189 research outputs found
Program in C for studying characteristic properties of two-body interactions in the framework of spectral distribution theory
We present a program in C that employs spectral distribution theory for
studies of characteristic properties of a many-particle quantum-mechanical
system and the underlying few-body interaction. In particular, the program
focuses on two-body nuclear interactions given in a JT-coupled harmonic
oscillator basis and calculates correlation coefficients, a measure of
similarity of any two interactions, as well as Hilbert-Schmidt norms specifying
interaction strengths. An important feature of the program is its ability to
identify the monopole part (centroid) of a 2-body interaction, as well as its
'density-dependent' one-body and two-body part, thereby providing key
information on the evolution of shell gaps and binding energies for larger
nuclear systems. As additional features, we provide statistical measures for
'density-dependent' interactions, as well as a mechanism to express an
interaction in terms of two other interactions. This, in turn, allows one to
identify, e.g., established features of the nuclear interaction (such as
pairing correlations) within a general Hamiltonian. The program handles the
radial degeneracy for 'density-dependent' one-body interactions and together
with an efficient linked list data structure, facilitates studies of nuclear
interactions in large model spaces that go beyond valence-shell applications.Comment: 22 pages, 3 figure
Exact isovector pairing in a shell-model framework: Role of proton-neutron correlations in isobaric analog states
We utilize a nuclear shell model Hamiltonian with only two adjustable
parameters to generate, for the first time, exact solutions for pairing
correlations for light to medium-mass nuclei, including the challenging
proton-neutron pairs, while also identifying the primary physics involved. In
addition to single-particle energy and Coulomb potential terms, the shell model
Hamiltonian consists of an isovector pairing interaction and an average
proton-neutron isoscalar interaction, where the term describes the
average interaction between non-paired protons and neutrons. This Hamiltonian
is exactly solvable, where, utilizing 3 to 7 single-particle energy levels, we
reproduce experimental data for 0 state energies for isotopes with mass
through exceptionally well including isotopes from He to Ge.
Additionally, we isolate effects due to like-particle and proton-neutron
pairing, provide estimates for the total and proton-neutron pairing gaps, and
reproduce (neutron) = (proton) irregularity. These results provide a
further understanding for the key role of proton-neutron pairing correlations
in nuclei, which is especially important for waiting-point nuclei on the
rp-path of nucleosynthesis.Comment: 10 pages, 4 figure
Ab initio Translationally Invariant Nonlocal One-body Densities from No-core Shell-model Theory
[Background:] It is well known that effective nuclear interactions are in
general nonlocal. Thus if nuclear densities obtained from {\it ab initio}
no-core-shell-model (NCSM) calculations are to be used in reaction
calculations, translationally invariant nonlocal densities must be available.
[Purpose:] Though it is standard to extract translationally invariant one-body
local densities from NCSM calculations to calculate local nuclear observables
like radii and transition amplitudes, the corresponding nonlocal one-body
densities have not been considered so far. A major reason for this is that the
procedure for removing the center-of-mass component from NCSM wavefunctions up
to now has only been developed for local densities. [Results:] A formulation
for removing center-of-mass contributions from nonlocal one-body densities
obtained from NCSM and symmetry-adapted NCSM (SA-NCSM) calculations is derived,
and applied to the ground state densities of He, Li, C, and
O. The nonlocality is studied as a function of angular momentum
components in momentum as well as coordinate space [Conclusions:] We find that
the nonlocality for the ground state densities of the nuclei under
consideration increases as a function of the angular momentum. The relative
magnitude of those contributions decreases with increasing angular momentum. In
general, the nonlocal structure of the one-body density matrices we studied is
given by the shell structure of the nucleus, and can not be described with
simple functional forms.Comment: 13 pages, 11 Figure
Ab initio symmetry-adapted no-core shell model
A multi-shell extension of the Elliott SU(3) model, the SU(3) symmetry-adapted version of the no-core shell model (SA-NCSM), is described. The significance of this SA-NCSM emerges from the physical relevance of its SU(3)-coupled basis, which - while it naturally manages center-of-mass spuriosity - provides a microscopic description of nuclei in terms of mixed shape configurations. Since typically configurations of maximum spatial deformation dominate, only a small part of the model space suffices to reproduce the low-energy nuclear dynamics and hence, offers an effective symmetry-guided framework for winnowing of model space. This is based on our recent findings of low-spin and high-deformation dominance in realistic NCSM results and, in turn, holds promise to significantly enhance the reach of ab initio shell models
Symplectic No-core Shell-model Approach to Intermediate-mass Nuclei
We present a microscopic description of nuclei in an intermediate-mass
region, including the proximity to the proton drip line, based on a no-core
shell model with a schematic many-nucleon long-range interaction with no
parameter adjustments. The outcome confirms the essential role played by the
symplectic symmetry to inform the interaction and the winnowing of shell-model
spaces. We show that it is imperative that model spaces be expanded well beyond
the current limits up through fifteen major shells to accommodate particle
excitations that appear critical to highly-deformed spatial structures and the
convergence of associated observables.Comment: 9 pages, 8 figure
Symmetry-adapted ab initio shell model for nuclear structure calculations
