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B. R. Barrett

Publications and source records attributed to B. R. Barrett.

At least 19 recordsLinked to original sources
arXiv2022

Effective operators for valence space calculations from the {\itshape ab initio} No-Core Shell Mode

In recent years, remarkable progress has been achieved in developing novel non-perturbative techniques for constructing valence space shell model Hamiltonians from realistic internucleon interactions. One of these methods is based on the Okubo--Lee--Suzuki (OLS) unitary transformation applied to no-core shell model (NCSM) solutions. In the present work, we implement the corresponding approach to solve for valence space effective electromagnetic operators. To this end, we use the NCSM results for $A=16-18$, obtained at $N_{\rm max}=4$, to derive a charge-dependent version of the effective interaction for the $sd$ shell, which allows us to exactly reproduce selected NCSM spectra of $^{18}$O, $^{18}$F and $^{18}$Ne within the two valence nucleon space. We then deduce effective single-particle matrix elements of electric quadrupole ($E2$) and magnetic dipole ($M1$) operators by matching them to the electromagnetic transitions and moments for $^{17}$O and $^{17}$F from the NCSM at $N_{\rm max}=4$. Thus, effective $E2$ and $M1$ operators are obtained as sets of single-particle matrix elements for the valence space ($sd$ shell) which allow us to reproduce the NCSM results for $A=17$ exactly. Systematic comparison of a large set of $sd$ shell results on quadrupole and magnetic dipole moments and transitions for $A=18$ using effective $E2$ and $M1$ operators that we derive from the full NCSM calculations demonstrates a remarkable agreement.

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arXiv2015

The No-Core Gamow Shell Model: Including the continuum in the NCSM

We are witnessing an era of intense experimental efforts that will provide information about the properties of nuclei far from the line of stability, regarding resonant and scattering states as well as (weakly) bound states. This talk describes our formalism for including these necessary ingredients into the No-Core Shell Model by using the Gamow Shell Model approach. Applications of this new approach, known as the No-Core Gamow Shell Model, both to benchmark cases as well as to unstable nuclei will be given.

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arXiv2015

Ab initio effective interactions for sd-shell valence nucleons

We perform \textit{ab initio} no-core shell-model calculations for $A=18$ and $19$ nuclei in a $4\hbarΩ$, or $N_{\rm max}=4$, model space by using the effective JISP16 and chiral N3LO nucleon-nucleon potentials and transform the many-body effective Hamiltonians into the $0\hbarΩ$ model space to construct the $A$-body effective Hamiltonians in the $sd$-shell. We separate the $A$-body effective Hamiltonians with $A=18$ and $A=19$ into inert core, one-, and two-body components. Then, we use these core, one-, and two-body components to perform standard shell-model calculations for the $A=18$ and $A=19$ systems with valence nucleons restricted to the $sd$ shell. Finally, we compare the standard shell-model results in the $0\hbarΩ$ model space with the exact no-core shell model results in the $4\hbarΩ$ model space for the $A=18$ and $A=19$ systems and find good agreement.

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arXiv2013

Ab-initio No-Core Gamow Shell Model calculations with realistic interactions

No-Core Gamow Shell Model (NCGSM) is applied for the first time to study selected well-bound and unbound states of helium isotopes. This model is formulated on the complex energy plane and, by using a complete Berggren ensemble, treats bound, resonant, and scattering states on equal footing. We use the Density Matrix Renormalization Group method to solve the many-body Schrödinger equation. To test the validity of our approach, we benchmarked the NCGSM results against Faddeev and Faddeev-Yakubovsky exact calculations for $^3$H and $^4$He nuclei. We also performed {\textit ab initio} NCGSM calculations for the unstable nucleus $^5$He and determined the ground state energy and decay width, starting from a realistic N$^3$LO chiral interaction.

