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 three 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. 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 199 ppm 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 17 ppm for a source mass consisting of four 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.

用于测量牛顿引力常数的原子干涉测量方法。为了提高精度，应该在原子垂直速度和坐标的极值处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分量也是极端的。我们建议使用由三个或更多部分组成的源质量，因为只有在这种情况下，才能找到所有原子变量都变得极端的部分排列。相位对那些极值附近的原子位置和速度的不确定性的非线性依赖性要求我们修改相位相对标准偏差的表达式。此外，考虑到原子坐标和速度的相位依赖性中的非线性项会导致相移。在最后一个用原子干涉法测量牛顿引力常数的实验中，没有包括这种偏移。我们考虑了这种变化，得到了 199 ppm 的值，这导致牛顿常数的值减少了 0.02%。此外，我们还表明，在垂直和水平方向上的原子云大小相等，以及原子垂直和横向温度相等时，由于云的有限大小和温度而导致的系统误差消失了。计算还表明，当使用最近提出的 13 吨源质量时，对于由四分之四组成的源质量，测量精度可以达到 17 ppm。我们假设由一组圆柱体组成的源质量用于测量。