Competition between neutron-proton rescattering and deuteron break-up in (d,np) reactions

Existing final-state interaction (FSI) theories predict observable rescattering effects in low-energy nuclear reactions with three or more particles in the final state. Obvious yields which could be attributed to this effect have only been reported in (d, np) reactions. However,n-p rescattering might be confused with the neutron-proton FSI following deuteron break-up since both contribute strongest at low relative neutron-proton energies. We have re-examined the (d, np) reactions on¹²C and⁴⁰Ca in a kinematically complete experiment making special effort to try to distinguish between rescattering and then-p FSI. Data have been taken within and outside the reaction plane at different bombarding energies. Attempts to simultaneously fit the detailed shapes of the proton spectra and the azimuthal angularn-p correlations with theoretical predictions in a consistent way were unsuccessful forboth reaction mechanisms. Improvements in the fits at particular energy and angle combinations were always at the expense of the agreement at other angles or energies. Therefore it must be concluded from our analysis that on the basis of calculations available at present the contributions fromn-p rescattering and deuteron break-up cannot be distinguished in a conclusive manner in the (d, np) experiments performed to date.     

Analytic continuation of the Regge pole residue function

We show that the Regge residue functiony(s) is particularly well suited for performing unitarity bootstrap calculations. The reason is that firstlyy(s) has only one, viz. the right hand, cut along which its value can be evaluated from direct channel unitarity using a parameterfree representation for the partial wave amplitudeS(l, s). Secondly its values for negative real argument follow directly from large-energy scattering with the exchange of one Regge pole in the crossed channel. These values can be evaluated from the sameS(l, s) representation by partial wave sums. Then all one needs for a bootstrap system is an analytic connection of these 2 different pieces of information. We show that this can be achieved by logarithmic dispersion relations. This bootstrap system is supposed to compete favorably with the old unitaryN/D calculations. We finally also propose a new parameter free representation ofS(l, s) which applies equally well as that of Cheng. One main result is that Im α(s) has to decrease exponentially for larges.     

Neutrino-induced deuteron disintegration in an experiment at the Krasnoyarsk nuclear reactor

The results of studying antineutrino interactions with deuterons (CCD and NCD reactions) and hydrogen (CCP) at the Krasnoyarsk underground reactor with the Deuteron detector are presented. The cross sections for NCD and CCD were measured with a precision of 9%. For CCP, the precision is 3%: σ _expt ^NCD =(3.35±0.31)×10^?44 cm²/fission ²³⁵U, σ _expt ^NCD =(1.08±0.09)×10^?44 cm²/fission ²³⁵U, and σ _expt ^NCD =(6.39±0.19)×10^?43 cm²/fission ²³⁵U. The precision of the experimental results is close to the theoretical one and is in good agreement with other experiments. The limit on the parameters of antineutrino oscillations into the sterile state was obtained: Δm ²≤4.7×10^?2 eV² for sin²(2?)=1.0 (68% C.L.). A comparison of the measured and theoretical cross section gives us the neutron-neutron scattering length of a _nn(S)=?17±6 fm in the approach of zero momentum transfers. The weak neutral current constant is in good agreement with the prediction of the Standard Model: G _A ^NC =G _A ^CC /0.932±0.056.     

Measurement of np and pp asymmetry with an accelerated polarized deuteron beam from 725 to 1000 MeV per nucleon

The accelerated polarized deuteron beam of Saturn II was used to measure the analyzing power for np elastic scattering at five energies. The left-right asymmetries ε = (L + R)/(L + R) for np and for pp elastic scattering were measured simultaneously by CH₂? carbon subtraction using one of the beam-line polarimeters. The analyzing power A_00n0(np) is given by the ratio ε_np^d/ε_pp^d multiplied by the known analyzing power for pp elastic scattering. Experimental evidence is consistent with the underlying assumption that in the kinetmatic region of the experiment the ratio of the np to pp analyzing powers for scattering of quasifree nucleons in deuterons is the same as for scattering of free neutrons and protons, respectively.     

Determination of the deuteron mean square radius

Three new methods are applied to the problem of extracting the deuteron rms matter radius from the experimental ratio of (e, d) to (e, p) scattering. A new value r_Ed = 1.953 (3) fm is obtained. The asymptotic method also yields 〈r⁴〉 = 54.5 ± 0.3 fm⁴ and 〈r⁶〉 = 1914 ± 20 fm⁶. Potential models of the deuteron are apparently unable to explain this r_Ed simultaneously with the low energy effective-range parameters of the neutron-proton system.     

Discrete ambiguities in phase-shift analysis

In two practical examples (α-³He and α-α scattering) we investigate to what extent the elastic amplitude above the first inelastic threshold, determined from phase-shift analysis, is subject to ambiguity. We find that it is extremely difficult to determine the correct physical amplitude uniquely.     

