Phenomenological wave functions for the massA=14 system and a consistent description of beta decay observables

A set of phenomenological wave functions has been derived to describe the¹⁴N ground state and the isospin triplet consisting of the¹⁴C ground state, the first excited state of¹⁴N at 2.313 MeV and the¹⁴O ground state. Elastic and inelastic electron scattering form factors, the magnetic moment of the¹⁴N ground state and the shape factors in the ^± decay have been employed in a multiparameter fitting procedure to determine the amplitudes of the wave functions inL-S coupling. The inclusion of the beta decay observables in the fit has become possible for the first time since exact formulas for the shape factor in higher order do exist. The set of wave functions deduced exhibit predominately anL=0 contribution for the 0⁺; 1 states andL=1 and 2 contributions of nearly equal weight for the 1⁺; 0 state. It was observed that the inclusion of the shape factors allowed a more stringent determination of the amplitudes compared to previous attempts reported in the literature and led in the case of the 0⁺; 1 states to wave functions that show a small but noticeable difference within the isospin triplet. Besides the observables used for the fit, the radiative width (M1) of the 2.313 MeV state in¹⁴N can be described quite well with the derived wave functions, and in addition it has become possible to predict the pathological largeft ^– value of the¹⁴C decay and theft ⁺ value of the¹⁴O decay precisely. The wave functions are also applied to calculate the¹⁴N(, ⁺) cross section.Dedicated to Prof. Dr. P. Kienle on the occasion of his 60th birthday. Supported by the German Federal Minister for Research and Technology (BMFT) under contract number 06DA 184I     

Muonic atom-nucleus collisions in the energy region of dtµ, resonant states

We calculated the (dµ) _n=1 +t scattering in the energy region of the (dtµ)^* resonant states below then=2 level of the tµ atom. From the cross sections, we estimated the resonant energies, widths and branching ratios. We found eleven resonant states with angular momentumJ=0, and some of their resonant energies relative to then=2 level of tµ are small enough to form the [(dtµ)^* dee] by the Vesman mechanism. These resonant states decay to (dµ)[inn=1 +t or (tµ) _n=1 + d scattering states. The total decay rates are about 10¹¹ s^–1 which is three orders of magnitude larger than the fusion rates of (dtµ)^*4 He + n+ 17.6 MeV + µ. The main part of the decaying channel from the shallow resonant states is the (dµ) _n=1 +t channel. The branching ratios of the (dµ) _n=1 +t decay channel are around 0.9. Most of the muons that reach to then=2 states of tµ can transfer to then=1 state of du through (tµ) _n=2 + D₂ [(dtµ)^*dee] and (dtµ)^* (dµ) _n=1 +t processes.     

Hard form factors for meson-baryon strong couplings as derived from deep inelastic lepton scattering

As stimulated by earlier attempts for obtaining theNN andN form factors from the deep inelastic lepton scattering data, we extend the analysis by taking into account effects of additional mesons including, , ,K, andK ^*, with the coupling constants fixed by the lowenergy nucleon-nucleon and hyperon-nucleon scattering data. Contrary to an earlier claim that the NN andN form factor must be very soft (e.g., with the cutoff mass less than 500 MeV in the monopole form), we find, for example, that with all form factors parametrized in the dipole form, a universal cutoff mass of 1150 MeV in the/N sector and 1400 MeV in the/ sector yields predictions in excellent agreement with recently published neutrino data on the momentum fractions carried by thes, , and¯d quarks, as well as consistent with the sea-to-valence ratio extracted from the CDHS data and the Femilab E615 experiment. Similar results can also be obtained by using exponential cutoffs for all couplings, or by using monopole forms for some vertices while retaining dipole forms for the rest. The success of the mesonexchange picture in generating the strangeness content in a proton suggests an alternative understanding of the origin of sea quarks in the proton.We wish to thank G. Garvey, K. Holinde, L.-C. Liu, M. B. Johnson, M. Strikman, A. W. Thomas and Jochen Wambach for helpful conversations. W-Y. P. Hwang wishes to acknowledge the Alexander von Humboldt Foundation for a fellowship to visit Jülich for conducting research. His research works was also supported in part by the National Science Council of the Republic of China. The work of G. E. Brown is supported in part by a Humboldt award, in part by NATO Grant RG85/0093, and in part by the U.S. Department of Energy.     

