First observation of P-odd asymmetry of α -particle emission in the 10 B ( n , α ) 7 Li nuclear reaction

We present measurements of P-odd asymmetry of emission of α -particles in the 10 B ( n , α ) 7 Li nuclear reaction, which are carried out using beams of polarized cold neutrons at Petersburg Nuclear Physics Institute (PNPI, Russia) and Institut von – Langevin (ILL, nuclear reactors. The α -particle detector is an ionization chamber with insensitive gaseous layer. We measured the P-odd asymmetry coeﬃcient to be equal to α 10 B , α P - odd = − ( 11 . 2 ± 3 . 4 ) · 10 − 8 . © 2017 The Author(s). by Elsevier B.V. This is an open access article under the CC BY license Funded by SCOAP 3 .


Introduction
Experimental investigation of spatial parity in reactions of polarized neutrons with light nuclei is an important topic in the framework of exploring the fundamental problem of manifestations of weak interaction in nuclear processes as well as evaluating constants of weak nucleon-nucleon (NN) potential. To describe the contribution of weak interaction, the problem is often parameterised in terms of single (π , ρ, ω) and multiple (ππ) meson exchange with one weak and one or more strong vertices (see [1,2] for reviews). Within this parameterisation, neutral and charged weak currents are described with coupling constants f π and h 0 ρ , respectively. Several models attempt to relate these couplings to more fundamental theory. The quark model by Desplanques, Donoughe and Holstein (DDH) predicts "best values" f π = 4.6 · 10 −7 and h 0 ρ = 11.4 · 10 −7 within "allowed ranges" [3].
The soliton model of nucleon by Kaiser and Meissner (KM) [4,5] predicts lower values for these couplings. During last years, the weak NN interaction effects have been analyzed actively in the framework of the effective field theory [6][7][8]. This approach is more general and systematic compared to the one-mesonexchange model. Another theoretical approach consists of calculating parity-violating NN force in the 1/N c (N c -number of colors) expansion [9,10]. It might be of particular interest for the present * Corresponding author.
E-mail address: nesvizhevsky@ill.eu (V.V. Nesvizhevsky). study as it naturally explains the smallness of f π compared to h 0 ρ observed experimentally [11][12][13][14][15]. Anyway, one needs new precise relevant experimental data in order to verify theories. While the observation of parity violation in proton-proton scattering is a manifestation of charged weak currents in accordance with theory [16,17], no nonzero observation has yet been claimed for neutral weak current contributions in NN-interaction in nuclei. A popular system for the theoretical and experimental investigation of P-odd effects is the radiative neutron capture by protons, (n, p) → (d, γ ). As shown in ref. [2], the coefficient A γ of the P-odd asymmetry for γ emission depends on the weak neutral current alone, A γ = −0.11 f π . The "best value" of the DDH model for f π corresponds to P-odd asymmetry of the order of 5 · 10 −8 .
The model of KM predicts an even smaller value. Such a tiny observable and the fact that the cross section for neutron absorption is much smaller than that for scattering, present considerable difficulties to perform a statistically significant measurement.
Until recently, effects of parity violation in reactions with neutron absorption had been observed only in reactions with medium and heavy nuclei, where peculiar enhancement effects may occur [18]. Measurements of P-odd asymmetry coefficients for such nuclei have not provided information on constants of weak interaction in view of the complexity of calculations and corresponding uncertainties [2]. On the other hand, considerable progress has been made in the theoretical description of light nuclear systems involving up to 10 nucleons, starting from phenomenological potential models for NN interactions and including three-body forces.  In the absence of parameter-free description of light nuclear systems, we analyze in the following our data using the cluster model. In case of lightest nuclei, corresponding calculation can probably be done with sufficient accuracy and reliability.
A set of light nuclei can be described up to the excitation energy of 20-25 MeV as combination of a limited number of clusters; a neutron reaction with such a light nucleus can be considered as reaction in the field of one or a few α-particles. Then the problem can be solved in terms of constants of meson-nucleon interaction. The coefficient α P -odd of P-odd asymmetry in triton (t) emission in the 6 Li(n, α) 3 H reaction is calculated in ref. [19] in terms of weak interaction constants; it is equal to α where f π and h 0 ρ are weak interaction constants corresponding to the exchange of π -meson and ρ-meson respectively. This coefficient was evaluated using "best values" of constants in the DDH quark model: f π = 4.6 · 10 −7 and h 0 ρ = 11.4 · 10 −7 [3]. The measured coefficient is α 3 H P -odd ( 6 Li, exp.) = −(8.8 ± 2.1) · 10 −8 [12]. This result constrained the neutral constant f π within the cluster nuclear model as 0 ≤ f π ≤ 1.1 · 10 −7 at the 90% confidence level; this value is smaller than the "best value" in the DDH model. Calculation [20] of P-odd asymmetry coefficient in P-odd emission of γ -quantum in the reaction 10 B(n, α) 7 Li * → γ → 7 Li(g.s.) (E γ = 0.478 MeV) provided the following expression: α γ P -odd ( 10 B) ≈ 0.16 f π − 0.028h 0 ρ = 1.1 · 10 −7 ; this value corresponds to "best values" of f π and h 0 ρ constants. Measured value of this P-odd asymmetry coefficient equals α γ P -odd ( 10 B, exp.) = (0.0 ± 2.6 stat ± 1.1 syst ) · 10 −8 [21]. Performed experiments would not contradict to calculations if the value of neutral current constant is smaller than the theoretical "best value" and close to zero. That is why a measurement of P-odd asymmetry in the emission of α-particle in the reaction 10 B(n, α) 7 Li, with the predicted effect as high as 10 −7 -10 −6 in the α-transition E = 1.78 MeV [22] is of interest. Observation of a non-zero effect in another nuclear reaction accompanied with theoretical calculations would allow one better evaluating neutral and charged current constants.

