arXiv subjects

Calvin W. Johnson

Publications and source records attributed to Calvin W. Johnson.

At least 73 records · Page 4Linked to original sources

arXiv2013

Comparison of Gamow-Teller strengths in the random phase approximation

The Gamow-Teller response is astrophysically important for a number of nuclides, particularly around iron. The random phase approximation (RPA) is an efficient way to generate strength distributions. In order to better understand both theoretical systematics and uncertainties, we compare the Gamow-Teller strength distributions for a suite of nuclides and for a suite of interactions, including semi-realistic interactions in the $1p$-$0f$ space with the RPA and a separable multi-shell interaction in the quasi-particle RPA. We also compare with experimental results for GT$_-$ on ${54}$Fe.

nucl-th↗

arXiv2012

Many-body approximations for atomic binding energies

We benchmark three standard approximations for the many-body problem -- the Hartree-Fock, projected Hartree-Fock, and random phase approximations -- against full numerical configuration-interaction calculations of the electronic structure of atoms, from Li through to Ne. These configuration-interaction calculations used up to $2 \times 10^8$ uncoupled basis states, equivalent to $ 10^7$ coupled basis states (configuration state functions.) Each method uses exactly the same input, i.e., the same single-particle basis and Coulomb matrix elements, so any differences are strictly due to the approximation itself. Although it consistently overestimates the ground state binding energy, the random phase approximation has the smallest overall errors; furthermore, we suggest it may be useful as a method for efficient optimization of single-particle basis functions.

physics.atom-ph↗

arXiv2012

The origin of order in random matrices with symmetries

From Noether's theorem we know symmetries lead to conservation laws. What is left to nature is the ordering of conserved quantities; for example, the quantum numbers of the ground state. In physical systems the ground state is generally associated with `low' quantum numbers and symmetric, low-dimensional irreps, but there is no \textit{a priori} reason to expect this. By constructing random matrices with nontrivial point-group symmetries, I find the ground state is always dominated by extremal low-dimensional irreps. Going further, I suggest this explains the dominance of J=0 g.s. even for random two-body interactions.

math-ph↗

arXiv2011

Random matrices, symmetries, and many-body states

All nuclei with even numbers of protons and of neutrons have ground states with zero angular momentum. This is ascribed to the pairing force between nucleons, but simulations with random interactions suggest a much broader many-body phenomenon. In this Letter I project out random Hermitian matrices that have good quantum numbers and, computing the width of the Hamiltonian in subspaces, find ground states dominated by low quantum numbers, e.g. J=0. Furthermore I find odd-$Z$, odd-$N$ systems with isospin conservation have relatively fewer J=0 ground states.

nucl-th↗

arXiv2010

Many-body fits of phase-equivalent effective interactions

In many-body theory it is often useful to renormalize short-distance, high-momentum components of an interaction via unitary transformations. Such transformations preserve the on-shell physical observables of the two-body system (mostly phase-shifts, hence unitarily-connected effective interactions are often called phase-equivalent), while modifying off-shell T-matrix elements influential in many-body systems. In this paper I lay out a general and systematic approach for controlling the off-shell behavior of an effective interaction, which can be adjusted to many-body properties, and present an application to trapped fermions at the unitary

nucl-th↗

arXiv2010

Sensitivity analysis of random two-body interactions

The input to the configuration-interaction shell model includes many dozens or hundreds of independent two-body matrix elements. Previous studies have shown that when fitting to experimental low-lying spectra, the greatest sensitivity is to only a few linear combinations of matrix elements. Here we consider interactions drawn from the two-body random ensemble, or TBRE, and find that the low-lying spectra are also most sensitive to only a few linear combinations of two-body matrix elements, in a fashion nearly indistinguishable from an interaction empirically fit to data. We find in particular the spectra for both the random and empirical interactions are sensitive to similar matrix elements, which we analyze using monopole and contact interactions.

nucl-th↗

arXiv2009

Collapse of the random phase approximation: examples and counter-examples from the shell model

The Hartree-Fock approximation to the many-fermion problem can break exact symmetries, and in some cases by changing a parameter in the interaction one can drive the Hartree-Fock minimum from a symmetry-breaking state to a symmetry-conserving state (also referred to as a ``phase transition'' in the literature). The order of the transition is important when one applies the random phase approximation (RPA) to the of the Hartree-Fock wavefunction: if first order, RPA is stable through the transition, but if second-order, then the RPA amplitudes become large and lead to unphysical results. The latter is known as ``collapse'' of the RPA. While the difference between first- and second-order transitions in the RPA was first pointed out by Thouless, we present for the first time non-trivial examples of both first- and second-order transitions in a uniform model, the interacting shell-model, where we can compare to exact numerical results.

nucl-th↗

arXiv2006

A new puzzle for random interaction

We continue a series of numerical experiments on many-body systems with random two-body interactions, by examining correlations in ratios in excitation energies of yrast $J$ = 0, 2, 4, 6, 8 states. Previous studies, limited only to $J$ = 0,2,4 states, had shown strong correlations in boson systems but not fermion systems. By including $J \ge 6$ states and considering different scatter plots, strong and realistic correlations appear in both boson and fermion systems. Such correlations are a challenge to explanations of random interactions.

