Effective field theory analysis of 3He–α scattering data

Poudel, Maheshwor; Phillips, Daniel R.

doi:10.1088/1361-6471/ac4da6

Title: Effective field theory analysis of ³He–α scattering data

Abstract

We treat low-energy ³He–α elastic scattering in an effective field theory (EFT) that exploits the separation of scales in this reaction. We compute the amplitude up to next-to-next-to-leading order, developing a hierarchy of the effective-range parameters (ERPs) that contribute at various orders. We use the resulting formalism to analyse data for recent measurements at center-of-mass energies of 0.38–3.12 MeV using the scattering of nuclei in inverse kinematics (SONIK) gas target at TRIUMF as well as older data in this energy regime. We employ a likelihood function that incorporates the theoretical uncertainty due to truncation of the EFT and use Markov chain Monte Carlo sampling to obtain the resulting posterior probability distribution. We find that the inclusion of a small amount of data on the analysing power A_y is crucial to determine the sign of the p-wave splitting in such an analysis. Here, the combination of A_y and SONIK data constrains all ERPs up to O(p⁴) in both s- and p-waves quite well. The asymptotic normalisation coefficients and s-wave scattering length are consistent with a recent EFT analysis of the capture reaction ³He(α, γ)⁷Be.

Authors:

^[1];

^[1]

Ohio Univ., Athens, OH (United States)

Publication Date:: Thu Mar 10 00:00:00 EST 2022

Research Org.:: Ohio Univ., Athens, OH (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP); USDOE National Nuclear Security Administration (NNSA); National Science Foundation (NSF)

OSTI Identifier:: 1872775

Grant/Contract Number:: FG02-93ER40756; NA0003883; PHY-2020275

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Physics. G, Nuclear and Particle Physics

Additional Journal Information:: Journal Volume: 49; Journal Issue: 4; Journal ID: ISSN 0954-3899

Publisher:: IOP Publishing

Country of Publication:: United States

Language:: English

Subject:: 73 NUCLEAR PHYSICS AND RADIATION PHYSICS

Citation Formats


                    Poudel, Maheshwor, and Phillips, Daniel R. Effective field theory analysis of 3He–α scattering data.  United States: N. p., 2022. 
Web.  doi:10.1088/1361-6471/ac4da6.

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                    Poudel, Maheshwor, & Phillips, Daniel R. Effective field theory analysis of 3He–α scattering data.  United States.  https://doi.org/10.1088/1361-6471/ac4da6

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                    Poudel, Maheshwor, and Phillips, Daniel R. Thu .  
"Effective field theory analysis of 3He–α scattering data".  United States.  https://doi.org/10.1088/1361-6471/ac4da6.  https://www.osti.gov/servlets/purl/1872775.

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@article{osti_1872775,

  title        = {Effective field theory analysis of 3He–α scattering data},

  author       = {Poudel, Maheshwor and Phillips, Daniel R.},

  abstractNote = {We treat low-energy 3He–α elastic scattering in an effective field theory (EFT) that exploits the separation of scales in this reaction. We compute the amplitude up to next-to-next-to-leading order, developing a hierarchy of the effective-range parameters (ERPs) that contribute at various orders. We use the resulting formalism to analyse data for recent measurements at center-of-mass energies of 0.38–3.12 MeV using the scattering of nuclei in inverse kinematics (SONIK) gas target at TRIUMF as well as older data in this energy regime. We employ a likelihood function that incorporates the theoretical uncertainty due to truncation of the EFT and use Markov chain Monte Carlo sampling to obtain the resulting posterior probability distribution. We find that the inclusion of a small amount of data on the analysing power Ay is crucial to determine the sign of the p-wave splitting in such an analysis. Here, the combination of Ay and SONIK data constrains all ERPs up to O(p4) in both s- and p-waves quite well. The asymptotic normalisation coefficients and s-wave scattering length are consistent with a recent EFT analysis of the capture reaction 3He(α, γ)7Be.},

  doi          = {10.1088/1361-6471/ac4da6},

  journal      = {Journal of Physics. G, Nuclear and Particle Physics},

  number       = 4,

  volume       = 49,

  place        = {United States},

  year         = {Thu Mar 10 00:00:00 EST 2022},

  month        = {Thu Mar 10 00:00:00 EST 2022}

}

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Title: Effective field theory analysis of 3He–α scattering data