Analytic solution of the covariant shell model of three dirac fermions with harmonic forces

A covariant shell model of three Dirac fermions in the center-of-mass frame is analytically solved for a particular spin-dependent harmonic-oscillator potential. Three equal-mass quarks are all assumed to be in states with identical quantum numbers ofj =1/2⁺ for the shell-model ground state. The sixtyfour-component composite wave function for three Dirac fermions is reduced to a set of four coupled differential equations for the four independent composite radial components. Hyperspherical coordinates are used. The two-body potential used vanish in the small component of the composite wave function. The various components of the composite wave function are found to have a ^l exp(– ² ) hyperradial dependence, where is the hyperradius, andl is the sum of the orbital angular momentum acting in the various components of the composite wave function. For an eigenergy equal to the proteon rest-mass energy, the root-mean-square radius calculated is about 0.84 fermi, about 80% of that calculated in an independent-particle harmonic-oscillator model with the same rest-mass energy for the system. A sixth-order polynomial equation is found for the rest-mass energy of the system in terms of the potential-strength parameter, and the quark mass, For a quark mass of zero, a quadratic equation inE ³ is obtained. One solution agrees with earlier work, and the other can be rejected on physical grounds. The various components of the composite three-body wave function are dominated by thel=0s-state component as the quark mass approaches one third of the system rest-mass energy. For zero quark mass thes-wave component is about 29% of the normalization, thep wave about 44%, thed wave about 22%, and thef wave 4% of the normalization.     

Dispersion approach to quark-binding effects in weak decays of heavy mesons

The dispersion approach based on the constituent quark picture and its applications to weak decays of heavy mesons are reviewed. Meson interaction amplitudes are represented within this approach as relativistic spectral integrals over the mass variables in terms of the meson wave functions and spectral densities of the corresponding Feynman diagrams. Various applications of this approach are discussed:Relativistic spectral representations for meson elastic and transition form factors at spacelike momentum transfers are constructed. Form factors at q² > 0 are obtained by the analytical continuation. As a result of this procedure, form factors are given in the full q² range of the weak decay in terms of the wave functions of the participating mesons.The 1/m_Q expansion of the obtained spectral representations for the form factors for the particular limits of the heavy-to-heavy and heavy-to-light transitions are analysed. Their full consistency with the constraints provided by QCD for these limits is demonstrated.Predictions for form factors for B_(s) and D_(s) decays to light mesons are given.The B → γℓν decay and the weak annihilation in rare radiative decays are considered. Nonfactorizable corrections to the B⁰ mixing are calculated.Inclusive weak B decays are analysed and the differential distributions are obtained in terms of the B meson wave function.     

QCD sum rules analysis of the rare B_{c}\rightarrow X\nu\bar{\nu} decays

Taking into account the gluon correction contributions to the correlation function, the form factors relevant to the rare decays are calculated in the framework of the three-point QCD sum rules, where X stands for axial vector particle, AV(D _s1), and vector particles, V(D ^*,D _s ^*). The total decay width as well as the branching ratio of these decays are evaluated using the q ² dependent expressions of the form factors. A comparison of our results with the predictions of the relativistic constituent quark model is presented.     

Study of short-lived silver isotopes with a laser ion source

The continuum part of the⁶Li (a,a)⁶Li (1.47–2.47 MeV) scattering data at E_a=50 MeV are extracted in two discretized bins. Coupled-channel calculations are carried out coupling the 1⁺ ground state of⁶Li with both the resonant, 3⁺ ₁ state, and two non-resonant continuum states. The discretized continuum of the⁶Li (p,p)⁶Li (1.75–3.25 MeV) scattering data at E_p=65 MeV are also analysed on the same footing. In both the cases the effect of coupling is found to be minimal.     

