NEW DATA ON THE SCATTERING OF HIGH-ENERGY POLARIZED PROTONS

The scattering of nucleons by nucleons at high energy is of exceptional interest, since, along with the scattering of $\pi$-mesons by nucleons, it is the simplest process, the study of which makes it possible to obtain, in the least obscured form, information on the properties of nuclear forces. Despite the large number of experimental and theoretical studies devoted to this question, only very incomplete information on the character of nuclear forces has so far been obtained. The recently discovered phenomenon of polarization of a proton beam in scattering by nuclei[^1] has made it possible to study the scattering of polarized beams of nucleons, thereby obtaining in this way

From Current Literature

more detailed information on the properties of nuclear forces. Usually the experiments are carried out by means of the successive scattering of a proton beam on two targets; in this case, after the first scattering, the beam becomes strongly polarized.

One of the most interesting experimental works published in recent months is the study of the scattering of polarized protons on hydrogen and deuterium \(^{2,3,9}\).

Fig. 1.
(Labels in the diagram: first target; cyclotron; vacuum chamber; focusing magnet; concrete shielding; second target.)

The scheme of the experimental setup is shown in Fig. 1. A beam of protons with an energy of \(340\) MeV from the cyclotron, after the first scattering on an internal target made of carbon or beryllium, became strongly polarized. The polarized beam was led out of the cyclotron by a deflecting magnet and directed into a shielded room, in which the scattering of the beam on the second target was investigated. During the experiments the angle of the primary scattering was varied from \(17\) to \(20^\circ\). The energy of the polarized beam was \(290\) and \(312\) MeV in different experiments. The absolute intensity of the polarized beam was equal to \(2\cdot 10^5\) protons per second over an area of \(5\ \text{cm}^2\).

In order to establish that after the primary scattering a truly polarized proton beam is obtained, control experiments were carried out. They consisted in measuring the asymmetry of the secondary scattering to the right and to the left in the case when both targets are made of the same material. If, in the primary scattering, the beam is scattered in the horizontal plane, then the secondary scattering of the beam is characterized by the scattering angle \(\theta\) and by the angle \(\varphi\) between the plane of the secondary scattering and the horizontal plane. The intensity of the secondary scattering depends only on one scattering angle \(\psi\), while the intensity \(J\) of the secondary scattering depends on the two angles \(\theta\) and \(\varphi\). For \(\theta = 15^\circ\) and identical carbon targets, the following values of \(J(\varphi)\) were obtained:

\[ J(0^\circ)=134.1\pm 4.06;\qquad J(90^\circ)=101.8\pm 3.7;\qquad J(180^\circ)=59.3\pm 4.3; \]

\[ J(270^\circ)=104.7\pm 3.3. \]

From this it is easy to obtain:

\[ \frac{J(0^\circ)-J(180^\circ)} {J(0^\circ)+J(180^\circ)} =0.39\pm 0.04; \qquad \frac{J(90^\circ)-J(180^\circ)} {J(90^\circ)+J(180^\circ)} =0.01\pm 0.02. \]

This indicates that, in the primary scattering, a polarized beam is indeed obtained. If the beam falls on the very same target without preliminary scattering, then, as should be expected, no scattering asymmetry is observed (the scattering does not depend on \(\varphi\)).

To use a polarized beam for quantitative measurements, one must know the degree of its polarization \(P=(F_+-F_-)(F_++F_-)^{-1}\), where \(F_+\) and \(F_-\) are the numbers of protons in the beam with spin directed respectively up and down. If targets made of one and the same material are used and the scattering is elastic, then for \(\theta=\psi\), \(P\approx\sqrt{\varepsilon}\) (neglecting the energy decrease in secondary scattering).

