扭秤周期法测G实验中的系统误差研究
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摘要
从1798年Cavendish的扭秤实验给出万有引力常数G的第一个值以来，过去两百多年里国际上测量出了三百多个G值，但精度仅提高不到两个数量级。国际科技数据委员会给出G的最新推荐值CODATA2010为6.67384(80)×10~(-11)m~3kg1s2，相对不确定度为120ppm。在CODATA2010推荐值收录的11个G值中声称精度小于50ppm的有6个，而它们之中最大值和最小值的差别达到了487ppm。测G的这种现状反应了对这个基本物理学常数进行精确测量的困难，以及在各种不同的测G方法中可能存在着不同的系统误差。
在我们实验室2009年测G实验（HUST-09）的基础上，通过一系列的改进措施，我们开展了新一轮基于高Q值石英丝的周期法测G实验。主要改进措施有：1、采用Q值约为5.00×10~4的石英丝取代钨丝来降低滞弹性效应和提高扭秤周期的稳定性。在HUST-09实验中，Q值约为1.7×10~3的涂钍钨丝贡献的滞弹性效应为-211.80(18.69) ppm。采用石英扭丝之后滞弹性效应降低至-6.37(0.50) ppm，这说明滞弹性不再是周期法测G中的主要系统误差来源；2、为了解决由于石英丝不导电带来的静电问题，我们在石英丝表面依次镀了厚度为8nm的锗和8nm的铋膜。目前三天扭秤数据的周期稳定性约为0.05ms，这比HUST-09实验中的周期稳定性提高了约4倍；3、对测G实验环境的背景引力场采用偶极对称扭秤进行了测量并用约800kg铅块进行了补偿。补偿之后，背景引力场对扭秤周期的影响降低了约5倍，同时扭秤的平衡位置处在背景场最平坦的地方，这使得背景场对扭秤周期的影响极大地降低。在72天的近、远程数据中，背景场贡献的效应只有0.38ppm；4、在扭丝周围安装了导热性良好的紫铜管用于均热，实验中铜管上、下端的温度差异小于0.02C，由它引起的热弹性效应贡献给G值的不确定度小于5ppm；5、优化磁阻尼单元。在保持磁阻尼单元对单摆运动模式的抑制能力前提下，将悬挂磁阻尼的钨丝直径和长度进行相应的优化之后，整个磁阻尼贡献给G值的效应从17.54(0.31)ppm减小至0.13(0.01) ppm；6、为了减小扭秤表面镀层对测G的贡献，镀层的材料选用密度更小的铝取代HUST-09中的铜和金之后，整个镀层贡献的效应从-24.28(4.33) ppm降低至-1.81(0.91) ppm。
目前我们已经完成了初步的测G实验，给出的G值相对不确定度为16.95ppm。其中两项主要的误差来源于Cg/I和ω2的测量精度，它们分别为9.56ppm和13.22ppm。为了使测量结果更加可靠，我们将进行重复的测G工作，因此目前暂不公布G值的测量结果。
本课题得到973计划课题“基于精密测量物理的引力及相关物理规律研究”的子课题：万有引力常数G的精确测量（2010CB832801）的资助。
The absolute value of G was first measured in the laboratory by Cavendish in1798, whichgave G=6.67(7)×10~11m3kg1s2with a relative uncertainty (ur) of about1%. Over the pasttwo centuries, nearly300different values of G have appeared, however, the measurement pre-cision of G value has improved only at the rate of about1order of magnitude per century. Thenewest recommended G value of CODATA2010(Committee on Data for Science and Tech-nology) is6.67384(80)×10~11m3kg1s2with ur=120ppm. The adopted G values in CO-DATA2010are in poor agreement in their claimed uncertainties, in which the largest differenceyields487ppm. This situation testifies the great difficulty in G measurements, and there maybesome unfound systematic errors.
Based on the HUST-09G measurement in our laboratory, we develop the new work onG measurement with the time-of-swing method by using a high-Q silica fiber. The main im-provements in the experiment are:1. A silica fiber with Q-factor of5.00×10~4is used as thesuspension fiber to reduce the fiber’s anelastic effect and advance the stability of the pendulum’speriod. Due to the fiber’s high Q, the anelastic effect is reduced from-211.80(18.69) ppm inHUST-09G measurement to only-6.37(0.50) ppm. This means that the anelasticity will not bea main error source in present G measurement;2. To reduce the potential electrostatic effect, thesilica fiber is coated with8-nm-thickness of germanium and8-nm-thickness of bismuth layers inturn. After coated, the period’s stability is about0.05ms yielded from one set of3-days data ofthe pendulum;3. The background gravitational field of the environment is measured by using adipolar pendulum. After compensated with～800kg lead blocks, the influence on the period dueto the background gravitational field is reduced to1/5of that of before compensating. Besides,the equilibrium position of the pendulum in G measurement is located at the peak value of thebackground gravitational field which leads to the least contribution to G value;4. A copper tubewith5-mm-thickness is installed around the fiber to decrease the temperature discrepancy, and6sensors are installed near the fiber to monitor the temperature change. In experiment, the largestdifference between the sensors is less than0.02C, which contribute an uncertainty of <5ppmto G value;5. The magnetic damper is designed to reduce its influence on the pendulum’s pe-riod. At present, the correction from the magnetic damper is reduced from17.54(0.31) ppm toonly0.13(0.01) ppm;6. Aluminum is chosen as the coating material of the pendulum instead ofgold and copper. After improved, the correction for G value from coating layer is reduced from-24.28(4.33) ppm to-1.81(0.91) ppm.