nucl-th↗

arXiv2006

Benchmark calculation of inclusive electromagnetic responses in the four-body nuclear system

Both the no-core shell model and the effective interaction hyperspherical harmonic approaches are applied to the calculation of different response functions to external electromagnetic probes, using the Lorentz integral transform method. The test is performed on the four-body nuclear system, within a simple potential model. The quality of the agreement in the various cases is discussed, together with the perspectives for rigorous ab initio calculations of cross sections of heavier nuclei.

nucl-th↗

arXiv2006

Simple models for shell-model configuration densities

We consider the secular behavior of shell-model configuration (partial) densities. When configuration densities are characterized by their moments, one often finds large third moments, which can make suitable parameterization of the secular behavior problematic. We review several parameterizations or models, and consider in depth three specific models: Cornish-Fisher, binomial, and modified Breit-Wigner distributions. Of these three the modified Breit-Wigner provides the best secular approximation to exact numerical configuration densities computed via full diagonalization from realistic interactions.

nucl-th↗

arXiv2006

Collective behavior in random interaction

Recent investigations have looked at the many-body spectra of random two-body interactions. In fermion systems, such as the interacting shell model, one finds pairing-like spectra, while in boson systems, such as IBM-1, one finds rotational and vibrational spectra. We discuss the search for random ensembles of fermion interactions that yield rotational and vibrational spectra, and in particular present results from a new ensemble, the ``random quadrupole-quadrupole ensemble''

nucl-th↗

arXiv2005

The nuclear density of states and the role of the residual interaction

We discuss the role of mean-field and moment methods in microscopic models for calculating the nuclear density of states (also known as the nuclear level density). Working in a shell-model framework, we use moments of the nuclear many-body Hamiltonian to illustrate the importance of the residual interaction for accurate representations.

nucl-th↗

arXiv2005

Behavior of shell-model configuration moments

An important input into reaction theory is the density of states or the level density. Spectral distribution theory (also known as nuclear statistical spectroscopy) characterizes the secular behavior of the density of states through moments of the Hamiltonian. One particular approach is to partition the model space into subspaces and find the moments in those subspaces; a convenient choice of subspaces are spherical shell-model configurations. We revisit these configuration moments and find, for complete $0\hbarω$ many-body spaces, the following behaviors: (a) the configuration width is nearly constant for all configurations; (b) the configuration asymmetry or third moment is strongly correlated with the configuration centroid; (c) the configuration fourth moment, or excess is linearly related to the square to the configuration asymmetry. Such universal behavior may allow for more efficient modeling of the density of states in a shell-model framework.

nucl-th↗

arXiv2005

Time-integrated supernova neutrino flux from a nearby cluster

The rate of gravitational collapse (type II) supernovae in our galaxy is uncertain by a factor of three or more. One way to determine the galactic supernova rate is through a radiogeochemical experiment (for example, the molybdenum-technetium experiment) that would integrate the neutrino flux over several million years. While such a measurement is designed to integrate the flux over the entire galaxy, nearby star-forming regions could skew the results. We model the flux from a recently identified such region, the Scorpius-Centaurus OB association, and compare with the flux from the rest of the galaxy.

astro-ph↗

arXiv2004

Shortcuts to nuclear structure: lessons in Hartree-Fock, RPA, and the no-core shell model

While the no-core shell model is a state-of-the-art microscopic approach to low-energy nuclear structure, its intense computational requirements lead us to consider time-honored approximations such as the Hartree-Fock (HF) approximation and the random phase approximation (RPA). We review RPA and point out some common misunderstandings, then apply HF+RPA to the no-core shell model. Here the main issue is appropriate treatment of contamination by spurious center-of-mass motion.

nucl-th↗

arXiv2004

Electromagnetic transitions with effective operators

In the no-core shell model formalism we compute effective one- and two-body operators, using the Lee-Suzuki procedure within the two-body cluster approximation. We evaluate the validity of the latter through calculations in reduced model spaces. In particular, we test the results for the two-body system and find that indeed the effective operators in the reduced space reproduce the expectation values or transition strengths computed in the full space. On the other hand, the renormalization for operators in the case of 6Li is very weak, suggesting the need for higher-body clusters in computing the effective interaction.

nucl-th↗

arXiv2003

Gamow-Teller transitions and deformation in the proton-neutron random phase approximation

We investigate reliability of Gamow-Teller transition strengths computed in the proton-neutron random phase approximation, comparing with exact results from diagonalization in full $0\hbarω$ shell-model spaces. By allowing the Hartree-Fock state to be deformed, we obtain good results for a wide variety of nuclides, even though we do not project onto good angular momentum. We suggest that deformation is as important or more so than pairing for Gamow-Teller transitions.

nucl-th↗

arXiv2003

Collectivity, chaos, and computers

Two important pieces of nuclear structure are many-body collective deformations and single-particle spin-orbit splitting. The former can be well-described microscopically by simple SU(3) irreps, but the latter mixes SU(3) irreps, which presents a challenge for large-scale, ab initio calculations on fast modern computers. Nonetheless, SU(3)-like phenomenology remains even in the face of strong mixing. The robustness of band structure is reminiscent of robust, pairing collectivity that arises from random two-body interactions.

nucl-th↗