A note on the use of the additivity rule for electron-molecule elastic scattering

For a sample of four molecules (O₂, CO, CO₂ and CF₄) investigated here it is found that the additivity rule gives almost the same values of the momentum transfer cross section (MTCS) as obtained within the framework of the independent atom model (IAM) for elastic scattering of electrons at intermediate and high incident energies. However, large differences are noted between the two values in the case of the integral elastic cross section.     

The use of fixed t analyticity in elastic proton-proton scattering

Several methods of exploiting fixed-t analyticity are described and compared with each other. For the forward amplitude the predictions of the real parts from the total cross section data — including the new NAL data — and dispersion relations are found to be in good agreement with the Coulomb interference data. It is also discussed how the results depend on the assumptions on the asymptotic behaviour of the cross section. Furthermore, the conventional dispersion relation approach is compared with the method of analytic parametrization and with the differential operator method. For the non-forward directions, information on the amplitude is extracted from a dispersion relation for the slopes and from a relation between the phase and the modulus of the amplitude.     

t/s scaling in exclusive and inclusive proton reactions

A model is developed in order to account for the previously observed large-angle behaviour in elastic scattering, and to predict the analogous inclusive effects. Data of (pp, p) distributions and pp → pN^* reactions are examined in regions of high transverse momenta and fitted by the functional forms of the model. The fits show the expected features of this new type of high-energy scaling.     

A new protocol for constructing nonlocal n-qubit controlled-U gates

We present a new protocol for constructing a nonlocal n-qubit controlled-U gate. In this protocol, no prior sharing of entanglement is needed and only one ancilla qubit is sent once from one party to another. Thus, the present protocol is very efficient for performing a nonlocal multiqubit controlled-U gate, which is important to network quantum information processing and communication.     

A note on the effect of non-elastic processes on elastic scattering

We study the effect of non-elastic processes on elastic scattering by means of Froissart's method. We derive the conditions under which this method leads to a unique solution and those under which inelastic processes lead to the creation of more resonances in the elastic channel. We derive further the generalization of Levinson's theorem for the case of the existence of nonelastic processes and we introduce an illustratrive explicitly solvable example.     

The K−p charge exchange and elastic scattering reactions at 4.2 GeV/c

In this letter results are presented on the reactions $\text{K}{}^{\mathrm{?}}\text{p →}\text{K}{}^0\text{n and K}{}^{\mathrm{?}}\text{p → K}{}^{\mathrm{?}}\text{p}$ from a high statistics CERN 2-metre hydrogen bubble chamber exposure at 4.15 GeV/c. The behaviour of the differential cross section as a function of four-momentum transfer shows remarkable similarities between the two reactions studied. From a comparison of our data with K⁺p elastic scattering at 4.27 GeV/c we draw some conclusions concerning the magnitude of the contributing amplitudes.     

A new formalism of inclusive breakup reactions and validity of the surface approximation

Austern and Vincent's formalism for the inclusive breakup reactions in DWBA is rewritten in a form in which the elastic and inelastic breakup processes are well discernible. This form is calculable exactly and hence we test the validity of the surface approximation used by Baur et al.     

Spin dependence of inclusive reactions from proton-proton collisions at 7.9 GeV/c

The spin dependence of inclusive proton and pion production by 7.9 GeV/c protons has been measured using a polarized proton target, for nominal values of x = p_L^cm/p_max^cm = 0.7 in the transverse momentum range 0.4 GeV/c <pp_t < 1.2 GeV/c, and for p_t = 0.4 GeV/c in the range 0.1 < x < 0.96. The results indicate a positive asymmetry of +5% over this kinematic region, which corresponds to fragmentation of the unpolarized proton.     

Semicoherent elastic pion-carbon scattering at 25 and 40 GeV/c

In the frame of a systematic study of hadron-nucleus interactions performed at the Serpukhov accelerator (CERN-IHEP 5th experiment), semicoherent elastic scattering on carbon $\text{π}{}^{\mathrm{?12}}\text{C}\text{a}\text{?}\text{π}{}^{\mathrm{?12}}\text{C}{}^1\text{(4.44}\text{MeV}\text{)}$ was investigated with 25 and 40 GeV/c incident pions.The experimental data were obtained with a counter technique, looking at the coincidence between the scattered pion and the 4.44 MeV photon from the J^P = 2⁺ carbon excited state detected by a NaI counter.The value obtained for the integrated cross section at 40 GeV/c in the 0.0032 ? |t| ? 0.27 (GeV/c)² four-momentum transfer range isσ = 1.16 ± 0.11 mb.According to the theoretical models, this t-range at 40 GeV/c covers more than 99% of the angular distribution, so the above value almost corresponds to the total semicoherent elastic cross section.     

