Nuclear effects on lepton polarization in charged-current quasielastic neutrino scattering

We use a correlated local Fermi gas (LFG) model, which accounts also for long distance corrections of the RPA type and final-state interactions, to compute the polarization of the final lepton in charged-current quasielastic neutrino scattering. The present model has been successfully used in recent studies of inclusive neutrino nucleus processes and muon capture. We investigate the relevance of nuclear effects in the particular case of τ polarization in tau-neutrino induced reactions for several kinematics of relevance for neutrino oscillation experiments.     

Shell-model study of partial muon-capture rates in light nuclei

The nuclear shell model is used to study ordinary muon capture of light nuclei in the p, sd and p-sd shell-model spaces. Several well-established two-body interactions are applied to calculate the involved nuclear matrix elements and the emerging results are compared with each other. The resulting theoretical partial muon-capture rates are compared with experimental data and their stability against different model spaces and interactions studied. The effects of the induced-pseudoscalar strength, C_p, on the capture rates is discussed. The relation between the allowed partial muon capture rates and the Gamow-Teller strength function is stressed.     

Energy spectra of neutrons emitted following muon capture in O and C

The energy spectra of neutrons emitted following muon capture in ¹⁶O and ¹²C are investigated using the continuum shell model. Nuclear wave functions, which have been shown by Ohtsubo and the author to describe the radiative pion capture reaction in the above nuclei well, are adopted. The calculated neutron energy spectra explain well the observed main peaks, at 5 MeV for ¹⁶O and 4 MeV for ¹²C, which are considered to be the giant resonances excited in the muon capture reaction. These peaks are interpreted as the 2⁻ state at 20.3 MeV for ¹⁶O and the 1⁻ state at 22.5 MeV for ¹²C. Comparisons with photon spectra in radiative pion capture reactions are also made. The calculated total capture rates exceed the experimental values by a factor of 2.5 for ¹⁶O and by 30–40% for ¹²C.     

Measurement of spin correlation in tt production using a matrix element approach

We determine the fraction of tt events with spin correlation, assuming that the spin of the top quark is either correlated with the spin of the top antiquark as predicted by the standard model or is uncorrelated. For the first time we use a matrix-element-based approach to study tt spin correlation. We use tt → W+ b W- b → ?+ νb?- ν b final states produced in pp collisions at a center-of-mass energy sqrt(s)=1.96 TeV, where ? denotes an electron or a muon. The data correspond to an integrated luminosity of 5.4 fb(-1) and were collected with the D0 detector at the Fermilab Tevatron collider. The result agrees with the standard model prediction. We exclude the hypothesis that the spins of the tt are uncorrelated at the 97.7% C.L.     

Muon capture revisited

The problem of inclusive muon capture in nuclei is studied by calculating the capture rate in asymmetric infinite nuclear matter and using the local density approximation to evaluate the capture rates in nuclei. It is shown that the method is rather reliable and allows one to improve on approximations used in the past. The need for a strong nuclear renormalization is shown, reducing the capture rates by about a factor two in medium and heavy nuclei. By using standard effective interactions in the spin-isospin channel one can account for this renormalization and one finds a remarkable overall agreement with the measured capture rates for a large list of nuclei through the periodic table.     

Study of the flavour violating (μ,e) conversion in nuclei

The muon number violating (μ⁻, e⁻) conversion in the presence of nuclei is investigated. The effective operators resulting from various mechanisms, both photonic and non-photonic, are expressed in terms of nuclear coordinates: (i) for intermediate neutrino models, and (ii) for supersymmetric theories. Using these operators the (A, Z) dependence of the corresponding widths is discussed throughout the periodic table. For the coherent process the dependence of the conversion rate on the nuclear parameters is given in terms of the elastic nuclear form factors, which are obtained in the context of shell model, taking into account finite nucleon-size effects. For the inclusive μ−e conversion process the total rates are calculated for closed-shell nuclei. The method of calculation utilizes microscopic non-energy-weighted sum rules (closure). The isospindependent part of the total (μ⁻, e⁻) rate is also related to that of the total (μ⁻, _vμ capture rate, the latter being calculated with Primakoff's phenomenological method. The agreement between the two provides a good test of the reliability of the shell-model closure calculations. For non-closed-shell nuclei the relevant rates can be obtained by interpolation techniques from the functions obtained in the present work for closed-shell nuclei. Finally the experimentally interesting ratio of the coherent to the total μ−e conversion rate is discussed.     

