Table of contents

The solution of the massless Schwinger model is discussed in the context of the gauge technique.

The plaquette-plaquette correlation functions are studied for compact U(1) gauge theory on a 6⁴ lattice. The author extracts the correlation length zeta for various values of the inverse temperature beta and examines the critical exponent near the critical temperature.

The critical exponent for compact U(1) gauge theory is calculated by examining the specific heat on 4⁴, 5⁴ and 6⁴ lattices. The height of the specific heat at the critical temperature as a function of the lattice size yields a critical exponent of 0.32.

By applying a unitary transformation to the Lagrangian density of the cloudy-bag model, the author obtains a generalisation of the Weinberg effective Lagrangian for pion-nucleon scattering. The new Lagrangian incorporates the Weinberg-Tomozawa result for s-wave pion scattering from any hadronic bag in a very simple but elegant fashion.

The authors have measured ( pi ^+or-, p) spectra for ^3,4He and ²⁷Al at theta =20 degrees and report on the two-nucleon pion absorption over the energy range 50-300 MeV. The pi ⁺NN to Np and pi ^-pp to pn yields for T=0 NN systems in ^3,4He are found to be larger than expected relative to pi ⁺d to pp while they are smaller for T=1 systems and show a significant difference between ³He and ⁴He.

A least-squares method is presented for determining the j_>, j_< components of sums of spectroscopic factors for one-nucleon transfer, and is applied to l=2 neutron pickup on ¹⁹F and l=2 proton stripping on ²⁹Si. Fractional d_5/2 occupancies thus derived are in good agreement with those obtained for adjacent even-even nucleui.

The existence of an effective coupling constant in QCD is discussed. A possible candidate for a renormalisation-scheme- and gauge-parameter-independent coupling constant, which was given previously at the one-loop level, turns out to be gauge-dependent at higher orders.

As a first step towards a unified treatment of hyperon-exchange reactions the authors study backward KN scattering. They present a simple Regge-pole model based on SU(3), duality and knowledge derived from the well studied backward pi N to pi N reactions and show that it gives a satisfactory fit to the data. Further tests of the model are suggested.

For pt.I see ibid., vol.7, p.1597-1609 (1981). A model for hyperon-exchange reactions, based on Regge theory, SU(3) and duality is applied to pi ^-p to Lambda ⁰K⁰. It provides a good fit to cross section, polarisation and spin correlation parameters.

Experimental data on large-angle p alpha elastic scattering at 200-450 MeV proton laboratory energies are compared with the theoretical predictions obtained using Feynman triangle diagrams with the virtual processes p+t( tau ) to alpha + pi and pN to pN.

The effects of propagation of isobaric nucleon states in the intermediate steps of multiple scattering processes have been studied and applied to proton-⁴He elastic scattering at 1 GeV. The calculations are performed within the Glauber model and results are given for the differential cross section, the polarisation and the spin rotation parameter. In the conclusions the authors stress the large cancellations observed between terms of various orders and the great sensitivity of the effects to the nucleon-nucleon amplitudes.

The spectral distribution method is applied to linear energy-weighted sum rules (LEWSR) for magnetic dipole transitions using a two-body, spin-dependent delta interaction. The authors learn that in evaluating the ground-state expectation value of the sum-rule double commutator operator, it is crucial to have accurate ground-state wavefunctions. For example, in ²⁸Si with a delta interaction, the expectation value would vanish if the ground state was taken to be the closed j shell d⁶₅2 nu /d⁶₅2 pi / (as shown by Traini). However, with the properly correlated ground-state wavefunction one obtains a substantial contribution to LEWSR. These correlations are automatically taken care of int the spectral distribution method.

Under the assumption of a single-step transfer process, sum rules are derived which relate relative cross sections to states of a given final spin to the matrix elements of two-nucleon multipole operators. For the transfer of pairs of identical nucleons of the type even in the target nucleus, the expected relative sizes of these matrix elements imply simplified sum rules, a prediction checked by calculations for two-neutron pick-up on ⁴⁵Sc.

The overall statistics of systems of fermions are reviewed. Apparent deviations from Fermi or Bose symmetrisation in scattering experiments can result if there are unobserved degrees of freedom and can be parametrised in terms of the parastatistics formalism of an earlier paper. Experiments at Yale of ¹²C on ¹²C and ¹⁶O on ¹⁶O exhibit this type of behaviour. They are analysed and an alternative explanation is given in terms of atomic processes.

The ¹²C+¹²C elastic scattering excitation function at a centre-of-mass (CM) angle of 90 degrees between 13 and 62 MeV CM energy is analysed with a complex molecular potential. Parameters of the real part of this potential are obtained from scaling the potential used for the ¹⁶O+¹⁶O case. Both the magnitude and general features of the data are reproduced quite well. Theoretical angular distributions at six typical energies, 70.7, 74-25, 78-85, 83.3, 102.1 and 112.0 MeV (lab), are also compared with data and are found to account for the general behaviour. In particular, both the sharp dip in the excitation function around 52 MeV (CM) and the angular distribution at that energy are well accounted for.