Reaction 10 B(n, α) 7 Li
Energy released in this reaction equals 2.79 MeV; it is distributed over reaction products as follows: E α 0 = 1.78 MeV, E Li 0 = 1.01 MeV for 7 Li in the ground state, and E α 1 = 1.47 MeV, E Li * = 0.84 MeV for the exited state of 7 Li; the excitation energy is In view of complexity of 10 B nucleus, theoretical calculations in terms of meson constants have not been performed; nevertheless, an observation of non-zero P-odd effect in this reaction (see Fig. 1 for the reaction scheme) is of interest.
In accordance with the model of S-P interference [23], S-and P-resonances with equal total momentum have to be mixed in order to provide P-odd asymmetry. Here, a single pair of resonances is present in the input channel: P-resonance (E P = 0.53 MeV, Fig. 2. A sketch of the ionisation chamber in the neutron beam: 1 -ionisation chamber; 2 -6 LiF beam-stop for absorption of neutrons at the chamber exit; 3 -solenoid for guiding the magnetic field; 4 -grids and 10 B targets; 5 -base plate of the ionisation chamber. [24]. The width of S-resonance α-decay with the energy E = 1.47 MeV equals zero; thus, P-odd asymmetry for this α-transition associated with the input channel is absent. A P-odd effect can be associated only with α 0 -transition with the energy E = 1.78 MeV (for the given method of introduction of weak interaction). A Podd effect in the exit reaction channel was evaluated in ref. [25]; it is an order of magnitude smaller than its expectation for the E = 1.78 MeV α-transition in the input channel. Besides, if P-odd asymmetry exists in α 1 -transition, a P-odd effect should exist also in E γ = 0.478 MeV γ -transition from first excited to ground state in 7 Li. Performed experiments [21] constrained the coefficient of P-odd asymmetry α γ P -odd 10 B < 4.3 · 10 −8 of γ -quanta emission at the 90% confidence level. Thus P-odd effect in α 1 -transition in the exit channel is absent in first approximation, and one could consider experiments with mixture of α-transitions, where α 1 is a background transition not contributing to the effect.
In first measurements of P-odd asymmetry, rather significant false effects were observed in nearly all neutron reactions with light nuclei accompanied with emission of charged particles. In later dedicated experiments with the neutron spin − → σ n set perpendicular to the charged particle momentum − → p p and to the neutron momentum − → p n , it was attributed to left-right asymmetry of a type The coefficient of left-right asymmetry for the E = 1.78 MeV transition in the reaction 10 B (n, α) 7 Li was measured to be equal to α lr (α 0 ) = (0.77 ± 0.06) · 10 −4 . The coefficient of left-right asymmetry for α 1 transition was estimated as α lr (α 1 ) = − (0.28 ± 0.14) · 10 −5 [26]. As left-right asymmetry has to accompany P-odd asymmetry, the later estimation also indicates that P-odd asymmetry is expected to be present only in α 0 transition. In order to provide that left-right asymmetry does not contribute to measured P-odd asymmetry, one should set vectors − → σ n , If the later condition is met with the accuracy of d ∼ 5 · 10 −3 , a contribution of left-right asymmetry into P-odd asymmetry does not exceed ∼ 3 · 10 −9 , as it is of the order of d 2 ; this condition can be easily provided experimentally. The experimental geometry and the experimental setup were the same as in ref. [12] studying the reaction 6 Li (n, α) 3 H (see Fig. 2).