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arXiv2013

Extrapolation uncertainties in the importance-truncated No-Core Shell Model

We report on Li-6 calculations performed with the IT-NCSM and compare them to full NCSM calculations. We employ the Entem and Machleidt chiral two-body N3LO interaction (regulated at 500 MeV/c), which has been modified to a phase-shift equivalent potential by the similarity renormalization group (SRG) procedure. We investigate the dependence of the procedure on the technique employed to extrapolate to the complete Nmax space, the harmonic oscillator energy, and investigate the dependence on the momentum-decoupling scale (λ) used in the SRG. We also investigate the use of one or several reference states from which the truncated basis is constructed. We find that the uncertainties generated from various extrapolating functions used to extrapolate to the complete Nmax space increase as Nmax increases. The extrapolation uncertainties range from a few keV for the smallest Nmax spaces to about 50 keV for the largest Nmax spaces. We note that the difference between extrapolated IT-NCSM and NCSM ground-state energies, however, can be as large as a 100-250 keV depending on the chosen harmonic oscillator energy. We also present the extrapolation of IT-NCSM results to Nmax infinity and compare these to similarly extrapolated full NCSM results.

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arXiv2011

Two and Three Nucleons in a Trap and the Continuum Limit

We describe systems of two and three nucleons trapped in a harmonic-oscillator potential with interactions from the pionless effective field theory up to next-to-leading order (NLO). We construct the two-nucleon interaction using two-nucleon scattering information. We calculate the trapped levels in the three-nucleon system with isospin $T=1/2$ and determine the three-nucleon force needed for stability of the triton. We extract neutron-deuteron phase shifts, and show that the quartet scattering length is in good agreement with experimental data.

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arXiv2010

Three and Four Harmonically Trapped Particles in an Effective Field Theory Framework

We study systems of few two-component fermions interacting via short-range interactions within a harmonic-oscillator trap. The dominant interactions, which are two-body, are organized according to the number of derivatives and defined in a two-body truncated model space made from a bound-state basis. Leading-order (LO) interactions are solved for exactly using the formalism of the No-Core Shell Model, whereas corrections are treated as many-body perturbations. We show explicitly that next-to-LO and next-to-next-to-LO interactions improve convergence as the model space increases. We present results at unitarity for three- and four-fermion systems, which show excellent agreement with the exact solution (for the three-body problem) and results obtained by others methods (in the four-body case). We also present results for finite scattering lengths and non-zero range of the interaction, including (at positive scattering length) observation of a change in the structure of the three-body ground state and extraction of the atom-dimer scattering length.

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arXiv2010

An effective field theory approach to two trapped particles

We discuss the problem of two particles interacting via short-range interactions within a harmonic-oscillator trap. The interactions are organized according to their number of derivatives and defined in truncated model spaces made from a bound-state basis. Leading-order (LO) interactions are iterated to all orders, while corrections are treated in perturbation theory. We show explicitly that next-to-LO and next-to-next-to-LO interactions improve convergence as the model space increases. In the large-model-space limit we regain results from a pseudopotential. Arbitrary scattering lengths are considered, as well as a generalization to include the non-vanishing range of the interaction.

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arXiv2009

Effective interactions for light nuclei: an effective (field theory) approach

One of the central open problems in nuclear physics is the construction of effective interactions suitable for many-body calculations. We discuss a recently developed approach to this problem, where one starts with an effective field theory containing only fermion fields and formulated directly in a no-core shell-model space. We present applications to light nuclei and to systems of a few atoms in a harmonic-oscillator trap. Future applications and extensions, as well as challenges, are also considered.

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arXiv2009

Concavity for nuclear binding energies, thermodynamical functions and density functionals

Sequences of experimental ground-state energies for both odd and even $A$ are mapped onto concave patterns cured from convexities due to pairing and/or shell effects. The same patterns, completed by a list of excitation energies, give numerical estimates of the grand potential $Ω(β,μ)$ for a mixture of nuclei at low or moderate temperatures $T=β^{-1}$ and at many chemical potentials $μ.$ The average nucleon number $<{\bf A} >(β,μ)$ then becomes a continuous variable, allowing extrapolations towards nuclear masses closer to drip lines. We study the possible concavity of several thermodynamical functions, such as the free energy and the average energy, as functions of $<{\bf A} >.$ Concavity, which always occur for the free energy and is usually present for the average energy, allows easy interpolations and extrapolations providing upper and lower bounds, respectively, to binding energies. Such bounds define an error bar for the prediction of binding energies. Finally we show how concavity and universality are related in the theory of the nuclear density functional.

