A possible non-Regge behaviour of the πN amplitude at high energies

The total cross sections up to 65 GeV/c and the experimental real parts of the isospin evenπN forward amplitude are compatible with the dispersion relation. However the arguments which led to the introduction of theP′ Regge pole (α _p′≈0.5) are not valid. The data are compatible with the existence of the integral in Lehmann's sum rule, which implies a finite real partD ⁺(∞) at infinity. — The isospin odd combinationσ ^? is still consistent with the reggeizedρ-exchange model and with Pomeranchuk's theorem.     

Is a subtraction really necessary in the isospin even πN dispersion relation?

It is shown that the assumption of anunsubtracted fixed-t dispersion relation for the isospin evenπN amplitudeA ⁺ is compatible with all data. The prediction for the subtraction function agrees reasonably well with independent determinations. The assumption has the consequence that the ratio of thes-channel helicity flip and non flip amplitudes vanishes in the high energy limit.     

Impact parameter expansion of πN scattering amplitudes at intermediate energies

Impact parameter transforms of isospin even no-flip πN-amplitudes and of the overlap function are calculated from the new CERN phase shifts. The results are compared with different models.—The approximate equality of the partial wave and the impact transform forbq=(l+ 1/2) is valid for smalll and not for largel as frequently assumed. The “optical potential” has a repulsive core in the real part and rather flat tails beyond 0.5 fermi in the real and imaginary parts.     

Pairing vibrational and isospin rotational states in a particle number and isospin projected generator coordinate method

Pairing vibrational and isospin rotational states are described in different approximations based on particle number and isospin projected, proton-proton, neutron-neutron and proton-neutron pairing wave functions and on the generator coordinate method (GCM). The investigations are performed in models for which an exact group theoretical solution exists. It turns out that a particle number and isospin projection is essential to yield a good approximation to the ground state or isospin yrast state energies. For strong pairing correlations (pairing force constant equal to the single-particle level distance) isospin cranking (-ωT_x) yields with particle number projected pairing wave function also good agreement with the exact energies. GCM wave functions generated by particle number and isospin projected BCS functions with different amounts of pairing correlations yield for the lowest T = 0 and T = 2 states energies which are practically indistinguishable from the exact solutions. But even the second and third lowest energies of charge-symmetric states are still very reliable. Thus we conclude that also in realistic cases isospin rotational and pairing vibrational states may be described in the framework of the GCM method with isospin and particle number projected generating wave functions.     

Time-evolution of isospin mixing in the unified exciton model

The unified exciton model, based on a master-equation approach, is extended to describe also the coupling between exciton states of different isospin. This allows the determination of the time evolution of the isospin mixing coefficient μ²(t). The equilibration of the excited nucleus, both in exciton number and isospin space, is discussed. It is shown that the nucleus essentially decays before full equilibrium is established.     

Isospin mixing observed in the reaction 12C(6Li, α)14N

The reaction ¹²C(¹²Li, α)¹⁴N was studied to investigate the isospin mixing of high-lying levels in ¹⁸F. Excitation functions and angular distributions of the α-transitions to the ground, first and second excited states in ¹⁴N were measured for bombarding energies from 3.2 to 8.0 MeV. The isospin-forbidden cross section for the excitation of the lowest T = 1 state in ¹⁴N at 2.31 MeV was found to lie between 1–2 % of that of the allowed transitions. A partial wave analysis of the α₁ angular distribution data revealed a strong resonance with J^π = 2⁺ at E_x = 15.99 MeV. Arguments are presented which tentatively identify this resonance as being due to two close-lying 2⁺ levels with different isospin.     

Zero trajectories of invariant πN amplitudes. I

Zero trajectories of invariant πN amplitudes have been calculated from the results of the recent phase shift analyses of the Karlsruhe-Helsinki and CMU-LBL groups. It is remarkable that the zero patterns of all invariant amplitudesA, B (for elastic π^± p scattering and also for the isospin even and odd combinations) are similar to each other. This is unexpected from dual models, in particular sinceB ⁺ contains the effects of diffraction. There are qualitative discrepancies with the zero pattern of Odorico's Linear Zero Model. The good agreement between the results derived from the two phase shift analyses indicates that the ambiguities have been resolved in the same way. The continuation of the trajectories to unphysical regions and several applications will be treated in the second part of this paper.     

Isospin and density waves in asymmetric nuclear matter

The excitation of small density oscillations (zero sound) and isospin oscillations (isospin sound) in cold asymmetric nuclear matter (in the ground state ?⁰_n> ?⁰_p, ?⁰ = ?⁰_n+?⁰_p = 0.17 nucleons/fm³) is investigated within the framework of the Landau theory of normal Fermi liquids. There is only one undamped mode of excitation, which consists predominantly of isospin oscillations, with some admixture of density oscillations. The phase velocity of this undamped wave depends very weakly on the neutron excess and is close to that of a pure isospin wave (isospin sound) in symmetric nuclear matter of the same density. At the neutron excess corresponding to that existing in heavy nuclei the amplitude of the density oscillations constitutes about 30 % of the amplitude of the neutron excess density oscillations. Calculation with a suitably parametrized charge dependent quasiparticle interaction in asymmetric nuclear matter shows that for (?⁰_n??⁰_p)/?⁰ > 0.63 both zero sound and isospin sound are strongly damped.     

