arXiv subjects

G. Hagen

Publications and source records attributed to G. Hagen.

At least 109 records · Page 6Linked to original sources

arXiv2011

Quenching of spectroscopic factors for proton removal in oxygen isotopes

We present microscopic coupled-cluster calculations of the spectroscopic factors for proton removal from the closed-shell oxygen isotopes $^{14,16,22,24,28}$O with the chiral nucleon-nucleon interaction at next-to-next-to-next-to-leading order. We include coupling-to-continuum degrees of freedom by using a Hartree-Fock basis built from a Woods-Saxon single-particle basis. This basis treats bound and continuum states on an equal footing. We find a significant quenching of spectroscopic factors in the neutron-rich oxygen isotopes, pointing to enhanced many-body correlations induced by strong coupling to the scattering continuum above the neutron emission thresholds.

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arXiv2011

Ab initio coupled-cluster theory for open-shell nuclei

We develop a new method to describe properties of truly open-shell nuclei. This method is based on single-reference coupled-cluster theory and the equation-of-motion method with extensions to nuclei with $A\pm 2$ nucleons outside a closed shell. We perform proof-of-principle calculations for the ground states of the helium isotopes $^{3-6}$He and the first excited $2^+$ state in $^6$He. The comparison with exact results from matrix diagonalization in small model spaces demonstrates the accuracy of the coupled-cluster methods. Three-particle--one-hole excitations of $^4$He play an important role for the accurate description of $^6$He. For the open-shell nucleus $^6$He, the computational cost of the method is comparable with the coupled-cluster singles-and-doubles approximation while its accuracy is similar to coupled-cluster with singles, doubles and triples excitations.

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arXiv2010

Closed-shell properties of $^{24}$O with {\em ab initio} coupled-cluster theory

We present an \emph{ab initio} calculation of spectroscopic factors for neutron and proton removal from $^{24}$O using the coupled-cluster method and a state-of-the-art chiral nucleon-nucleon interaction at next-to-next-to-next-to-leading order. In order to account for the coupling to the scattering continuum we use a Berggren single-particle basis that treats bound, resonant, and continuum states on an equal footing. We report neutron removal spectroscopic factors for the $^{23}$O states $J^π = 1/2^+$, $5/2^+$, $3/2^-$ and $1/2^-$, and proton removal spectroscopic factors for the $^{23}$N states $1/2^-$ and $3/2^-$. Our calculations support the accumulated experimental evidence that $^{24}$O is a closed-shell nucleus.

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arXiv2010

Ab initio computation of circular quantum dots

We perform coupled-cluster and diffusion Monte Carlo calculations of the energies of circular quantum dots up to 20 electrons. The coupled-cluster calculations include triples corrections and a renormalized Coulomb interaction defined for a given number of low-lying oscillator shells. Using such a renormalized Coulomb interaction brings the coupled-cluster calculations with triples correlations in excellent agreement with the diffusion Monte Carlo calculations. This opens up perspectives for doing ab initio calculations for much larger systems of electrons.

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arXiv2010

Ab initio coupled-cluster approach to nuclear structure with modern nucleon-nucleon interactions

We perform coupled-cluster calculations for the doubly magic nuclei 4He, 16O, 40Ca and 48Ca, for neutron-rich isotopes of oxygen and fluorine, and employ "bare" and secondary renormalized nucleon-nucleon interactions. For the nucleon-nucleon interaction from chiral effective field theory at order next-to-next-to-next-to leading order, we find that the coupled-cluster approximation including triples corrections binds nuclei within 0.4 MeV per nucleon compared to data. We employ interactions from a resolution-scale dependent similarity renormalization group transformations and assess the validity of power counting estimates in medium-mass nuclei. We find that the missing contributions due to three-nucleon forces are consistent with these estimates. For the unitary correlator model potential, we find a slow convergence with respect to increasing the size of the model space. For the G-matrix approach, we find a weak dependence of ground-state energies on the starting energy combined with a rather slow convergence with respect to increasing model spaces. We also analyze the center-of-mass problem and present a practical and efficient solution.