Gamow-Teller beta decay of the very neutron-deficientN=50 nuclide98Cd

For the first time, detailed decay-spectroscopic investigations were performed for the very neutron-deficientN=50 nuclide⁹⁸Cd. The⁹⁸Cd activity was produced in spallation reactions between 600 MeV protons and a natural tin target, yielding a⁹⁸Cd beam intensity of 10 to 60 atoms/s at the collector of the ISOLDE massseparator. By means of-ray and conversion-electron spectroscopy, 19 transitions were found to follow the ⁺/EC decay⁹⁸Cd⁹⁸Ag. The transitions at 61 and 107 keV were shown to beM1(+E2) andE2, respectively, and the⁹⁸Cd half-life was measured as 9.2±0.3 s. TheQ _EC value of⁹⁸Cd is determined semiempirically and is compared to model predictions together with the measuredQ _EC values of the neighbouring cadmium isotopes^100,102Cd and theN=50 isotones⁹²Mo,⁹⁴Ru, and⁹⁶Pd, taken from the literature. The newly established decay scheme of⁹⁸Cd includes 9 excited states of⁹⁸Ag. Four states at 1691, 1861, 2164, and 2544 keV are directly fed by 0⁺ 1⁺ Gamow-Teller beta transitions with a summed strength of 3.5 _–0.7 ^+0.8 . This value corresponds to 25±5% of the strength predicted for the GT transformation of a g_9/2 proton (in⁹⁸Cd) into a g_7/2 neutron (in⁹⁸Ag) by the extreme single-particle shell model. The GT-strength splitting and quenching, observed for⁹⁸Cd, are compared with the corresponding data for lighter even-even N=50 isotones, and are discussed with reference to the predictions of more sophisticated nuclear models. We find that only in some cases it is possible to explain qualitatively the observed GT strength distribution and its total magnitude without renormalizing the free-neutron value of the axial-vector coupling constant.Dedicated to Prof. P. Armbruster on the occasion of his 60th birthday     

Proton decay of spin isospin modes excited by the12C(6Li,6He)12N reaction

First investigations of the reaction¹²C(⁶Li,⁶He)-¹²N(p)¹¹C were used to study spin-isospin strength in the nucleus¹²N at E_Li=156 MeV. While the⁶He ejectiles were detected at _He=0° using a magnetic spectrograph, the decay protons were analysed in a wide range of backward angles (100°_p<170°) with=" an=" arrangement=" of=" semiconductor=" strip=" detectors.=" singles=" spectra=" were=" extracted=" as=" well=" as=" coincident=" excitation=" strength=" for=" the=" decay=" to=" low=" lying=" levels=">¹¹C. For the decay to the¹¹C ground state angular correlations were evaluated for six different energy regions in¹²N^*.The authors wish to thank the staff of the Karlsruhe Cyclotron Laboratory for their cooperation. This work has been funded by the German Federal Minister for Research and Technology (BMFT) under contract no. 06ER262I and by the Kernforschungs-zentrum Karlsruhe.     

The vibrational relaxation time constant for theB v=0 level of XeCl

The vibrational relaxation time constant for theB _v=0 vibrational level of XeCl^* has been investigated by observing the coupling between theB _v=1 andB _v=0 vibrational levels under saturated lasing conditions. Based on this observation, estimates of the expected extraction efficiency from theB-state have been made.     

The proton g9/2 isomer in theN=50 nucleus87Rb and M2 transition rates in85,87Rb

Low-lying states of theN=50 nucleus⁸⁷Rb have been investigated in the (, ') reaction measuring- and delayed-rf-coincidences. A half-life ofT _1/2=6(1) ns was obtained for the level at 1578.1 keV. This experimental result confirms the 9/2⁺ assignment and the proton 1g_9/2 single-particle character of this state. Experimental M2 transition strengths in^85,87Rb are compared with predictions of the shell model and the particle-core coupling model.This work was partly supported by the Bulgarian National Research Foundation.     

Multi-exponential analysis of DLTS

Deep-level transient spectroscopy (DLTS), which is widely used to characterize deep impurity centers in semiconductors, assumes a single exponential wave form for the transient junction capacitance. When there are several closely spaced energy levels this assumption is no more valid, and the conventional DLTS may lead to errorneous results. To overcome this difficulty we propose here a novel method which we call the multi-exponential DLTS(MEDLTS). The transient wave form of the junction capacitance is directly analysed into multi-exponential compouents using the nonlinear least-squares analysis program DISCRETE developed by Provencher. The resolved time constants of these components are then displayed in the form of aT ²–1/T plot. According to the results of simulation with various parameters MEDLTS is shown quite effective to resolve closely spaced energy levels which can not be resolved by the conventional DLTS. As an example of the application of this method deep levels in Si: Au were investigated. The results have shown that a single peak in conventional DLTS actually consists of two adjacent levels with activation energies and capture cross-sectionsE _B1=0.49 eV, _B1=1.1×10^–14cm² andE _B2=0.46 eV, _B2=1.3×10^–15 cm² and with amplitude ratio 11.     

