New determination of the neutron-proton scattering amplitude and precise measurements of the scattering amplitudes on carbon, chlorine, fluorine and bromine

Abstract

Abstract. After an improvement on the theory of the neutron-gravity-refractometer and after refinements of the experimental procedure we have performed new measurements of the absolute value of the neutron-proton scattering amplitude at low neutron energies. In order to obtain and to confirm a very high accuracy we carried out neutron-reflection experiments on 18 various liquids of 11 different organic substances containing the elements carbon, hydrogen and/or chlorine. Compounds with fluorine and bromine were used to measure the scattering amplitudes of these elements. We found the coherent scattering amplitudes of the bound atoms to be: a, = -3.7409 (11)fm, ac=6.6484(13)fm, acl=9.5792(8)fm, av= 5.66(2)fm and a~r=6.79(2)fm. The low energy (n, p)-parameters a t and a~ were calculated with the present a H and a new value of the (n, p) scattering cross-section cr 0. By comparing the measured a c with values obtained from precise transmission experiments we could determine the gravitational acceleration gj of the free neutron in terms of the local value g. We found the two values to be equal: gf =0.9996(7)g.

Determination of low-energy parameters of neutron-proton scattering on the basis of modern experimental data from partial-wave analyses

“…It should be emphasized, however, that this agreement is not accidental; it is directly related to the fact that, in the partial-wave analysis of the Nijmegen group, the cross-section values obtained by Houk [12] and Dilg [13] and the coherent-scattering-length value obtained by Koester and Nistler [22] were used as input experimental parameters. It is precisely the reason why all of the experimental lowenergy parameters in (17), with the exception of the singlet effective range, agree within the experimental error with the corresponding parameters in (19), which were calculated on the basis of the Nijmegen phase shifts.…”

“…Using expressions (18) and (19) for the scattering lengths and relying on formulas (2) and [22]. It should be emphasized, however, that this agreement is not accidental; it is directly related to the fact that, in the partial-wave analysis of the Nijmegen group, the cross-section values obtained by Houk [12] and Dilg [13] and the coherent-scattering-length value obtained by Koester and Nistler [22] were used as input experimental parameters.…”

“…The coherent scattering length f , which is determined by relation (3), is found either from experiments where slow neutrons are scattered by pure para-hydrogen [8,14,15] or by crystals [16] or -and this is a more precise method -from experiments where neutrons are reflected by a liquid mirror and where use is made of a number of pure hydrocarbons [9,10,[17][18][19][20][21][22]. Also, a method for determining the coherent scattering length by means of neutron interferometry from experiments to study neutron scattering on molecular hydrogen was proposed in [23].…”

“…Table 3 presents values obtained in a number of previous studies [9,10,13,18,21,22,[24][25][26][27][28] for the scattering lengths and effective ranges in the triplet and singlet spin states. All of them have been used as experimental values.…”

Effective field theory of3He

“…(15), (16), and (17). The two-body input is provided by γ = 45.703 MeV , a np = −23.749 ± 0.008 fm [14] , a nn = −18.5 ± 0.4 fm [15] . (23) We adjust the three-body force to fit the triton binding energy,…”