Isospin sum rules and discontinuity formulae for inclusive reactions

This paper describes a functional method of deriving families of sum rules that express the full content of isospin conservation. In particular, it is shown that there seem to be no isospin relations involving inclusive cross sections beyond those that follow from I_z conservation alone.     

The role of isospin on the N=Z line

The role played by isospin in nuclear structure phenomena encountered on the N=Z line is discussed. New results on Coulomb energy differences (CED) at high spin for odd-A nuclei in the f _7/2 shell are presented and interpreted in the framework of a simple Cranked Shell Model treatment involving an exact numerical diagonalisation. Results for the CED between the A=46 even-even mirror pairs are also discussed. The CED between the T=1 states in N=Z odd-odd nuclei and their isobaric analogues are suggested as a possible probe of np pairing on the N=Z line. First results from a numerical diagonalization of IBM-4 are cited.     

Spin and isospin in a gauge theory with monopoles

The mechanism by which systems of spinless bosons with isospin and spinless magnetic monopoles acquire a spin in their ground states is investigated in the context of SU(2) gauge models. Contrary to recent claims, it is demonstrated that isospin degrees of freedom are not converted into spin degrees of freedom. For a spin $\text{1}\text{2}$ state, solutions are explicitly constructed, exhibiting the isospin degree of freedom.     

Low mass πN enhancement in inelastic αp interaction

Evidence for an enhancement in the isospin $\text{I =}\text{1}\text{2}\text{π}\text{N}$ system at M = 1130 MeV/c² (Γ = 80 MeV/c²) has been found in the reaction αp → αx at an incident α-momentum of 4.00 and 5.08 GeV/c. A strong t-dependence of the cross section and a mass-slope correlation are seen as the main features of the data.     

The decay of theτ lepton to six pions

We present the branching ratio predictions of an isospin statistical model forτ decays to four, five and six pions. Limits on the branching ratios of the three possible six pionτ decay modes using the Conserved Vector Current (CVC) Hypothesis and thee ⁺ e ^?→6π cross section data are also presented. We find that the isospin model prediction is in good agreement with the well-measured four pion decay modes and consistent with the five pion decay modes. However, we find that some of the recent six pionτ measurements do not agree with the isospin model and the CVC prediction.     

Study of the Isospin Mixing in 6Li with α + p + n Three-Body Model

We calculate the isospin mixing probabilities for both T = 0 and T = 1 states of ⁶Li systematically, and compare them to clarify the relation between the structure of ⁶Li and the isospin mixing probabilities. As a result, the effect of halo structure on the isospin mixing cannot be seen clearly. The effect of the coupling to the continuum states such as of ⁵He + p and ⁵Li + n is suggested.     

On the use of ibm-2 in a shell of neutrons and protons

We discuss the role of isospin in boson approximations for a system with neutrons and protons in the same shell. The lack of isospin symmetry in the IBM-2 model can be approximately corrected by using an N, T-dependent hamiltonian.     

Isospin mixing between low-lying states of the odd-odd N = Z nucleus 54Co

Isospin mixing of the recently discovered doublet of 4(+) states with isospin quantum numbers T = 0 and T = 1 in 54Co is analyzed. It is shown that the measured E2/M1 multipole mixing ratios can be used to estimate the isospin mixing of these states. Combining the new experimental data with results of a shell model calculation, the amount of isospin mixing is found to be approximately 0.2%.     

Saturation of isospin bounds and constraints on experimental data and amplitude analysis in πN-scattering

In this paper we prove new and interesting isospin bounds in pion-nucleon scattering and we investigate their saturations using the CERN-phase shift analysis. These isospin bounds are saturated exactly along certain lines in the (P_LAB, cosθ)-plane and impose strong constraints on experimental data and amplitude analyses. Also, we obtain all constraints on data and amplitude analysis when different isospin bounds are saturated or degenerated.     

Pion properties at finite isospin chemical potential with isospin symmetry breaking

Pion properties at finite temperature, finite isospin and baryon chemical potentials are investigated within the SU(2) NJL model. In the mean field approximation for quarks and random phase approximation fpr mesons, we calculate the pion mass, the decay constant and the phase diagram with different quark masses for the u quark and d quark, related to QCD corrections, for the first time. Our results show an asymmetry between μI 0 and μI 0 in the phase diagram, and different values for the charged pion mass(or decay constant) and neutral pion mass(or decay constant) at finite temperature and finite isospin chemical potential. This is caused by the effect of isospin symmetry breaking, which is from different quark masses.