Liquid ⁴He: Equation of State, Compressibility and Velocity of First Sound

Abstract

In calculations for liquid 4 He, an investigation is made to check the accuracy of a lowestorder constrained variational (LOCV) method, using modified "healing" conditions on the two-body Jastrow wave function. Results obtained for the ground-state energy for four different interaction models are fitted by a polynomial expression, whereby the pressure, compressibility and velocity of first sound are obtained. The theoretical results are found to be in fair agreement with experimental results.PACS number(s): 67.20.+k, 67.40.Mj

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

“…The LOCV method may be used for Bose systems as well as Fermi systems, previous results for liquid 4 He [2,3] being in excellent agreement with Monte Carlo results [4]. In the case of Fermi systems, results for both the unpolarized and fully spin-polarized phases of liquid 3 He [5] were also found to be in excellent agreement with variational Monte Carlo (VMC) and Fermi hypernetted-chain (FHNC) results [6,7].…”

“…The helium liquids have long been a favourite testing ground for many-body methods in quantum physics. In recent years an increasing amount of attention has been directed towards spin-polarized quantum systems, notably liquid 3 He. Some systems, however, such as electronspin-polarized atomic hydrogen, will exhibit properties with a quantum behaviour even more extreme than that observed in liquid 3 He.…”

“…In recent years an increasing amount of attention has been directed towards spin-polarized quantum systems, notably liquid 3 He. Some systems, however, such as electronspin-polarized atomic hydrogen, will exhibit properties with a quantum behaviour even more extreme than that observed in liquid 3 He. This can be visualized using the 'quantum parameter', i.e., η = h2 /(m σ 2 ), where and σ are related to the depth and repulsive core range, respectively, of the two-body interaction [1].…”

“…Access to a given state of polarization should then be possible by the controlled application of an external magnetic field. With only one spin state occupied, bulk ↓D B Skjetne and E Østgaard be bulk ↓D ↑ 2 and ↓D ↑ 3 , respectively, where the former is analogous to unpolarized 3 He, i.e., liquid 3 He ↑ 2 , and the latter has no such analogue. Results for the ground-state energy levels of many-body ↓D ↑ 1 , ↓D ↑ 2 and ↓D ↑ 3 are here obtained in calculations with a constrained variational approach, which improves upon the basic Jastrow function without going explicitly beyond second order.…”

“…The LOCV method may be used for Bose systems as well as Fermi systems, previous results for liquid 4 He [2,3] being in excellent agreement with Monte Carlo results [4]. In the case of Fermi systems, results for both the unpolarized and fully spin-polarized phases of liquid 3 He [5] were also found to be in excellent agreement with variational Monte Carlo (VMC) and Fermi hypernetted-chain (FHNC) results [6,7]. Our aim in this work, then, has been to determine how well the current benchmark results reported in VMC many-body calculations [8] for ↓D ↑ 1 , ↓D ↑ 2 and ↓D ↑ 3 can be reproduced in the constrained variational approach.…”