Atomic parity nonconservation and neutron radii in cesium isotopes

Abstract

The interpretation of future precise experiments on atomic parity violation in terms of parameters of the Standard Model could be hampered by uncertainties in the atomic and nuclear structure. While the former can be overcome by measurement in a series of isotopes, the nuclear structure requires knowledge of the neutron density.We use the nuclear Hartree-Fock method, which includes deformation effects, to calculate the proton and neutron densities in 125 Cs -139 Cs. We argue that the good agreement with the experimental charge radii, binding energies, and ground state spins signifies that the phenomenological nuclear force and the method of calculation that we use is adequate. Based on this agreement, and on calculations involving different effective interactions, we estimate the uncertainties in the differences of the neutron radii δ r 2 N,N ′ and conclude that they cause uncertainties in the ratio of weak charges, the quantities determined in the atomic parity nonconservation experiments, of less than 10 −3 . Such an uncertainty is smaller than the anticipated experimental error.

Neutron skin thickness ofZr90determined by charge exchange reactions

“…It is also known that the neutron skin thickness is strongly correlated with the nuclear symmetry energy [7,9]. Reliable neutron distributions are also needed for analyses of atomic parity violation experiments [10,11] and of pionic states in nuclei [12].Several attempts have been made to determine neutron distributions [2,13,14,15,16]. Ray et al analyzed proton elastic scattering on several nuclei at 800 MeV using impulse approximation and obtained a neutron thickness of 0.09 ± 0.07 fm for An alternative method for determining the neutron rms radius is provided by the model-independent sum rule strength of charge exchange spin-dipole (SD) excitations [19].…”

“…It is also known that the neutron skin thickness is strongly correlated with the nuclear symmetry energy [7,9]. Reliable neutron distributions are also needed for analyses of atomic parity violation experiments [10,11] and of pionic states in nuclei [12].…”

Neutron density distributions for atomic parity nonconservation experiments

“…11. We notice that while the isotope trend is similar, the actual values of r n /r p calculated with the RHB NL3+D1S model are considerably larger than those obtained in the Hartre-Fock Skyrme calculations for Pb [8] and Cs [2,9]. In particular, for 133 Cs we calculate r n /r p = 1.046, as compared to the HartreFock values: 1.022 for SkM * , and 1.016 for SkIII.…”

Electrons, new physics, and the future of parity-violation

“…To set the scale of the level of accuracy nuclear theory must achieve to make the isotope ratio measurements useful, supposed we require the uncertainty in the neutron radius term to be as small as the prospective experimental uncertainty in the value of R, namely, 0.1 %. Pollock [25] and Chen and Vogel [26,27] have analyzed the nuclear model spread in ∆X N ; from their analyses, we learn that nuclear theory is at least a factor of two away from achieivng the requisite precision (for a summary of the theoretical situation, see Ref. [13]).…”