In the first communication\(^2\) the results of experiments on the scattering of protons by protons and by carbon were presented. The energy of the polarized beam was 290 MeV. In the second communication\(^3\) it is indicated that the authors were able to obtain a sufficiently polarized neutron beam for studying neutron scattering by protons, and had to extract information on the neutron-proton interaction from experiments on the interaction of protons with deuterons. To a first approximation one may neglect the binding energy of the deuteron, regarding the proton and neutron as free. Then, when deuterons are bombarded with protons, the processes of proton-proton, proton-neutron scattering and scattering of the proton by the deuteron as a whole are possible. These three processes can be distinguished by the emission of different pairs of particles, using the coincidence technique. In the experiments the asymmetry of proton-proton and proton-neutron scattering was measured. The asymmetric part of the cross section \(P\sigma=\frac12[\sigma(\theta,0^\circ)-\sigma(\theta,180^\circ)]\); here \(\sigma(\theta,\varphi)\) is the scattering cross section for a polarized beam and an unpolarized target—was calculated from the formula \(P\sigma=\varepsilon\sigma_{\text{unpol}}/P'\). The degree of beam polarization was \(P'=0.73\). The cross section for the unpolarized beam and proton-proton scattering was taken to be

Fig. 2.

\(3.75\cdot10^{-27}\ \text{cm}^2\) per steradian\(^4\), while for neutron-proton scattering it was taken from work\(^5\). It should be noted that for proton-proton scattering \(\sigma(90^\circ)=0\); this may serve as still another method of checking for the presence of polarization effects. The measurement results are shown in Figs. 2 and 3. The solid curves correspond to the formulas \((P\sigma)_{pp}=0.3595\sin2\theta+0.0645\sin4\theta+0.0309\sin6\theta\); \((P\sigma)_{pn}=-0.016\sin\theta+0.95\sin2\theta+0.324\sin3\theta\).

The results of the experiment are of great significance because they provide new information about which partial waves play the main role in scattering at an energy of about 300 MeV. Recently several attempts have been made to describe the experimental data on nucleon-nucleon scattering using a small number of phase shifts\(^6,7\). In particular, in work\(^6\) it is shown that, using seven phases with orbital

with angular momentum \(l \leq 2\), one can obtain good agreement with the experimental value of the differential scattering cross section of unpolarized protons on protons and on neutrons for an energy of 260 MeV. In deriving this, the authors assumed that triplet \(D\)-phases are equal and neglected the admixture of \({}^3S\)- and \({}^3D\)-waves arising in the case of a noncentral interaction. An analysis of the results of the scattering of polarized nucleons by nucleons\(^8\) shows that

Fig. 3.

the set of phases obtained in Ref. 6 cannot describe the scattering of polarized protons. The experimental results presented indicate the necessity of partial waves with orbital angular momentum greater than two. In particular, at least a \({}^3F\)-phase is required. The Fourier expansion of the differential-cross-section curve leads to eighteen Fourier coefficients. The course of the cross section can be explained with the aid of eleven phases with \(l \leq 2\), one \({}^3F\)-phase, and one mixing parameter for \(J = 1\) and \(l = 0\); thus, in all, 13 real parameters are required\(^8\). Taking into account the experimental errors, one may assert that several sets of phases are possible which describe the experiment equally well. In Ref. 8 it is reported that the author is carrying out calculations of the phases from the experimental data.

M. I. R.

CITED LITERATURE

1. C. L. Oxley, W. Cartwright, J. Rouvina, E. Baskir, D. Klein, J. Ring, W. Skillman, Phys. Rev. 91, 419 (1953); see also the collection Problems of Modern Physics, 1954, No. 7.
2. O. Chamberlain, E. Segre, R. Tripp, C. Wiegand, Ypsilantis, Phys. Rev. 93, 1430 (1954).
3. O. Chamberlain, E. Segre, R. Tripp, C. Wiegand, Donaldson, Ypsilantis, Phys. Rev. 95, 850 (1954); 83, 929 (1951).
4. O. Chamberlain, E. Segre, C. Wiegand, Phys. Rev. 93, 1424 (1954).
5. Kelly, Leith, Segre, Wiegand, Phys. Rev. 79, 96 (1950).
6. Thaler, Bengston, Phys. Rev. 94, 683 (1954).
7. Garren, Phys. Rev. 92, 213 (1953).
8. B. Fried, Phys. Rev. 95, 851 (1954).
9. O. Chamberlain, Pettengill, E. Segre, C. Wiegand, Phys. Rev. 95, 1348 (1954).