An innovative concept, the symmetry-adapted ab initio shell model, that capitalizes on partial as well as exact symmetries that underpin the structure of nuclei, is discussed. This framework is expected to inform the leading features of nuclear structure and reaction data for light and medium mass nuclei, which are currently inaccessible by theory and experiment and for which predictions of modern phenomenological models often diverge. We use powerful computational and group-theoretical algorithms to perform ab initio CI (configuration-interaction) calculations in a model space spanned by SU(3) symmetry-adapted many-body configurations with the JISP16 nucleon-nucleon interaction. We demonstrate that the results for the ground states of light nuclei up through A = 16 exhibit a strong dominance of low-spin and high-deformation configurations together with an evident symplectic structure. This, in turn, points to the importance of using a symmetry-adapted framework, one based on an LS coupling scheme with the associated spatial configurations organized according to deformation
Symmetry-adapted Ab initio theory for many-body correlations in nuclei
We demonstrate that no-core shell-model results for low-lying states of light and medium mass nuclei, whether they are dilute or dense systems, reveal a strong dominance of low-spin and high-deformation configurations. This result is independent of whether the system Hamiltonian is phenomenological in nature or derived from a realistic interaction. It implies that only a small fraction of the complete model space is required for a description of such states, and this in turn points to the importance of using a symmetry-adapted, no-core shell-model framework for describing such nuclei, one based on an LS coupling scheme with the associated spatial configurations organized according to deformation. These results confirm that the pioneering work of early developers of the field, J. P. Elliott with his SU(3) model and M. Moshinsky with his U(3) many-body oscillator work, extends to more open, multi-shell environments. Specifically, algebraic methods are both relevant in such an environment and they can be used to quell the combinatorial growth in dimensionality that comes with the addition of oscillator shells to a model space. Indeed, our findings demonstrate the utility of a symmetry-adapted, no-core shell-model approach, one that takes advantage of group theoretical as well as advanced computational methods. And importantly, what at first glance appear to be a daunting task - casting complex algebraic expressions of a symmetry-adapted scheme into a user-friendly and efficient shell-mode code, turns out to be not only doable, but a logical framework that embraces constructs that can be made to execute efficiently on massively parallel, multi-processor (and core) systems. Early results for some light p-shell nuclei are presented. In addition, we will show that the method can be extended to heavier nuclei of the sd-shell and beyond, including some cases of special astrophysical interest in the upper fp- and lower gds-shells, like isotopes of Ge, Se, and even Kr. © Published under licence by IOP Publishing Ltd
Ab initio Folding Potentials for Nucleon-Nucleus Scattering based on NCSM One-Body Densities
Calculating microscopic optical potentials for elastic nucleon-nucleus
scattering has already led to large body of work in the past. For folding
first-order calculations the nucleon-nucleon (NN) interaction and the one-body
density of the nucleus were taken as input to rigorous calculations in a
spectator expansion of the multiple scattering series.
Based on the Watson expansion of the multiple scattering series we employ a
nonlocal translationally invariant nuclear density derived from a chiral
next-to-next-to-leading order (NNLO) and the very same interaction for
consistent full-folding calculation of the effective (optical) potential for
nucleon-nucleus scattering for light nuclei.
We calculate scattering observables, such as total, reaction, and
differential cross sections as well as the analyzing power and the
spin-rotation parameter, for elastic scattering of protons and neutrons from
He, He, C, and O, in the energy regime between 100 and
200~MeV projectile kinetic energy, and compare to available data.
Our calculations show that the effective nucleon-nucleus potential obtained
from the first-order term in the spectator expansion of the multiple scattering
expansion describes experiments very well to about 60 degrees in the
center-of-mass frame, which coincides roughly with the validity of the NNLO
chiral interaction used to calculate both the NN amplitudes and the one-body
nuclear density.Comment: 10 pages, 14 figures, 1 tabl
Ab initio No-core Shell Model Calculations in a SU(3)-based Coupling Scheme
We use powerful algorithms of computational group theory to perform ab initio configuration-interaction calculations in a SU(3)-based symmetry-adapted many-particle basis. We demonstrate that eigenfunctions for the low-lying states of 6Li, 8Be, 12C, and 16O exhibit a strong dominance of low proton, neutron, and total intrinsic spins that carry the same spatial deformation as the leading symplectic Sp(3,) irreducible representations. Our findings imply that only a small fraction of the complete model space is needed to model nuclear collective dynamics, deformation, and α-particle clustering even if one uses modern realistic interactions that do not preserve SU(3) symmetry. This in turn points to the importance of using a symmetry-adapted framework, one based on a LS coupling scheme with the associated spatial configurations organized according to deformation. © Published under licence by IOP Publishing Ltd
Ab initio symmetry-adapted emulator for studying emergent collectivity and clustering in nuclei
We discuss emulators from the ab initio symmetry-adapted no-core shell-model framework for studying the formation of alpha clustering and collective properties without effective charges. We present a new type of an emulator, one that utilizes the eigenvector continuation technique but is based on the use of symplectic symmetry considerations. This is achieved by using physically relevant degrees of freedom, namely, the symmetry-adapted basis, which exploits the almost perfect symplectic symmetry in nuclei. Specifically, we study excitation energies, point-proton root-mean-square radii, along with electric quadrupole moments and transitions for 6Li and 12C. We show that the set of parameterizations of the chiral potential used to train the emulators has no significant effect on predictions of dominant nuclear features, such as shape and the associated symplectic symmetry, along with cluster formation, but slightly varies details that affect collective quadrupole moments, asymptotic normalization coefficients, and alpha partial widths up to a factor of two. This makes these types of emulators important for further constraining the nuclear force for high-precision nuclear structure and reaction observables
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