Search for long-range force between a neutron and an atom with a trap of ultracold neutrons

A method of using a gravitational ultracold neutron (UCN) spectrometer for the search for long-range forces between neutrons and atoms is proposed. The constraints on the strength of long-range forces within the range of 10${}^{-10}$--10${}^{-4}$ cm can be obtained from experiments on measurements of the total cross section of the interaction of UCN with atoms of noble gases (He, Ne, Ar, Kr) and data on the coherent neutron-scattering length of the nucleus. The first result of such an analysis is presented. Further prospects for the UCN method are discussed.

Figure 1

The experiment setup: 1, entrance foil with critical energy $E_{\mathrm{UCN}}^{\mathrm{foil}}$ = $m_{n}gh$; 2, the entrance valve; 3, UCN trap with the critical energy $E_{\mathrm{UCN}}^{\mathrm{trap}}$; 4, the absorber for formation of UCN spectrum; 5, the exit valve; 6, exit foil with critical energy $E_{\mathrm{UCN}}^{\mathrm{foil}}$ = $m_{n}gh$; 7, the UCN detector.

Figure 2

Dependence of the differential cross section on recoil energy ${\varepsilon }_R$ transferred to a neutron for various values of parameter l. (a) The case of a repulsive potential and (b) the case of an attractive potential.

Figure 3

Dependence of an expected experimental effect ${\Delta }_1^{P\tau \mathrm{nucl}}$ on parameters $g^2$ and $\lambda$ for He. (a) The case of a repulsive potential, i.e., an exchange by a vector boson. (b) Correlation between parameters $g^2$ and $\lambda$ for a repulsive potential if the effect ${\Delta }_1^{P\tau \mathrm{nucl}}$ is equal to 0.3, 0.03, and 0.003. (c) The case of an attractive potential, i.e., an exchange by a scalar boson. (d) Correlation between parameters $g^2$ and $\lambda$ for an attractive potential if the effect ${\Delta }_1^{P\tau \mathrm{nucl}}$ is equal to $\pm$0.3, $\pm$0.03, and $\pm$0.003.

Figure 4

The dark shaded area corresponds to constraints for $g^2$and $\lambda$ from our preliminary measurements of the $P\tau$ value for He [$P\tau =(427\pm 4)\mathrm{mbr}\mathrm{s}$] and the nuclear scattering cross section ${\sigma }_{\mathrm{free}\text{−}\mathrm{nucl}}^{\mathrm{He}}$ (0.76$\pm$0.01$\times$10${}^{-24}$ cm${}^2$) measured by the neutron transmission [26, 27, 28]. The light shaded area corresponds to constraints for $g^2$and $\lambda$ from Refs. [9, 10]. The upper inclined area ${\Delta }_{2,\mathrm{He}}^{P\tau \mathrm{int}}$ corresponds to values of $g^2$and $\lambda$ from a comparison of the $P\tau$ method for He [$P\tau =(427\pm 4)\mathrm{mbr}\mathrm{s}$] and the interferometer method [29] for He. The other inclined areas ${\Delta }_{\mathrm{He}}^{\mathrm{int}\text{−}\mathrm{nucl}}$, ${\Delta }_{\mathrm{Ar}}^{\mathrm{int}\text{−}\mathrm{nucl}}$, and ${\Delta }_{\mathrm{Kr}}^{\mathrm{int}\text{−}\mathrm{nucl}}$correspond to values of $g^2$ and $\lambda$ from a comparison of the scattering cross sections measured by the transmission method [26] and by mean interferometer [29] for He, Ar, and Kr. For all cases ${\Delta }_{2,\mathrm{He}}^{P\tau \mathrm{int}}$, ${\Delta }_{\mathrm{He}}^{\mathrm{int}\text{−}\mathrm{nucl}}$, ${\Delta }_{\mathrm{Ar}}^{\mathrm{int}\text{−}\mathrm{nucl}}$, and ${\Delta }_{\mathrm{Kr}}^{\mathrm{int}\text{−}\mathrm{nucl}}$ the solution exists only for repulsive potential.

Figure 5

Dependence of ${\Delta }_3^{\mathrm{low}\text{−}\mathrm{energ}\text{−}\mathrm{nucl}}$on $g^2$and $\lambda$: (a) for $\varphi >0$ and (b) for $\varphi <0$.

Figure 6

The comparison of the constrains (95% C.L.) from the $\left(P\tau \right)$ method and the method of above-barrier neutrons for two cases of analysis: with $b_{}^{}=b_{\mathrm{free}\text{−}\mathrm{nucl}}^{}$ and with $b=b_{\mathrm{free}\text{−}\mathrm{int}}^{}$ for the case of ${}^{86}\mathrm{Kr}$. (a) $\varphi >0$, ${\Delta }_1^{P\tau \mathrm{nucl}}$ = 0.03, ${\Delta }_3^{\mathrm{low}\text{−}\mathrm{energ}\text{−}\mathrm{nucl}}$ = 0.03; (b) $\varphi <0$, ${\Delta }_1^{P\tau \mathrm{nucl}}$ = 0.03 or −0.03, ${\Delta }_3^{\mathrm{low}\text{−}\mathrm{energ}\text{−}\mathrm{nucl}}$ = 0.03 or −0.03; (c) $\varphi >0$, ${\Delta }_2^{P\tau \mathrm{int}}$ = 0.03 or −0.03, ${\Delta }_4^{\mathrm{low}\text{−}\mathrm{energ}\text{−}\mathrm{int}}$ = 0.03 or −0.03; (d) $\varphi <0$, ${\Delta }_2^{P\tau \mathrm{int}}$ = 0.03, ${\Delta }_4^{\mathrm{low}\text{−}\mathrm{energ}\text{−}\mathrm{int}}$ = 0.03. The shaded area shows excluded values of $g^2$and $\lambda$ from Refs. [9, 10].