论文标题
牛顿引力恒定测量。当使用由3个或更多零件组成的源质量时，所有原子变量都变得极端
Newtonian gravitational constant measurement. All atomic variables become extreme when using a source mass consisting of 3 or more parts
论文作者
论文摘要
原子干涉法用于测量牛顿引力常数。为了提高准确性，应在原子垂直速度和坐标的极端值下测量原子干涉仪的相位。由于对称性，原子速度和坐标的水平成分也很极高。我们建议使用由3个或更多零件组成的源质量，因为只有在这种情况下，才能找到这样的零件排列，使所有原子变量变得极端。在这些极端值附近的原子位置和速度的不确定性的非线性依赖性需要我们修改相对标准偏差（RSD）的表达式。此外，考虑到对原子坐标和速度的阶段依赖性中的非线性项会导致相移。在最后一个通过原子干涉测量牛顿重力常数测量的实验中，不包括这种转移。我们考虑了这一转变，为此获得了199ppm的价值，这导致牛顿常数的价值下降了0.02％。此外，我们表明，在垂直和水平方向上的原子云的大小相等，以及在相等的原子垂直和横向温度下，由于云的有限尺寸和温度消失了，因此系统误差消失了。该计算还表明，在最近提出的13吨源质量质量时，对于由4个季度组成的源质量，测量精度可以达到17ppm。我们假设由一组圆柱体组成的源质量用于测量。我们为均匀圆柱体的重力场获得了新的分析表达。
Atomic interferometry methods used to measure the Newtonian gravitational constant. To improve the accuracy, one should measure the phase of an atomic interferometer at extreme values of atomic vertical velocities and coordinates. Owing to symmetry, the horizontal components of atomic velocities and coordinates are also extreme. We propose using a source mass consisting of 3 or more parts, since only in this case one can find such an arrangement of parts that all atomic variables become extreme. Nonlinear dependences of the phase on the uncertainties of atomic positions and velocities near those extreme values required us to modify the expression for the phase relative standard deviation (RSD). Moreover, taking into account nonlinear terms in the phase dependence on the atomic coordinates and velocities leads to a phase shift. In the last experiment to measure the Newtonian gravitational constant by atomic interferometry, this shift was not included. We took the shift into account, got a value of 199ppm for it, and this leads to a decrease in the value of the Newton constant by 0.02%. In addition, we showed that at equal sizes of the atomic cloud in the vertical and horizontal directions, as well as at equal atomic vertical and transverse temperatures, systematic errors due to the finite size and temperature of the cloud disappear. The calculation also showed that when using the 13-ton source mass proposed recently, the measurement accuracy can reach 17ppm for a source mass consisting of 4 quarters. We assumed that the source mass consisting of a set of cylinders is used for measurements. We have obtained a new analytical expression for the gravitational field of a homogeneous cylinder.
