arXiv subjects

Calvin W. Johnson

Publications and source records attributed to Calvin W. Johnson.

84 records · Page 5Linked to original sources

arXiv2003

Tests of the random phase approximation for transition strengths

We investigate the reliability of transition strengths computed in the random-phase approximation (RPA), comparing with exact results from diagonalization in full $0\hbarω$ shell-model spaces. The RPA and shell-model results are in reasonable agreement for most transitions; however some very low-lying collective transitions, such as isoscalar quadrupole, are in serious disagreement. We suggest the failure lies with incomplete restoration of broken symmetries in the RPA. Furthermore we prove, analytically and numerically, that standard statements regarding the energy-weighted sum rule in the RPA do not hold if an exact symmetry is broken.

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arXiv2002

Scalar ground-state observables in the random phase approximation

We calculate the ground-state expectation value of scalar observables in the matrix formulation of the random phase approximation (RPA). Our expression, derived using the quasiboson approximation, is a straightforward generalization of the RPA correlation energy. We test the reliability of our expression by comparing against full diagonalization in 0 h-bar omega shell-model spaces. In general the RPA values are an improvement over mean-field (Hartree-Fock) results, but are not always consistent with shell-model results. We also consider exact symmetries broken in the mean-field state and whether or not they are restored in RPA.

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arXiv2002

SU(3) versus deformed Hartree-Fock

Deformation is fundamental to understanding nuclear structure. We compare two ways to efficiently realize deformation for many-fermion wavefunctions, the leading SU(3) irrep and the angular-momentum projected Hartree-Fock state. In the absence of single-particle spin-orbit splitting the two are nearly identical. With realistic forces, however, the difference between the two is non-trivial, with the angular-momentum projected Hartree-Fock state better approximating an ``exact'' wavefunction calculated in the fully interacting shell model. The difference is driven almost entirely by the single-particle spin-orbit splitting.

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arXiv2002

RPA vs. exact shell-model correlation energies

The random phase approximation (RPA) builds in correlations left out by mean-field theory. In full 0-hbar-omega shell-model spaces we calculate the Hartree-Fock + RPA binding energy, and compare it to exact diagonalization. We find that in general HF+RPA gives a very good approximation to the ``exact'' ground state energy. In those cases where RPA is less satisfactory, however, there is no obvious correlation with properties of the HF state, such as deformation or overlap with the exact ground state wavefunction.

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arXiv2001

Reliable calculations of level densities using statistical spectroscopy

Nucleosynthesis calculations require nuclear level densities for hundreds or even thousands of nuclides. Ideally one would like to constrain these level densities by microscopically motivated yet computationally cheap models. A statistical approach suggests that low moments of the Hamiltonian might be sufficient. Recently Zuker proposed a simple combinatoric formula for level densities based upon the binomial distribution. We rigorously test the binomial formula against full scale shell-model diagonalization calculations for selected $sd$- and $pf$-shell nuclides and also against Monte Carlo path integration calculations. We find that the fourth moment is as important as the third moment to a good description of the level density, as well as partitioning of the model space into subspaces.

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arXiv2001

Statistical spectroscopic calculation of expectation values and spin-cutoff factors

Recently we proposed a formalism, based in nuclear statistical spectroscopy, for efficient computation of nuclear level density, or densities of states, through a sum of partitioned binomial functions (SUPARB). In this Letter we extend the formalism to the calculation of locally averaged expectation values, with specific application to spin-cutoff factors and the angular momentum dependence of the nuclear density of states.

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arXiv2001

Statistical models of nuclear level densities

We present calculations of nuclear level densities that are based upon the detailed microphysics of the interacting shell model yet are also computationally tractable. To do this, we combine in a novel fashion several previously disparate ideas from statistical spectroscopy, namely partitioning of the model space into subspaces, analytic calculations of moments up to fourth order directly from the two-body interaction, and Zuker's binomial distribution. We get excellent agreement with full scale interacting shell model calculations. We also calculate ``ab initio'' the level densities for $^{29}$Si and $^{57}$Co and get reasonable agreement with experiment.

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arXiv2000

Spin Structure of Many-Body Systems with Two-Body Random Interactions

We investigate the spin structure of many-fermion systems with a spin-conserving two-body random interaction. We find a strong dominance of spin-0 ground states and considerable correlations between energies and wave functions of low-lying states with different spin, but no indication of pairing. The spectral densities exhibit spin-dependent shapes and widths, and depend on the relative strengths of the spin-0 and spin-1 couplings in the two-body random matrix. The spin structure of low-lying states can largely be explained analytically.

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arXiv1994

Theory of fermion to boson mappings: old wine in new bottles

After a brief review of various mappings of fermion pairs to bosons, we rigorously derive a general approach. Following the methods of Marumori and Otsuka, Arima, and Iachello, our approach begins with mapping states and constructs boson representations that preserve fermion matrix elements. In several cases these representations factor into finite, Hermitian boson images times a projection or norm operator that embodies the Pauli principle. We pay particular attention to truncated boson spaces, and describe general methods for constructing Hermitian and approximately finite boson image Hamiltonians, including effective operator theory to account for excluded states. This method is akin to that of Otsuka, Arima, and Iachello introduced in connection with the Interacting Boson Model, but is more rigorous, general, and systematic.

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arXiv1994

Fermion to boson mappings revisited

We briefly review various mappings of fermion pairs to bosons, including those based on mapping operators, such as Belyaev-Zelevinskii, and those on mapping states, such as Marumori; in particular we consider the work of Otsuka-Arima-Iachello, aimed at deriving the Interacting Boson Model. We then give a rigorous and unified description of state-mapping procedures which allows one to systematically go beyond Otsuka-Arima-Iachello and related approaches, along with several exact results.

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arXiv1994

Hermitian boson mapping and finite truncation

Starting from a general, microscopic fermion-to-boson mapping that preserves Hermitian conjugation, we discuss truncations of the boson Fock space basis. We give conditions under which the exact boson images of finite fermion operators are also finite (e.g., a 1+2-body fermion Hamiltonian is mapped to a 1+2-body boson Hamiltonian) in the truncated basis. For the most general case, where the image is not necessarily exactly finite, we discuss how to make practical and controlled approximations.

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arXiv1993

Exact, finite, and Hermitian fermion-pair-to-boson mapping

We discuss a general, exact (in that matrix elements are preserved) mapping of fermion pairs to bosons, and find a simple factorization of the boson representation of fermion operators. This leads to boson Hamiltonians that are Hermitian and finite, with no more than two-body operators if the fermion Hamiltonian has at most two-body operators, and one-body boson transition operators if the fermion transition operator is one-body.

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