论文标题
中子 - 中子散射长度从$π^+$ $ $ $ photoductuntion the Deuteron
Neutron-neutron scattering length from $π^+$ photoproduction on the deuteron
论文作者
论文摘要
我们讨论了从横截面数据中提取中子中的散射长度$ a_ {nn} $和有效范围$ r_ {nn} $（$ d^2σ/dm_ {nn}/dΩ_π$），作为$ nn $ nn $ nn $ nn $ nn $ nn nn} $ $ phote $ phote $ phote $ pottut的函数（ π^+nn $）。该分析基于$γd\至π^+nn $反应模型，其中$γp\ toπ^+n $，$ nn \ to nn $和$πn\toπn$的现实基本振幅内置。我们显示了$ m_ {nn} $依赖（line} $ __的$ r} $ rm rm rm rm rm rm r rm r rm $ d^2σ/dm_ {nn}/dΩ_π$由$dσ/dΩ_π$归一化$γp\toπ^+ n $以及deuteron内部的核能动量分布，在$θ_π= 0^\ Circ $和$e_γ\ sim 250 $ a___________________________________________________________________________________________________ $ r_ {nn} $从相应的数据$ r _ {\ rm exp} $。发现$ r _ {\ rm exp} $带有2％的误差，分为$ m_ {nn} $ bin宽度为0.04 meV（对应于0.05 mev $/c $的$p_π$ bin宽度，可以确定，可以确定$ a_ {nn} $ $ r_ nnn} $ nnn} $ 0.2对于$ a_ {nn} = - 18.9 $ fm和$ r_ {nn} = 2.75 $ fm的情况，分别为0.06 $ fm。这种狭窄的垃圾箱宽度的要求表明，必须以高分辨率来测量入射光子和发射的$π^+$的动量。这可以通过利用Mainz Mami设施中电子散射的非常小的$ Q^2 $的虚拟光子来实现。从$γd\到π^+ nn $确定$ a_ {nn} $和$ r_ {nn} $的提议方法比上一个利用$π^ - d \toγnn$的实验优势具有很大的实验优势，因为它可以免于控制中子检测效率和其不确定的强大任务。
We discuss the possibility of extracting the neutron-neutron scattering length $a_{nn}$ and effective range $r_{nn}$ from cross section data ($d^2σ/dM_{nn}/dΩ_π$), as a function of the $nn$ invariant mass $M_{nn}$, for $π^+$ photoproduction on the deuteron ($γd\to π^+nn$). The analysis is based on a $γd\to π^+nn$ reaction model in which realistic elementary amplitudes for $γp\to π^+n$, $NN\to NN$, and $πN\to πN$ are built in. We show that $M_{nn}$ dependence (lineshape) of a ratio $R_{\rm th}$, $d^2σ/dM_{nn}/dΩ_π$ normalized by $dσ/dΩ_π$ for $γp\toπ^+ n$ and the nucleon momentum distribution inside the deuteron, at the kinematics with $θ_π=0^\circ$ and $E_γ\sim 250$ MeV is particularly useful for extracting $a_{nn}$ and $r_{nn}$ from the corresponding data $R_{\rm exp}$. It is found that $R_{\rm exp}$ with 2% error, resolved into the $M_{nn}$ bin width of 0.04 MeV (corresponding to the $p_π$ bin width of 0.05 MeV$/c$), can determine $a_{nn}$ and $r_{nn}$ with uncertainties of $\pm 0.21$ fm and $\pm 0.06$ fm, respectively, for the case of $a_{nn}=-18.9$ fm and $r_{nn}=2.75$ fm. The requirement of such narrow bin widths indicates that the momenta of the incident photon and the emitted $π^+$ have to be measured with high resolutions. This can be achieved by utilizing virtual photons of very small $Q^2$ from electron scattering at Mainz MAMI facility. The proposed method for determining $a_{nn}$ and $r_{nn}$ from $γd\to π^+ nn$ has a great experimental advantage over the previous one utilizing $π^- d\toγnn$ for being free from the formidable task of controlling the neutron detection efficiency and its uncertainty.
