Mesonic Corrections Research Articles

Competition between Allowed and First-Forbidden β Decay: The Case of ^{208}Hg→^{208}Tl.

The β decay of ^{208}Hg into the one-proton hole, one neutron-particle _{81}^{208}Tl_{127} nucleus was investigated at CERN-ISOLDE. Shell-model calculations describe well the level scheme deduced, validating the proton-neutron interactions used, with implications for the whole of the N>126, Z<82 quadrant of neutron-rich nuclei. While both negative and positive parity states with spin 0 and 1 are expected within the Q_{β} window, only three negative parity states are populated directly in the β decay. The data provide a unique test of the competition between allowed Gamow-Teller and Fermi, and first-forbidden β decays, essential for the understanding of the nucleosynthesis of heavy nuclei in the rapid neutron capture process. Furthermore, the observation of the parity changing 0^{+}→0^{-}β decay where the daughter state is core excited is unique, and can provide information on mesonic corrections of effective operators.

Meson loop effect on high density chiral phase transition

Abstract We test the stability of the mean field solution in the Nambu-Jona-Lasinio model in a semi-quantitative manner. For stable solutions with respect to both the σ and π directions, we investigate effects of the mesonic loop corrections of 1/N c, which correspond to the next-to-leading order in the 1/N c expansion, on the high density chiral phase transition. The corrections weaken the first order phase transition and shift the critical chemical potential to a lower value. At N c = 3, however, instability of the mean field effective potential prevents us from determining the minimum of the corrected one.

Mesonic corrections to the quark propagator in the Nambu-Jona-Lasinio model

Corrections to the chiral condensate and quark mass in the Nambu-Jona-Lasinio model for the four-dimensional cutoff and dimensional-analytical regularizations are calculated within the mean-field expansion in the bilocal quark-source formalism. It is shown that pion corrections to quark masses are zero in both regularizations. This coincidence of the results suggests that the zero pion contribution to the quark mass is a fact of the Nambu-Jona-Lasinio model and is independent of regularization.

Electromagnetic corrections to baryon masses

We analyze the electromagnetic contributions to the octet and decuplet baryon masses using the heavy-baryon approximation in chiral effective field theory and methods we developed in earlier analyses of the baryon masses and magnetic moments. Our methods connect simply to Morpurgo's general parametrization of the electromagnetic contributions and to semirelativistic quark models. Our calculations are carried out including the one-loop mesonic corrections to the basic electromagnetic interactions, so to two loops overall. We find that to this order in the chiral loop expansion there are no three-body contributions. The Coleman-Glashow relation and other sum rules derived in quark models with only two-body terms therefore continue to hold, and violations involve at least three-loop processes and can be expected to be quite small. We present the complete formal results and some estimates of the matrix elements here. Numerical calculations will be presented separately.

Mesonic corrections to the shape of quark distributions

We compute the full x dependence of the proton and neutron spin structure functions in the MIT bag model, including the effect of gluon exchange and the meson cloud. Impressive agreement is found for x larger than 0.1, where polarised gluons are not expected to play a significant role.

Proton spin and baryon octet axial couplings

Peripheral spin structure of the nucleon generated by the soft mesonic radiative corrections is studied within the light-cone perturbation theory. Starting with the tree-levelSU (6) symmetry, we find good description of the axial-vector couplings in β-decay of hyperons. We study the proton helicity flow from the baryonic core to the angular momentum of the pionic cloud. It is found that in the relativistic light-cone approach the spin-flip pattern is different from that in the conventional nonrelativistic models. The axial-vector current matrix elements are shown to receive large corrections from beyond the conventional static limit. The important virtue of using the light-cone vertex functions of the meson-baryon Fock components of the proton is that the local gauge invariance and the energy-momentum sum rule are satisfied automatically. We infer the radius of the light-cone form factor from an analysis of the experimental data on the fragmentation of high-energy protons into nucleons and hyperons-the process dominated by stripping off the mesons of the meson-baryon Fock states.

DeuteronA(q 2) structure function in the low and mediumq 2 range

The deuteronA(q 2 ) structure function is calculated up toq 2=20 fm−2 with the Paris potential including relativistic nucleonic and mesonic corrections. Different parametrizations (Iachello et al., Galster et al., Hohler et al., Gari and Krumpelmann (GK)) of the nucleon electromagnetic form factors (emff) are used. Unlike the data of Simon et al., those recently taken at Saclay are reasonably well reproduced by our full predictions for the first three emff considered. On the contrary, the predictions for the GK model fail to fit the Saclay data. The dependence ofA(q 2 ) on the cut-off masses of the hadronic form factors is also investigated.

