Limits on Anomalous Spin-Spin Couplings between Neutrons

We report experimental limits on new spin-dependent macroscopic forces between neutrons. We measured the nuclear Zeeman frequencies of a ${}^3\mathrm{He}/{}^{129}\mathrm{Xe}$ maser while modulating the nuclear spin polarization of a nearby ${}^3\mathrm{He}$ ensemble in a separate glass cell. We place limits on the coupling strength of neutron spin-spin interactions mediated by light pseudoscalar particles like the axion [$g_p{g}_p/(4\pi \hslash c)$] at the $3\times {10}^{-7}$ level for interaction ranges longer than about 40 cm. This limit is about ${10}^{-5}$ the size of the magnetic dipole-dipole interaction between neutrons.

Figure 1

Experimental schematic showing the ${}^3\mathrm{He}$ spin source on top and the ${}^3\mathrm{He}/{}^{129}\mathrm{Xe}$ maser on the bottom (not to scale).

Figure 2

Noise spectrum of the ${}^3\mathrm{He}$ Zeeman maser frequency averaged from three weeks of data. The modulation period of the spin orientation of the spin source was chosen to lie in the white frequency noise dominated part of the spectrum to avoid phase noise at high frequencies and drift at low frequencies.

Figure 3

Distribution of frequency modulation amplitudes from the fit of the ${}^3\mathrm{He}$ Zeeman maser frequency to the modulated spin orientation of the spin source. The amplitudes have a Gaussian distribution that agrees well with the noise spectrum shown in Fig. 2.

Figure 4

$1\sigma$ excluded region from the present experiment for the dimensionless coupling constant $g_p^n{g}_p^n/(4\pi \hslash c)$ as a function of interaction range for a neutron-neutron spin interaction mediated by the axion or an axionlike pseudoscalar particle [see Eq. (1)].

Figure 5

Calculation of amplitude $A(\alpha ,\gamma ,{\theta }_v)$ for $\gamma =0$ for the Goldstone boson mediated potential between two parallel spins [see Eq. (2)]. The dashed line is the parabolic approximation for the boundary between the shadow and shock wave regions.

Figure 6

$1\sigma$ excluded region from the present experiment for neutron-neutron spin coupling as described by Eq. (2) (see text).