Effective field theory analysis of 3He–α scattering data

Poudel, Maheshwor; Phillips, Daniel R.

doi:10.1088/1361-6471/ac4da6

Effective field theory analysis of ³He–α scattering data

Journal Article · Wed Mar 09 23:00:00 EST 2022 · Journal of Physics. G, Nuclear and Particle Physics

DOI:https://doi.org/10.1088/1361-6471/ac4da6· OSTI ID:1872775

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Ohio Univ., Athens, OH (United States); Ohio University
Ohio Univ., Athens, OH (United States)

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.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP); USDOE National Nuclear Security Administration (NNSA); US NSF

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

OSTI ID:: 1872775

Journal Information:: Journal of Physics. G, Nuclear and Particle Physics, Journal Name: Journal of Physics. G, Nuclear and Particle Physics Journal Issue: 4 Vol. 49; ISSN 0954-3899

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United States

Language:: English

References (43)

The scattering of He3 by He4 Barnard, A. C. L.; Jones, C. M.; Phillips, G. C. Nuclear Physics, Vol. 50 https://doi.org/10.1016/0029-5582(64)90235-4	journal	January 1964
the elastic scattering reactions 4He(t, t)4He and 4He(τ, τ)4He near 2 MeV Chuang, L. S. Nuclear Physics A, Vol. 174, Issue 2 https://doi.org/10.1016/0375-9474(71)90672-5	journal	October 1971
Scattering of 3He and 4He from polarized 3He between 4 and 10 MeV Boykin, W. R.; Baker, S. D.; Hardy, D. M. Nuclear Physics A, Vol. 195, Issue 1 https://doi.org/10.1016/0375-9474(72)90732-4	journal	November 1972
Phenomenological Lagrangians Weinberg, Steven Physica A: Statistical Mechanics and its Applications, Vol. 96, Issue 1-2 https://doi.org/10.1016/0378-4371(79)90223-1	journal	April 1979
Coulomb corrections in non-relativistic scattering Hamilton, J.; Øverbö, I.; Tromborg, B. Nuclear Physics B, Vol. 60 https://doi.org/10.1016/0550-3213(73)90193-4	journal	January 1973
αα scattering in halo effective field theory Higa, R.; Hammer, H. -W.; van Kolck, U. Nuclear Physics A, Vol. 809, Issue 3-4 https://doi.org/10.1016/j.nuclphysa.2008.06.003	journal	September 2008
Electric properties of the Beryllium-11 system in Halo EFT Hammer, H. -W.; Phillips, D. R. Nuclear Physics A, Vol. 865, Issue 1 https://doi.org/10.1016/j.nuclphysa.2011.06.028	journal	August 2011
Analysis of the 3He(α,γ)7Be and 3H(α,γ)7Li astrophysical direct capture reactions in a modified potential-model approach Tursunov, E. M.; Turakulov, S. A.; Kadyrov, A. S. Nuclear Physics A, Vol. 1006 https://doi.org/10.1016/j.nuclphysa.2020.122108	journal	February 2021
Narrow resonances in effective field theory Bedaque, P. F.; Hammer, H. -W.; van Kolck, U. Physics Letters B, Vol. 569, Issue 3-4 https://doi.org/10.1016/j.physletb.2003.07.049	journal	September 2003
He 3 ( α , γ ) Be 7 and H 3 ( α , γ ) Li 7 astrophysical S factors from the no-core shell model with continuum Dohet-Eraly, Jérémy; Navrátil, Petr; Quaglioni, Sofia Physics Letters B, Vol. 757 https://doi.org/10.1016/j.physletb.2016.04.021	journal	June 2016
Energy levels of light nuclei A=5, 6, 7 Tilley, D. R.; Cheves, C. M.; Godwin, J. L. Nuclear Physics A, Vol. 708, Issue 1-2 https://doi.org/10.1016/s0375-9474(02)00597-3	journal	September 2002
Coulomb effects in low energy proton–proton scattering Kong, Xinwei; Ravndal, Finn Nuclear Physics A, Vol. 665, Issue 1-2 https://doi.org/10.1016/s0375-9474(99)00406-6	journal	February 2000