Up to now we have finished the primary experiment, and the combined uncertainty of Gvalue is16.95ppm. After repeating the G measurement time after time, we will report the final G value with the hoped uncertainty of <20ppm.
This work is supported in part by the National Basic Research Program of China underGrant No.2010CB832801.
在我们实验室2009年测G实验（HUST-09）的基础上，通过一系列的改进措施，我们开展了新一轮基于高Q值石英丝的周期法测G实验。主要改进措施有：1、采用Q值约为5.00×10~4的石英丝取代钨丝来降低滞弹性效应和提高扭秤周期的稳定性。在HUST-09实验中，Q值约为1.7×10~3的涂钍钨丝贡献的滞弹性效应为-211.80(18.69) ppm。采用石英扭丝之后滞弹性效应降低至-6.37(0.50) ppm，这说明滞弹性不再是周期法测G中的主要系统误差来源；2、为了解决由于石英丝不导电带来的静电问题，我们在石英丝表面依次镀了厚度为8nm的锗和8nm的铋膜。目前三天扭秤数据的周期稳定性约为0.05ms，这比HUST-09实验中的周期稳定性提高了约4倍；3、对测G实验环境的背景引力场采用偶极对称扭秤进行了测量并用约800kg铅块进行了补偿。补偿之后，背景引力场对扭秤周期的影响降低了约5倍，同时扭秤的平衡位置处在背景场最平坦的地方，这使得背景场对扭秤周期的影响极大地降低。在72天的近、远程数据中，背景场贡献的效应只有0.38ppm；4、在扭丝周围安装了导热性良好的紫铜管用于均热，实验中铜管上、下端的温度差异小于0.02C，由它引起的热弹性效应贡献给G值的不确定度小于5ppm；5、优化磁阻尼单元。在保持磁阻尼单元对单摆运动模式的抑制能力前提下，将悬挂磁阻尼的钨丝直径和长度进行相应的优化之后，整个磁阻尼贡献给G值的效应从17.54(0.31)ppm减小至0.13(0.01) ppm；6、为了减小扭秤表面镀层对测G的贡献，镀层的材料选用密度更小的铝取代HUST-09中的铜和金之后，整个镀层贡献的效应从-24.28(4.33) ppm降低至-1.81(0.91) ppm。
目前我们已经完成了初步的测G实验，给出的G值相对不确定度为16.95ppm。其中两项主要的误差来源于Cg/I和ω2的测量精度，它们分别为9.56ppm和13.22ppm。为了使测量结果更加可靠，我们将进行重复的测G工作，因此目前暂不公布G值的测量结果。
本课题得到973计划课题“基于精密测量物理的引力及相关物理规律研究”的子课题：万有引力常数G的精确测量（2010CB832801）的资助。
The absolute value of G was first measured in the laboratory by Cavendish in1798, whichgave G=6.67(7)×10~11m3kg1s2with a relative uncertainty (ur) of about1%. Over the pasttwo centuries, nearly300different values of G have appeared, however, the measurement pre-cision of G value has improved only at the rate of about1order of magnitude per century. Thenewest recommended G value of CODATA2010(Committee on Data for Science and Tech-nology) is6.67384(80)×10~11m3kg1s2with ur=120ppm. The adopted G values in CO-DATA2010are in poor agreement in their claimed uncertainties, in which the largest differenceyields487ppm. This situation testifies the great difficulty in G measurements, and there maybesome unfound systematic errors.
Based on the HUST-09G measurement in our laboratory, we develop the new work onG measurement with the time-of-swing method by using a high-Q silica fiber. The main im-provements in the experiment are:1. A silica fiber with Q-factor of5.00×10~4is used as thesuspension fiber to reduce the fiber’s anelastic effect and advance the stability of the pendulum’speriod. Due to the fiber’s high Q, the anelastic effect is reduced from-211.80(18.69) ppm inHUST-09G measurement to only-6.37(0.50) ppm. This means that the anelasticity will not bea main error source in present G measurement;2. To reduce the potential electrostatic effect, thesilica fiber is coated with8-nm-thickness of germanium and8-nm-thickness of bismuth layers inturn. After coated, the period’s stability is about0.05ms yielded from one set of3-days data ofthe pendulum;3. The background gravitational field of the environment is measured by using adipolar pendulum. After compensated with～800kg lead blocks, the influence on the period dueto the background gravitational field is reduced to1/5of that of before compensating. Besides,the equilibrium position of the pendulum in G measurement is located at the peak value of thebackground gravitational field which leads to the least contribution to G value;4. A copper tubewith5-mm-thickness is installed around the fiber to decrease the temperature discrepancy, and6sensors are installed near the fiber to monitor the temperature change. In experiment, the largestdifference between the sensors is less than0.02C, which contribute an uncertainty of <5ppmto G value;5. The magnetic damper is designed to reduce its influence on the pendulum’s pe-riod. At present, the correction from the magnetic damper is reduced from17.54(0.31) ppm toonly0.13(0.01) ppm;6. Aluminum is chosen as the coating material of the pendulum instead ofgold and copper. After improved, the correction for G value from coating layer is reduced from-24.28(4.33) ppm to-1.81(0.91) ppm.
Up to now we have finished the primary experiment, and the combined uncertainty of Gvalue is16.95ppm. After repeating the G measurement time after time, we will report the final G value with the hoped uncertainty of <20ppm.
This work is supported in part by the National Basic Research Program of China underGrant No.2010CB832801.
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