We address the issue of determining an effective two-body interaction for mean-field calculations of the energies of many-body systems. We show that the effective interaction is proportional to the phase shift and demonstrate this result in the quasiclassical approximation when there is a trapping potential in addition to the short-range interaction between a pair of particles. We calculate numerically energy levels for the case of an interaction with a short-range square well and a harmonic trapping potential and show that the numerical results agree well with the analytical expression. We derive a generalized Gross-Pitaevskii equation which includes effective range corrections and discuss the form of the electron-atom effective interaction to be used in calculations of Rydberg atoms and molecules.We address the issue of determining an effective two-body interaction for mean-field calculations of the energies of many-body systems. We show that the effective interaction is proportional to the phase shift and demonstrate this result in the quasiclassical approximation when there is a trapping potential in addition to the short-range interaction between a pair of particles. We calculate numerically energy levels for the case of an interaction with a short-range square well and a harmonic trapping potential and show that the numerical results agree well with the analytical expression. We derive a generalized Gross-Pitaevskii equation which includes effective range corrections and discuss the form of the electron-atom effective interaction to be used in calculations of Rydberg atoms and molecules.

arXiv:cond-mat/0610314Physical Review AJan 12, 200768 citations

Accelerating Quantum Many Body Calculations for Strongly Correlated Systems

Evan Sheridan

Dec 1, 20210 citations

Exact calculation of three-body contact interaction to second order1

Norbert Kaiser

For a system of fermions with a three-body contact interaction the second-order contributions to the energy per particle $\ensuremath \bar E(k_f)$ are calculated exactly. The three-particle scattering amplitude in the medium is derived in closed analytical form from the corresponding two-loop rescattering diagram. We compare the (genuine) second-order three-body contribution to $\ensuremath \bar E(k_f)\sim k_f^{10}$ with the second-order term due to the density-dependent effective two-body interaction, and find that the latter term dominates. The results of the present study are of interest for nuclear many-body calculations where chiral three-nucleon forces are treated beyond leading order via a density-dependent effective two-body interaction.For a system of fermions with a three-body contact interaction the second-order contributions to the energy per particle $\ensuremath \bar E(k_f)$ are calculated exactly. The three-particle scattering amplitude in the medium is derived in closed analytical form from the corresponding two-loop rescattering diagram. We compare the (genuine) second-order three-body contribution to $\ensuremath \bar E(k_f)\sim k_f^{10}$ with the second-order term due to the density-dependent effective two-body interaction, and find that the latter term dominates. The results of the present study are of interest for nuclear many-body calculations where chiral three-nucleon forces are treated beyond leading order via a density-dependent effective two-body interaction.

Aug 16, 201611 citations

The State Dependence Calculation of Three-body Cluster Energy for Nuclear Matter

H. R. Moshfegh, Majid Modarres

It is shown that the method of lowest order contrained variational (LOCV) which is based on the cluster expansion theory is a reliable many-body technique to calculate the nuclear matter equation of states. In this respect the state-dependence correlation functions and effective interactions which have been produce by LOCV calculation with the Reid Soft Core and $Δ$ -Reid interactions are used to estimate the size of higher order cluster terms such as the effect of three body cluster energy in nuclear matter. We find that the three-body cluster energy is less than 1 MeV beyond the nuclear matter saturation density and it has weaker density dependence than our previous calculation with the state-averaged coorrelation functions and effective interactions. Finally, we conclude that the LOCV method is good enough to calculate other propertiesn of quantal fluids.It is shown that the method of lowest order contrained variational (LOCV) which is based on the cluster expansion theory is a reliable many-body technique to calculate the nuclear matter equation of states. In this respect the state-dependence correlation functions and effective interactions which have been produce by LOCV calculation with the Reid Soft Core and $Δ$-Reid interactions are used to estimate the size of higher order cluster terms such as the effect of three body cluster energy in nuclear matter. We find that the three-body cluster energy is less than 1 MeV beyond the nuclear matter saturation density and it has weaker density dependence than our previous calculation with the state-averaged coorrelation functions and effective interactions. Finally, we conclude that the LOCV method is good enough to calculate other propertiesn of quantal fluids.

arXiv:nucl-th/9907044Jul 11, 19990 citations

Three-body interactions in many-body effective field theory

R. J. Furnstahl

arXiv:nucl-th/0307099Nuclear Physics AJun 1, 20040 citations

Δ

-Reid interactions are used to estimate the size of higher order cluster terms such as the effect of three body cluster energy in nuclear matter. We find that the three-body cluster energy is less than 1 MeV beyond the nuclear matter saturation density and it has weaker density dependence than our previous calculation with the state-averaged coorrelation functions and effective interactions. Finally, we conclude that the LOCV method is good enough to calculate other propertiesn of quantal fluids.