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M. Hjorth-Jensen

Publications and source records attributed to M. Hjorth-Jensen.

At least 55 records · Page 3Linked to original sources

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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Effective interactions and shell model studies of heavy tin isotopes

We present results from large-scale shell-model calculations of even and odd tin isotopes from 134Sn to 142}Sn with a shell-model space defined by the 1f7/2,2p3/2,0h9/2,2p1/2,1f5/2,0i13/2 single-particle orbits. An effective two-body interaction based on modern nucleon-nucleon interactions is employed. The shell-model results are in turn analyzed for their pairing content using a generalized seniority approach. Our results indicate that a pairing-model picture captures a great deal of the structure and the correlations of the lowest lying states for even and odd isotopes.

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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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Quantum and Classical Calculations of Ground State Properties of Parabolic Quantum Dots

We report calculations for electronic ground states of parabolically confined quantum dots for up to 30 electrons based on the quantum Monte Carlo method. Effects of the electron-electron interaction and the response to a magnetic field are exposed. The wavefunctions and the ground state energies are compared with purely classical calculations performed with a comprehensive Molecular Dynamics code. For the chosen well parameters a close correspondence in the overall shape of electron density distribution is found even for small number of electrons, while the detailed radial distributions show the effects of Pauli principle in the quantal case.

cond-mat.str-el↗

Coupled-cluster calculations for valence systems around O-16

We study the ground and low-lying excited states of O-15, O-17, N-15, and F-17 using modern two-body nucleon-nucleon interactions and the suitably designed variants of the ab initio equation-of-motion coupled-cluster theory aimed at an accurate description of systems with valence particles and holes. A number of properties of O-15, O-17, N-15, and F-17, including ways the energies of ground and excited states of valence systems around O-16 change as functions of the number of nucleons, are correctly reproduced by the equation-of-motion coupled-cluster calculations. Within a harmonic oscillator basis and large effective model spaces, our results are converged for the chosen two-body Hamiltonians. Thus, all disagreements with experiment are, most likely, due to the degrees of freedom such as three-body interactions not accounted for in our effective two-body Hamiltonians. In particular, the calculated binding energies of O-15/N-15 and O-17/F-17 enable us to rationalize the discrepancy between the experimental and recently published [Phys. Rev. Lett. 94, 212501 (2005)] equation-of-motion coupled-cluster excitation energies for the Jpi=3- state of O-16. The results demonstrate the feasibility of the equation-of-motion coupled-cluster methods to deal with valence systems around closed-shell nuclei and to provide precise results for systems beyond A=16.

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Dominant g(9/2)^2 neutron configuration in the 4+1 state of 68Zn based on new g factor measurements

The $g$ factor of the $4_1^+$ state in $^{68}$Zn has been remeasured with improved energy resolution of the detectors used. The value obtained is consistent with the previous result of a negative $g$ factor thus confirming the dominant $0g_{9/2}$ neutron nature of the $4_1^+$ state. In addition, the accuracy of the $g$ factors of the $2_1^+$, $2_2^+$ and $3_1^-$ states has been improved an d their lifetimes were well reproduced. New large-scale shell model calculations based on a $^{56}$Ni core and an $0f_{5/2}1pg_{9/2}$ model space yield a theoretical value, $g(4_1^+) = +0.008$. Although the calculated value is small, it cannot fully explain the experimental value, $g(4_1^+) = -0.37(17)$. The magnitude of the deduced B(E2) of the $4_1^+$ and $2_1^+$ transition is, however, rather well described. These results demonstrate again the importance of $g$ factor measurements for nuclear structure determination s due to their specific sensitivity to detailed proton and neutron components in the nuclear wave functions.

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Numerical Methods as an Integrated Part of Physics Education

During the last decade we have witnessed an impressive development in so-called interpreted languages and computational environments such as Maple, Mathematica, IDL, Matlab etc. Problems which until recently were typically solved on mainframe machines and written in computing languages such as Fortran or C/C++, can now easily be solved on standard PCs with the bonus of immediate visualizations of the results. In our undergraduate programs an often posed question is how to incorporate and exploit efficiently these advances in the standard physics and mathematics curriculum, without detracting the attention from the classical and basic theoretical and experimental topics to be covered. Furthermore, if students are trained to use such tools at early stages in their education, do such tools really enhance and improve the learning environment? And, perhaps even more important, does it lead to a better physics understanding? Here we present one possible approach, where computational topics are gradually baked into our undergraduate curriculum in Mathematics and Physics, Astronomy and Meteorology. We focus on training our students to use general programming tools in solving physics problems, in addition to the classical analytic problems. By this approach, the students gain an expertise that they can build upon in their future studies and careers. We use mainly Java, Matlab and Maple as computational environments. Our students are now capable of handling at an early stage in their education more realistic physics problems than before. We believe firmly that, in addition to educating modern scientists, this promotes a better physics understanding for a majority of the students.

physics.ed-ph↗

Vortices in Atomic Bose-Einstein Condensates in the Large Gas Parameter Region

In this work we compare the results of the Gross-Pitaevskii and modified Gross-Pitaevskii equations with ab initio variational Monte Carlo calculations for Bose-Einstein condensates of atoms in axially symmetric traps. We examine both the ground state and excited states having a vortex line along the z-axis at high values of the gas parameter and demonstrate an excellent agreement between the modified Gross-Pitaevskii and ab initio Monte Carlo methods, both for the ground and vortex states.

cond-mat.other↗

Ab initio coupled-cluster study of 16-O

We report converged results for the ground and excited states and matter density of 16-O using realistic two-body nucleon-nucleon interactions and coupled-cluster methods and formalism developed in quantum chemistry. Most of the binding is obtained with the coupled-cluster singles and doubles approach. Additional binding due to three-body clusters (triples) is minimal. The coupled-cluster method with singles and doubles provides a good description of the matter density, charge radius, charge form factor, and excited states of a 1-particle-1-hole nature, but it cannot describe the first excited 0+ state. Incorporation of triples has no effect on the latter finding.