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arXiv2010

Computation of spectroscopic factors with the coupled-cluster method

We present a calculation of spectroscopic factors within coupled-cluster theory. Our derivation of algebraic equations for the one-body overlap functions are based on coupled-cluster equation-of-motion solutions for the ground and excited states of the doubly magic nucleus with mass number $A$ and the odd-mass neighbor with mass $A-1$. As a proof-of-principle calculation, we consider $^{16}$O and the odd neighbors $^{15}$O and $^{15}$N, and compute the spectroscopic factor for nucleon removal from $^{16}$O. We employ a renormalized low-momentum interaction of the $V_{\mathrm{low-}k}$ type derived from a chiral interaction at next-to-next-to-next-to-leading order. We study the sensitivity of our results by variation of the momentum cutoff, and then discuss the treatment of the center of mass.

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arXiv2010

Ab initio computation of the 17F proton-halo state and resonances in A = 17 nuclei

We perform coupled-cluster calculations of the energies and lifetimes of single-particle states around the doubly magic nucleus 16O based on chiral nucleon-nucleon interactions at next-to-next- to-next-to-leading order. To incorporate effects from the scattering continuum, we solve the coupled- cluster equations with a Gamow-Hartree-Fock basis. Our calculations for the 1/2+ proton-halo state in 17F and the 1/2+ state in 17O agree well with experiment, while the calculated spin-orbit splitting between d5/2 and d3/2 states is too small due to the lack of three-nucleon forces. We find that continuum effects yield a significant amount of additional binding energy for the 1/2+ and 3/2+ states in 17O and 17F.

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arXiv2010

Many-body interactions and nuclear structure

This article presents several challenges to nuclear many-body theory and our understanding of the stability of nuclear matte r. In order to achieve this, we present five different cases, starting with an idealized toy model. These cases expose problems that need to be understood in order to match recent advances in nuclear theory with current experimental programs in low-energy nuclear physics. In particular, we focus on our current understanding, or lack thereof, of many-body forces, and how they evolve as functions of the number of particles . We provide examples of discrepancies between theory and experiment and outline some selected perspectives for future research directions.

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arXiv2009

Gamow shell-model calculations of drip-line oxygen isotopes

We employ the Gamow shell model (GSM) to describe low-lying states of the oxygen isotopes 24O and 25O. The many-body Schrodinger equation is solved starting from a two-body Hamiltonian defined by a renormalized low-momentum nucleon-nucleon (NN) interaction, and a spherical Berggren basis. The Berggren basis treats bound, resonant, and continuum states on an equal footing, and is therefore an appropriate representation of loosely bound and unbound nuclear states near threshold. We show that such a basis is necessary in order to obtain a detailed and correct description of the low-lying 1+ and 2+ excited states in 24O. On the other hand, we find that a correct description of binding energy systematics of the ground states is driven by proper treatment and inclusion of many-body correlation effects. This is supported by the fact that we get 25O unstable with respect to 24O in both oscillator and Berggren representations starting from a 22O core. Furthermore, we show that the structure of these loosely bound or unbound isotopes are strongly influenced by the 1S0 component of the NN interaction. This has important consequences for our understanding of nuclear stability.

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arXiv2009

Ab-initio computation of neutron-rich oxygen isotopes

We compute the binding energy of neutron-rich oxygen isotopes and employ the coupled-cluster method and chiral nucleon-nucleon interactions at next-to-next-to-next-to-leading order with two different cutoffs. We obtain rather well-converged results in model spaces consisting of up to 21 oscillator shells. For interactions with a momentum cutoff of 500 MeV, we find that 28O is stable with respect to 24O, while calculations with a momentum cutoff of 600 MeV result in a slightly unbound 28O. The theoretical error estimates due to the omission of the three-nucleon forces and the truncation of excitations beyond three-particle-three-hole clusters indicate that the stability of 28O cannot be ruled out from ab-initio calculations, and that three-nucleon forces and continuum effects play the dominant role in deciding this question.

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arXiv2009

Solution of the center-of-mass problem in nuclear structure calculations

The coupled-cluster wave function factorizes to a very good approximation into a product of an intrinsic wave function and a Gaussian for the center-of-mass coordinate. The width of the Gaussian is in general not identical to the oscillator length of the underlying single-particle basis. The quality of the separation can be verified by a simple procedure.

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arXiv2009

Helium halo nuclei from low-momentum interactions

We present ground-state energies of helium halo nuclei based on chiral low-momentum interactions, using the hyperspherical-harmonics method for 6He and coupled-cluster theory for 8He, with correct asymptotics for the extended halo structure.