`emcee` : The MCMC Hammer Foreman-Mackey, Daniel; Hogg, David W.; Lang, Dustin Publications of the Astronomical Society of the Pacific, Vol. 125, Issue 925 https://doi.org/10.1086/670067	journal	March 2013
Effective field theory description of halo nuclei Hammer, H-W; Ji, C.; Phillips, D. R. Journal of Physics G: Nuclear and Particle Physics, Vol. 44, Issue 10 https://doi.org/10.1088/1361-6471/aa83db	journal	September 2017
Exploring Bayesian parameter estimation for chiral effective field theory using nucleon–nucleon phase shifts Wesolowski, S.; Furnstahl, R. J.; Melendez, J. A. Journal of Physics G: Nuclear and Particle Physics, Vol. 46, Issue 4 https://doi.org/10.1088/1361-6471/aaf5fc	journal	February 2019
Electric structure of shallow D -wave states in Halo EFT Braun, J.; Elkamhawy, W.; Roth, R. Journal of Physics G: Nuclear and Particle Physics, Vol. 46, Issue 11 https://doi.org/10.1088/1361-6471/ab368f	journal	September 2019
S -factor and scattering-parameter extractions from ${}^{3}\mathrm{He}+{}^{4}\mathrm{He}{ \rightarrow }^{7}\mathrm{Be}+\gamma $ Zhang, Xilin; Nollett, Kenneth M.; Phillips, D. R. Journal of Physics G: Nuclear and Particle Physics, Vol. 47, Issue 5 https://doi.org/10.1088/1361-6471/ab6a71	journal	March 2020
Theory of the Effective Range in Nuclear Scattering Bethe, H. A. Physical Review, Vol. 76, Issue 1 https://doi.org/10.1103/PhysRev.76.38	journal	July 1949
Scattering of He 3 from He 4 and States in Be 7 Miller, Philip D.; Phillips, G. C. Physical Review, Vol. 112, Issue 6 https://doi.org/10.1103/physrev.112.2048	journal	December 1958
Scattering of He 3 from He 4 Tombrello, T. A.; Parker, P. D. Physical Review, Vol. 130, Issue 3 https://doi.org/10.1103/physrev.130.1112	journal	May 1963
Scattering of He 3 by He 4 and of He 4 by Tritium Spiger, R. J.; Tombrello, T. A. Physical Review, Vol. 163, Issue 4 https://doi.org/10.1103/physrev.163.964	journal	November 1967
Phase Shifts in Proton-Alpha-Scattering Critchfield, C. L.; Dodder, D. C. Physical Review, Vol. 76, Issue 5 https://doi.org/10.1103/physrev.76.602	journal	September 1949
Quantifying correlated truncation errors in effective field theory Melendez, J. A.; Furnstahl, R. J.; Phillips, D. R. Physical Review C, Vol. 100, Issue 4 https://doi.org/10.1103/physrevc.100.044001	journal	October 2019
Spectroscopic factors, overlaps, and isospin symmetry from an R -matrix point of view Brune, Carl R. Physical Review C, Vol. 102, Issue 3 https://doi.org/10.1103/physrevc.102.034328	journal	September 2020
He 3 + He 4 elastic scattering at E c . m . = 60.2 and 113.1 MeV Roos, P. G.; Nadasen, A.; Frisbee, P. E. Physical Review C, Vol. 21, Issue 3 https://doi.org/10.1103/physrevc.21.799	journal	March 1980
Alpha scattering and capture reactions in the A =7 system at low energies Mohr, P.; Abele, H.; Zwiebel, R. Physical Review C, Vol. 48, Issue 3 https://doi.org/10.1103/physrevc.48.1420	journal	September 1993
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 Tursunmahatov, Q. I.; Yarmukhamedov, R. Physical Review C, Vol. 85, Issue 4 https://doi.org/10.1103/physrevc.85.045807	journal	April 2012
Field theory of the d + t → n + α reaction dominated by a 5 He * unstable particle Brown, Lowell S.; Hale, Gerald M. Physical Review C, Vol. 89, Issue 1 https://doi.org/10.1103/physrevc.89.014622	journal	January 2014
