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arXiv 0810.1941nucl-th
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一π和二π范围的电磁二体电流

Electromagnetic two-body currents of one- and two-pion range

S. Pastore, R. Schiavilla, J. L. Goity

摘要:

核电磁流是在有效场论框架内的时间序微扰理论中推导出来的,有效场论框架包括显式核子、$Δ$等压线和π介子,直到一个环,或N $^3$ LO。在N $^2$ LO处获得的电流{ \it,即}忽略回路修正,用于研究中子辐射俘获质子和氘在热能,和$A$ =2和3核磁矩。$A$ =2的波函数是从薛定谔方程的解中导出的,其势为Argonne $v_{18}$(AV 18)或CD-Bonn(CDB)势,而$A$ =3的波函数是用超球谐函数展开法从一个实际的哈密顿量中得到的,该哈密顿量除了AV 18或CDB的双核子势外,还包括一个三核子势。通过确定N $^2$ LO处的$Δ$ -激发电流的强度来再现$n$ - $p$截面和三核子磁矩的等矢量组合,我们发现在$n$ - $d$和$\vec{n}$ - $d$过程中测量的截面和光子圆偏振参数都低于理论预测值,例如,当截止能量从500 MeV增加到800 MeV时,截面增加(11- 38)%。一个完整的分析结果,特别是他们的大截止依赖,提出。

英文摘要:

Nuclear electromagnetic currents are derived in time-ordered perturbation theory within an effective-field-theory framework including explicit nucleons, $Δ$ isobars, and pions up to one loop, or N$^3$LO. The currents obtained at N$^2$LO, {\it i.e.} ignoring loop corrections, are used in a study of neutron radiative captures on protons and deuterons at thermal energies, and of $A$=2 and 3 nuclei magnetic moments. The wave functions for $A$=2 are derived from solutions of the Schrödinger equation with the Argonne $v_{18}$ (AV18) or CD-Bonn (CDB) potentials, while those for $A$=3 are obtained with the hyperspherical-harmonics-expansion method from a realistic Hamiltonian including, in addition to the AV18 or CDB two-nucleon, also a three-nucleon potential. With the strengths of the $Δ$-excitation currents occurring at N$^2$LO determined to reproduce the $n$-$p$ cross section and isovector combination of the trinucleon magnetic moments, we find that the cross section and photon circular polarization parameter, measured in $n$-$d$ and $\vec{n}$-$d$ processes, are underpredicted by theory, for example the cross section by (11--38)% as the cutoff is increased from 500 to 800 MeV. A complete analysis of the results, in particular their large cutoff dependence, is presented.

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