Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review C

Inclusion of Pauli principle constraints in equations-of-motion methods for the nuclear many-body problem

Pranab K. Chattopadhyay, Abraham Klein

Published Feb 1, 1975• 0 citations
Publisher

Abstract

The effort to isolate and study the dominant collective modes of a nuclear many-body system by generalized equations-of-motion methods (algebraic methods) confronts the inherent difficulty that such modes are correlated with each other and with noncollective modes by kinematic constraints traceable to the Pauli principle. This problem has previously been solved for simplified nuclear models. A solution is proposed for the general shell model problem of a number of interacting levels.

DOI
10.1103/physrevc.11.610

Related papers

On an Algebraic Foundation of Kinematical Constraints of Pair Operators in a Many-Nucleon System

Seiya Nishiyama

Various kinds of kinematical constraints of pair operators play important roles in an algebraic approach to the theory of nuclear collective motion. The algebraic foundation of these constraints is given with the use of algebraic recursion formulas.

Progress of Theoretical Physics•Apr 1, 1976•4 citations

Algebraic approach to vibrational collective motion in a model with both collective and noncollective degrees of freedom

Moyez G. Vassanji, Abraham Klein, C.H. Dasso

An algebraic approach, within a framework using equations of motion, is applied to the study of vibrational collective motion in exactly soluble shell models with symmetry R(5) and R(5) \ifmmode\times\else\texttimes\fi{} R(5). The latter exhibits two phonon branches, permitting the study of the effect of the noncollective on the collective branch. The results of this method, including the splitting of the two-phonon degeneracy, agree satisfactorily with exact results for a range of parameters well into the transition region between vibrational and rotational motion.[NUCLEAR STRUCTURE Approximate many-body methods applied to a solvable model. Vibrational spectrum. Equations of motion method.]

Physical Review C•Feb 1, 1978•4 citations

Many-body formalism for fermions: Enforcing the Pauli principle on paper

D. K. Watson

Confined quantum systems involving $N$ identical interacting fermions are found in many areas of physics, including condensed matter, atomic, nuclear, and chemical physics. In a previous series of papers, a many-body perturbation method that is applicable to both weakly and strongly interacting systems of bosons has been set forth by the author and coworkers. A symmetry-invariant perturbation theory was developed that uses group theory coupled with the dimension of space as the perturbation parameter to obtain an analytic correlated wave function through first order for a system under spherical confinement with a general two-body interaction. In the present paper, we extend this formalism to large systems of fermions, circumventing the numerical demands of applying the Pauli principle by enforcing the Pauli principle on paper. The method does not scale in complexity with $N$ and has minimal numerical cost. We apply the method to a unitary Fermi gas and compare to recent Monte Carlo values.

Physical Review A•Jul 23, 2015•5 citations

Revisiting the Equation-of-Motion Method: A Universal Framework for Correlated Quantum Systems

Andrea Porro

A general implementation of the equation-of-motion (EOM) formalism for correlated many-body states is presented and applied to the description of collective excitations in atomic nuclei. While EOM approaches are traditionally formulated on top of independent-particle reference states, the present work extends the method to correlated reference states generated by modern many-body solvers. This formulation enables a consistent treatment of ground-state correlations and excited-state dynamics within a unified framework. Particular emphasis is placed on collective nuclear excitations employing chiral nuclear Hamiltonians in an ab initio context. The approach is motivated by the renewed interest in EOM techniques across several fields, including quantum chemistry and quantum computing, where they provide efficient and systematically improvable descriptions of excitation spectra. The present results demonstrate that the EOM framework offers a flexible and powerful tool for the microscopic description of nuclear spectroscopy beyond the traditional mean-field paradigm.

nucl-thCross-listedarXiv:2607.29396•Aug 3, 2026•0 citations

Collective Motion in Finite Many-Particle Systems. II

Abraham Klein, Arthur K. Kerman

This is the second of a series of papers aimed at exploiting a generalized self-consistent approach to the study of collective excited states in finite many-particle systems. It contains: (i) A restatement of the equations of the method with further discussion of the basic approximations involved; (ii) a study, through the medium of the exactly soluble problem of uniform translational motion, of the inherent limitations in accuracy of the method when applied to the "strong-coupling" limit for which it was designed. A mode of approximation which can be made self-consistent is indicated. (iii) This approximation is applied to the problem of rotational motion in a plane. In the further limit in which one assumes the spectrum of the rigid rotator, one regains the results of the self-consistent cranking model. In contrast to previous work, the possibility of removing this limitation is indicated, but remains to be carried through.