Deep-inelastic scattering on nuclei: Impulse approximation and mesonic corrections

We present a unified relativistic covariant description of nucleon binding and mesonic corrections to nuclear structure functions in terms of a Feynman diagram approach. The connection between considerations in the infinite momentum frame, where the parton model can be applied, and in the nucleus rest frame is discussed. A new method to estimate mesonic corrections in terms of a nuclear model based on effective meson-nucleon theory is proposed. We apply this method to evaluate the mean mesonic excess in nuclei n mes , the mean mesonic momentum squared k mes 2 , and to derive the bounds on pion distribution function in nuclei. We find that the bulk of the EMC effect at x > 0.1 is reproduced within the impulse approximation with mesonic corrections, while this approximation fails to explain new EMC data at x < 0.1.

DeuteronA(q 2 ) structure function in the low and mediumq 2 range

The deuteronA(q 2 ) structure function is calculated up toq 2=20 fm−2 with the Paris potential including relativistic nucleonic and mesonic corrections. Different parametrizations (Iachello et al., Galster et al., Hohler et al., Gari and Krumpelmann (GK)) of the nucleon electromagnetic form factors (emff) are used. Unlike the data of Simon et al., those recently taken at Saclay are reasonably well reproduced by our full predictions for the first three emff considered. On the contrary, the predictions for the GK model fail to fit the Saclay data. The dependence ofA(q 2 ) on the cut-off masses of the hadronic form factors is also investigated.

Mesonic and relativistic corrections to electromagnetic form factors of the deuteron

Observables of the elastic electron-deuteron scattering are calculated with the deuteron wavefunctions of the Paris potential including mesonic and relativistic corrections. It is shown that the theoretical result is in agreement with experimental data up to a momentum transfer of q2 approximately=1 fm-2.

Covariant soliton dynamics: Structure of the nucleon.

We present a model of nucleon structure that is fully covariant. We begin with a Lagrangian that describes quarks coupled to various mesonic fields (\ensuremath{\sigma},\ensuremath{\pi},\ensuremath{\rho},\ensuremath{\omega}) and an additional field, \ensuremath{\chi}, which is required to bind the quarks into a nucleon. The couplings of the \ensuremath{\sigma}, \ensuremath{\pi}, \ensuremath{\rho}, and \ensuremath{\omega} fields to the quarks are fixed so as to reproduce the empirically determined coupling of these mesons to the nucleon. The latter couplings are taken from fits to nucleon-nucleon scattering data made using one-boson-exchange models. Therefore the free parameters of the model are the mass and coupling constant of the \ensuremath{\chi} field and the quark mass, ${m}_{q}$. In order to simplify the problem, the nucleon is assumed to virtually decay into a quark and a diquark. Equations which specify this amplitude are found by using the equations for the quark and meson field operators obtained from our Lagrangian. The equations which we solve are fully covariant and nonlinear and are solved by iteration. In this model the quark dynamics is governed by the mesonic fields whose source is the nucleon itself. The amplitudes for the emission of these fields by the nucleon depend upon the (nucleon)\ensuremath{\rightarrow}(quark + diquark) amplitudes whose structures we are attempting to determine. This model therefore requires a self-consistent solution and leads to the nonlinear equations noted above. At this point we have not calculated mesonic corrections to the nucleon observables such as the magnetic moments, form factors, and ${g}_{A}$, although we have included the effects of all the mesonic fields in the calculation of the nucleon mass. However, the calculation of nucleon observables, using current operators which contain only quark fields, yields a surprisingly good fit to electromagnetic form factors, magnetic moments, ${g}_{A}$, etc. (It is possible that some aspects of these results will be less satisfactory when mesonic corrections are calculated.) The model has the further virtue of generalizing the SU(6) quark model of the nucleon so as to be consistent with the covariance requirements of the theory of special relativity. It is clear that the major limitation of the model, other than the use of the diquark approximation, is the lack of a satisfactory description of the confinement mechanism as the \ensuremath{\chi} field serves to bind the system but does not actually confine the quarks.

