Many-particle Model Research Articles

Theory of atomic ordering in copper-platinum alloys

An expression is obtained for the energy of a binary system with an hcp lattice using a many-particle model. This expression is used for calculating regions of relative stability of modifications of the copper-platinum alloy. The effect of a many-particle interatomic interaction on the order-disorder phase equilibrium diagram and on order parameters is studied. Agreement between theory and experiment has been achieved for the first time for the phase diagram as well as for short-range order parameters in the two spheres of copper-platinum alloy. It is shown, within the framework of the model used, that such a comprehensive agreement between theory and experiment is possible only if many-particle interaction and the trigonal character of L11 phase are taken into account. Calculations were performed with the help of the multicluster version of the Kikuchi method in the tetrahedron + triangle approximation. Results obtained clarify significantly the Understanding of the interatomic interaction in copper-platinum alloy.

The Lipkin pseudospin model in the variational exp S formalism

The variational extended exp S formulation of the coupled-cluster method is numerically studied and applied to the many-particle model of Lipkin, Meshkov and Glick.In contrast to the standard exp S scheme the new method is shown to give good results even in the deformed phase without explicit introduction of a new single-particle basis. The ground-state energies are found to satisfy the variational property of being upper limits to the exact energies. Also the excitation energies are in satisfactory overall agreement with the true ones for arbitrary interaction strengths. Special attention is paid to the phase-transition region of the interaction strength parameter.

Nuclear structure study of51V

The spins and electromagnetic properties of levels up to 3,700 keV in51V were studied by means of inelastic proton scattering. Results are discussed with reference to the many-particle shell model using effective surface delta and realistic Kuo-Brown interactions.

The nuclear surface studied with a momentum-dependent interaction in the Thomas-Fermi and Hartree approximations

A self-consistent many-particle model containing a two-body interaction with a quadratic momentum dependence is developed in the Hartree approximation. The various possible algebraic forms of the momentum dependence are studied in parallel. A simple modification of the standard Thomas-Fermi approximation is formulated for the treatment of models with momentum-dependent interactions. Numerical calculations are carried out for symmetric semi-infinite nuclear matter. The modified Thomas-Fermi approximation, as compared with the Hartree approximation, is found to underestimate the surface diffuseness and the surface energy by typically 10%. It is demonstrated that the surface properties are very sensitive to the particular algebraic form of the quadratic momentum dependence.

Photoneutron cross sections for 9Be obtained with quasi-monoenerget1c photons

Absolute ( γ, xn) cross sections for 9Be were measured with monochromatic photons from positron annihilation in flight in the energy range from 17 to 37 MeV. No pronounced structure was found in the cross sections in contrast to recent experiments performed with bremsstrahlung sources. The results are compared with many-particle shell model calculations.

Polynomial expansions for excitation strengths

Rapidly convergent expansions for the strength function of an excitation in a many-particle model space are given in terms of orthogonal polynomials defined by the state or partial state densities of the system. Convergence is assured in a wide range of circumstances by the operation of a central limit theorem. Level-to-level fluctuations are in many cases small, their automatic elimination in the statistical smoothing generated by truncating the series then leading to only small errors.

Beta decay of 23Mg and 27Si

The β-decays of 23Mg and 27Si have been studied by observing the delayed γ-radiation. The following branches (and log ft values) have been found for 23 Mg(β +) 23 Na: 0 keV, 0.914 ± 0.002 (3.67); 440 keV, 0.086 ± 0.002 (4.40); and 2391 keVa (6.9 ± 0.9) × 10 −5 (4.98); and for 27 Si(β +) 27 Al: 0 keV, 0.9977 ± 0.0002 (3.61); 1014 keV, (4.9 ± 2.4) × 10 −5 (7.3); 2211 keV, (1.80 ± 0.13) × 10 −3 (4.68); 2734 keV, (1.55 ± 0.17) × 10 −4 (5.02); and 2981 keV, (2.59 ± 0.24) × 10 −4 (4.33) . The branches to the 2391 keV level from the 23Mg decay and to the 2734 keV level from the 27Si decay have not been previously reported. A comparison is made between the experimental results and the predictions of the many-particle shell model.

Investigation of the reaction at Eτ = 15 MeV

Abstract Angular distributions of α-particle groups, corresponding to 34 levels observed in the reaction 31P(τ, α)30P at Eτ = 15 MeV, have been measured with a split-pole magnetic spectrograph equipped with position sensitive detectors. New 30P levels were found at 5890 ± 12, 5930 ± 8, 6050 ± 10 and 6090 ± 6 keV. For 27 levels the ln value could be deduced. Experimental spectroscopic factors from a DWBA analysis are compared with those from recent many-particle shell model calculations.

Electromagnetic transition rates and vibrational modes in34S

States in34S up to 6 MeV excitation energy, populated by the reaction31P(α, pγ), have been investigated by Doppler shift and line shape analysis andpγ andγγ angular correlation measurements. The strengths of electromagnetic transitions between even parity levels are compared with theoretical predictions of the weak coupling unified model and the many-particle shell model. The experimental evidence for a weak coupling of the single particle motion to vibrational modes is discussed.

