Measurement of the γ-anisotropy in n+pd+γ

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Abstract

The study of the radiative neutron capture by protons, n+p→d+γ, provides valuable information about the nucleon–nucleon interaction. So far, no experimental value has existed for the γ-anisotropy which may appear if neutrons and protons both are polarised. A non-vanishing γ-anisotropy η is a clear-cut signal for the existence of transitions 3S13d1 from the triplet initial state to the ground state of the deuteron. We report the first measurement of this observable. The result is η=(1.0±2.5)×10−4 at 50.5% polarisation of neutrons and protons.

Introduction

The radiative capture of neutrons by protons, n+p→d+γ (2.2246 MeV), can be considered as a prototype process of nuclear physics. It reveals information about the interaction between two nucleons which can be interpreted without having to take into account effects due to a complicated nuclear structure. Owing to its absence of a level scheme, the deuteron is too simple an object to play a similar role in strong interaction physics as the hydrogen atom does in studies of the electromagnetic interaction. However, valuable information is contained in the single electromagnetic transition from the ionised state of the two nucleons to the ground state of the deuteron. Not all experimentally accessible observables in this process were subjected to measurement yet. Owing to the low center-of-mass energy, the process takes place in a s-wave either in a singlet, 1S0, or a triplet initial state, 3S1. Since the spin of the ground state of the deuteron is one, three electromagnetic transitions are possible in principle, with according matrix elements M1(1S0), M1(3S1) and E2(3S1), where the radiation is classified as belonging to the magnetic dipolar or electric quadrupolar type. Experiment and theory are challenged to provide the values of these matrix elements.

Experimentally, radiative neutron capture by protons can be studied under three conditions of nucleon polarisation, resulting in three basic observables. (i) With both nucleons unpolarised one obtains the capture cross section σc, which is known since long to high precision, σc=0.3342(5)×10−24 cm2 [1]. (ii) With polarised neutrons captured by unpolarised protons one can detect a circular polarisation Pγ of the γ quanta [2]. (iii) With both nucleons polarised in the initial state, one can search for an anisotropy η of the γ-emission. The latter is defined asη=I−I||I+I||.I and I|| is the gamma flux, emitted per solid angle by a point source in the direction perpendicular, respectively, parallel to the axis of nuclear polarisation. The three observables σc, Pγ and η have a different dependence on the three matrix elements. Therefore, it is desirable to have experimental information about each of them. However, up to now no experimental value of η has been published.

The appearance of a γ-anisotropy can be understood from Fig. 1. The shown transitions from the 1S0 and 3S1 initial states to the ground state 3d1 can be classified as belonging to the σ or the π type, which have different angular distribution; Iσ(θ)=(1+cos2θ)/2, respective Iπ(θ)=sin2θ, where θ is the angle of emission relative to the axis of nuclear polarisation. For unpolarised nucleons, or in absence of any 3S13d1 transition, the ratio of σ to π amplitudes is 2:1 which corresponds to isotropic γ-emission. Polarisation of both nucleons populates one of the outer Zeeman levels in the triplet initial state and a γ-anisotropy may be observed which depends on the size of the triplet admixture to the capture cross section and on the nuclear polarisation. In order to get an idea of this dependence, it is useful to consider a simplified picture with magnetic dipole radiation only. The γ-anisotropy η can be calculated from a density matrix analysis given in Ref. [3], and be shown to depend only on the product of the polarisation values p of neutrons and P of the protons, as well as on the ratio R=σct/σcs of the capture cross sections from the triplet and the singlet initial states, respectively,η=pPR(4+pP)R+4−4pP(M1-radiationonly).As is evident from Fig. 2, in order to measure a non-vanishing anisotropy even for a very small R, a high polarisation of protons and neutrons is desirable.

The simplest model describes neutron capture by protons as a pure M1(1S0)→3d1 transition. The basic assumption is that the same spin-dependent interaction potential between two point-like nucleons is present in the initial and final states. The ground state of the deuteron is predominantly 3S1 (with a small admixture of 3d1, giving rise to the small quadrupole moment of the deuteron). The near absence of 3S13d1 transitions is then caused by the orthogonality of two wave functions which belong to the same Hamiltonian (see e.g. Ref. [4]).

Until 1972, theory could not explain the size of σc, theoretical values were 10% lower than the experimental value. There have been attempts to explain the discrepancy as being due to an “interaction effect”, removing the orthogonality argument and thereby leading to a sizeable contribution to the absorption cross section from 3S13S1 transitions [5]. In 1971 Breit and Rustgi proposed to measure the γ-anisotropy η in order to detect these transitions [3]. However, the 10% discrepancy was removed from the theoretical side only one year later by inclusion of meson exchange currents in the deuteron [6], and probably for this reason a measurement of η was never attempted. Also the value for the observable Pγ measured later seems to rule out the possibility to observe 3S13d1 transitions in a measurement of η at the level initially suspected. However, since there are three matrix elements involved and only two of the experimentally accessible independent parameters were measured so far, we felt challenged to measure also the third, missing one. In the present article we give the first experimental value of the γ-anisotropy η.

Section snippets

The experimental technique

In order to exclude uncertainties steming from not precisely known absolute efficiencies of the γ-detectors, a procedure with two sets of measurements (i) with polarised neutrons and polarised protons, and (ii) with unpolarised neutrons and unpolarised protons was applied.

The experimental count rates are related to the idealized count rates I|| and I of Eq. (1) byN||||I||andNIwhere ε|| and ε are the corresponding detector efficiencies, which, among other things, contain the effective

Corrections and systematic effects

A representative example of a gamma spectrum is shown in Fig. 6. The background of the 2.2246 MeV γ-line consists of a non-hydrogen part (an offset due to multiple scattering of high-energy gamma quanta) and a part caused by hydrogen not belonging to the target (there is no line from another material with energy close to the hydrogen peak at 2.2246 MeV within the detector resolution). The first one was obtained from a standard extrapolation procedure described in Ref. [11]. This type of

Result and conclusion

Including all the corrections and uncertainties, the final result of our measurement of the γ-anisotropy isη=(1.0±2.5)×10−4which was obtained for a neutron and proton polarisation of 50.5±2.1%. This small value of η excludes a large contribution of the 3S1 capture channel to the total capture cross section. Unfortunately, the result cannot challenge modern theories using one boson exchange potentials [12] or chiral perturbation theory [13] which predict some 10−7 for the anisotropy at the

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