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arXiv2009

Effective operators from exact many-body renormalization

We construct effective two-body Hamiltonians and E2 operators for the p-shell by performing $16\hbarΩ$ ab initio no-core shell model (NCSM) calculations for A=5 and A=6 nuclei and explicitly projecting the many-body Hamiltonians and E2 operator onto the $0\hbarΩ$ space. We then separate the effective E2 operator into one-body and two-body contributions employing the two-body valence cluster approximation. We analyze the convergence of proton and neutron valence one-body contributions with increasing model space size and explore the role of valence two-body contributions. We show that the constructed effective E2 operator can be parametrized in terms of one-body effective charges giving a good estimate of the NCSM result for heavier p-shell nuclei.

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arXiv2009

Determining the Energy Barrier for Decay out of Superdeformed Bands

An asymptotically exact quantum mechanical calculation of the matrix elements for tunneling through an asymmetric barrier is combined with the two-state statistical model for decay out of superdeformed bands to determine the energy barrier (as a function of spin) separating the superdeformed and normal-deformed wells for several nuclei in the 190 and 150 mass regions. The spin-dependence of the barrier leading to sudden decay out is shown to be consistent with the decrease of a centrifugal barrier with decreasing angular momentum. Values of the barrier frequency in the two mass regions are predicted.

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arXiv2009

Ab initio shell-model calculation for ^{18}O in a restricted no-core model space

We perform an ab initio shell-model calculation for ^{18}O in a restricted no-core model space, microscopically deriving a two-body effective interaction and introducing a minimal refinement of one-body energies in the spsd or spsdpf model space. Low-lying energy levels, except for the experimental 0_{2}^{+} and 2_{3}^{+} states, are better described in the spsdpf space than in the spsd space. The structure of low-lying energy levels is discussed with an emphasis on many-particle many-hole states beyond the four-particle two-hole configuration.

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arXiv2008

Ab-initio shell model with a core

We construct effective 2- and 3-body Hamiltonians for the p-shell by performing 12\hbarΩab initio no-core shell model (NCSM) calculations for A=6 and 7 nuclei and explicitly projecting the many-body Hamiltonians onto the 0\hbarΩspace. We then separate these effective Hamiltonians into 0-, 1- and 2-body contributions (also 3-body for A=7) and analyze the systematic behavior of these different parts as a function of the mass number A and size of the NCSM basis space. The role of effective 3- and higher-body interactions for A>6 is investigated and discussed.

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arXiv2007

Universality of Decay out of Superdeformed Bands in the 190 Mass Region

Superdeformed nuclei in the 190 mass region exhibit a striking universality in their decay-out profiles. We show that this universality can be explained in the two-level model of superdeformed decay as related to a strong separation of energy scales: a higher scale related to the nuclear interactions, and a lower scale caused by electromagnetic decay. Furthermore, we present the results of the two-level model for all decays for which sufficient data are known, including statistical extraction of the matrix element for tunneling through the potential barrier.

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arXiv2007

Bounds to binding energies from the concavity of thermodynamical functions

Sequences of experimental ground-state energies are mapped onto concave patterns cured from convexities due to pairing and/or shell effects. The same patterns, completed by a list of excitation energies, can be used to give numerical estimates of the grand potential $Ω(β,μ)$ for a mixture of nuclei at low or moderate temperatures $T=β^{-1}$ and at many chemical potentials $μ.$ The average nucleon number $<{\bf A} >(β,μ)$ then becomes a continuous variable, allowing extrapolations towards nuclear masses closer to drip lines. We study the possible concavity of several thermodynamical functions, such as the free energy and the average energy, as functions of $<{\bf A} >.$ Concavity, when present in such functions, allows trivial interpolations and extrapolations providing upper and lower bounds, respectively, to binding energies. Such bounds define an error bar for the prediction of binding energies. An extrapolation scheme for such concave functions is tested. We conclude with numerical estimates of the binding energies of a few nuclei closer to drip lines.

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