Magnetic moments of [formula omitted] isomers in neutron-deficient lead isotopes

The magnetic moments of the 12 + isomers in 192, 196, 198, 200, 206Pb and of the 33 2 + isomer in 205Pb have been measured using the PAD technique. The results for the g-factors are: g(192) = −0.173(2), g(196) = −0.1600(15), g(198) = −0.1552(15), g(200) = −0.1512(15), g(206) = −0.1496(18), and g(205) = −0.148(5). As all states have a rather pure (νi 13 2 ) −n configuration, the values reflect directly the νi 13 2 orbital. They show a decrease towards the more neutron-deficient isotopes attributed to the reduced core polarisation as a result of decreasing occupation of the i 13 2 neutron shell. The measured systematics are discussed regarding core polarisation, mesonic corrections, and small admixtures of core-excited states to the i 13 2 wave function.

Mesonic and relativistic corrections to the deuteron charge radius and quadrupole moment

The mesonic and relativistic corrections to the deuteron charge radius and quadrupole moment are re-examined in the light of recent developments. Using the deuteron wavefunction of the Paris potential, the results are Delta r=0.0036 fm and Delta Q=0.0063 fm2.

Muon capture by the deuteron with outgoing neutrinos of very small momentum

Large mesonic exchange current corrections are obtained in the calculation of the rate of muon capture by the deuteron with outgoing neutrinos of very small momentum. Detailed results are given for ${m}_{\ensuremath{\nu}}=0$. No difference sufficiently large to be observed with present techniques is predicted for ${m}_{\ensuremath{\nu}}\ensuremath{\le}2.5$ MeV/${\mathit{c}}^{2}$.RADIOACTIVITY Muon capture $^{2}\mathrm{H}+{\ensuremath{\mu}}^{\ensuremath{-}}\ensuremath{\rightarrow}n+n+{\ensuremath{\nu}}_{\ensuremath{\mu}}$, mesonic exchange contribution, small neutrino momentum.

Relativistic and Mesonic Corrections to the Forward Cross Section ford(γ, p)n

The discrepancy between the theoretical and the experimental values of the forward deuteron photodisintegration cross section is found to be sensibly reduced by the inclusion of the relativistic corrections (Darwin-Foldy and spin-orbit terms) in the charge density. On the contrary, the pionic corrections calculated in the pseudoscalar $\ensuremath{\pi}\mathrm{NN}$ coupling are in the opposite direction.

Mesonic corrections to the baryon mass spectrum

We here investigate possible pi mesonic contributions to the masses of the light baryons. The description of the spectrum is improved in particular for the Σ-Λ splitting. However, the meson and gluon exchange contributions are difficult to distinguish one from the other. The role of the pion field in the spectrum of P-wave baryons and for the charge radius of the neutron is also briefly discussed.

One-pion exchange currents effect on the allowed beta-decays in the 1p shell nuclei

A calculation is performed of theft- values for beta-decay allowed transitions in theA=6 −14 nuclei. The 1p-shell model and the one-pion exchange model are used. It is found that the mesonic corrections are state dependent and may take large values when logft>4.0.

Asymmetry of Beta-Ray Angular Distribution in Polarized Nuclei andG-Parity Nonconservation

We have derived an equation for the $\ensuremath{\beta}$-ray angular distribution including Coulomb corrections, radiative corrections, induced effect, and higher-order nuclear matrices. With this equation and the experimental data on $\ensuremath{\beta}$-ray asymmetries in polarized $^{12}\mathrm{B}$ and $^{12}\mathrm{N}$, we conclude that the strength of the second-class induced tensor is $\frac{{f}_{T}}{{f}_{A}}=\ensuremath{-}(0.96\ifmmode\pm\else\textpm\fi{}0.35)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ in the limit of the impulse approximation. A possible modification of this value due to mesonic corrections is discussed.

Second-class currents in 0−→0+ and unique nuclear β transitions

The induced pseudotensor contribution to 0− → 0+ and uniqueβ transitions has been analyzed starting from two possible forms of the nonrelativistic Hamiltonian. The role of mesonic corrections and mesonic second-class currents has been discussed

Trinucleon bound state properties and form factors with the B.K.R. potential

The triton binding energy, S′ - and D-state probabilities are determined using the B.K.R. potential. Neglecting mesonic corrections, the charge and magnetic form factors are computed for 3H and 3He. They show a diffraction minimum at q 2 = 14.4 fm −2.