Vertex form factors of the rho-meson nucleon interaction at low momentum transfer

We calculated the one pion loop contributions to the form factors of the rho-nucleon interaction within a field theoretical model using effective Lagrangians. The results show that the tensor interaction is likely to be described well within such an approach. We obtain a magnetic coupling in the range of 3.5–7.1 atQ ²=0, depending on the choice of pion-nucleon form factor and a dipole form for theQ ² dependence tensor form factor with a scale of roughly 900 MeV for space-like momentum transfer. The results agree with the findings of the recent analysis of thep-N interaction and support a small scale parameter (0.5 GeV) for the pion-nucleon form factor.This work is supported by BMFT (06BO7027) and COSY-KFA Jülich (41140512)     

Calculation of quasi-stationary state parameters within the algebraic version of the resonating-group method

The dynamical equations of the algebraic version of the resonatinggroup method are used to determine the positionsE _res,l and the widths _l of quasi-stationary states or, what is equivalent, to find the polesE _l =E _resl –i _l /2 of theS-matrix in the fourth quadrant of thek-plane. Concrete calculations are performed for the -decay of⁸Be. A comparison with the results of other authors and with experiment is made.     

Neutron scattering study of the two-dimensional spinS=1/2 square-lattice Heisenberg antiferromagnet Sr2CuO2Cl2

We have carried out a neutron scattering investigation of the static structure factorS(q _2D ) (q _2D is the in-plane wave vector) in the two-dimensional spinS=1/2 square-lattice Heisenberg antiferromagnet Sr₂CuO₂Cl₂. For the spin correlation length we find quantitative agreement with Monte Carlo results over a wide range of temperature. The combined Sr₂CuO₂Cl₂-Monte Carlo data, which cover the length scale from 1 to 200 lattice constants, are predicted without adjustable parameteres by renormalized classical theory for the quantum nonlinear sigma model. For the structure factor peakS(0), on the other hand, we findS(0) ² for the reduced temperature range 0.16<T/2 _s <0.36, whereas current theories predict that at low temperaturesS(0)T ^{2 2}. This discrepancy has important implications for the interpretation of many derivative quantities such as NMR relaxation rates. In the ordered phase, we have measured the temperature dependence of the out-of-plane spin-wave gap. Its low-temperature value of 5.0 meV corresponds to an XY anisotropyJ _XY /J=1.4×10^–4. From measurements of the sublattice mangetization we obtain =0.22±0.01 for the order parameter exponent. This may either reflect tricricality as in La₂CuO₄, or it may indicate finite-size two-dimensional XY behavior as suggested by Bramwell and Holdsworth. As in theS=1 system K₂NiF₄, the gap energy in Sr₂CuO₂Cl₂ scales linearly with the order parameter up to the Néel temperature. We also reanalyze static structure factor data for K₂NiF₄ using the exact low temperature result for the correlation length of Hasenfratz and Niedermayer and including the Ising anisotropy explicitly. Excellent agreement between experiment and theory is obtained for the correlation length, albeit with the spin-stiffness _s reduced by 20% from the spin-wave value. As in Sr₂CuO₂Cl₂ we find thatS(0) ² for the reduced temperature range 0.22<T/2 _s <0.47.     

On the role of theΔ -isobar in deep inelastic scattering on the deuteron

The role of the nuclear structure effects, viz. the boundness of nucleons and-isobar components, in the deep inelastic scattering of leptons on the deuteron is considered. It is shown that small admixture of the-isobar configurations to the deuteron wave function may lead to significant effects in the spin structure functions of the deuteronb ₁ ^D andg ₁ ^D (x): up to 4% in g ₁ ^D (x) dx and up to 10% ing ₁ ^D (x) at smallx.One of the authors (A.U.) thanks Prof. F.C. Khanna for helpful discussions and for kind offering the information used in our calculations.     