Mesures de Rapports d'Embranchement et de Vies Moyennes dans 30Si

Gamma rays from the decay of 30Si levels with excitation energies less than 6.0 MeV have been studied by the 27Al(α, pγ)30Si reaction. The γ rays were detected in a Ge(Li) detector in coincidence with protons observed in an annular detector placed at 180°. Branching ratios and lifetimes have been extracted. The lifetimes have been measured by the Doppler-shift attenuation method.The electromagnetic matrix elements for some of the observed levels were compared with recent many-particle shell model and core-coupling calculations.

Many-particle shell model calculation of electromagnetic transition rates and multipole moments in A = 30–34 nuclei

Many-particle shell model wavefunctions have been used to calculate magnetic dipole and electric quadrupole transition probabilities and moments as well as log ft values for even-parity states in the A = 30–34 region. The calculations were performed: (i) for bare-nucleon g factors and charges; (ii) for effective g factors and charges obtained from a least-squares fit to experimental data; (iii) for effective single-particle matrix elements obtained from an analogous fit. For the magnetic dipole transitions and moments it appeared necessary to perform separate fits for the A = 30–32 and 33–34 regions. The final best fits for strong transitions are excellent. The average deviation between theory and experiment with three effective single-particle matrix elements for M1 transitions and effective charges for E2 transitions is about 30 %, only slightly larger than the average experimental error. Show cases are 31Si and 33S where the calculated lifetimes, branching ratios and mixing ratios (including the sign) all agree with the measured values within the experimental error. Poor fits, however, are obtained for transitions involving 1 + states and, more generally, states for which the experimental and theoretical spectroscopic factors are in disagreement. Strong M1 transitions generally have a pronounced singe-particle character (with one contribution in the matrix element predominating), whereas all E2 transitions have a collective character (many small contributions).

A many-particle dipole interaction model with finite anhysteretic susceptibility

A many-particle dipole interaction model with finite anhysteretic susceptibility

The photodisintegration of9Be

The absorption spectrum for dipole γ quanta with energies below 35 MeV is calculated using the many-particle nuclear-shell model. The cross-sections of the partial photonuclear reactions (γ, n), (γ, p), (γ, d) and (γ, α) and the photonucleon spectra are calculated. Spin-orbital interactions are neglected and it is assumed that the residual pairing interaction is well described by Serber forces. The supermultiplet structure of the considered spectrum of excited levels is thus preserved and the matrix of the Hamiltonian decomposes into a number of submatrices having considerably lower order, each of which can be diagonalized separately. This circumstance made it possible to consider states which are not directly excited in γ-quantum absorption, which however do considerably influence the structure of the absorption curve and especially the decay properties of the excited levels and the spectrum of emitted particles. The agreement with the experimental data is very satisfactory.

Intrinsic motion and translational invariance in shell-model calculations

The nuclear Hamiltonian has been replaced by another one which is identical with respect to the motion of the nucleons in their centre-of-mass-system, i.e. to their intrinsic motion. The new Hamiltonian can be diagonalized in a shell-model basis without destroying translational invariance or giving rise to spurious effects due to the c.m. motion. This provides an alternative to the usual variational approach for handling very light nuclei provided difficulties arising from the hard core in the nucleon-nucleon potential are somehow circumvented. The method is extended to the nuclear Hamiltonian within the framework of the many-particle shell model, where corrective terms are found to arise when a non-local central potential is used. Finally the method is applied to the many-particle shell model in the Tamm-Dancoff approximation. Matrix elements of the terms, which take properly into account the c.m. motion, are found to be very important for 1 − states. It is shown in a quite general way that in the usual many-particle shell model 1 −, T = 1 excited states approximately describe the intrinsic motions, while 1 −, T = 0 excited states are generally spurious.

Many-Particle Self-Consistent Model

The number and general nature of the self-consistency equations that may arise in a universal bootstrap theory of all strongly interacting particles is discussed. There are more equations than there are variables to be determined, so that it may be possible to bypass some of the divergence difficulties of dispersion theory by making use of a sufficient number of the equations. A general method of attacking the difficulties associated with the many-particle aspect of the problem is discussed. A simple first approximation to the method is applied to a model of four multiplets (pseudoscalar meson, vector meson, baryon ground state, and $j={\frac{3}{2}}^{+}$ baryon excited state), under the assumption that unitary symmetry is approximately valid. It is argued that comparison with experiment of the calculated differences in masses of particles within the same multiplet will provide experimental tests that are meaningful in a low-order approximation to the model. It is shown that if the mass splitting of the baryon octet is assumed to be partly self-generating (i.e., not resulting completely from the mass splitting of the meson multiplets), a nondegenerate solution to the model is most likely if there is a large violation of $R$ invariance.