Abstract

Citation Formats

Ensemble samplers with affine invariance journal, January 2010

He 3 + He 4 elastic scattering at E c . m . = 60.2 and 113.1 MeV journal, March 1980

Combining ab initio calculations and low-energy effective field theory for halo nuclear systems: The case of 7 Li + n → 8 Li + γ journal, February 2014

Bayesian analysis of capture reactions $$\varvec{^3}\hbox {He}\varvec{(\alpha ,\gamma )^7}\hbox {Be}$$ and $$\varvec{^3}\hbox {H}\varvec{(\alpha ,\gamma )^7}\hbox {Li}$$ journal, June 2020

Verification of R-matrix calculations for charged-particle reactions in the resolved resonance region for the 7Be system journal, June 2019

Scattering of 3He and 4He from polarized 3He between 4 and 10 MeV journal, November 1972

Analysis of the 3He(α,γ)7Be and 3H(α,γ)7Li astrophysical direct capture reactions in a modified potential-model approach journal, February 2021

Theory of the Effective Range in Nuclear Scattering journal, July 1949

Scattering of He 3 by He 4 and of He 4 by Tritium journal, November 1967

Determination of the 3 He + α → 7 Be asymptotic normalization coefficients, the nuclear vertex constants, and their application for the extrapolation of the 3 He( α , γ ) 7 Be astrophysical S factors to the solar energy region journal, April 2012

Electric properties of the Beryllium-11 system in Halo EFT journal, August 2011

Effective field theory description of halo nuclei journal, September 2017

Field theory of the d + t → n + α reaction dominated by a 5 He * unstable particle journal, January 2014

He 3 ( α , γ ) Be 7 and H 3 ( α , γ ) Li 7 astrophysical S factors from the no-core shell model with continuum journal, June 2016

Alpha scattering and capture reactions in the A =7 system at low energies journal, September 1993

Monte Carlo uncertainty of the He 3 ( α , γ ) Be 7 reaction rate journal, September 2014

Spectroscopic factors, overlaps, and isospin symmetry from an R -matrix point of view journal, September 2020

Solar fusion cross sections. II. The p p chain and CNO cycles journal, April 2011

Scattering of He 3 from He 4 journal, May 1963

αα scattering in halo effective field theory journal, September 2008

Microscopic Calculation of the He 3 ( α , γ ) Be 7 and H 3 ( α , γ ) Li 7 Capture Cross Sections Using Realistic Interactions journal, January 2011

emcee : The MCMC Hammer journal, March 2013

Scattering of He 3 from He 4 and States in Be 7 journal, December 1958

Narrow resonances in effective field theory journal, September 2003

Phase Shifts in Proton-Alpha-Scattering journal, September 1949

Coulomb corrections in non-relativistic scattering journal, January 1973

The scattering of He3 by He4 journal, January 1964

Phenomenological Lagrangians journal, April 1979

S -factor and scattering-parameter extractions from ${}^{3}\mathrm{He}+{}^{4}\mathrm{He}{ \rightarrow }^{7}\mathrm{Be}+\gamma $ journal, March 2020

the elastic scattering reactions 4He(t, t)4He and 4He(τ, τ)4He near 2 MeV journal, October 1971

Radiative 3He( $\alpha , \gamma$ α , γ )7Be reaction in halo effective field theory journal, May 2018

Halo structure of 17C journal, November 2018

Exploring Bayesian parameter estimation for chiral effective field theory using nucleon–nucleon phase shifts journal, February 2019

A New Generation of Standard Solar Models journal, January 2017

Electric structure of shallow D -wave states in Halo EFT journal, September 2019

Title: Effective field theory analysis of ³He–α scattering data

Ensemble samplers with affine invariance
journal, January 2010

${}^{3}{He}$ + ${}^{4}{He}$ elastic scattering at $E_{c . m .} = 60.2 and 113.1$ MeV
journal, March 1980