Ionization chamber
Due to large partial ionization losses, passes of α-particles are small, 0.7-0.8 mg/cm 2 , thus solid film absorbers cannot be used for absorbing the heavy component and defining certain mean cosine of α-particle emission. Instead, insensitive layer is provided with gas layer (argon ( Ar) at the pressure of 0.3 bar) with the thickness of 9 mm; Li ions and α-particles emitted to certain angles are absorbed in this layer. Operation of the ionization chamber is simulated using Monte-Carlo method for these parameters and for the actual detector geometry; the target thickness is assumed to be distributed non-uniformly in accordance with the normal statistical law; the mean target thickness is 180 μg/cm 2 . The mean cosine of α (α 0 )-particle emission angle is calculated to be equal to cos − → σ n , − → p p = 0.77. Calculated contributions of the reaction products (energies taken into account) into the current measured in the detector are equal: To shape the neutron beam, we installed three collimators made of 6 Li F ceramics inserted in Al foil envelopes inside the chamber along its total length. The beam is smaller than the target size at both the entrance to and the exit from the chamber. The deviation of the neutron beam along the vertical axis is smaller than 5 mm. The chamber is installed on concrete blocks so that the horizontal misalignment between the neutron beam and the chamber axis is smaller than 5 mm/m. A solenoid wired around the ionization chamber produced the longitudinal magnetic field, which guided the neutron spin. The direction of magnetic field in the chamber is aligned along the chamber axis with the accuracy better than 1 • . For this geometry, a contribution of left-right asymmetry into P-odd effect is suppressed by 4-5 orders of magnitude compared to its maximum value.
24 double targets and detection chambers are installed inside the ionization chamber along the longitudinally polarized neutron beam. Targets are produced using sedimentation of amorphous B suspended in acetone to Al foils with the thickness of 20 μm. Each double chamber is equipped with two targets folded back to back so that each B-coated side looks to its own chamber. Target substrates totally absorb reaction products. One half of a double chamber detects α-particles emitted along the neutron momentum ("forward"), another half detects α-particles emitted against the neutron momentum ("backward"). Due to the correlation − → σ n , − → p p , P-odd effects in "forward" and "backward" particle emission are of opposite signs. Signal electrodes of chambers are connected to two common electronic lines: "forward" for chambers detecting α-particles emitted along the neutron momentum and "backward" for chambers detecting α-particles emitted in the opposite direction. Signals of all detector chambers "forward" ("backward") are sent to respective preamplifiers (PA), which transform ionization chamber current into voltage proportional to α-particle current.
The voltage at the PA exit is recorded in PC using programmable analog-digit converter.
PA divides signals into variable and constant parts. Variable part is amplified and then recorded. The amplification coefficient is calibrated sending a rectangular-step signal of known amplitude to the PA entrance.