μ-介子在He3原子核上的俘获

本文计算了μ介子在He³核上俘获的几率、末态H³核的角分布和极化。所采用的理论是带有重正化效应(包含弱磁矩及赝标项)的V-A普适弱作用理论。在计算中考虑了μ和He³核在始态有极化及处于不同超精细态上的情况。在计算中假定了He³核的基态是纯S态,这时忽略了由张量力以及其他自旋轨道耦合力引起的其他态。介子交换电流的效应也没有考虑。在以上这两个假定下,我们证明了俘获几率中只包含一个未知的原子核矩阵元,这个矩阵元恰好是原子核密度函数的富氏分量。利用μ介子(或电子)与He³(或H³)原子核的散射可以确定这个未知矩阵元。     

原子核对光电离截面的影响

利用Dirac-Slater相对论平均自洽场理论,研究了不同原子体系光电离截面在不同核模型下的差异.考虑原子核大小时,核的尺寸效应使电子所感受到的有效核电荷减小,并进而影响到电子的概率分布及光电离截面等;对没有考虑原子核大小的点模型,由于不存在核的尺寸效应,出射光电子的波函数有较大相移,从而有可能出现Cooper极小.当入射光子的能量远大于相关电子的电离能时,不同核模型下电子束缚能及平均半径等的差异将相对减小,从而使光电离截面随入射光子能量的变化趋于一致.     

On the continuity in energy of the free-bound one-photon cross-sections

For a charged particle in a central field of force we discuss the continuity in energy of the cross-sections for the related processes of ground state photoeffect and radiative capture. This continuity follows from general arguments, while for a Coulomb potential, where exact analytic expressions are available, the continuity can also be traced explicitly through the calculation. Our analysis allows us to identify an error in papers on radiative muon capture in the ground state which claim the existence of a discontinuity in the cross-section, occurring in hydrogen for muon energies in the neighbourhood of 2.8 keV. As a discontinuity in radiative capture would imply a discontinuity in atomic photoeffect, we note that in the latter case there are extensive experimental results in good qualitative agreement with the usual continuous result (Stobbe formula) for the cross-section. Received: 13 February 1998 / Accepted: 14 May 1998     

Effects of kinematical constraints in nuclear muon capture

Muon capture is discussed in the framework of linear response theory. This approach allows a general discussion of the role played by kinematical constraints in determining which features of nuclear dynamics are actually probed in the capture event. It is argued that the muon momentum spread can increase the capture rate at large energy transfer.     

Giant M2 and transversal E1 resonances in light nuclei

The cross section for inelastic backward electron scattering on 1p shell nuclei at incident energy E_e = 70 MeV is calculated in the shell model. Comparison is made with radiative pion capture and muon capture. It is shown that the T_> branch of the M2 resonance in (e, e') and the main maxima in the (π^?, γ) response function are formed by identical partial transitions. We consider the basic features of the M2 resonance excitation in 1p shell nuclei and predict configurational and isospin splitting of this mode.     

Effects of nuclear structure in double charge exchange reactions on 16O and 40Ca

The energy dependence of forward double charge exchange (DCX) reaction is studied for the doubly closed shell nuclei ¹⁶O and ⁴⁰Ca. A common characteristic of the two DCX reactions is a resonance-like peak around 50 MeV pion lab energy. While some authors have interpreted this peak as the evidence of a dibaryon resonance state, we show that it arises naturally in a two-step process in the conventional pion—nucleon system with proper handling of nuclear structure. The effects of nuclear structure are demonstrated through a comparison among different nuclear structure models: the symmetry model SU(4) ? SU(3), the single particle shell model and the «realistic” shell model.     

Anomalously suppressed localization in the two-channel Anderson model

We study numerically the localization properties of a two-channel quasi-one-dimensional Anderson model with uncorrelated diagonal disorder within the nearest-neighbor tight-binding approximation. We calculate and analyze the disorder-averaged transmittance and the Lyapunov exponent. We find that the localization of the entire system is enhanced by increasing the interchain hopping strength t?. From the numerical investigation of the energy dependence of the Lyapunov exponent for many different interchain hopping strengths, we find that apart from the band center anomaly, which usually occurs in strictly one-dimensional disordered systems, additional anomalies appear at special spectral points. They are found to be associated with the interchain hopping strength and occur at E = ± t?/2 and ± t?. We find that the anomalies at E = ± t? are associated with the π-coupling occurring within one energy band and those at E = ± t?/2 are associated with the π-coupling occurring between two different energy bands. Despite having a similar origin, these two anomalies have distinct characteristics in their dependence on the strength of disorder. We also show that for a suitable range of parameter values, effectively delocalized states are observed in finite-size systems.     