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arXiv2008

Medium-mass nuclei from chiral nucleon-nucleon interactions

We compute the binding energies, radii, and densities for selected medium-mass nuclei within coupled-cluster theory and employ the "bare" chiral nucleon-nucleon interaction at order N3LO. We find rather well-converged results in model spaces consisting of 15 oscillator shells, and the doubly magic nuclei 40Ca, 48Ca, and the exotic 48Ni are underbound by about 1 MeV per nucleon within the CCSD approximation. The binding-energy difference between the mirror nuclei 48Ca and 48Ni is close to theoretical mass table evaluations. Our computation of the one-body density matrices and the corresponding natural orbitals and occupation numbers provides a first step to a microscopic foundation of the nuclear shell model.

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arXiv2007

Coupled-cluster theory for three-body Hamiltonians

We derive coupled-cluster equations for three-body Hamiltonians. The equations for the one- and two-body cluster amplitudes are presented in a factorized form that leads to an efficient numerical implementation. We employ low-momentum two- and three-nucleon interactions and calculate the binding energy of He-4. The results show that the main contribution of the three-nucleon interaction stems from its density-dependent zero-, one-, and two-body terms that result from the normal ordering of the Hamiltonian in coupled-cluster theory. The residual three-body terms that remain after normal ordering can be neglected.

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arXiv2007

Comment on "Ab Initio study of 40-Ca with an importance-truncated no-core shell model"

In a recent Letter [Phys. Rev. Lett. 99, 092501 (2007)], Roth and Navratil present an importance-truncation scheme for the no-core shell model. The authors claim that their truncation scheme leads to converged results for the ground state of 40-Ca. We believe that this conclusion cannot be drawn from the results presented in the Letter. Furthermore, the claimed convergence is at variance with expectations of many-body theory. In particular, coupled-cluster calculations indicate that a significant fraction of the correlation energy is missing.

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arXiv2007

Benchmark calculations for 3H, 4He, 16O and 40Ca with ab-initio coupled-cluster theory

We present ab-initio calculations for 3H, 4He, 16O, and 40Ca based on two-nucleon low-momentum interactions Vlowk within coupled-cluster theory. For 3H and 4He, our results 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-particle basis. For the heavier nuclei, we report practically converged binding energies and compare with other approaches.

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arXiv2006

Complex coupled-cluster approach to an ab-initio description of open quantum systems

We develop ab-initio coupled-cluster theory to describe resonant and weakly bound states along the neutron drip line. We compute the ground states of the helium chain 3-10He within coupled-cluster theory in singles and doubles (CCSD) approximation. We employ a spherical Gamow-Hartree-Fock basis generated from the low-momentum N3LO nucleon-nucleon interaction. This basis treats bound, resonant, and continuum states on equal footing, and is therefore optimal for the description of properties of drip line nuclei where continuum features play an essential role. Within this formalism, we present an ab-initio calculation of energies and decay widths of unstable nuclei starting from realistic interactions.

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arXiv2006

Gamow shell model and realistic nucleon-nucleon interactions

We present a new and efficient method to obtain a Gamow shell-model basis and matrix elements generated by realistic nucleon-nucleon interactions. We derive a self-consistent Hartree-Fock potential from the renormalized N3LO interaction model. The corresponding Gamow one-body eigenstates are generated in a plane wave basis in order to build a Gamow shell-model set of basis states for the closed shell nuclei 4He and 16O. We address also the problem of representing a realistic nucleon-nucleon interaction in a two-particle Berggren basis in the laboratory frame. To achieve this, an expansion of matrix elements of the residual nucleon-nucleon interaction in a finite set of harmonic oscillator wave functions is used. We show that all loosely bound and narrow resonant states converge surprisingly fast. Even broad resonances in these two-particle valence systems converge within a reasonable number of harmonic oscillator functions. Examples of 6He and 18O Gamow shell-model calculations using 4He and 16}O as closed shell cores are presented. This procedure allows Gamow shell-model calculations to be performed with all realistic nucleon-nucleon interactions and with either momentum or position space representations for the Gamow basis. The possibility to remove the center of mass spuriosity of Gamow shell-model nuclear states with this method is also discussed. Perspectives for nuclear structure calculations of dripline nuclei are outlined.

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