287 (1977).

Multi-Channel Calculations in Molecular Physics: Study of Coupled Square Wells, an Exactly Soluble Model - A. Noyola, A. Fierros, S. Y. Larsen and J. Franklin. J. Chem. Phys. 66, 1744 (1977).

Note on Miller's Method to Compute Partition Functions for the Case of Hard Spheres - M. Berrondo and S. Y. Larsen. J. Chem. Phys. 68, 5302 (1978).

Third Cluster Coefficient for Square Well Discs, S. Y. Larsen and J. E. Kilpatrick - 8th International Conference, Few Body Systems and Nuclear Forces: 497 (1978,Springer-Verlag).

The Ramsauer-Townsend effect in Molecular Systems of Electron-Spin-Polarized Hydrogen and Helium and their Isotopes - T. K. Lim and S. Y. Larsen. J. Chem. Phys. 74, 4997 (1981).

The Q.M. Second Virial Coefficients of Electron Spin-Polarized Atomic Hydrogen and its Admixtures with the Isotopes of Helium - T.K. Lim and S.Y. Larsen. J. Chem. Phys. 75, 955 (1981).

WKB for Coupled Equations and Virial Coefficients - S.Y. Larsen, A. Palma and M. Berrondo. J. Chem. Phys. 77, 5816 (1982).

The Hyperspherical Way - an extensive review of the field, together with the presentation of new results - Few-Body Methods, World Scientific Publishing Co., August 1986, p. 467-506.

Useful Amendments and Observations on the Algorithm of Davidson for Eigenvalues and Eigenvectors of Large Real Symmetric Matrices - A. D. Klemm and S. Y. Larsen. Division of Comp. \& Math. Tech. Report 4M, Deakin University (1986).

Asymptotic Behaviour of the Many Body Wave Function - M. Fabre de la Ripelle and S.Y. Larsen. Contributions to the International Conference on Atomic Physics and Few Body Systems. Sendai, Japan, August 1986. Published in the Proceedings.

Hyperspherical Harmonics in One Dimension. I. Adiabatic Effective Potentials for Three Particles with Delta-Function Interactions - W. Gibson, S. Y. Larsen, and J. Popiel. Phys Rev. 35, 4919 (1987).

Asymptotic Behavior of the Eigenpotentials in the Hyperspherical Adiabatic Approximation - M. Fabre de la Ripelle and S. Y. Larsen. XI European Few Body Conference, Fontrevault, France. Resume des communications, 24 (1987).

A set of Hyperspherical Harmonics Especially suited for Three Body Collisions in a Plane - J. E. Kilpatrick and S. Y. Larsen. Few-Body Systems 3, 75 (1987).

Low Energy Behaviour of a 3 Body Phase Shift - S. Y. Larsen and J. Zhen. Mol. Phys. 63, 581 (1988).

Three 3-Body Scattering Calculations using Hyperspherical Harmonics and Adiabatic Bases - S.Y. Larsen. Int. Workshop on Microscopic Methods in Few-Body Systems, Kalinin, USSR. Abstracts, 24 (1988).

The Quantum Mechanical Third Cluster for a Binary Step Potential - S. Y. Larsen and J. Zhen. Mol. Phys. 65, 237 (1988).

Asymptotic High Energy Expansion for the Relative Density of States of Hard Spheres - M. Berrondo and S. Y. Larsen. Mol. Phys. 65, 345 (1988).

Three-Body Scattering Calculations using Hyperspherical Harmonics And Adiabatic Bases - Sigurd Larsen. Int. Workshop on Microscopic Methods in Few-Body Systems, Kalinin, USSR. Vol. 2, 115 (1988).

Discontinuous Magnetization in Mean Field Theory - M. Berrondo and S. Y. Larsen. Eur. J. Phys. 10, 205 (1989).

Expansion of a Three-Body S-Matrix at low energies Using an Adiabatic Basis - S. Y. Larsen and J. J. Popiel. Triumph, Contributed papers from Few Body XII, F15 (1989).

Yes, Potential Harmonics Provide Atomic Accuracy! - M. Fabre de la Ripelle and S. Y. Larsen. Triumph, Contributed papers from Few Body XII, A3 (1989).

Many-Body Bound States with Potential Harmonics - M. Fabre de la Ripelle, A. D. Klemm and S. Y. Larsen. Triumph, Contributed papers from Few Body XII, B44 (1989).

Behaviour of Adiabatic Potentials in the Scattering of Three Particles - A. D. Klemm and S. Y. Larsen. Few-Body Systems 9, 123 (1990).

Some Integrals Involving Legendre Polynomials Providing Combinatorial Identities - A. D. Klemm and S.Y. Larsen. J. Austral. Math. Soc. Ser. B 32, 304 (1991).

Potential Harmonic Calculations of the Binding Energies of Bosons and Fermions in Nuclear Physics - M. Fabre de la Ripelle, Young-Ju Jee, A. D. Klemm and S. Y. Larsen. Annals of Physics 212, 195 (1991).