Pion production in nuclear collisions

The production of pions in nuclear collisions is analyzed in terms of a microscopic reaction model, where the free energy of the entrance channel is transferred to the final channel through the coupling of the relative motion to the internal excitation of N^*-resonances. Such a model allows quite naturally for a consistent analysis of the exclusive and the inclusive production of pions. It turns out that the pionic fusion cross section is determined predominantly by the spectroscopic parentage between the initial target projectile combination and the final nucleus, whereas the inclusive part is dominated by the energy dependence of the phase space factor, i.e. by the number of the degrees of freedom which are relevant in a given kinematical situation. This model is applied to the analysis of available experimental data from threshold to the (1232)-region. A consistent analysis of both the inclusive and the exclusive part of the pion spectrum is presented.Dedicated to Prof. Dr. P. Kienle on the occasion of his 60th birthday     

Total muon capture rates for N = Z nuclei in the 1p shell

The approach to total muon capture rates by means of sum rule techniques is applied systematically to 1p shell nuclei. Explicit calculations involve ground-state wave functions extracted from Cohen-Kurath effective interactions. For the double commutator expectation value we use a form of the potential consistent with the effective interaction and the giant dipole resonance energy.Results are given for N = Z nuclei, studying the minimal sensitivity with the parameter of the improved closure approach. The manifestations of SU(4) breaking are quantitatively shown. Within the uncertainties of the model the rates thus obtained compare reasonably well with experiment.     

The nuclear excitations and particle emission following muon capture

The nuclear muon capture process is studied as an excitation of the analogues of various harmonics of the multipole giant resonance. The excitation energy distribution is calculated with the use of the hydrodynamical model of the nucleus. The following particle emission cascade (including precompound states) is considered and the obtained particle spectra as well as yields of various residual nuclei are in a fair agreement with the existing experimental data.     

Neutrino mass effect on the nuclear muon capture

Multipole expansion of the partial transition amplitude in the nuclear muon capture with massive lefthanded Dirac neutrino has been derived. The multipole amplitudes for the partial nuclear transitions are given as the explicit functions of the neutrino mass parameter. As an example, the capture rate, the recoil asymmetry and the neutrino polarization are investigated in terms of these multipole amplitudes. The transversal neutrino polarization provides a connection between theT-violation and the neutrino mass: ifT-odd component in the neutrino polarization is observed, then neutrino must be a massive particle. It turns out that in the capture rate and recoil polarization, the effects due to very small neutrino mass can be proportional to the square ratio of the neutrino mass to its momentum, while the neutrino transversal polarization is proportional to this ratio only. Under the recent limits on the muon neutrino mass, the observable effects inthe partial transition may be below the order of ?10^?3.     

Hadron final states in deep-inelastic leptoproduction on nuclei

We discuss some aspects of the formation of inclusive hadron final states in deep-inelastic electro-, muo- and neutrinoproduction on nuclear targets.The inclusive final states are known to possess a remarkable Q² independence in interactions with free nucleons. Nevertheless, we prove that the nuclear spectra and mean multiplicities should have a rather specific and appreciable dependence on Q². In leptoproduction on heavy nuclei the yields of particles in nucleus fragmentation rise by a factor of two, as at the fixed energy transfer v one passes from incoherent scattering to diffraction scattering, and the total multiplicities change by 20–40%. The effects predicted seem to be detectable with the current and the near-future experimental facilities. Fermilab bubble chamber neutrino experiments and the coming SPS muon and neutrino experiments deserve special attention in this respect. We also comment on the possibilities offered by leptoproduction on nuclei for testing some absorption models.     

Meson exchange currents for nuclear muon capture by3He leading to the triton final state

We have calculated exchange corrections for nuclear muon capture by³He using the hard-pion model and realistic nuclear wavefunctions. These currents modify the vector and axial part of the weak nuclear current. In their absence the rate is found to be about 12% smaller than experiment. Our aim is to test the hard-pion model by making a realistic estimate of the theoretical uncertainty and comparing the calculated rate with its experimental value. Results for the rate and spin observables will be presented at the symposium. The recent precise measurement of the rate (see the contributions of A.A. Vorobyov and W. Prymas in these proceedings) allows the most stringent test of exchange currents for muon capture to date.Supported by the Sir James Knott Fellowship.Supported by grants nos. 202/94/0370 (GA CR) and 148410 (GA ASC CR).