Perturbation Theory and the Nuclear Many Body Problem

Kumar, K. Vinod; Folk, R.

doi:10.1119/1.1969674

Cited by 15 publications

(11 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…may be written in terms of the reaction matrix of Brillouin-Wigner perturbation theory as (see, e.g., Kumar 1962, Starace 1972, 1974, Wendin 1976a…”

Section: Wavefunctions and Energy Levels In A Strong-interaction Regimementioning

confidence: 99%

Perturbation theory in a strong-interaction regime with application to 4d-subshell spectra of Ba and La

Wendin

Starace

1978

J. Phys. B: At. Mol. Phys.

View full text Add to dashboard Cite

“…may be written in terms of the reaction matrix of Brillouin-Wigner perturbation theory as (see, e.g., Kumar 1962, Starace 1972, 1974, Wendin 1976a…”

Section: Wavefunctions and Energy Levels In A Strong-interaction Regimementioning

confidence: 99%

Perturbation theory in a strong-interaction regime with application to 4d-subshell spectra of Ba and La

Wendin

Starace

1978

J. Phys. B: At. Mol. Phys.

View full text Add to dashboard Cite

“…However, the integral identity of Equation (35) is valid for an arbitrary switching function, allowing the factorization of Equations (37) and (38) It is also of interest to note that the customary assertion [20] that the vacuum amplitude of Equations (24) and (37) can be written as the exponential of connected diagrams in the form is, strictly speaking, irrelevant to the cancellation of Brueckner terms in the energy [Equation (24a)I. In order to clarify this, note that when the amplitude of Equation (39) is expanded one obtains, among others, third-order product terms of the form (3) which, as we have indicated, arise from three distinct time orderings of disconnected vacuum diagrams in the customary perturbation series of Equations (23)- (27). When the diagrams corresponding to the three distinct time orderings are evaluated in the limit of ideal adiabatic switching, the correct Brueckner unlinked terms in the third-order energy appear, and cancel when the time orderings are summed; that is ( t 3 0),…”

Section: = ( L + O ---X +~--O + @ + ( J --G --+(Yj --mentioning

confidence: 97%

“…we shall define, in accordance with common usage [27], the Brueckner unlinked part of the second-order static perturbation function by Of course, the third-order perturbation energy Es (3) also contains closely related canceling Brueckner unlinked terms of the form Note that while the secular and normalization terms of Equations (12)- (16) are identified for an arbitrary perturbation Hamiltonian H , (l), the canceling Brueckner unlinked terms are only identified in the first quantized development when the matrix elements of Equation (20) are evaluated in the case of a many-electron perturbation, as in Equations (21) and (22).…”

Section: H~o ( ' ) H K O (~) mentioning

confidence: 99%

“…Introducing Equations (28) and (29) into Equations (23)- (27) results in a set of ordinary and time-ordered products of creation and destruction operators in Equations (26a) and (26b), respectively. The use of Wick's algebra [29] in this connection provides a set of rules for constructing and evaluating Feynman-Goldstone diagrams for the wave function and energy of Equations (23) and (24), respectively.…”

Section: Wave Function Diagramsmentioning

confidence: 99%

See 1 more Smart Citation

On the brueckner and goldstone forms of the linked-cluster theorem

Langhoff

Hernández

2009

Int. J. Quantum Chem.

View full text Add to dashboard Cite

Connections between the Brueckner and Goldstone forms of the linked-cluster theorem are clarified in an elementary fashion employing a finite many-body system of electrons interacting via two-body forces as an illustrative example. It is shown that the order-by-order cancellations of Brueckner unlinked terms in the many-body wave function and energy occur in the Goldstone development upon the additions of the different time orderings of Feynman-Goldstone diagrams having disconnected vacuum parts. The factoring of the vacuum amplitude from the wave function, upon which customary presentations of the theorem focus attention, is seen to be irrelevant to the cancellations of Brueckner unlinked terms, and has to do, rather, with the presence of secular and normalization terms in the time-dependent perturbation functions for an adiabatically switched static perturbation. Similarly, the equivalence of the vacuum amplitude with the exponential of all connected vacuum diagrams, originally demonstrated by Feynman in the case of hole theory, is seen to be irrelevant to the cancellations of Brueckner unlinked terms in the energy, which occur in the Goldstone development upon the summations over all time orderings of disconnected vacuum diagrams. The distinction between Brueckner unlinked terms on the one hand, and secular and normalization terms on the other, is confused in customary presentations of the linked-cluster theorem by the use of exponential switching, following Gell-Mann and Low, and is clarified in the present development by considering the Friedrichs limit of ideal adiabatic switching.

show abstract

“…For non zero pressure in nuclear matter the Fermi energy is not equal to the average binding energy but there are the well known correction (see for example) [18]:…”

Section: Rmf Models Eos and Parton Sfmentioning

confidence: 99%

The Modification of the Scalar Field in Dense Nuclear Matter

Rożynek

2010

Int. J. Mod. Phys. E

View full text Add to dashboard Cite

Abstract.We show the possible evolution of the nuclear deep inelastic structure function with nuclear density ρ. The nucleon deep inelastic structure function represents distribution of quarks as function of Björken variable x which measures the longitudinal fraction of momentum carried by them during the Deep Inelastic Scattering (DIS) of electrons on nuclear targets. Starting with small density and negative pressure in Nuclear Matter (NM) we have relatively large inter-nucleon distances and increasing role of nuclear interaction mediated by virtual mesons.When the density approaches the saturation point, ρ = ρ 0 , we have no longer separate mesons and nucleons but eventually modified nucleon Structure Function (SF) in medium. The ratio of nuclear to nucleon SF measured at saturation point is well known as "EMC effect". For larger density, ρ > ρ 0 , when the localization of quarks is smaller then 0.3 fm, the nucleons overlap. We argue that nucleon mass should start to decrease in order to satisfy the Momentum Sum Rule (MSR) of DIS. These modifications of the nucleon Structure Function (SF) are calculated in the frame of the nuclear Relativistic Mean Field (RMF) convolution model. The correction to the Fermi energy from term proportional to the pressure is very important and its inclusion modifies the Equation of State (EoS) for nuclear matter.

show abstract

Perturbation Theory and the Nuclear Many Body Problem

Cited by 15 publications

References 0 publications

Perturbation theory in a strong-interaction regime with application to 4d-subshell spectra of Ba and La

Perturbation theory in a strong-interaction regime with application to 4d-subshell spectra of Ba and La

On the brueckner and goldstone forms of the linked-cluster theorem

The Modification of the Scalar Field in Dense Nuclear Matter

Contact Info

Product

Resources

About