Measuring procedure
To achieve maximum accuracy, we used the scheme of two detectors ("forward" and "backward") and special procedure of measurements. The principle of the scheme is based on the fact that both detector channels measure simultaneously the same process, however the signs of real effects are opposite while the effect of synchronous fluctuations is the same.
Studies effects α of P-odd asymmetry in nuclear reactions with polarized neutrons are defined as: where N + and N − are detector counts corresponding to the emitted particle momentum parallel and antiparallel to the neutron spin, respectively. For the integral measuring method applied, "number of events" per time interval is equivalent to the sum of variable U and constant U C parts of the signal integrated over this interval and thus the asymmetry coefficient α P -odd is written as follows: Here U + C , U − C , U + , U − are respectively constant and variable parts of the signal for different neutron spins relative to the detected particle momentum. Coefficient "K " is introduced as the variable part amplified in PA by a factor of K . As U C >> U and U + C ∼ = U − C = U C , thus normalized asymmetry coefficient equals: Time diagram of measurements is shown in Fig. 3. For each detector channel, tetrads U + 1 , U − 2 , U − 3 , U + 4 of variable parts of signals from PA averaged over period T are combined in single measurements and calculated as follows: Signs "+" and "−" correspond to different neutron spin directions. This combination allows eliminating linear drifts in amplifies. The asymmetry is calculated for single measurement for each detector. N consequent single measurements in both channels are combined in one series; constant signal part is measured ones in each interval T ; mean, over the series, values of constant signals are used in the normalized asymmetry coefficient. Results are treated after the series.
Synchronous fluctuations of reactor power in measured signals are compensated due to subtraction of asymmetry coefficients for single measurements in two detectors (measuring effects of opposite sign) and summation of these differences at the end of series. Thus, the effect is doubled while reactor power fluctuations are subtracted.
The procedure of data treatment and relevant formulas are described in detail in ref. [12]. To avoid false asymmetries, the direction of magnetic field in the chamber (guiding the neutron spin) is reversed after each series; the numbers of series with opposite directions of the guiding field are equal. Averaging procedure takes into account that reversion of magnetic field changes the sign of P-odd effect to the opposite one.
Thus, combined treatment of data for two detectors and two magnetic field directions eliminates parasitic effects as repeatedly verified in experiments [22,27,11].
Earth's magnetic field and external stationary magnetic fields from surrounding are not compensated for; they can increase the contribution of left-right asymmetry into P-odd asymmetry. The sign of corresponding left-right asymmetry does not change when the guiding magnetic field reverses [27]; subtraction of results for opposite directions of guiding field eliminates the contribution of this effect.
This experiment was carried out at the vertical polarized neutron beam at the PNPI reactor (Gatchina, Russia). The integral neutron intensity was ∼ (1-3) · 10 10 s −1 ; the mean neutron polarization was P = 0.8.
Second experiment is carried out at the horizontal polarized neutron beam of PF1B [28] facility at the ILL (Grenoble, France).
The mean neutron wavelength is λ = 4.7 Å; the integral flux of polarized neutrons is 4-5 · 10 10 s −1 ; the neutron polarization is P = 92 ± 2%. Neutron polarization is flipped using an adiabatic spin-flipper with the efficiency close to 100%.
The two results provide the value of P-odd asymmetry coefficient of α-particle emission in the reaction 10 B (n, α) 7 Li equal to α α 0 +α 1 P -odd ( 10 B, exp.) = −(11.2 ± 3.4) · 10 −8 . Fig. 4 shows experimental results; explanations in the caption. Table 1 lists possible systematic effects and the estimation of their potential contribution.

Control experiments
Ref. [12] presents detailed analysis of possible background Podd effects in different reactions of neutrons with the construction materials of the experimental setup. As reliable calculation of these effects is complicated, we had to verify experimentally the contribution of possible false asymmetry caused by neutron reactions with other-then-B nuclei. Thus, we measured P-odd asymmetry with all targets covered with foils completely absorbing reaction products. We performed this experiment in the studies of P-odd asymmetry of t emission in the reaction 6 Li(n, α) 3 H [12]. The Table 1 Possible systematic effects. chamber and all surrounding of the chamber in the two experiments are equivalent. Taking into account earlier analogous measurements at PNPI [22], the result is This value can be used also for experiments with B, as the detector of charged particles, the ionization chamber, is the same. Note that the initial beam is shaped precisely enough to provide that any effects of the beam tails are negligible to the scattering of neutrons on the targets.
Thus, it is at least 10 times lower. A contribution of L-R asymmetry to the P-odd asymmetry is below 0.3 · 10 −8 for the measured reaction in the geometry used for this experiment [27]. The L-R contribution associated with the magnetic field of the Earth and experimental installations around is the same in each detector, provided the "parasitic" field does not change; it cancels when measured for two directions of the guiding magnetic field. We did not observe any influence of the guiding magnetic field (∼5 Oe) to the ionization chambers [27]. Anyway, such a false effect associated with the interference of the detector current with the guiding magnetic field would be equivalent to the effect of electromagnetic noise.
The procedure of compensation of synchronous fluctuations of the signals in the two detectors reduced the effect of fluctuations of the neutron flux, as illustrated in Fig. 5.
Thus, we can state that the effect of P-odd asymmetry in the presented experiment is associated with the reaction 10 B(n, α) 7 Li.

Conclusion
The precision of measurement of P-odd asymmetry in the emission of α-particles in the reaction 10  is obtained for the first time. 10 B is the second light nucleus, after 6 Li, where P-odd effect has been observed.
P-odd effect in the reaction 10 B(n, α) 7 Li can be theoretically calculated within the cluster model; it would be of high importance to describe the considered reaction also from "first principles".