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Magnetic moments of the 2${^+_1}$ states around $^{132}$Sn

Development of neutron-rich radioactive beams at the HRIBF facility has stimulated experimental and theoretical activity in heavy Sn and Te isotopes. Recently, the g-factor of the first 2$^+$ state in $^{132}$Te has been measured. We report here new shell-model calculation of magnetic moments for selected Sn and Te isotopes. The residual interaction is based on the CD-Bonn renormalized $ G $-matrix. Single-particle spin and orbital effective g-factors are evaluated microscopically including core polarization and meson exchange currents effects.

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Model Calculation of Effective Three-Body Forces

We propose a scheme for extracting an effective three-body interaction originating from a two-nucleon interaction. This is based on the Q-box method of Kuo and collaborators, where folded diagrams are obtained by differentiating a sum of non-folded diagrams with respect to the starting energy. To gain insight we have studied several examples using the Lipkin model where the perturbative approach can be compared with exact results. Numerically the three-body interactions can be significant and in a matrix example good accuracy was not obtained simultaneously for both eigenvalues with two-body interactions alone.

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Effective Interaction Techniques for the Gamow Shell Model

We apply a contour deformation technique in momentum space to the newly developed Gamow shell model, and study the drip-line nuclei 5He, 6He and 7He. A major problem in Gamow shell-model studies of nuclear many-body systems is the increasing dimensionality of many-body configurations due to the large number of resonant and complex continuum states necessary to reproduce bound and resonant state energies. We address this problem using two different effective operator approaches generalized to the complex momentum plane. These are the Lee-Suzuki similarity transformation method for complex interactions and the multi-reference perturbation theory method. The combination of these two approaches results in a large truncation of the relevant configurations compared with direct diagonalization. This offers interesting perspectives for studies of weakly bound systems.

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Nuclear Structure Calculations with Coupled Cluster Methods from Quantum Chemistry

We present several coupled-cluster calculations of ground and excited states of 4He and 16O employing methods from quantum chemistry. A comparison of coupled cluster results with the results of exact diagonalization of the hamiltonian in the same model space and other truncated shell-model calculations shows that the quantum chemistry inspired coupled cluster approximations provide an excellent description of ground and excited states of nuclei, with much less computational effort than traditional large-scale shell-model approaches. Unless truncations are made, for nuclei like 16O, full-fledged shell-model calculations with four or more major shells are not possible. However, these and even larger systems can be studied with the coupled cluster methods due to the polynomial rather than factorial scaling inherent in standard shell-model studies. This makes the coupled cluster approaches, developed in quantum chemistry, viable methods for describing weakly bound systems of interest for future nuclear facilities.

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Effective interactions and the nuclear shell-model

This review aims at a critical discussion of the interplay between effective interactions derived from various many-body approaches and spectroscopic data extracted from large scale shell-model studies. To achieve this, our many-body scheme starts with the free nucleon-nucleon (NN) interaction, typically modelled on various meson exchanges. The NN interaction is in turn renormalized in order to derive an effective medium dependent interaction. The latter is in turn used in shell-model calculations of selected nuclei. We also describe how to sum up the parquet class of diagrams and present initial uses of the effective interactions in coupled cluster many-body theory.

nucl-th↗

Coupled cluster calculations of ground and excited states of nuclei

The standard and renormalized coupled cluster methods with singles, doubles, and noniterative triples and their generalizations to excited states, based on the equation of motion coupled cluster approach, are applied to the He-4 and O-16 nuclei. A comparison of coupled cluster results with the results of the exact diagonalization of the Hamiltonian in the same model space shows that the quantum chemistry inspired coupled cluster approximations provide an excellent description of ground and excited states of nuclei. The bulk of the correlation effects is obtained at the coupled cluster singles and doubles level. Triples, treated noniteratively, provide the virtually exact description.

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Pairing correlations and transitions in nuclear systems

We discuss several pairing-related phenomena in nuclear systems, ranging from superfluidity in neutron stars to the gradual breaking of pairs in finite nuclei. We describe recent experimental evidence that points to a relation between pairing and phase transitions (or transformations) in finite nuclear systems. A simple pairing interaction model is used in order to study and classify an eventual pairing phase transition in finite fermionic systems such as nuclei. We show that systems with as few as 10-16 fermions can exhibit clear features reminiscent of a phase transition.

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Coupled cluster approach to nuclear physics

Using many-body perturbation theory and coupled-cluster theory, we calculate the ground-state energy of He-4 and O-16. We perform these calculations using a no-core G-matrix interaction derived from a realistic nucleon-nucleon potential. Our calculations employ up to two-particle-two-hole coupled-cluster amplitudes.

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Free energy and criticality in the nucleon pair breaking process

Experimental level densities for 171,172Yb, 166,167Er, 161,162Dy, and 148,149Sm are analyzed within the microcanonical ensemble. In the even isotopes at excitation energies E < 2 MeV, the Helmholtz free energy F signals the transition from zero to two quasiparticles. For E > 2 MeV, the odd and even isotopes reveal a surprisingly constant F at a critical temperature Tc of appr. 0.5 MeV, indicating the continuous melting of nucleon Cooper pairs as function of excitation energy.

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