Correlation structure of the wave function and the expansion of the ground- state energy of nuclear matter

A nonperturbative derivation of the Brueckner approximation to the ground-state energy of nuclear matter (with standard choice of hole and particle energies) is given within the framework of the method of correlated basis functions. The structure of the factor-cluster (FIY) expansion of the expectation value of the Hamiltonian with respect to a trial function incorporating short-range correlations in a general fashion, is analyzed for a uniform extended medium of fermions. With a special choice of correlated wave function, the Brueckner approximation is extracted from the FIY expansion by selective summation of two-body combination terms to all orders in the smallness parameter $\ensuremath{\kappa}$ associated, in this case, with both Brueckner-Bethe-Goldstone and FIY energy expansions. A reexamination of the numerical comparison of conventional Brueckner and Jastrow methods carried out earlier for two simple models of nuclear matter leads to the conclusion that it is inadvisable, at least in a Jastrow calculation satisfying the average Pauli condition, to incorporate the $O(\ensuremath{\kappa})$ contribution of the analog of the dispersion correction of reaction-matrix theory without at the same time including the $O(\ensuremath{\kappa})$ contribution of the analog of the Bethe-Faddeev term. For the uniform extended medium for the Jastrow choice of wave function, there is a formal cancellation of these two three-body contributions, the scale of this cancellation being governed by the size of $\ensuremath{\kappa}$. In the numerical example considered, $\ensuremath{\kappa}$ is about 0.22 and the cancellation goes something like +14 MeV-15 MeV=-1 MeV. These findings, when juxtaposed with the standard Brueckner results for the simple models in question, suggest that a departure from the standard prescription of hole and particle energies in reaction-matrix theory may be necessary when $\ensuremath{\kappa}$ is sizeable-as in liquid $^{3}\mathrm{He}$ and the high-density neutron gas, as well as equilibrium nuclear matter described with some potentials.A nonperturbative derivation of the Brueckner approximation to the ground-state energy of nuclear matter (with standard choice of hole and particle energies) is given within the framework of the method of correlated basis functions. The structure of the factor-cluster (FIY) expansion of the expectation value of the Hamiltonian with respect to a trial function incorporating short-range correlations in a general fashion, is analyzed for a uniform extended medium of fermions. With a special choice of correlated wave function, the Brueckner approximation is extracted from the FIY expansion by selective summation of two-body combination terms to all orders in the smallness parameter $\ensuremath{\kappa}$ associated, in this case, with both Brueckner-Bethe-Goldstone and FIY energy expansions. A reexamination of the numerical comparison of conventional Brueckner and Jastrow methods carried out earlier for two simple models of nuclear matter leads to the conclusion that it is inadvisable, at least in a Jastrow calculation satisfying the average Pauli condition, to incorporate the $O(\ensuremath{\kappa})$ contribution of the analog of the dispersion correction of reaction-matrix theory without at the same time including the $O(\ensuremath{\kappa})$ contribution of the analog of the Bethe-Faddeev term. For the uniform extended medium for the Jastrow choice of wave function, there is a formal cancellation of these two three-body contributions, the scale of this cancellation being governed by the size of $\ensuremath{\kappa}$. In the numerical example considered, $\ensuremath{\kappa}$ is about 0.22 and the cancellation goes something like +14 MeV-15 MeV=-1 MeV. These findings, when juxtaposed with the standard Brueckner results for the simple models in question, suggest that a departure from the standard prescription of hole and particle energies in reaction-matrix theory may be necessary when $\ensuremath{\kappa}$ is sizeable-as in liquid $^{3}\mathrm{He}$ and the high-density neutron gas, as well as equilibrium nuclear matter described with some potentials.

Physical Review CMay 1, 197319 citations

Short-range expansion for the quantum many-body problem

R. Weiss, Diego Lonardoni, Stefano Gandolfi

In this work we derive a systematic short-range expansion of the many-body wave function. At leading order, the wave function is factorized to a zero-energy s -wave correlated pair and spectator particles, while terms that include energy derivatives and larger orbital angular momentum two-body functions appear at subleading orders. The validity of the expansion is tested for the two-body case, as well as the many-body case, where infinite neutron matter is considered. An accurate and consistent description of both coordinate-space two-body densities and the one-body momentum distribution is obtained. These results show the possibility to utilize such an expansion for describing different observables in strongly-interacting many-body systems, including nuclear, atomic and condensed-matter systems. This work also opens the path for a systematic description of large momentum transfer reactions in nuclear systems sensitive to short-range correlations, provides a link between such experiments and low-energy nuclear physics, and motivates measurement of new observables in these experiments.In this work we derive a systematic short-range expansion of the many-body wave function. At leading order, the wave function is factorized to a zero-energy s -wave correlated pair and spectator particles, while terms that include energy derivatives and larger orbital angular momentum two-body functions appear at subleading orders. The validity of the expansion is tested for the two-body case, as well as the many-body case, where infinite neutron matter is considered. An accurate and consistent description of both coordinate-space two-body densities and the one-body momentum distribution is obtained. These results show the possibility to utilize such an expansion for describing different observables in strongly-interacting many-body systems, including nuclear, atomic and condensed-matter systems. This work also opens the path for a systematic description of large momentum transfer reactions in nuclear systems sensitive to short-range correlations, provides a link between such experiments and low-energy nuclear physics, and motivates measurement of new observables in these experiments.

arXiv:2307.05910Physics Letters BAug 23, 20241 citation

The correlated wave function approach to finite nuclear systems

J. W. Clark

Springer eBooksApr 6, 200824 citations

Theory of Nuclear Matter

Franz Mohling

The methods of quantum statistics previously developed by the author are applied to the determination of properties of the ground state of nuclear matter. An expansion in powers of the pair-function of quantum statistics is made and expressions are derived for the momentum distribution, pair-correlation function, binding energy, and effective single-particle energies. The leading terms of these expressions can be interpreted in terms of an effective two-body interaction, and a model of nuclear matter which consists of interacting quasi-particles whose energies are the effective single-particle energies is thereby suggested. The theory is compared with Brueckner's theory and also with Landau's phenomenological theory of the Fermi liquid.The methods of quantum statistics previously developed by the author are applied to the determination of properties of the ground state of nuclear matter. An expansion in powers of the pair-function of quantum statistics is made and expressions are derived for the momentum distribution, pair-correlation function, binding energy, and effective single-particle energies. The leading terms of these expressions can be interpreted in terms of an effective two-body interaction, and a model of nuclear matter which consists of interacting quasi-particles whose energies are the effective single-particle energies is thereby suggested. The theory is compared with Brueckner's theory and also with Landau's phenomenological theory of the Fermi liquid.

Physical ReviewOct 15, 196126 citations

^{3}\mathrm{He}

and the high-density neutron gas, as well as equilibrium nuclear matter described with some potentials.