The ab initio no-core shell model (NCSM) is extended to include a realistic three-body interaction in calculations for p-shell nuclei. The NCSM formalism is reviewed and new features needed in ...calculations with three-body forces are discussed in detail. We present results of first applications to 6,7Li, 6He, 7,8,10Be, 10,11,12B, 12N and 10,11,12,13C using the Argonne V8' nucleon-nucleon (NN) potential and the Tucson-Melbourne TM'(99) three-nucleon interaction (TNI). In addition to increasing the total binding energy, we observe a substantial sensitivity in the low-lying spectra to the presence of the realistic three-body force and an overall improvement in the level-ordering and level-spacing in comparison to experiment. The greatest sensitivity occurs for states where the spin-orbit interaction strength is known to play a role. In particular, with the TNI we obtain the correct ground-state spin for 10,11,12B and 12N, contrary to calculations with NN potentials only.
We report the first no-core shell model results for \(^{48}Ca\), \(^{48}Sc\) and \(^{48}Ti\) with derived and modified two-body Hamiltonians. We use an oscillator basis with a limited \(\hbar\Omega\) ...range around \(45/A^{1/3}-25/A^{2/3} = 10.5 MeV\) and a limited model space up to \(1\hbar\Omega\). No single-particle energies are used. We find that the charge dependence of the bulk binding energy of eight A=48 nuclei is reasonably described with an effective Hamiltonian derived from the CD-Bonn interaction while there is an overall underbinding by about 0.4 MeV/nucleon. However, the resulting spectra exhibit deficiencies that are anticipated due to: (1) basis space limitations and/or the absence of effective many-body interactions; and, (2) the absence of genuine three-nucleon interactions. We then introduce additive isospin-dependent central terms plus a tensor force to our Hamiltonian and achieve accurate binding energies and reasonable spectra for all three nuclei. The resulting no-core shell model opens a path for applications to the double-beta (\(\beta\beta\)) decay process.
Phys.Rev. C59 (1999) 1906-1918 We use equations for Faddeev amplitudes to solve the shell-model problem for
four nucleons in the model space that includes up to 14 hbar Omega
harmonic-oscillator ...excitations above the unperturbed ground state. Two- and
three-body effective interactions derived from the Reid93 and Argonne V8'
nucleon-nucleon potentials are used in the calculations. Binding energies,
excitations energies, point-nucleon radii and electromagnetic and strangeness
charge form factors for 4He are studied. The structure of the Faddeev-like
equations is discussed and a formula for matrix elements of the permutation
operators in a harmonic-oscillator basis is given. The dependence on
harmonic-oscillator excitations allowed in the model space and on the
harmonic-oscillator frequency is investigated. It is demonstrated that the use
of the three-body effective interactions improves the convergence of the
results.
Phys.Rev.C57:3119-3128,1998 Results of large-basis shell-model calculations for nuclei with A=7-11 are
presented. The effective interactions used in the study were derived
microscopically from the ...Reid93 potential and take into account the Coulomb
potential as well as the charge dependence of T=1 partial waves. For A=7, a
$6\hbar\Omega$ model space was used, while for the rest of the studied
nuclides, the calculations were performed in a $4\hbar\Omega$ model space. It
is demonstrated that the shell model combined with microscopic effective
interactions derived from modern nucleon-nucleon potentials is capable of
providing good agreement with the experimental properties of the ground state
as well as with those of the low-lying excited states.
Phys.Rev. C71 (2005) 044312 We are presenting the first ab initio structure investigation of the loosely
bound 11-Be nucleus, together with a study of the lighter isotope 9-Be. The
nuclear structure ...of these isotopes is particularly interesting due to the
appearance of a parity-inverted ground state in 11-Be. Our study is performed
in the framework of the ab initio no-core shell model. Results obtained using
four different, high-precision two-nucleon interactions, in model spaces up to
9\hbar\Omega, are shown. For both nuclei, and all potentials, we reach
convergence in the level ordering of positive- and negative-parity spectra
separately. Concerning their relative position, the positive-parity states are
always too high in excitation energy, but a fast drop with respect to the
negative-parity spectrum is observed when the model space is increased. This
behavior is most dramatic for 11-Be. In the largest model space we were able to
reach, the 1/2+ level has dropped down to become either the first or the second
excited state, depending on which interaction we use. We also observe a
contrasting behavior in the convergence patterns for different two-nucleon
potentials, and argue that a three-nucleon interaction is needed to explain the
parity inversion. Furthermore, large-basis calculations of 13-C and 11-B are
performed. This allows us to study the systematics of the position of the first
unnatural-parity state in the N=7 isotone and the A=11 isobar. The 11-B run in
the 9\hbar\Omega model space involves a matrix with dimension exceeding 1.1 x
10^9, and is our largest calculation so far. We present results on binding
energies, excitation spectra, level configurations, radii, electromagnetic
observables, and 10-Be+n overlap functions.