Potential Harmonic Expansion for Atomic Wave Functions - M. Fabre de la Ripelle, M. Haftel and S. Y. Larsen. Phys. Rev. A 44, 7084 (1991).

Effect of a Spurious Potential appearing in Faddeev type Equations - M. Fabre de la Ripelle and S. Y. Larsen. Few-Body Systems 13, 199 (1992).

Low Energy Three-Body Scattering In a Hyperspherical Adiabatic Basis - J. J. Popiel and S. Y. Larsen. Few-Body Systems 15, 129 (1993).

Pathologies in Three-Body Molecular Clusters when using Delta-Shell Potentials - YoungJu Jee, Sigurd Y. Larsen, Robert Intemann and M. Fabre de la Ripelle. Phys. Rev. A 49, 1912 (1994).

Three-Body Phase Shifts in One Dimensional 2 + 1 Scattering - A. Amaya-Tapia, S. Y. Larsen, and J. Popiel. Few-Body Systems 23, 87 (1997).

Hyperspherical Adiabatic Formalism of the Boltzmann Third Virial Coefficient - Sigurd Larsen. Proceedings of the Bogoliubov Conference on Problems of Theoretical and Mathematical Physics, 1999. $\;$ physics$/0105074$ \\ Phys. Elem. Part. and Atom. Nucl., Part. and Nucl. \, 31, \, 7B, 156 (2000)

The Effective Adiabatic Approximation Of Three-Body Problem with Short-Range Potentials - D. V. Proskurin, D. V. Pavlov, S. Y. Larsen, S. I. Vinitsky. Preprint E4-99-140 of the Joint Institute for Nuclear Research, Dubna, 1999. Also: Yadernaya Fizika 64, 37 (2001).

The Effective Adiabatic Approximation in the Problem of Three-Bodies coupled via Short-Range Potentials S. I. Vinitsky, S. Y. Larsen, D. V. Pavlov, D. V. Proskurin. Phys. At. Nucl. 64, 27 (2001).

Ghost components in the Jost Function and a new class of phase equivalent potentials - M. Lassaut, S. Y. Larsen, S. A. Sofianos and S. A. Rakityansky. J. Phys. A: Math. Gen. 34, 1 (2001).

S matrix poles and the second virial coefficient - A. Amaya-Tapia, S. Y. Larsen, J. Baxter, M. Lassaut and M. Berrondo. Molecular Physics 100, No. 16, 2605 (2002).

Results in One, Two, and Three Dimensions, for Delta Functions, Square Wells, and Delta Shells, Respectively - S. Y. Larsen. Few-Body Systems 31, No. 2-4, 91 (2002).

Three identical particles on a line: comparisons of some exact and approximate calculations - O. Chuluunbaatar, A. A. Gusev, S. Y. Larsen, S. I. Vinitsky. J. Phys. A35, L513 (2002)

Newtonian iteration schemes for solving the three-body scattering problem on a line - O. Chuluunbaatar, I. V. Puzynin, D. V. Pavlov, A. A. Gusev, S. Y. Larsen and S. I. Vinitsky. JINR preprint P11-01-255, Dubna 2001; Proceeding SPIE, 4706 (2002)

A variational-iteration approach to the three-body scattering problem - O. Chuluunbaatar, A. A. Gusev, I. V. Puzynin, S. Y. Larsen and S. I. Vinitsky. JINR D4-2003-89, Dubna, 2003

The Effective Adiabatic Approach to the Three-Body Problem - A. A. Gusev, O. Chuluunbaatar, D. V. Pavlov, S. Y. Larsen and S. I. Vinitsky. Journal of Computational Methods in Sciences and Engineering 2, 3 (2004)

Integral representation of one dimensional three particle scattering for delta-function interactions. - A. Amaya-Tapia, G. Gasaneo, S. Ovchinnikov, J. H. Macek and S. Y. Larsen. J. Math. Phys. 45, 3498 (2004)

Second virial coefficient in one dimension, as a function of asymptotic quantities - A. Amaya-Tapia, S. Y. Larsen and M. Lassaut. physics/0405150 and submitted to Molecular Physics

PREPRINTS - archived (xxx.lanl.gov)

Analytical Expressions for a Hyperspherical Adiabatic Basis. Three Particles in 2 Dimensions - Anthony D. Klemm and Sigurd Yves Larsen. physics/0105041

Potential Harmonic Calculations of Helium Triplet States - Anthony D. Klemm, Michel Fabre de la Ripelle and S. Y. Larsen. physics/0105076

S-Matrix Poles and the Second Virial Coefficient - A. Amaya-Tapia, S. Y. Larsen and J. Baxter, Monique Lassaut and Manuel Berrondo. physics/0105001

Second virial coefficient in one dimension, as a function of asymptotic quantities - A. Amaya-Tapia, S. Y. Larsen and M. Lassaut. physics/0405150