Proton-neutron correlation in the deuteron breakup at 56 MeV and prior-form DWBA analysis

Proton-neutron angular correlations in the ¹²C, ⁵¹V and ¹¹⁸Sn(d, pn) reactions have been measured at 56 MeV to investigate the deuteron breakup process. The elastic breakup which leaves the target nucleus in its ground state dominates the coincident spectra. The elastic breakup cross sections are estimated to be 36–48% of the inclusive breakup yields at 15° or 17.5°. In the angular correlations the protons are emitted predominantly on the side of the beam opposite to the neutrons. The experimental data have been analyzed using the prior-form DWBA. For both nuclear and Coulomb breakup, sufficient convergence of the calculations is obtained by including the pn angular momenta up to l = 2. For the nuclear breakup calculations, the l = 0 and 2 contributions dominate the cross sections. For the Coulomb breakup the l = 1 contribution is predominant. In the calculations the effect of the Coulomb breakup is seen at forward angles of the angular correlation. The DWBA calculations reproduce fairly well the coincident energy spectra and the angular correlations in the angular region where the protons are emitted on the side of the beam opposite to the neutrons. On the other hand the calculations overestimate the break-up cross sections by a factor of 2 to 10 in the angular region where the protons are emitted on the same side of the beam as the neutrons. The distributions of deuteron c.m. angular momenta that contribute to the breakup amplitude are examined to obtain information on the region of space in which the breakup reactions takes place.     

Truncation of continuum ambiguities in phase-shift analysis

The continuum ambiguity in the determination of phase shifts from scattering data consists of a family of amplitudes which have in general an infinite number of partial waves. In practical computations, however, the partial wave series is necessarily truncated. We discuss the relation of the resulting (truncated) amplitudes to those representing the true continuum ambiguity. In particular, we show that each of the latter is approximated increasingly well, as the cut-off tends to infinity, uniformly inside an ellipse in the cos plane.     

From the deuteron to deusons,an analysis of deuteronlike meson-meson bound states

A systematic study of possible deuteronlike twomeson bound states,deusons, is presented. Previous arguments that many such bound states may exist are elaborated with detailed arguments and numerical calculations including, in particular, the tensor potential. This tensor potential which is crucial for the deuteron binding is shown to be very important also in the mesonic case. Especially, in the pseudoscalar³ P ₀ pseudoscalar-vector and vector-vector channels the important observation is made that the centrifugal barrier from theP-wave can be overcome by the 1/r ² and 1/r ³ terms of the tensor potential. In the heavy meson sector one-pion exchange alone is strong enough to form at least deuteronlike and composites bound by approximately 50 MeV. Composites of and states bound by pion exchange alone are expected near the thresholds, while in the light meson sector one generally needs some additional short range attraction to form bound states. The quantum numbers of these states areI=0, andJ ^PC=0^–+, 1⁺⁺ for the states andI=0,J ^PC=0⁺⁺, O^–+, 1^+– and 2⁺⁺ for the composites. In the states: ^b (10545), _b1(10562) are predicted and in , one finds the states: ^b (10590), _bQ (10582),h _b(10608), _b2(10602). Near the threshold the states: ^c (3870), _c0(3870) are predicted, and near the threshold one finds the states: _b0(4015), ^c (4015),h _c(4015), _c2(4015). Within the light meson sector pion exchange gives strong attraction for and systems with quantum numbers where the best non- candidates exist, although pion exchange alone is not strong enough to support such bound states. Thus, although one cannot conclude with certainty it to be the case, this fact does favour the picture that the (1440) and thef ₁ (1420) are mainly composites and thef ₀(1710) mainly a bound state, while thef ₀(1515) andf ₂(1520) could be predominantly composites. If the predicted and states are found, these would support this interpretation of the light states. In channels with exotic flavour orCP quantum numbers pion exchange is generally repulsive or quite weak. Therefore one does not expect that such deuteronlike bound states exist, althoughB*B* may be an exception.     

A study of the proton momentum spectrum from deuteron fragmentation at 8.9 GeV/c and an estimate of admixture parameters for the six-quark state in the deuteron

The momentum spectrum of protons emitted at small angles in the stripping reaction d + ¹²C → p + X has been measured at a deuteron momentum of 8.9 GeV/c. The data are described in the framework of the Glauber-Sitenko theory using the hybrid model of the deuteron wave function which includes a six-quark state. The parameters of this state are determined. A shoulder in the spectrum has been observed in the proton momenta region which kinematically corresponds to the production of a dibaryon resonance with a mass from 2.0 to 2.2 GeV.     

The problem of the unambiguity of phase-shift analysis I

For the discrimination of phase-shift solutions, the new so-calledτ-criterion, based on the calculation of some functionτ of the experimental data, is used. This method can be applied, in general, to an arbitrary ambiguous phase-shift analysis. Theτ-criterion is more powerful than theχ ²-criterion, e.g. for rejecting a less probable set it is necessary to have a smaller quantity of experimental points (in statistics this means that theτ-criterion gives a smaller Type II error). For the calculation of the quantityτ, the standard programme for phase-shift analysis with a small additional part can be used. A computer time of about only 5–10 min. on a computer of M-20 type is needed. A Type I error is then obtained from the tables of the normal distribution function.     