Nuclear structure of 7Be, 8B and 7,8Li is studied within the ab initio no-core shell model (NCSM). Starting from high-precision nucleon-nucleon (NN) interactions, wave functions of 7Be and 8B bound ...states are obtained in basis spaces up to 10 hbar Omega and used to calculate channel cluster form factors (overlap integrals) of the 8B ground state with 7Be+p. Due to the use of the harmonic oscillator (HO) basis, the overlap integrals have incorrect asymptotic properties. We fix this problem in two alternative ways. First, by a Woods-Saxon (WS) potential solution fit to the interior of the NCSM overlap integrals. Second, by a direct matching with the Whittaker function. The corrected overlap integrals are then used for the 7Be(p,gamma)8B S-factor calculation. We study the convergence of the S-factor with respect to the NCSM HO frequency and the model space size. Our S-factor results are in agreement with recent direct measurement data. We also test the spectroscopic factors and the corrected overlap integrals from the NCSM in describing the momentum distributions in knockout reactions with 8B projectiles. A good agreement with the available experimental data is also found, attesting the overall consistency of the calculations.
Nuclear structure of 7Be, 8B and 7,8Li is studied within the ab initio no-core shell model (NCSM). Starting from the high-precision CD-Bonn 2000 nucleon-nucleon (NN) interaction, wave functions of ...7Be and 8B bound states are obtained in basis spaces up to 10 hbar Omega and used to calculate channel cluster form factors (overlap integrals) of the 8B ground state with 7Be+p. Due to the use of the harmonic oscillator (HO) basis, the overlap integrals have incorrect asymptotic properties. We fix this problem in two alternative ways. First, by a Woods-Saxon (WS) potential solution fit to the interior of the NCSM overlap integrals. Second, by a direct matching with the Whittaker function. The corrected overlap integrals are then used for the 7Be(p,gamma)8B S-factor calculation. We study the convergence of the S-factor with respect to the NCSM HO frequency and the model space size. Our S-factor results are in agreement with recent direct measurement data.
Phys.Rev.C57:562-568,1998 We use Faddeev's decomposition to solve the shell-model problem for three
nucleons. The dependence on harmonic-oscillator excitations allowed in the
model space, up to $32 ...\hbar\Omega$ in the present calculations, and on the
harmonic-oscillator frequency is studied. Effective interactions derived from
Nijmegen II and Reid93 potentials are used in the calculations. The binding
energies obtained are close to those calculated by other methods. The structure
of the Faddeev equations is discussed and a simple formula for matrix elements
of the permutation operators in a harmonic-oscillator basis is given. The Pauli
principle is properly treated in the calculations.
Phys.Rev.Lett.99:042501,2007 Properties of finite nuclei are evaluated with two-nucleon (NN) and
three-nucleon (NNN) interactions derived within chiral effective field theory
(EFT). The nuclear ...Hamiltonian is fixed by properties of the A=2 system, except
for two low-energy constants (LECs) that parameterize the short range NNN
interaction. We constrain those two LECs by a fit to the A=3 system binding
energy and investigate sensitivity of 4He, 6Li, 10,11B and 12,13C properties to
the variation of the constrained LECs. We identify a preferred choice that
gives globally the best description. We demonstrate that the NNN interaction
terms significantly improve the binding energies and spectra of mid-p-shell
nuclei not just with the preferred choice of the LECs but even within a wide
range of the constrained LECs. At the same time, we find that a very high
quality description of these nuclei requires further improvements to the chiral
Hamiltonian.
Deep Brain Stimulation can improve tremor, bradykinesia, rigidity, and axial symptoms in patients with Parkinson's disease. Potentially, improving each symptom may require stimulation of different ...white matter tracts. Here, we study a large cohort of patients (N = 237 from five centers) to identify tracts associated with improvements in each of the four symptom domains. Tremor improvements were associated with stimulation of tracts connected to primary motor cortex and cerebellum. In contrast, axial symptoms are associated with stimulation of tracts connected to the supplementary motor cortex and brainstem. Bradykinesia and rigidity improvements are associated with the stimulation of tracts connected to the supplementary motor and premotor cortices, respectively. We introduce an algorithm that uses these symptom-response tracts to suggest optimal stimulation parameters for DBS based on individual patient's symptom profiles. Application of the algorithm illustrates that our symptom-tract library may bear potential in personalizing stimulation treatment based on the symptoms that are most burdensome in an individual patient.