Theu=0 structure theorem

The previous theorem of the author on the analytic structure of the bubble diagram functions that occur in unitary equations (and are kernels of products of connected scattering operatorsS _m,n ^c or (S ^–1) _m,n ^c , and related quantities), is extended to a class of situations, called here in generalu=0 points, that were not covered by this earlier result.This new theorem, which is proved on the basis of a refined macrocausality condition, resolves one of the remaining crucial problems in the derivation of discontinuity formulae and related results inS-matrix theory: all points are in factu=0 points for some of the bubble diagram functions, such as ((S ^–1) _3,3 ^c S _3,3 ^c ), that are encountered even in the simplest cases. In all previous approaches, ad hoc technical assumptions with no a priori physical basis were required for these terms.The origin of theu=0 problem is the absence of information, in general, on a product of distributions that are boundary values of analytic functions from opposite directions, and more generally on the essential support, or singular spectrum, of a product of distributions whose essential supports contain opposite directions. On the other hand, the recent results obtained by Kashiwara-Kawai-Stapp in the framework of hyperfunction theory apply mainly to phase-space factors, whose bubbles are constants times conservation -functions rather than actual scattering operators. The present work has basically required the development of new physical and mathematical ideas and methods. In particular, a new general result on the essential support of a product of bounded operators is presented inu=0 situations, under a general regularity property on individual terms. The latter follows in the application from the refined macrocausality condition, in the same time as information on the essential support ofS-matrix kernels.     

On the behavior of the πN partial wave amplitudes ats=0

The behavior of theπN partial wave amplitudes in the limitss→+0 ands→? 0 is related to backward scattering in thes- andt-channel, respectively. Assuming Mandelstam analyticity we prove with the aid of the Phragmen-Lindelöf theorem that the amplitudes for high energy backward scattering inπN→πN andππ→N¯N are equal and therefore dominated by the same exchange mechanism, namely Reggeized Fermion exchange. The dominating Regge trajectory is the Δ_δ-trajectory, and it is shown that theπN partial wave amplitudes diverge fors→±0 as \(s^{ - \alpha \Delta _\delta (0) - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} \) . — Reduced amplitudes are defined which are regular ats=0. — Using recent results ofπN backward scattering real and imaginary part of thes-wave amplitudef ₀₊ ^(?) are calculated in the interval 0≦s≦7.     

Study of the centrally producer ππ andK \bar K systems at 85 and 300 GeV/c

We have studied the andK systems centrally produced in proton proton collisions at 300 GeV/c and ⁺/p proton collisions at 85 GeV/c using the CERN spectrometer. Clear evidence forS ^*/f _o(975) production is observed. An analysis performed on the ^{+ –} mass spectrum in the 1.0 GeV region, using a coupled channel formalism, shows that it is possible to describe theS ^*/f _o(975) effect with one single resonance once interference of theS ^*/f _o(975) with theS-wave background is introduced. The resultingS ^*/f _o(975) parameters arem _o =979±4MeV,g =0.28±0.04,g _K =0.56±0.18 corresponding to a pole position on sheet II at (1001±2)–i(36±4) MeV. Evidence is also found for a structure having a mass of 1472±12 MeV and a width of 195±33 MeV.     

The decay of theT=1 isospin triplet inA=12 systems

A complete theoretical study is carried out of the beta decays of the¹²B and¹²N ground states to the¹²C ground state. We calculated the form factor coefficientsF _KLs ^N (k_e, m, n, ρ) using the Cohen-Kurath wave functions. In particular, we obtained reasonable values for the form factor coefficients ^A F ₁₀₁ ⁰ and ^v F ₁₁₁ ⁰ whose ratio contains the influence of the weak magnetism coupling constant. It is shown that in this way the measurements of the shape factors presented by Wu and coworkers can be explained. In addition, it is demonstrated that the contribution of the term proportional to (WR)² cannot be completely neglected because of the large end point energyW ₀. From our value of ^v F ₁₁₁ ⁰ we have derived the radiative widthΓ _γ (M1) of the isobaric analogγ transition from the excited state¹²C^* to the ground state of¹²C. The result is in good agreement with the experimental data. For both beta transitions we have evaluated theft values which are in good agreement with the experimental values. It is confirmed that the difference between theft values for both beta transitions can be accounted for by binding energies effects.