On representations of the groups Sp(n, 1) and Sp(n)

New classes of unitary irreducible representations of Sp(n, 1) which can be useful for applications in physics are obtained. The infinitesimal operators of these representations of Sp(n, 1) and of irreducible representations of Sp(n+1) with highest weights (m, m, m₃,…,m_n+1) and (m₁, m₂, 0,…,0) are expressed in terms of the simple Clebsch–Gordancoefficients for Sp(n). For Sp(3) and Sp(2, 1) they are found in an explicit form.     

A new “parametrization” of the differential cross section for elastic scattering

A new parametrization of the differential cross section for elastic scattering is proposed. The parametrization incorporates correct analytic properties of the differential cross section and is based on optimized polynomial expansions of an analytic function. It is, in principle, valid for all energies and all angles. The parametrization has been tested for pp, $\text{p}\text{p}$, pd, π^± and K^±p elastic scattering at high energies and small angles. The results of the new fits are compared with those of the old ones. It has been found that with the same number of parameters one obtains practically the same values of χ². However, the new values of physical quantities, such as slope, α and (dσ/dt)₀, in most cases differ considerably from those obtained by the old parametrization. In particular, it has been found that the slope of the differential cross section for pp, $\text{p}\text{p}$, pd and K^±p elastic scattering increases continuously as the forward direction is approached.     

A non-elliptic solution of the Lane-Emden equation for index n=5

A condition for the existence of non-elliptic solutions of the Lane-Emden equation of index 5 is obtained. It is shown that for a particular non-zero value of the integration constant D the equation admits a non-elliptic solution and thus leads to the modification of the statement of Chandrashekhar [1] that the solution of the Lane-Emden equation of index 5 for non-zero values of D is complicated and involves elliptic integrals. Some characteristics of the new solution curves are also discussed.     

A systematic search for a realistic SU(n) tumbling gauge model

Within the framework of the dynamical symmetry breaking and the tumbling ideas, a systematic search was carried out in SU(n) groups with the ultimate aim of determining if a realistic and phenomenologically acceptable model exists which tumbles down to SU(3)_c ? U(1), or a suitable large group. To do so all the anomaly free and the asymptotically free fermion contents for any SU(n) were first determined. In order to have nontrivial tumbling the real and the pseudo-real representations have been eliminated, and the tumbling patterns of all the allowed complex ones in detail have been examined. No such realistic model has been found. These results combined with those of Srednicki's concerning the SO(4n + 2) and E₆ groups establish the fact that there cannot be any realistic tumbling gauge model within the context of the original tumbling hypotheses. Having thus established the need for a change of these hypotheses some suggestions and comment on various ways of remedying the problem are made.     

On a resolution of the multiplicity problem for U(n)

The Borel-Weil theory of holomorphic induction is used to provide a resolution of the multiplicity problem occuring in the tensor product decomposition of representations of the U(n) groups.     

Canonical realizations of the lie algebras gl(n, R) and sl(n, R) I. Formulae and classification

The generators of the Lie algebra of the general linear group GL(n, R) and of the special linear group SL(n, R) are, recurrently, expressed through polynomials in the quantum canonical variables p_t and q_t. These realizations are skew-Hermitian, the Casimir operations are realized by constant multiples of identity element and, in dependence on the number of the canonical pairs used, they depend on d(d?1 for sl (n,R)), d = 2, …, n, free real parameters.     

Measurement of the polarization parameter in pp elastic scattering at 150 GeV/c

The polarization parameter in pp elastic scattering at 150 GeV/c, and in the momentum transfer interval 0.4 ? ?t ? 3.0 GeV², has been measured in an MWPC and scintillation counter experiment at the CERN SPS using a polarized proton target. The polarization is decreasing steadily from zero to ≈ ? 10% in the range 0.4 < ?t < 1.3 GeV²; for higher |t| the data suggests a change of sign. Results are also given for the differential cross section, which exhibits a small dip at ?t = (1.46 ± 0.01) GeV.     

A new parametrization for the N/D method

A new treatment of the left-hand cut for N/D problems is presented whereby, instead of poles, the cut is parametrized by a Legendre expansion which fixes the discontinuity. The method is tested through the use of analytic forms, and is found to work very well in a wide variety of circumstances. An extension is made to situations where there are errors in the input, and resulting problems are discussed. The method is applied to elastic pion-pion scattering. Both the rho and f₀ mesons are produced dynamically, but trouble is encountered for the s-waves. The relation of this trouble to ambiguities found in other s-wave calculations is discussed.