Cluster expansion of the wave function. Electron correlations in the ground state, valence and Rydberg excited states, ionized states, and electron attached states of formaldehyde by SAC and SAC–CI theories

1981 ◽  
Vol 75 (6) ◽  
pp. 2952-2958 ◽  
Author(s):  
H. Nakatsuji ◽  
K. Ohta ◽  
K. Hirao
Keyword(s):  
Wave Function ◽  
Excited States ◽  
Cluster Expansion ◽  
Ground State ◽  
Electron Correlations

The effects of ground state correlations in 16O on the muonuclear sum rule

1982 ◽  
Vol 60 (3) ◽  
pp. 321-328 ◽  
Author(s):  
D. Duplain ◽  
B. Goulard
Keyword(s):  
Wave Function ◽  
Cluster Expansion ◽  
Ground State ◽  
Neutrino Energy ◽  
Tensor Component ◽  
Second Order ◽  
Muon Capture ◽  
Total Rate ◽  
Sum Rule ◽  
The Mean

The total rate of muon capture by 16O is calculated using the linked cluster expansion to introduce ground state correlations. All diagrams up to the second order in the number of hole-lines are included. [Formula: see text] is reduced by some 15% and is shown to behave like σ−1,. [Formula: see text] and [Formula: see text] are strongly increased by about 30%. This enhancement is related to that part of the defect wave function which arises directly from the tensor component of the N–N potential. It is suggested that, for those transitions that are induced by spin operators, the mean neutrino energy may be smaller than usually thought.

DESCRIPTION OF 8Be AS DEFORMED GAS-LIKE TWO-ALPHA-PARTICLE STATES

2003 ◽  
Vol 18 (02n06) ◽  
pp. 170-173
Author(s):  
Y. FUNAKI ◽  
H. HORIUCHI ◽  
A. TOHSAKI ◽  
P. SCHUCK ◽  
G. RÖPKE
Keyword(s):  
Wave Function ◽  
Excited States ◽  
Ground State ◽  
Cluster Structure ◽  
Test Case ◽  
Weakly Bound ◽  
Generator Coordinate Method ◽  
Spatial Deformation ◽  
Generator Coordinate ◽  
Spin Excitations

In order to study non-zero spin excitations of the recently proposed α-cluster condensation in the self-conjugate 4n nuclei, spatial deformation is introduced into the model wave function of the α-cluster condensate. The rotational band states of 8 Be are investigated as a first step of a test case for the study of the deformation of the α-cluster condensate. Calculations reproduce well the binding energy of the 0+ ground state and also the excitation energy of the 2+ state. Our 0+ wave function is found to be exactly equal to the 0+ wave function obtained by the generator coordinate method using Brink's 2α wave function. The study shows that both the 0+ ground and 2+ excited states can be considered as having a gas-like (i.e. weakly bound) 2α-cluster structure.

Correlated Atomic Pair Functions by the e-ϱ-Method. I. Ground State 11S and Lowest Excited States n1S (n > 1) and n3S of Helium

1999 ◽  
Vol 54 (12) ◽  
pp. 711-717
Author(s):  
F. F. Seelig ◽  
G. A. Becker
Keyword(s):  
Integral Equation ◽  
Wave Function ◽  
Helium Atom ◽  
Excited States ◽  
Ground State ◽  
Single Parent ◽  
Hartree Fock ◽  
Atomic Pair ◽  
Electronic Wave Function ◽  
S States

Abstract Some low n1S and n3S states of the helium atom are computed with the aid of the e-e method which formulates the electronic wave function of the 2 electrons ψ = e-e F, where ϱ=Z(r1+r2)–½r12 and here Z = 2. Both the differential and the integral equation for F contain a pseudopotential Ṽ instead of the true potential V that contrary to V is finite. For the ground state, F = 1 yields nearly the Hartree-Fock SCF accuracy, whereas a multinomial expansion in r1, r2 , r2 yields a relative error of about 10-7 . All integrals can be computed analytically and are derived from one single “parent” integral.

Exact Numerical Procedure for the Binding Energy of Hydrogen Impurities in Quantum Dots with Parabolic Confinements

2013 ◽  
Vol 475-476 ◽  
pp. 1355-1358
Author(s):  
Arnold Abramov
Keyword(s):  
Quantum Dots ◽  
Wave Function ◽  
Binding Energy ◽  
Quantum Dot ◽  
Excited States ◽  
Ground State ◽  
Qualitative Agreement ◽  
Numerical Procedure ◽  
Impurity States ◽  
Parabolic Confinement

In this paper we present exact numerical procedure to calculate the binding energy and wave function of impurity states in a quantum dot with parabolic confinement. The developed method allows control the accuracy of obtained results, as well as calculates the characteristics of not only ground state, but also of the excited states. Comparison of our results with data obtained by other methods is in quantitative and qualitative agreement. We studied the effects of impurity position on the binding energy.

Generator Coordinate Method and Short Range Correlations

1973 ◽  
Vol 28 (3-4) ◽  
pp. 393-395
Author(s):  
J. da Providência ◽  
C. M. Shakin
Keyword(s):  
Excited States ◽  
Cluster Expansion ◽  
Ground State ◽  
Short Range ◽  
Generator Coordinate Method ◽  
Correlated Systems ◽  
Coordinate Method ◽  
Generator Coordinate ◽  
Singular Interactions ◽  
Short Range Correlations

AbstractIt is shown that the cluster expansion formalism previously developed as a basis for a theory of the ground state of correlated systems may be generalised in such a way as to enable the application of the generator coordinate method in the presence of singular interactions, thereby providing also a theory for excited states.

scholarly journals A NEW REALISTIC MANY-BODY APPROACH FOR THE DESCRIPTION OF HIGH-ENERGY SCATTERING PROCESSES OFF COMPLEX NUCLEI

2006 ◽  
Vol 20 (30n31) ◽  
pp. 5325-5329
Author(s):  
M. ALVIOLI ◽  
C. CIOFI DEGLI ATTI ◽  
H. MORITA
Keyword(s):  
Wave Function ◽  
Momentum Distribution ◽  
Cluster Expansion ◽  
Ground State ◽  
Final State Interaction ◽  
High Energy ◽  
Many Body ◽  
Energy Scattering ◽  
High Energy Scattering ◽  
Complex Nuclei

A new linked cluster expansion for the calculation of ground state observables of many-body nuclei with realistic interactions has been developed, in order to single out the major contributions to the relevant quantities when Nucleon-Nucleon correlations are taken into account in the wave function. Using the V8′ potential the ground state energy, density and momentum distribution of complex nuclei have been calculated and found to be in good agreement with the results obtained within the Fermi Hyper Netted Chain, and Variational Monte Carlo approaches. Using the same cluster expansion, with wave function and correlations parameters fixed from the calculation of the ground-state observables, we have calculated various high energy scattering processes off complex nuclei. We made use of the Glauber multiple scattering theory, which can be readily included into the cluster expansion we have developed, to take into account final state interaction effects in the semi-inclusive reaction A(e,e′p)X, and calculated the distorted momentum distribution, which is a necessary ingredient to estimate the cross section.

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