Recently, the $n{}^3\mathrm{He}$ Collaboration reported a measurement of the parity-violating (PV) proton directional asymmetry $A_{\mathrm{PV}}=[1.55\pm 0.97\left(\mathrm{stat}\right)\pm 0.24\left(\mathrm{sys}\right)]\times {10}^{-8}$ in the capture reaction of ${}^3\mathrm{He}(\vec{n},p){}^3\mathrm{H}$ at meV incident neutron energies. The result increased the limited inventory of precisely measured and calculable PV observables in few-body systems required to further understand the structure of hadronic weak interaction. In this Letter, we report the experimental and theoretical investigation of a parity conserving (PC) asymmetry $A_{\mathrm{PC}}$ in the same reaction (the first ever measured PC observable at meV neutron energies). As a result of S- and P-wave mixing in the reaction, the $A_{\mathrm{PC}}$ is inversely proportional to the neutron wavelength $\lambda$. The experimental value is $(\lambda \times A_{\mathrm{PC}})\equiv \beta =[-1.97\pm 0.28\left(\mathrm{stat}\right)\pm 0.12\left(\mathrm{sys}\right)]\times {10}^{-6}\AA$. We present results for a theoretical analysis of this reaction by solving the four-body scattering problem within the hyperspherical harmonic method. We find that in the ${}^3\mathrm{He}(\vec{n},p){}^3\mathrm{H}$ reaction, $A_{\mathrm{PC}}$ depends critically on the energy and width of the close $0^{-}$ resonant state of ${}^4\mathrm{He}$, resulting in a large sensitivity to the spin-orbit components of the nucleon-nucleon force and even to the three-nucleon force. The analysis of the accurately measured $A_{\mathrm{PC}}$ and $A_{\mathrm{PV}}$ using the same few-body theoretical models gives essential information needed to interpret the PV asymmetry in the ${}^3\mathrm{He}(\vec{n},p){}^3\mathrm{H}$ reaction.

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• Charge-exchange reactions
• Nuclear forces
• Nucleon induced nuclear reactions
• Polarization phenomena
• A ≤ 5
• Few-body systems
• Hyperspherical method
• Nuclear data analysis & compilation
• Particle sources & targets