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Title: Benchmark Calculations for 3H, 4He, 16O, and 40Ca with ab-initio Coupled-Cluster Theory

Abstract

We present ab-initio calculations for 3H, 4He, 16O, and 40Ca based on two-nucleon low-momentum interactions V_{low k} within coupled-cluster theory. For 3H and 4He, our reesults are within 70 keV and 10 keV of the corresponding Faddeev and Faddeev-Yakubovsky energies. We study in detail the convergence with respect to the size of the model space and the single-partcle basis. For the heavier nuclei, we report practically converged binding energies and compare with other approaches.

Authors:
 [1];  [2];  [3];  [2];  [4]
  1. University of Tennessee, Knoxville (UTK) & Oak Ridge National Laboratory (ORNL)
  2. ORNL
  3. University of Oslo, Norway
  4. TRIUMF, Canada
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
932093
DOE Contract Number:
DE-AC05-00OR22725
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review C; Journal Volume: 76; Journal Issue: 4
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS; BENCHMARKS; CONVERGENCE; TRITIUM; HELIUM 4; OXYGEN 16; CALCIUM 40; BINDING ENERGY; TWO-BODY PROBLEM

Citation Formats

Hagen, G., Dean, David Jarvis, Hjorth-Jensen, M., Papenbrock, Thomas F, and Schwenk, A.. Benchmark Calculations for 3H, 4He, 16O, and 40Ca with ab-initio Coupled-Cluster Theory. United States: N. p., 2007. Web. doi:10.1103/PhysRevC.76.044305.
Hagen, G., Dean, David Jarvis, Hjorth-Jensen, M., Papenbrock, Thomas F, & Schwenk, A.. Benchmark Calculations for 3H, 4He, 16O, and 40Ca with ab-initio Coupled-Cluster Theory. United States. doi:10.1103/PhysRevC.76.044305.
Hagen, G., Dean, David Jarvis, Hjorth-Jensen, M., Papenbrock, Thomas F, and Schwenk, A.. Mon . "Benchmark Calculations for 3H, 4He, 16O, and 40Ca with ab-initio Coupled-Cluster Theory". United States. doi:10.1103/PhysRevC.76.044305.
@article{osti_932093,
title = {Benchmark Calculations for 3H, 4He, 16O, and 40Ca with ab-initio Coupled-Cluster Theory},
author = {Hagen, G. and Dean, David Jarvis and Hjorth-Jensen, M. and Papenbrock, Thomas F and Schwenk, A.},
abstractNote = {We present ab-initio calculations for 3H, 4He, 16O, and 40Ca based on two-nucleon low-momentum interactions V_{low k} within coupled-cluster theory. For 3H and 4He, our reesults are within 70 keV and 10 keV of the corresponding Faddeev and Faddeev-Yakubovsky energies. We study in detail the convergence with respect to the size of the model space and the single-partcle basis. For the heavier nuclei, we report practically converged binding energies and compare with other approaches.},
doi = {10.1103/PhysRevC.76.044305},
journal = {Physical Review C},
number = 4,
volume = 76,
place = {United States},
year = {Mon Jan 01 00:00:00 EST 2007},
month = {Mon Jan 01 00:00:00 EST 2007}
}
  • We present ab initio calculations for {sup 3}H, {sup 4}He, {sup 16}O, and {sup 40}Ca based on two-nucleon low-momentum interactions V{sub lowk} within coupled-cluster theory. For {sup 3}H and {sup 4}He, our results are within 70 and 10 keV of the corresponding Faddeev and Faddeev-Yakubovsky energies. We study in detail the convergence with respect to the size of the model space and the single-particle basis. For the heavier nuclei, we report practically converged binding energies and compare with other approaches.
  • Using the ground-state energy of {sup 16}O obtained with the realistic V{sub UCOM} interaction as a test case, we present a comprehensive comparison of different configuration interaction (CI) and coupled-cluster (CC) methods, analyzing the intrinsic advantages and limitations of each of the approaches. In particular, we use the importance-truncated (IT) CI and no-core shell model (NCSM) schemes with up to 4-particle-4-hole (4p4h) excitations, with and without the Davidson extensivity corrections, as well as the size extensive CC methods with a complete treatment of one- and two-body clusters (CCSD) and a noniterative treatment of connected three-body clusters via the completely renormalizedmore » correction to the CCSD energy defining the CR-CC(2,3) approach, which are all capable of handling larger systems with dozens of explicitly correlated fermions. We discuss the impact of the center-of-mass contaminations, the choice of the single-particle basis, and size-extensivity on the resulting energies. When the IT-CI and IT-NCSM methods include the 4p4h excitations and when the CC calculations include the 1p1h, 2p2h, and 3p3h clusters, as in the CR-CC(2,3) approach, we observe an excellent agreement among the different methodologies, particularly when the Davidson extensivity corrections are added to the IT-CI energies and the effects of the connected three-body clusters are accounted for in the CC calculations. This shows that despite their individual limitations, the IT-CI, IT-NCSM, and CC methods can provide precise and consistent ab initio nuclear structure predictions. Furthermore, the IT-CI, IT-NCSM, and CC ground-state energy values obtained for {sup 16}O are in reasonable agreement with the experimental value, providing further evidence that the V{sub UCOM} two-body interaction may allow for a good description of binding energies for heavier nuclei and that all of the methods used in this study account for most of the relevant particle correlation effects.« less
  • We combine a recently developed ab initio many-body approach capable of describing simultaneously both bound and scattering states, the ab initio no-core shell model/resonating-group method (NCSM/RGM), with an importance-truncation scheme for the cluster eigenstate basis and demonstrate its applicability to nuclei with mass numbers as high as 17. By using soft similarity renormalization-group-evolved chiral nucleon-nucleon interactions, we first calculate nucleon-{sup 4}He phase shifts, cross sections, and analyzing powers. Next, we investigate nucleon scattering on {sup 7}Li, {sup 7}Be, {sup 12}C, and {sup 16}O in coupled-channel NCSM/RGM calculations that include low-lying excited states of these nuclei. We check the convergence ofmore » phase shifts with the basis size and study A=8,13, and 17 bound and unbound states. Our calculations predict low-lying resonances in {sup 8}Li and {sup 8}B that have not been experimentally clearly identified yet. We are able to reproduce reasonably well the structure of the A=13 low-lying states. However, we find that A=17 states cannot be described without an improved treatment of {sup 16}O one-particle-one-hole excitations and {alpha} clustering.« less
  • The {sup 2}H(d,p){sup 3}H, {sup 2}H(d,n){sup 3}He, and {sup 2}H(d,{gamma}){sup 4}He reactions at low energies are studied with realistic nucleon-nucleon interactions in an ab initio approach. The obtained astrophysical S-factors are all in very good agreement with experiment. The most important channels for both transfer and radiative capture are all found to dominate thanks to the tensor force.
  • The {sup 2}H(d,p){sup 3}H, {sup 2}H(d,n){sup 3}He, and {sup 2}H(d,{gamma}){sup 4}He reactions are studied at low energies in a multichannel ab initio model that takes into account the distortions of the nuclei. The internal wave functions of these nuclei are given by the stochastic variational method with the AV8{sup '} realistic interaction and a phenomenological three-body force included to reproduce the two-body thresholds. The obtained astrophysical S factors are all in very good agreement with the experiment. The most important channels for both transfer and radiative capture are identified by comparing to calculations with an effective central force. They aremore » all found to dominate thanks to the tensor force.« less