Physical Review•Jun 7, 1965•36 citations

MAXIMAL-DECOUPLING VARIATIONAL PRINCIPLE AND OPTIMAL AUXILIARY HAMILTONIANS FOR NUCLEAR COLLECTIVE MOTIONS

Ching‐Teh Li

A variational principle of maximal decoupling between the collective and noncollective subspaces has recently been proposed to pin down the collective degrees of freedom of the nuclear many-body problem. This maximal-decoupling variational principle is further utilized here to determine in an optimal way the auxiliary Hamiltonians to be used in severely truncated boson-space calculations for nuclear collective motions. In the present method one treats the spurious-state problem in truncated boson-space calculations by using appropriate auxiliary boson Hamiltonians. The viability of the method is demonstrated through its application to a simplified shell model containing only the monopole pairing interactions.

International Journal of Modern Physics E•Jan 1, 1993•0 citations
The effort to isolate and study the dominant collective modes of a nuclear many-body system by generalized equations-of-motion methods (algebraic methods) confronts the inherent difficulty that such modes are correlated with each other and with noncollective modes by kinematic constraints traceable to the Pauli principle. This problem has previously been solved for simplified nuclear models. A solution is proposed for the general shell model problem of a number of interacting levels.
An algebraic approach, within a framework using equations of motion, is applied to the study of vibrational collective motion in exactly soluble shell models with symmetry R(5) and R(5) \ifmmode\times\else\texttimes\fi{} R(5). The latter exhibits two phonon branches, permitting the study of the effect of the noncollective on the collective branch. The results of this method, including the splitting of the two-phonon degeneracy, agree satisfactorily with exact results for a range of parameters well into the transition region between vibrational and rotational motion.[NUCLEAR STRUCTURE Approximate many-body methods applied to a solvable model. Vibrational spectrum. Equations of motion method.]
Confined quantum systems involving NNN identical interacting fermions are found in many areas of physics, including condensed matter, atomic, nuclear, and chemical physics. In a previous series of papers, a many-body perturbation method that is applicable to both weakly and strongly interacting systems of bosons has been set forth by the author and coworkers. A symmetry-invariant perturbation theory was developed that uses group theory coupled with the dimension of space as the perturbation parameter to obtain an analytic correlated wave function through first order for a system under spherical confinement with a general two-body interaction. In the present paper, we extend this formalism to large systems of fermions, circumventing the numerical demands of applying the Pauli principle by enforcing the Pauli principle on paper. The method does not scale in complexity with NNN and has minimal numerical cost. We apply the method to a unitary Fermi gas and compare to recent Monte Carlo values.
A general implementation of the equation-of-motion (EOM) formalism for correlated many-body states is presented and applied to the description of collective excitations in atomic nuclei. While EOM approaches are traditionally formulated on top of independent-particle reference states, the present work extends the method to correlated reference states generated by modern many-body solvers. This formulation enables a consistent treatment of ground-state correlations and excited-state dynamics within a unified framework. Particular emphasis is placed on collective nuclear excitations employing chiral nuclear Hamiltonians in an ab initio context. The approach is motivated by the renewed interest in EOM techniques across several fields, including quantum chemistry and quantum computing, where they provide efficient and systematically improvable descriptions of excitation spectra. The present results demonstrate that the EOM framework offers a flexible and powerful tool for the microscopic description of nuclear spectroscopy beyond the traditional mean-field paradigm.
This is the second of a series of papers aimed at exploiting a generalized self-consistent approach to the study of collective excited states in finite many-particle systems. It contains: (i) A restatement of the equations of the method with further discussion of the basic approximations involved; (ii) a study, through the medium of the exactly soluble problem of uniform translational motion, of the inherent limitations in accuracy of the method when applied to the "strong-coupling" limit for which it was designed. A mode of approximation which can be made self-consistent is indicated. (iii) This approximation is applied to the problem of rotational motion in a plane. In the further limit in which one assumes the spectrum of the rigid rotator, one regains the results of the self-consistent cranking model. In contrast to previous work, the possibility of removing this limitation is indicated, but remains to be carried through.
A variational principle of maximal decoupling between the collective and noncollective subspaces has recently been proposed to pin down the collective degrees of freedom of the nuclear many-body problem. This maximal-decoupling variational principle is further utilized here to determine in an optimal way the auxiliary Hamiltonians to be used in severely truncated boson-space calculations for nuclear collective motions. In the present method one treats the spurious-state problem in truncated boson-space calculations by using appropriate auxiliary boson Hamiltonians. The viability of the method is demonstrated through its application to a simplified shell model containing only the monopole pairing interactions.