Ground-state properties of nuclear-spin-aligned deuterium are studied within the method of correlated basis functions (CBF), using Fermi-hypernetted-chain (FHNC) techniques to evaluate the requisite matrix elements of the Hamiltonian and identity attendant to a Jastrow choice of correlation operator. Results are presented for the ground-state energies of three hypothetical species of this system, calculated to low order in CBF perturbation theory, taking account of two- and three-body CBF effective interactions. Also included are data on the Jastrow momentum distribution and radial distribution function, computed using the FHNC scheme. These findings are supplemented by benchmark variational Monte Carlo results on the energy and radial distribution function. The three deuterium species provide examples of strongly interacting Fermi fluids, intermediate in coupling strength between nuclear matter and liquid $^{3}\mathrm{He}$ .Ground-state properties of nuclear-spin-aligned deuterium are studied within the method of correlated basis functions (CBF), using Fermi-hypernetted-chain (FHNC) techniques to evaluate the requisite matrix elements of the Hamiltonian and identity attendant to a Jastrow choice of correlation operator. Results are presented for the ground-state energies of three hypothetical species of this system, calculated to low order in CBF perturbation theory, taking account of two- and three-body CBF effective interactions. Also included are data on the Jastrow momentum distribution and radial distribution function, computed using the FHNC scheme. These findings are supplemented by benchmark variational Monte Carlo results on the energy and radial distribution function. The three deuterium species provide examples of strongly interacting Fermi fluids, intermediate in coupling strength between nuclear matter and liquid $^{3}\mathrm{He}$.

Physical review. B, Condensed matterSep 1, 198518 citations

Planar Theory Made Variational

Andrew David Jackson, Alexander Lande, R. A. Smith

Within the framework of boson parquet-diagram summations in perturbation theory, we show analytically that several simple approximations lead inevitably to the radial distribution function $g(r)$ which would be obtained with the Jastrow hypernetted-chain variational method. This is the first derivation of the Jastrow result from perturbation theory. Without mentioning pair-correlation functions, we have a clear interpretation of $g(r)$ and the structure function, $S(k)$ , in terms of diagram sums.Within the framework of boson parquet-diagram summations in perturbation theory, we show analytically that several simple approximations lead inevitably to the radial distribution function $g(r)$ which would be obtained with the Jastrow hypernetted-chain variational method. This is the first derivation of the Jastrow result from perturbation theory. Without mentioning pair-correlation functions, we have a clear interpretation of $g(r)$ and the structure function, $S(k)$, in terms of diagram sums.

Physical Review LettersApr 8, 198565 citations

ON THE THEORY OF THE FERMI LIQUID

Elsevier eBooksJan 1, 19652 citations

Density matrix of quantum fluids

MANFRED L. RISTIG, J. W. Clark

An elaborate cluster analysis of the single-particle occupation probability ${n}_{\stackrel{^}{q}}$ and associated one-body density matrix $n(r)$ is performed for a Fermi system described by a Jastrow wave function. A diagrammatic formalism rooted in Ursell-Mayer theory facilitates the analysis. It is conjectured, and demonstrated to convincingly high cluster order, that ${n}_{\stackrel{^}{q}}$ may be written as $n[N(q)+{N}_{1}(q)]$ , where $n$ is a strength factor independent of wave number $q$ and the quantities $N(q)$ and ${N}_{1}(q)$ may be expressed as series of irreducible cluster contributions. The strength factor $n$ has the form $n={e}^{Q}$ , where $Q$ may also be expressed as a series of irreducible cluster contributions. Massive partial summations on the latter series yield a compact expression for $Q$ in terms of the spatial distribution functions corresponding to the Jastrow wave function. Working with the Fourier inverse of ${n}_{\stackrel{^}{q}}$, it is further demonstrated that $n(r)$ may be cast in the form $\ensuremath{\rho}n[{N}_{1}(r)+{N}_{2}(r)]\mathrm{exp}\mathcal{Q}(r)$, where $\ensuremath{\rho}$ is the particle density and the functions ${N}_{1}(r)$ , ${N}_{2}(r)$ , and $\mathcal{Q}(r)$ are all given by irreducible cluster series. Massive partial summations are executed in the $\mathcal{Q}(r)$ series to achieve a compact expression of this quantity in terms of the aforementioned spatial distribution functions. One has $\mathcal{Q}(0)=Q$ . The leading diagrams necessary for a quantitative evaluation of the momentum distribution of liquid $^{3}\mathrm{He}$ and nuclear matter are displayed. Specialization to infinite degeneracy of the single-particle levels, while shrinking the Fermi wave number to zero (Bose limit), allows liquid $^{4}\mathrm{He}$ to be treated as well. In this limit off-diagonal long-range order appears, the condensate fraction ${\ensuremath{\rho}}^{\ensuremath{-}1}n(\ensuremath{\infty})={n}_{c}$ being just the strength factor $n$ . It may also be shown (under certain reasonable assumptions) that the customary ${r}^{\ensuremath{-}2}$ long-range behavior of the two-body correlations implies a singular behavior ${n}_{q}={n}_{c}(\frac{\mathrm{mc}}{2\ensuremath{\hbar}}){q}^{\ensuremath{-}1}$ of the Bose momentum distribution for small $q$ .An elaborate cluster analysis of the single-particle occupation probability ${n}_{\stackrel{^}{q}}$ and associated one-body density matrix $n(r)$ is performed for a Fermi system described by a Jastrow wave function. A diagrammatic formalism rooted in Ursell-Mayer theory facilitates the analysis. It is conjectured, and demonstrated to convincingly high cluster order, that ${n}_{\stackrel{^}{q}}$ may be written as $n[N(q)+{N}_{1}(q)]$, where $n$ is a strength factor independent of wave number $q$ and the quantities $N(q)$ and ${N}_{1}(q)$ may be expressed as series of irreducible cluster contributions. The strength factor $n$ has the form $n={e}^{Q}$, where $Q$ may also be expressed as a series of irreducible cluster contributions. Massive partial summations on the latter series yield a compact expression for $Q$ in terms of the spatial distribution functions corresponding to the Jastrow wave function. Working with the Fourier inverse of ${n}_{\stackrel{^}{q}}$, it is further demonstrated that $n(r)$ may be cast in the form $\ensuremath{\rho}n[{N}_{1}(r)+{N}_{2}(r)]\mathrm{exp}\mathcal{Q}(r)$, where $\ensuremath{\rho}$ is the particle density and the functions ${N}_{1}(r)$, ${N}_{2}(r)$, and $\mathcal{Q}(r)$ are all given by irreducible cluster series. Massive partial summations are executed in the $\mathcal{Q}(r)$ series to achieve a compact expression of this quantity in terms of the aforementioned spatial distribution functions. One has $\mathcal{Q}(0)=Q$. The leading diagrams necessary for a quantitative evaluation of the momentum distribution of liquid $^{3}\mathrm{He}$ and nuclear matter are displayed. Specialization to infinite degeneracy of the single-particle levels, while shrinking the Fermi wave number to zero (Bose limit), allows liquid $^{4}\mathrm{He}$ to be treated as well. In this limit off-diagonal long-range order appears, the condensate fraction ${\ensuremath{\rho}}^{\ensuremath{-}1}n(\ensuremath{\infty})={n}_{c}$ being just the strength factor $n$. It may also be shown (under certain reasonable assumptions) that the customary ${r}^{\ensuremath{-}2}$ long-range behavior of the two-body correlations implies a singular behavior ${n}_{q}={n}_{c}(\frac{\mathrm{mc}}{2\ensuremath{\hbar}}){q}^{\ensuremath{-}1}$ of the Bose momentum distribution for small $q$.

