Charged Particle Scattering in Renormalizable Pionless Effective Field Theory at Next-to-Leading Order: The $pd$, $dd$, and $p^3\mathrm{He}$ Case
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| Format: | Preprint |
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2025
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| _version_ | 1866915404226494464 |
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| author | Rojik, Matúš Schäfer, Martin Bagnarol, Mirko Barnea, Nir |
| author_facet | Rojik, Matúš Schäfer, Martin Bagnarol, Mirko Barnea, Nir |
| contents | We formulate a renormalizable pionless effective field theory (Pionless EFT) with a non-perturbative treatment of the Coulomb interaction up to next-to-leading order (NLO) for few-nucleon systems. We extract scattering observables for charged clusters by employing two-, three-, and four-body contact interactions and using the stochastic variational method with a Coulomb-corrected harmonic oscillator trap. Our NLO results yield a $pd$ spin-quartet scattering length and effective range of $a_{pd}^{3/2} = 12.76(29)\,\mathrm{fm}$ and $r_{pd}^{3/2} = 1.17(7)\,\mathrm{fm}$; for $dd$ scattering in the spin-quintet channel, we find $a_{dd}^{2} = 6.26(3)\,\mathrm{fm}$ and $r_{dd}^{2} = 1.41(7)\,\mathrm{fm}$; and for $p^3\mathrm{He}$ scattering, the spin-singlet and spin-triplet channels are characterized by $a_{p^3\mathrm{He}}^0 = 11.26(4)\,\mathrm{fm}$, $r_{p^3\mathrm{He}}^0 = 1.65(26)\,\mathrm{fm}$ and $a_{p^3\mathrm{He}}^1 = 9.06(4)\,\mathrm{fm}$, $r_{p^3\mathrm{He}}^1 = 1.36(25)\,\mathrm{fm}$, respectively. Our predictions exhibit mild cutoff dependence and agree well with existing experimental phase shift analyses and potential model calculations. This demonstrates the predictive power of (Pionless EFT) for charged few-nucleon systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_16250 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Charged Particle Scattering in Renormalizable Pionless Effective Field Theory at Next-to-Leading Order: The $pd$, $dd$, and $p^3\mathrm{He}$ Case Rojik, Matúš Schäfer, Martin Bagnarol, Mirko Barnea, Nir Nuclear Theory We formulate a renormalizable pionless effective field theory (Pionless EFT) with a non-perturbative treatment of the Coulomb interaction up to next-to-leading order (NLO) for few-nucleon systems. We extract scattering observables for charged clusters by employing two-, three-, and four-body contact interactions and using the stochastic variational method with a Coulomb-corrected harmonic oscillator trap. Our NLO results yield a $pd$ spin-quartet scattering length and effective range of $a_{pd}^{3/2} = 12.76(29)\,\mathrm{fm}$ and $r_{pd}^{3/2} = 1.17(7)\,\mathrm{fm}$; for $dd$ scattering in the spin-quintet channel, we find $a_{dd}^{2} = 6.26(3)\,\mathrm{fm}$ and $r_{dd}^{2} = 1.41(7)\,\mathrm{fm}$; and for $p^3\mathrm{He}$ scattering, the spin-singlet and spin-triplet channels are characterized by $a_{p^3\mathrm{He}}^0 = 11.26(4)\,\mathrm{fm}$, $r_{p^3\mathrm{He}}^0 = 1.65(26)\,\mathrm{fm}$ and $a_{p^3\mathrm{He}}^1 = 9.06(4)\,\mathrm{fm}$, $r_{p^3\mathrm{He}}^1 = 1.36(25)\,\mathrm{fm}$, respectively. Our predictions exhibit mild cutoff dependence and agree well with existing experimental phase shift analyses and potential model calculations. This demonstrates the predictive power of (Pionless EFT) for charged few-nucleon systems. |
| title | Charged Particle Scattering in Renormalizable Pionless Effective Field Theory at Next-to-Leading Order: The $pd$, $dd$, and $p^3\mathrm{He}$ Case |
| topic | Nuclear Theory |
| url | https://arxiv.org/abs/2507.16250 |