A time-dependent Hartree-Fock analysis of the collision of ³²S with ²⁷Al is carried out for a laboratory energy of 175 MeV. Using the sharp cut-off approximation a total nuclear reaction cross section of 2.27 b is obtained, corresponding to a grazing angular momentum of approximately 64h(cross). A complete fusion cross section of 1.06 b arises from an angular momentum fusion window 17h(cross)<or approximately=l_in<or approximately=47h(cross). The deep inelastic reactions on either side of the fusion window lead to two separate components in the energy spectrum of the products of strongly damped collisions with distinct Q values.

The K-shell internal ionisation in beta decay has been calculated relativistically using the wavefunction proposed by Greenland and Irvine (1972) and taking into account the effect of the indistinguishability of the two continuum electrons in the final state. The calculated results are compared with the experimental data and a possible reason for the discrepancy between theory and experiment is discussed.

The intensities of X-rays and gammas emitted per beta decay of ¹⁵¹Sm are measured using singles and coincidence methods. The K-shell internal ionisation probability in the decay to the ground state of ¹⁵¹Eu is found to be (1.59+or-0.13)*10^-6. The internal ionisation probabilities in the L₁, L₂ and L₃ subshells in the decay to the ground state are found to be (6+or-0.6)*10^-4, (9+or-0.9)*10^-4 and (15+or-1.5)*10^-4 respectively. The total L-shell internal ionisation probability in the decay to the first excited state is measured to be (31+or-6)*10^-4.

Positive-parity levels in ⁴⁹V were studied using the ⁴⁶Ti( alpha ,p gamma ) reaction of E_alpha =8 MeV. A gamma - gamma angular correlation measurement yielded the mixing ratio 1.4_-0.8⁺¹⁰ for the transition between the 1646 keV level (1/2₁⁺) and the 748 keV level (3/2₁⁺). These levels were considered to be the band-heads of the ¹/₂(200) and ³/₂(202) bands. The mean lifetime of the 1646 keV level was measured to be 9.5_-1.1^+1.5 ps by the recoil-distance method. A B(M1) value of (1.6_-1.5^+2.4)*10^-5 e² fm² was deduced for the 1/2₁⁺ to 3/2₁⁺ transition from these data. Furthermore, a Doppler-shift attenuation experiment gives 0.7_-0.2^+0.3 ps as the mean lifetime of the 1995 keV (3/2₂⁺) level. The present results combined with previous data indicate that the B(M1) value for the 1/2₁⁺ to 3/2₁⁺ transition is 1/30-1/50 of those for other M1 transitions between the positive-parity levels in ⁴⁹V. A strong-coupling model calculation with band mixing shows that this hindered M1 transition is the result of the cancellation of M1 matrix elements at beta approximately=0.2.

The total reaction cross sections for the target nuclei ⁴⁵Sc, ⁴⁸Ti, ⁵¹V and ^52,53,54Cr induced by 13.6 MeV deuterons and 27.2 MeV alpha particles were measured. The deuteron-induced total reaction cross sections for ⁴⁸Ti and ^52,54Cr are well reproduced by optical-model calculations. Ambiguity of parameters for these nuclei is reduced considerably. The total reaction cross sections corresponding to alpha particles are analysed in the quasiclassical approximation. It is shown that isotopic-isotonic effects may be explained quantitatively if one assumes that the diffuseness of the nuclear density distribution for the nucleus ⁵²Cr is less than that for ⁵¹V by Delta a=0.28+or-0.11 fm, and the diffuseness of the isotope ⁵⁴Cr is greater than that for ⁵²Cr by Delta a=0.13+or-0.11 fm. The optical-model analysis of elastic scattering and total reaction cross sections for the nuclei ⁴⁵Sc, ⁴⁸Ti and ⁵¹V was carried out concurrently. The experimental data are explained successfully using a six-parameter optical potential.

The anisotropies of 10 gamma rays in the decay of ¹⁹¹Pt oriented at 2.7 mK in Fe have been measured. The nuclear magnetic moment of ¹⁹¹Pt has been determined to be 0.498(11) mu _N from the gamma-ray anisotropies and also from observing NMR on oriented ¹⁹¹Pt. Multipole mixing ratios of the gamma rays were deduced and used to obtain a set of absolute E2 and M1 multipole matrix elements for transitions in ¹⁹¹Ir. Comparison of the deduced matrix elements with calculated values suggests that the Nilsson model, including Coriolis mixing, gives a reasonable basis for understanding low-lying ¹⁹¹Ir even-parity states.