Combining ab initio calculations and low-energy effective field theory for halo nuclear systems: The case of $^{7} Li + n \to^{8} Li + γ$
journal, February 2014

Bayesian analysis of capture reactions $$\varvec{^3}\hbox {He}\varvec{(\alpha ,\gamma )^7}\hbox {Be}$$ and $$\varvec{^3}\hbox {H}\varvec{(\alpha ,\gamma )^7}\hbox {Li}$$
journal, June 2020

Verification of R-matrix calculations for charged-particle reactions in the resolved resonance region for the 7Be system
journal, June 2019

Scattering of 3He and 4He from polarized 3He between 4 and 10 MeV
journal, November 1972

Analysis of the 3He(α,γ)7Be and 3H(α,γ)7Li astrophysical direct capture reactions in a modified potential-model approach
journal, February 2021

Theory of the Effective Range in Nuclear Scattering
journal, July 1949

Scattering of ${He}^{3}$ by ${He}^{4}$ and of ${He}^{4}$ by Tritium
journal, November 1967

Determination of the $^{3} He + α \to^{7}$ Be asymptotic normalization coefficients, the nuclear vertex constants, and their application for the extrapolation of the $^{3}$ He( ${α, γ)}^{7}$ Be astrophysical $S$ factors to the solar energy region
journal, April 2012

Electric properties of the Beryllium-11 system in Halo EFT
journal, August 2011

Effective field theory description of halo nuclei
journal, September 2017

Field theory of the $d + t \to n + α$ reaction dominated by a $^{5}$ He $^{*}$ unstable particle
journal, January 2014

${}^{3}{He} (α, γ) {}^{7}{Be}$ and ${}^{3}H (α, γ) {}^{7}{Li}$ astrophysical S factors from the no-core shell model with continuum
journal, June 2016

Alpha scattering and capture reactions in the A =7 system at low energies
journal, September 1993

Monte Carlo uncertainty of the ${}^{3}{He} (α, γ) {}^{7}{Be}$ reaction rate
journal, September 2014

Spectroscopic factors, overlaps, and isospin symmetry from an $R$ -matrix point of view
journal, September 2020

Solar fusion cross sections. II. The $p p$ chain and CNO cycles
journal, April 2011

Scattering of ${He}^{3}$ from ${He}^{4}$
journal, May 1963

αα scattering in halo effective field theory
journal, September 2008

Microscopic Calculation of the ${}^{3}{He} (α, γ) {}^{7}{Be}$ and ${}^{3}H (α, γ) {}^{7}{Li}$ Capture Cross Sections Using Realistic Interactions
journal, January 2011

`emcee` : The MCMC Hammer
journal, March 2013

Scattering of ${He}^{3}$ from ${He}^{4}$ and States in ${Be}^{7}$
journal, December 1958

Narrow resonances in effective field theory
journal, September 2003

Phase Shifts in Proton-Alpha-Scattering
journal, September 1949

Coulomb corrections in non-relativistic scattering
journal, January 1973

The scattering of He3 by He4
journal, January 1964

Phenomenological Lagrangians
journal, April 1979

S -factor and scattering-parameter extractions from ${}^{3}\mathrm{He}+{}^{4}\mathrm{He}{ \rightarrow }^{7}\mathrm{Be}+\gamma $
journal, March 2020

the elastic scattering reactions 4He(t, t)4He and 4He(τ, τ)4He near 2 MeV
journal, October 1971

Radiative 3He( $\alpha , \gamma$ α , γ )7Be reaction in halo effective field theory
journal, May 2018

Halo structure of 17C
journal, November 2018

Exploring Bayesian parameter estimation for chiral effective field theory using nucleon–nucleon phase shifts
journal, February 2019

A New Generation of Standard Solar Models
journal, January 2017

Electric structure of shallow D -wave states in Halo EFT
journal, September 2019