Theoretical Study On Hyperfine Splittings And Isotope Shifts Of Light Helium-like Ions

Helium and helium-like ions have always been the focus of precision measurement physics.The high-precision theoretical calculation of its energy level plays an important role in the determination of basic physical constants,testing of quantum electrodynam-ics and exploration of nuclear physics.As the precision of experimental measurement increasing,more and more nuclear effects have been revealed,the study of precision spectroscopy has become an important platform to detect the nuclear structure.For ex-ample,Combining experimental and theoretical study of hyperfine splittings and isotope shifts,we can extract the nuclear electromagnetic radius(Zemach radius)and nuclear quadrupole moment,as well as the difference of the square of the nuclear charge radius.These parameters are the external manifestations of the internal structure and motion of the nucleus,thus their high-precision determinations are of great significance in test-ing the nuclear structure model and exploring the accurate nuclear force theory.This thesis focuses on the hyperfine splittings and isotope shifts of helium and helium-like ions.The corrections of hyperfine splittings and isotope shifts of three body system up to the order of m?6 are studied systematically in the frame of NRQED theory.The main contents are as follows:(1)The hyperfine structures of the 23S1 states of the 6Li+and 7Li+ ions are inves-tigated theoretically to extract the Zemach radii of the 6Li and 7Li nuclei by comparing with precision measurements.The obtained Zemach radii are larger than the previous values of Puchalski and Pachucki and disagree with them by about 1.5 and 2.2 standard deviations for 6Li and 7Li,respectively.Furthermore,our Zemach radius of 6Li differs significantly from the nuclear physics value,derived from the nuclear charge and mag-netic radii,by more than 6 sigma,indicating an anomalous nuclear structure for 6Li.This anomalous phenomena of 6Li nucleus can not be explained by the current theory.The obtained Zemach radii are used to calculate the hyperfine splittings of the 23PJ states of 6,7Li+,where an order of magnitude improvement over the previous theory has been achieved for 7Li+.This work will further promote the study of Li+ and Li precision spectroscopy,and provide a theoretical basis for high precision experimental measurement of Li+ions in the future.(2)The isotope shifts of 2 1S0-23S1 and 23S1-23PJ transitions for 6Li+and 7Li+are calculated with the standard perturbation theory.An order of magnitude im-provement over the previous theory has been achieved for mass shifts.The results can be used for determining the nuclear charge radius difference of 6Li and 7Li in the future.Through the calculation of isotope shifts 2 3PJ in fine structure splittings,we analyze the reason for the disagreement between experiment and theory.Combining with the exper-imental measurements of the isotope shifts of the 23S1-23PJ transitions,we obtain the difference of the square of the nuclear charge radius between 6Li and 7Li as 0.768(65)fm2.Comparing with the value of Drake et al.,this result is updated obviously.It is expected improve the determination of 6Li-7Li nuclear charge radii difference with high accuracy,once the measurement accuracy of the experiment is improved by one order of magnitude,which will supply more information on the Li nuclear.(3)We extend our calculations to helium-like Be2+,the hyperfine structures of the 2 3S1 and 2 3PJ states of the 7Be2+and 9Be2+ions are investigated.The uncertainties of our hyperfine splitting results of 9Be2+ are in the order of tens of ppm,where two orders of magnitude improvement over the previous theory and experiment has been achieved.In addition,the results of 7Be2+ without the contribution of nuclear electric quadrupole moment are presented,where the uncertainties are less than 100ppm.A scheme for determining the properties of Be nuclei based on precise spectra is proposed,which opens a new window for the study of Be nuclei.Once the experimental measurements reach the same accuracy,the Zemach radius of 9Be can be determined with the predicted uncertainty being under 3%.The nuclear electric quadrupole moment of 7Be can be then derived as well.