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The nuclear magnetic moment of the ground state of 57 Cu(I π = 3/2 − , T 1/2 = 196.3 ms) has been measured to be |µ( 57 Cu)| = (2.00 ± 0.05)µN using the β-NMR technique. Together with the known magnetic moment of the mirror partner 57 Ni, the spin expectation value was extracted as Σσz = −0.78 ± 0.13. This is the heaviest isospin T = 1/2 mirror pair above the 40 Ca region for which both ground state magnetic moments have been determined. Discrepancy between present results and shell model calculations in full f p shell giving µ( 57 Cu) ∼ 2.4µN and Σσz ∼ 0.5 implies significant shell breaking at 56 Ni with the neutron number N = 28. The magnetic moment is one of the important fundamental properties of the nucleus and provides key information to understand nuclear structure, especially ideas built on core polarization and the meson exchange effects in the shell model. While the magnetic moments near the stability line in the nuclear chart are well known, we have only limited information on the magnetic moments far from the stability line. Some of the challenges facing ground state nuclear moment measurements include the small spin polarization and low cross sections encountered in the production mechanism for nuclei far removed from the stability line. It is important, however, to go far from the stability line in order to test predictive powers of theoretical models and to find possible variations of nuclear structure from the stability line.In this Letter, we report the first measurement of the magnetic moment of 57 Cu. Since 57 Cu has one proton outside of the 56 Ni core and the magnetic moment of T = 1/2 mirror partner 57 Ni is known, the current result completes the mirror pair and contributes important information for this shell region. The difficulties in the small polarization and low cross section were overcome by using a proton pick up reaction of an intermediate-energy primary beam. The small value for the 57 Cu magnetic moment, discussed later in this paper, implies possible shell breaking at the neutron number N = 28.The magnetic moment can be expressed as the sum of isoscalar Σµ 0 and isovector Σµ z components aswhere l and σ are the orbital and spin angularmomentum operators of the nucleon, respectively, τ is the isospin operator, µ p and µ n are the magnetic moments of free proton and neutron, respectively, and the sum is over all nucleons. The isovector Σµ z part is proportional to the isospin, T z , and changes its sign for T = ±T z . Provided that isospin is a good quantum number, the spin expectation value Σσ z , which is a contribution from nucleon spins to the magnetic moment, can be extracted [1] from the sum of mirror pair magnetic moments aswhere the total spin is I = Σl z + Σσ z /2. In the sd shell, all of the ground state magnetic moments of T = 1/2 mirror nuclei have been measured and there remain several T = 1 and 3/2 isospin multiplets to be measured. There exists, however, virtually no information regarding similar T = 1/2 pairs in the f p shell. A systematic trend of the spin expect...

Background: The systematic trend in mean-square charge radii as a function of proton or neutron number exhibits a discontinuity at the nucleon-shell closures. While the established N = 28 shell closure is evident in the 10 charge radii of the isotopic chains of K through Mn, a similar signature of the N = 20 shell-closure is absent in the Ca region.Purpose: The isotope shift between neutron-deficient 36 K and 37 K was determined to investigate the change of the mean-square charge radii across N = 20 in the K isotopic chain.Methods: The D1 atomic hyperfine spectra of 36 K and 37 K were measured using an optical pumping and 15 subsequent β-decay asymmetry detection technique. Atomic rate equations were solved to fit the resonant line shape. The result was compared to Skyrme energy-density functional and shell-model calculations.Results: The isotope shift was obtained as δν 37,36 = −139(4)(3) MHz. Using a re-evaluated isotope shift, δν 39,37 = −264(2)(3) MHz, the isotope shift relative to 39 K was determined to be δν 39,36 = −403(5)(4) MHz. The differential mean-square charge radius was then deduced as δ r 2 39,36 = −0.16 (5)(8) Conclusions:The absence of the shell-closure signature at N = 20 in the K isotopic chain is understood as a balance between the monopole and the quadrupole proton-core polarizations below and above N = 20, respectively.