To the question of electron angular distribution at Μ-meson decay

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    Faculty of Technical and Nuclear Phyxice, Pra~e

    The paper describes the measurement of the angular distribution of electrons at the decay of/t-mesons in a longitudinal magnetic field. The results of measurement indicate that electrons are emitted with preference not only in the direction parallel to the spin orientation of fz-meson but also in the antiparallel direction in disagreement with the angular distribution predicted by theory.


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    In the theory of a two-component neutrino, in the same way as in the theory of a four-component neutrino, the angular distribution of the electrons emitted at the decay of polarized it-mesons is derived in the form

    (1) N(O) dO - - K(1 + a cos O) sin O dO

    where K is a constant, a the asymmetry coefficient and O the angle between ~he direction of the it-meson spin and the electron momentum [1], [2].

    In paper [3] we compared the exper imental values obtained by us with those of an analogical paper [4]. We arr ived at the conclusion that agreement between the values of the asymmetry coefficients of both measurements can be reached if the asymmetry coefficient is calculated in the same way as in [5]. This method of determining the asymmetry coefficient, however, assumes that the cases of it-meson decay with an electron emitted in the direction of it-meson emission and in the anti-paral lel direction have greater statistical weight than other cases. However, this does not agree with the distr ibution given by Eq. (1). In order to determine whether deviations from this distribu- t ion really exist, we measured the angular distr ibutions of electrons at it-meson decay in a longitudinal magnet ic field, which orientates the it-meson spins into certain precessional angles.


    The experiment was performed according to our suggestion in the Joint Institute of Nuclear Research in Dubna. The experimental arrangement is shown schematically in Fig. 1.

    554 qex. ~t3 . H~. B 11 (1961)

  • To the Question oJ Electron Angular Distribution...

    A beam of ~--mesons having an energy of 80 MeV was led from the syn- ehrocyclotron and from it the ~*-mesons were separated by a graphite and aluminium filter (d, e). The most suitable filter thickness was found by means of the coincidences of three scintillation counters, two of which (a, b) were placed in front of the filter and one (c) behind it. The initial thickness of the filter was 19"8 g/em ~ of graphite. The optimum thickness of the additional filter was determined from the absorption curve (measurement of coincidences a, b and a, c) at 7.8 g/era 2 of alumi- nium. Graphite and aluminium were used on account of the small depo- larization of the ~-mesons in ~ight materials. The intensity of the ~- -meson beam was approximately 650 particles per 1 cm 2 per minute. Nuclear emulsions NIKFI -R (/), 10 10 cm ~ and 400 ~ thick, which were placed in the longitudinal mag- netic field of the solenoid (g), were

    Fig. 1. D iagram of exper iment w i th ~-meson decay in long i tud ina l magnet ic f ield: a, b, c - - sc in t i l l a t ion counters ; d, e - - f i l ter (d g raph i te , e a lumin ium) ; f - - nuc lear emuls -

    ions; g solenoid.

    used to detect the ~-meson decays. One part of the emulsion (stack I; 82 layers) was irradiated in a magnetic field anti-parallel to the direction of motion of the particles and the other part (stack II; 84 layers) in a magnetic field parallel to the motion of the particles. In both cases the intensity of the magnetic field was 6300 Oe. The emulsions were placed so that one edge of each emulsion was parallel to the direction of the magnetic field and to the direction of motion of the beam of particles. The thickness of each emulsion was measured before developing them.


    Of all the decays of positive ~-mesons we chose for measurement those cases which satisfied the following conditions:

    a) the ~-meson track formed an angle smaller than 5 ~ with the direction of the magnetic field;

    b) the projection of the electron track on the plane of the emulsion was at least 20 ~x in one emulsion;

    e) the electron track formed an angle with the plane of the emulsion of less than 68 ~ .