Physical review. B, Solid stateOct 1, 197670 citations

^{3}\mathrm{He}

Within the framework of boson parquet-diagram summations in perturbation theory, we show analytically that several simple approximations lead inevitably to the radial distribution function

g(r)

which would be obtained with the Jastrow hypernetted-chain variational method. This is the first derivation of the Jastrow result from perturbation theory. Without mentioning pair-correlation functions, we have a clear interpretation of

g(r)

and the structure function,

S(k)

, in terms of diagram sums.

An elaborate cluster analysis of the single-particle occupation probability ${n}_{\stackrel{^}{q}}$ and associated one-body density matrix

n(r)

is performed for a Fermi system described by a Jastrow wave function. A diagrammatic formalism rooted in Ursell-Mayer theory facilitates the analysis. It is conjectured, and demonstrated to convincingly high cluster order, that ${n}_{\stackrel{^}{q}}$ may be written as

n[N(q)+{N}_{1}(q)]

, where

n

is a strength factor independent of wave number

q

and the quantities

N(q)

and

{N}_{1}(q)

may be expressed as series of irreducible cluster contributions. The strength factor

n

has the form

n={e}^{Q}

, where

Q

may also be expressed as a series of irreducible cluster contributions. Massive partial summations on the latter series yield a compact expression for

Q

in terms of the spatial distribution functions corresponding to the Jastrow wave function. Working with the Fourier inverse of ${n}_{\stackrel{^}{q}}$, it is further demonstrated that

n(r)

may be cast in the form $\ensuremath{\rho}n[{N}_{1}(r)+{N}_{2}(r)]\mathrm{exp}\mathcal{Q}(r)$, where $\ensuremath{\rho}$ is the particle density and the functions

{N}_{1}(r)

{N}_{2}(r)

, and

\mathcal{Q}(r)

are all given by irreducible cluster series. Massive partial summations are executed in the

\mathcal{Q}(r)

series to achieve a compact expression of this quantity in terms of the aforementioned spatial distribution functions. One has

\mathcal{Q}(0)=Q

. The leading diagrams necessary for a quantitative evaluation of the momentum distribution of liquid

^{3}\mathrm{He}

and nuclear matter are displayed. Specialization to infinite degeneracy of the single-particle levels, while shrinking the Fermi wave number to zero (Bose limit), allows liquid

^{4}\mathrm{He}

to be treated as well. In this limit off-diagonal long-range order appears, the condensate fraction ${\ensuremath{\rho}}^{\ensuremath{-}1}n(\ensuremath{\infty})={n}_{c}$ being just the strength factor

n

. It may also be shown (under certain reasonable assumptions) that the customary ${r}^{\ensuremath{-}2}$ long-range behavior of the two-body correlations implies a singular behavior ${n}_{q}={n}_{c}(\frac{\mathrm{mc}}{2\ensuremath{\hbar}}){q}^{\ensuremath{-}1}$ of the Bose momentum distribution for small

q