Combining ab initio calculations and low-energy effective field theory for halo nuclear systems: The case of 7 Li + n → 8 Li + γ Zhang, Xilin; Nollett, Kenneth M.; Phillips, D. R. Physical Review C, Vol. 89, Issue 2 https://doi.org/10.1103/physrevc.89.024613	journal	February 2014
Monte Carlo uncertainty of the He 3 ( α , γ ) Be 7 reaction rate deBoer, R. J.; Görres, J.; Smith, K. Physical Review C, Vol. 90, Issue 3 https://doi.org/10.1103/physrevc.90.035804	journal	September 2014
Quantifying truncation errors in effective field theory Furnstahl, R. J.; Klco, N.; Phillips, D. R. Physical Review C, Vol. 92, Issue 2 https://doi.org/10.1103/physrevc.92.024005	journal	August 2015
Bayesian truncation errors in chiral effective field theory: Nucleon-nucleon observables Melendez, J. A.; Wesolowski, S.; Furnstahl, R. J. Physical Review C, Vol. 96, Issue 2 https://doi.org/10.1103/physrevc.96.024003	journal	August 2017
Microscopic Calculation of the He 3 ( α , γ ) Be 7 and H 3 ( α , γ ) Li 7 Capture Cross Sections Using Realistic Interactions Neff, Thomas Physical Review Letters, Vol. 106, Issue 4 https://doi.org/10.1103/physrevlett.106.042502	journal	January 2011
R-Matrix Theory of Nuclear Reactions Lane, A. M.; Thomas, R. G. Reviews of Modern Physics, Vol. 30, Issue 2 https://doi.org/10.1103/revmodphys.30.257	journal	April 1958
Modern theory of nuclear forces Epelbaum, E.; Hammer, H. -W.; Meißner, Ulf-G. Reviews of Modern Physics, Vol. 81, Issue 4 https://doi.org/10.1103/revmodphys.81.1773	journal	December 2009
Solar fusion cross sections. II. The p p chain and CNO cycles Adelberger, E. G.; García, A.; Robertson, R. G. Hamish Reviews of Modern Physics, Vol. 83, Issue 1 https://doi.org/10.1103/revmodphys.83.195	journal	April 2011
Nuclear effective field theory: Status and perspectives Hammer, H. -W.; König, Sebastian; van Kolck, U. Reviews of Modern Physics, Vol. 92, Issue 2 https://doi.org/10.1103/revmodphys.92.025004	journal	June 2020
Radiative 3He( $\alpha , \gamma$ α , γ )7Be reaction in halo effective field theory Higa, Renato; Rupak, Gautam; Vaghani, Akshay The European Physical Journal A, Vol. 54, Issue 5 https://doi.org/10.1140/epja/i2018-12486-5	journal	May 2018
Halo structure of 17C Braun, J.; Hammer, H. -W.; Platter, L. The European Physical Journal A, Vol. 54, Issue 11 https://doi.org/10.1140/epja/i2018-12630-3	journal	November 2018
Verification of R-matrix calculations for charged-particle reactions in the resolved resonance region for the 7Be system Thompson, Ian J.; deBoer, R. J.; Dimitriou, P. The European Physical Journal A, Vol. 55, Issue 6 https://doi.org/10.1140/epja/i2019-12753-y	journal	June 2019
Bayesian analysis of capture reactions $$\varvec{^3}\hbox {He}\varvec{(\alpha ,\gamma )^7}\hbox {Be}$$ and $$\varvec{^3}\hbox {H}\varvec{(\alpha ,\gamma )^7}\hbox {Li}$$ Premarathna, Pradeepa; Rupak, Gautam The European Physical Journal A, Vol. 56, Issue 6 https://doi.org/10.1140/epja/s10050-020-00113-z	journal	June 2020
Ensemble samplers with affine invariance Goodman, Jonathan; Weare, Jonathan Communications in Applied Mathematics and Computational Science, Vol. 5, Issue 1 https://doi.org/10.2140/camcos.2010.5.65	journal	January 2010
A New Generation of Standard Solar Models Vinyoles, Núria; Serenelli, Aldo M.; Villante, Francesco L. The Astrophysical Journal, Vol. 835, Issue 2 https://doi.org/10.3847/1538-4357/835/2/202	journal	January 2017

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