Nuclear magnetic moment is highly sensitive to the underlying structure of atomic nuclei and therefore serves as a stringent test of nuclear models. The advanced nuclear structure models have been successful in analyzing many nuclear structure properties, but they still cannot provide a satisfactory description of nuclear magnetic moments. Recently attempts to summarize the present understanding on nuclear magnetic moments in both relativistic and non-relativistic theoretical models have been made. The detailed contents are covered in the issue entitled "Nuclear magnetic moments and related topics" (in Sci China Phys Mech Astron, Vol. 54, No. 2, 2011). In this paper some of the related achievements will be highlighted. nuclear magnetic moments, status and progress, relativistic and non-relativistic many-body models Citation: Zhao E G. Recent progress in theoretical studies of nuclear magnetic moments. Chin Sci Bull, 2012Bull, , 57: 4394-4399, doi: 10.1007 Nuclear magnetic moment is an important physical observable that reflects the interplay between collective and singleparticle degrees of freedom in atomic nuclei. It therefore provides a stringent test of various nuclear structure models. A concise but interesting history and present understanding of nuclear magnetic moments have been provided in [1].Since the successes of the nuclear shell model established in 1949 by Mayer and Jensen for the explanation of the magic numbers (Z or N = 2, 8, 20, 28, 50, 82, . . . ), the understanding of the magnetic moment of an odd-A nucleus has been done in the extreme single-particle picture which leads to the well known Schmidt values [2]. It was observed in the early 1950s [3], however, that almost all nuclear magnetic moments are sandwiched between the two Schmidt lines.The pion, predicted by Yukawa in 1935, and discovered experimentally by Powell in 1947, was pointed out to be very important for understanding nuclear magnetic moments by Miyazawa in 1951 [4] and by Villars in 1952 [5] via the one-pion exchange currents, which can be understood as a medium correction in comparison with the free nuclear magnetic moments. Besides the pion effect, the first-order configuration mixing was pointed out to be also important in the email: egzhao@mail.itp.ac.cn odd-A nuclei with a j j-closed core by Arima and Horie in 1954 [6,7]. This effect is also called the first-order core polarization or Arima-Horie effect. However, for the nuclei with a LS -closed core ± 1 nucleon, the first-order configuration mixing does not contribute to nuclear magnetic moments. In order to understand the difference between Schmidt values and experiment data in this type of nuclei, it was realized that one has to take into account the second-order configuration mixing, which is also called the tensor correlation. The isoscalar magnetic moments provide us the best evidence of the tensor correlations. There were also lots of discussion on whether the Δ-hole mixing can explain the magnetic moments [8][9][10].In the past decades, covariant density functio...