    Measurement consisted in determining the direction of electron emission in the point of ~-meson decay. The cosine of the angle between the direction of electron emission and the direction of the magnetic field was calculated for each measurable case (i.e. the case satisfying the above conditions). In this way 1030 cases were elaborated for stack I and 1002 for stack II. Correction

    Czech. J. Phys. B 11 (1961) 555

  • M. Friml, A. Mazur

    for the finite thickness of the emulsions used was made for the measured angular distributions. The shrinkage factor was found for each emulsion separately. The histograms of the angular distributions are shown in Fig. 2.

    If we turn the angular distribution given by Eq. (1) about a precessional angle a with respect to the direction of the magnetic field we get a distribution

    (2) N(v ~) dv ~ -- K(1 -~ a cos ~ cos v ~) sin v~ dye,

    i.e. again a linear function of the space angle (v~ is the angle between the direc- tion of the magnetic field and the direction of electron emission). Figure 2 shows this distribution as lines Pl (histogram I, i.e. measurement on stack I) and PH (histogram II, i.e. measurement on stack II).








    IO 0.5 0 -0.5 -1.0 5 0 - -1.0 cos L~ COS




    Fig. 2. Histograms of angular distributions of electrons from ~-meson decay in longitudinal magnetic field. Histogram I is for case of anti-parallel orientation of magnetic field with respect to direction of motion of particles, histogram II for parallel orientation of magnetic field. Lines P1 and PII represent distribution predicted by theory (i.e. distribution given

    by Eq. (2)).

    The results of our measurements can be summed up as follows:

    1. The experimental values of the two angular distributions (I and II) do not agree with the lines PI and PI1 which represent the distribution given by Eq. (2).

    2. Distribution I (anti-parallel orientation of magnetic field with respect to direction of motion of beam of particles) and distribution I I (parallel orient- ation) differ qualitatively from one another. Histogram I has the greatest deviations from the theoretical line around the angle v ~ = ~:; the experimental

    556 "qex. c~:~3 ~ B 1! (1961)

  • To the Question o/Electron Angular Distributior, . . . .

    distribution I I has two pronounced maxima. This is an unexpected and sur- prising result.

    3. It is obvious that in case I the asymmetry of the angular distribution is greater than in case II. This means that in case I (anti-parallel orientation of magnetic field) the depolarization is smaller. It can be inferred from this that the polarization of ~+-mesons with respect to the direction of their emission at ::*-meson decay is negative. This agrees well with the results of paper [6].


    It is seen f rom Fig. 2 that angular distribution II, in particular, does not agree with Eq. (2). It can be shown that for the above-ment ioned transform- ation (transition f rom expression (1) to expression (2)) the two max ima cannot be given by a linear function of the space angle (i.e. a linear function of the cosine of the angle) but only by a non-monotonous distribution with respec~ to the space angle with two sharp max ima in distance of an angle 7:, i.e. in both direetion-wises of a given direction.

    When measuring angular distribution in a longitudinal magnetic field it is usually assumed that the angular distribution is described very well by Eq. (1). All cases when the ~-meson trajectory made a relatively large angle (30 ~ and more) with the magnetic field were therefore chosen for the measurement [5], [7]. With such a choice apparent deviations from the distribution given by Eq. (1) could not be determined. It can be assumed of the angular distributions measured without using a magnetic field that for the most part they are the result of the depolarization of ~-mesons. This hypothesis is supported by the fact that the asymmetry coefficients, measured in different laboratories under conditions which differed relatively little, are very different.

    The dependence of the form of the angular distribution on the mutual orientation of the magnetic field and the polarization of ~-mesons can be inferred from the qualitative difference in distributions I and II. It points to the asymmetry of the electromagnetic interaction of the ~-meson with the magnetic field. This can be understood, for example, to mean that the precessional motions of ~=mesons for parallel and anti-parallel spin orient- ation of the particle with respect to the direction of the magnetic field are qualitativelydifferent.

    The conclusions reached from our experiment can be summed up in three points:

    I. The angular distribution of electrons at ~-meson decay in a longitudinal magnetic field is not a linear function of the spac