We study Compton scattering at helium atom exposed to an electromagnetic field with a central frequency of 80 a.u. (\(\sim 2.18\) keV). We consider the situation where the incident light and scattered light are polarized along the same direction with small relative propagation angle \(\beta \). The energy of the emitted electron ranges from 0.2 to 2.1 a.u. (\(\sim 5.44\)–57.14 eV). The approach is based on previous works on stimulated Compton scattering (see Bachau et al. Phys Rev Lett 112:073001, 2014). We consider a field intensity of \(3.51\times 10^{16}\) W/cm\(^2\), where stimulated Compton scattering can be treated in perturbative regime. In lowest order perturbation theory, the process results from the contribution of \(\mathbf{A\cdot \mathbf{P}}\) in second order and \(\mathbf{A}^2\) in first order (\(\mathbf{P}\) is the electron momentum operator and \(\mathbf{A}\) the vector potential of the field); both terms induce two-photon transitions. The Compton matrix element \(|{{\mathcal {M}}}_{fg}|^2\) is extracted numerically resolving the time-dependent Schrödinger equation, and in perturbation theory, emphasis is put on the calculation of the second-order amplitude associated with \(\mathbf{A\cdot \mathbf{P}}\). We investigate the cases of relative propagation angle \(\beta =0\) and 10 degrees. The photoelectron energy distributions are dominated by the nondipole term \(\mathbf{A}^2\); they increase by orders of magnitude when \(\beta \) grows from 0 to 10 degrees. At \(\beta =0\) degree, both \(\mathbf{A\cdot \mathbf{P}}\) and \(\mathbf{A}^2\) are at play and we show that the electrons are emitted in the (forward) direction of the momentum transfer \({{\mathcal {Q}}}\) and to a lesser extent in the backward direction. When \(\beta \) increases, the nondipole contribution \(\mathbf{A}^2\) tends to dominate and the forward/backward asymmetry vanishes.

我们研究了中心频率为80 au（\（\ sim 2.18 \） keV）暴露于电磁场的氦原子上的康普顿散射。我们考虑入射光和散射光沿相同方向偏振且相对传播角为\（\ beta \）较小的情况。发射电子的能量范围为0.2到2.1 au（\（\ sim 5.44 \）– 57.14 eV）。该方法基于先前关于受激康普顿散射的研究（参见Bachau等人，Phys Rev Lett 112：073001，2014）。我们认为场强为\（3.51 \乘以10 ^ {16} \） W / cm \（^ 2 \），可以在摄动状态下处理刺激的康普顿散射。在最低阶扰动理论中，该过程是由第二阶\（\ mathbf {A \ cdot \ mathbf {P}} \\）和第一阶\（\ mathbf {A} ^ 2 \）（\（ \ mathbf {P} \）是电子动量算子，\（\ mathbf {A} \）是电场的矢量势。这两个术语都会引起双光子跃迁。数值提取康普顿矩阵元素\（| {{\ mathcal {M}}} _ {fg} | ^ 2 \）来解析时间相关的Schrödinger方程，并且在扰动理论中，重点放在第二维的计算上与\（\ mathbf {A \ cdot \ mathbf {P}} \）相关的幅度振幅。我们调查了相对传播角\（\ beta = 0 \）和10度的情况。光电子能量分布由非偶极子项\（\ mathbf {A} ^ 2 \）支配；当\（\ beta \）从0度增加到10度时，它们以数量级增加。在\（\ beta = 0 \）度下，\（\ mathbf {A \ cdot \ mathbf {P}} \）和\（\ mathbf {A} ^ 2 \）都在起作用，我们证明电子是在动量传递\（{{\ mathcal {Q}}} \）的（正向）方向上发射，并在向后方向上较小程度地发射。当\（\ beta \）增加时，非偶极贡献\（\ mathbf {A} ^ 2 \） 往往占主导地位，向前/向后的不对称性消失了。