The problem of the unambiguity of phase-shift analysis II

The new results of phase-shift analysis at energies of 23·1 and 18·2 MeV are discussed. Two and three solutions remain at these energies respectively. The measurements of triple n-p scattering parameters are necessary for obtaining the unambiguity of the solutions. It is shown that the Berkeley p-p polarization data at 19·7 MeV are in disagreement with other results.For the discrimination of phase shift solutions the so-called-criterion (described in Part I) was used.In conclusion the authors express their deep gratitude to P. Catillon and M. H. MacGregor for useful discussions and for sending us this results before their publication and to E. Dudova for help in our work.     

A phase-shift analysis of elastic pion-deuteron scattering

Recent data on differential and total cross sections in the region 82 < T_π (MeV) < 292 from SIN and CERN and an isolated polarization measurement formed the material for a πd phase-shift analysis. For virtually all cases χ² < 1 could be reached, but extracted phase parameters are not unique. We emphasize the strong constraints polarization data would exert on presently ambiguous phase parameters. We present our results in Argand plots and briefly discuss their behaviour.     

Polarization transfer in the deuteron break-up reaction at 56 MeV

The polarization transfer coefficients K^yy′ of the break-up spectra in the reactions ¹²C, ⁵⁸Ni, ²⁰⁹Bi($\text{d}$, $\text{p}$X) were measured at 56 MeV. In the forwardd angles (13.5° and 20.0°), the K_y^y′ data at the break-up peak are nearly equal to $\text{2}\text{3}$ (the spectator model prediction) and they decrease at both sides of the peak. The deviation due to the deuteron D-state is estimated, using PWBA and DWBA.     

The four-momentum transfer distribution for the deuteron break up at 3.3 GeV/c incident deuteron momentum

The differential cross section (dσ/dt) for the dp → ppn charge retention reaction at 3.3 GeV/c deuteron momentum is studied and compared with the Glauber multiple scattering theory. Within the limits of the uncertainties of the existing elementary nucleon-nucleon data, the simple Glauber model calculations give, in general, a fair agreement with experiment, except for the low |t| region where possible spin effects may play a role.     

Forward photodisintegration of the deuteron at 10.74 MeV photon energy

The absolute differential cross section for the photodisintegration of the deuteron at 0° for the outgoing proton has been measured at 10.74 MeV lab photon energy using a bremsstrahlung beam, a deuterated target, a magnet system, and a surface barrier detector. The absolute cross section is (4.7±0.85) b/sr and was determined with an angular resolution of 1.25°. The result, pertaining to a 4.6 MeV wide photon energy interval, favours a minimum in the differential cross section around 10 MeV photon energy.Supported in part by the Deutsche Forschungsgemeinschaft (SFB 201)     

Polyspectral analysis and optimization of the frequency-domain differential phase-shift keying

Using the mathematical tool of high-order spectra (polyspectra), we consider the synthesis of optimal variants of high-order differential phase-shift keying in the frequency domain. The proposed approach allows all possible variants of the second-order differential phase-shift keying to be reduced to phase modulation of a special form of the fourth-order spectrum (trispectrum) — triphase modulation. The optimal triphase shift keying variants which have the best spectral efficiency and outperform the known variants of the second-order differential phase-shift keying in noise immunity are devised. It is shown that the noise immunity of proposed modulation is higher than that of the first-order differential phase-shift keying in the channels with simultaneous time and frequency offsets.     

A semirelativistic calculation of the deuteron electrodisintegration at the quasielastic peak

The cross section for inelastic electron deuteron scattering at the quasielastic peak is calculated in the laboratory system, using complete relativistic kinematics. The difference between the exact cross section formula andDurand's simple sum rule expression is found to be approximately 1.2% for 4-momentum transfers of 2.5 to 4f^?1 and the influence of the deuteron wave function on the final results to be smaller than 1% for reasonable deuteron models. Final state corrections are introduced through a simple correction term in the cross section formula.     

Determination of A FB b at the Z pole using inclusive charge reconstruction and lifetime tagging

A novel high precision method measures the b-quark forward-backward asymmetry at the Z pole on a sample of 3,560,890 hadronic events collected with the DELPHI detector in 1992 to 2000. An enhanced impact parameter tag provides a high purity b sample. For event hemispheres with a reconstructed secondary vertex the charge of the corresponding quark or anti-quark is determined using a neural network which combines in an optimal way the full available charge information from the vertex charge, the jet charge and from identified leptons and hadrons. The probability of correctly identifying b-quarks and anti-quarks is measured on the data themselves comparing the rates of double hemisphere tagged like-sign and unlike-sign events. The b-quark forward-backward asymmetry is determined from the differential asymmetry, taking small corrections due to hemisphere correlations and background contributions into account. The results for different centre-of-mass energies are: .Combining these results yields the b-quark pole asymmetry Received: 22 July 2004, Revised: 9 December 2004, Published online: 4 February 2005