Calculation of the wave functions of the ground and weakly excited states of helium II
Abstract
The wave functions of the ground ({psi}{sub 0}) and the first excited ({psi}{sub k}) states of He II in the secondorder approximation, i.e., up to the first two corrections to the corresponding solutions for a weakly nonideal Bose gas, are determined by the collective variable method, which was proposed by Bogolyubov and Zubarev and developed in the studies by Yukhnovskii and Vakarchuk. The functions {psi}{sub 0} and {psi}{sub k} = {psi}{sub k}{psi}{sub 0} are determined as the eigenfunctions of the Nparticle Schroedinger equation from a system of coupled equations for {psi}{sub 0}, {psi}{sub k}, and the quasiparticle spectrum E(k) of helium II. The results consist in the following: (1) these equations are solved numerically for a higher order approximation compared with those investigated earlier (the firstorder approximation), and (2) {psi}{sub 0} and {psi}{sub k} are derived from a model potential of interaction between He{sup 4} atoms (rather than from the structure factor as earlier) in which the potential barrier is joined with the attractive potential found from experiment. The height V{sub 0} of the potential barrier is a free parameter. Except for V{sub 0}, the model does not have any free parameters or functions. The calculated values of the structuremore »
 Authors:
 National Academy of Sciences of Ukraine, Bogolyubov Institute of Theoretical Physics (Ukraine), Email: mtomchenko@bitp.kiev.ua
 Publication Date:
 OSTI Identifier:
 21067753
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Experimental and Theoretical Physics; Journal Volume: 102; Journal Issue: 1; Other Information: DOI: 10.1134/S106377610601016X; Copyright (c) 2006 Nauka/Interperiodica; Article Copyright (c) 2006 Pleiades Publishing, Inc; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; ASYMPTOTIC SOLUTIONS; BOSEEINSTEIN GAS; CORRECTIONS; EIGENFUNCTIONS; EXCITED STATES; GROUND STATES; HELIUM II; MICROSTRUCTURE; PARTICLES; POTENTIALS; SCHROEDINGER EQUATION; STRUCTURE FACTORS; WAVE FUNCTIONS
Citation Formats
Tomchenko, M. D.. Calculation of the wave functions of the ground and weakly excited states of helium II. United States: N. p., 2006.
Web. doi:10.1134/S106377610601016X.
Tomchenko, M. D.. Calculation of the wave functions of the ground and weakly excited states of helium II. United States. doi:10.1134/S106377610601016X.
Tomchenko, M. D.. Sun .
"Calculation of the wave functions of the ground and weakly excited states of helium II". United States.
doi:10.1134/S106377610601016X.
@article{osti_21067753,
title = {Calculation of the wave functions of the ground and weakly excited states of helium II},
author = {Tomchenko, M. D.},
abstractNote = {The wave functions of the ground ({psi}{sub 0}) and the first excited ({psi}{sub k}) states of He II in the secondorder approximation, i.e., up to the first two corrections to the corresponding solutions for a weakly nonideal Bose gas, are determined by the collective variable method, which was proposed by Bogolyubov and Zubarev and developed in the studies by Yukhnovskii and Vakarchuk. The functions {psi}{sub 0} and {psi}{sub k} = {psi}{sub k}{psi}{sub 0} are determined as the eigenfunctions of the Nparticle Schroedinger equation from a system of coupled equations for {psi}{sub 0}, {psi}{sub k}, and the quasiparticle spectrum E(k) of helium II. The results consist in the following: (1) these equations are solved numerically for a higher order approximation compared with those investigated earlier (the firstorder approximation), and (2) {psi}{sub 0} and {psi}{sub k} are derived from a model potential of interaction between He{sup 4} atoms (rather than from the structure factor as earlier) in which the potential barrier is joined with the attractive potential found from experiment. The height V{sub 0} of the potential barrier is a free parameter. Except for V{sub 0}, the model does not have any free parameters or functions. The calculated values of the structure factor, the groundstate energy E{sub 0}, and the quasiparticle spectrum E(k) of He II are in agreement with the experimental values for V{sub 0} {approx} 100 K. The secondorder correction to the logarithm of {psi}{sub 0} significantly affects the value of E{sub 0} and provides the asymptotics E(k {sup {yields}} 0) = ck, while the secondorder correction to {psi}{sub k} slightly affects the E(k). The secondorder corrections to {psi}{sub 0} and {psi}{sub k} have a smaller effect on the results compared with the firstorder corrections, whereby the theory is in agreement with experiment; therefore, one may assume that the truncated {psi}{sub 0} and {psi}{sub k} well describe the microstructure of He II. Thus, the series for {psi}{sub 0} and {psi}{sub k} can be truncated in spite of the fact that the expansion parameter is not very small ({approx}1/2)},
doi = {10.1134/S106377610601016X},
journal = {Journal of Experimental and Theoretical Physics},
number = 1,
volume = 102,
place = {United States},
year = {Sun Jan 15 00:00:00 EST 2006},
month = {Sun Jan 15 00:00:00 EST 2006}
}

ASE wave functions containing singly excited (SE) configurations for each space orbital of the principal configuration are compared with similarly constructed pairexcitation (PE) wave functions. The energies are exactly or almost the same. Nearredundant configurations are removed, and the equivalence of SE with PE wave functions is investigated for special cases. (auth)