Low Angular Momentum States Research Articles

Giant dipole resonance in excited 120Sn and 208Pb nuclei populated by inelastic alpha scattering

The evolution of the giant dipole resonance (GDR) in hot 120Sn and 208Pb nuclei was studied by measuring high energy γ-rays from the decay of the resonance. The excited nuclei were populated by inelastic scattering of α-particles at 40 and 50 MeV/nucleon. The resonance width was observed to increase systematically with excitation energy in both systems. Inelastic scattering populates low angular momentum states in the target. The observed width increase is thus attributed to fluctuations in the nuclear shape induced by temperature.

Long- and short-range interactions in the temperature dependent collisional excitation of the antisymmetric stretching CO2(001) level by highly vibrationally excited pyrazine

The relaxation of highly vibrationally excited pyrazine, C4H4N2, by collisions with CO2 that produce molecules in the vibrationally excited antisymmetric stretch state (0001) has been investigated using high resolution infrared transient absorption spectroscopy at a series of ambient cell temperatures. The vibrationally hot (Evib≊5 eV) pyrazine molecules are formed by 248 nm excimer laser pumping, followed by rapid radiationless decay to the ground electronic state. The nascent rotational and translational product state distributions of the vibrationally excited CO2 molecules are probed at short times following the excitation of pyrazine. The temperature dependence of this process, along with the CO2 product state distributions, strongly suggest that the vibrational excitation of CO2 occurs via two mechanisms. The vibrational energy transfer is dominated by a long-range attractive force interaction, which is accompanied by almost no rotational and translational excitation. However, the CO2(0001) product state distribution also reveals a smaller contribution from a short-range interaction that results in vibrational excitation accompanied by substantial rotational and translational excitation. The long-range interaction dominates scattering into low angular momentum (J) states while the short-range interaction is most important for molecules scattering into high J states. The implications of these results for our understanding of the relaxation of molecules with chemically significant amounts of vibrational energy are discussed.

Magnetic point vortex and parasupersymmetry

We develop a formalism for point vortex interaction in parasupersymmetry. It is shown that vortices are compatible with parasupersymmetry and there are zero range interactions in some low angular momentum states.

Rotational state distribution of oriented NO molecules scattered from Ag(111) surfaces

Both classical and quantum calculations are made for the steric effect with respect to the rotational state distribution of oriented NO scattered from Ag(111) with the use of a Morse type potential including angle dependence between the molecular axis and the surface normal. It is shown that the steric effect for rotational states of low angular momentum depends strongly on the anisotropic property in the repulsive part of the potential. The results of numerical calculations seem to reproduce the characteristics of the steric effect observed experimentally.

Strong coupling and quasispinor representations of the SU(3) rotor model

We define a coupling scheme, in close parallel to the coupling scheme of Elliott and Wilsdon, in which nucleonic intrinsic spins are strongly coupled to SU(3) spatial wave functions. The scheme is proposed for shell-model calculations in strongly deformed nuclei and for semimicroscopic analyses of rotations in odd-mass nuclei and other nuclei for which the spin-orbit interaction is believed to play an important role. The coupling scheme extends the domain of utility of the SU(3) model, and the symplectic model, to heavy nuclei and odd-mass nuclei. It is based on the observation that the low angular-momentum states of an SU(3) irrep have properties that mimic those of a corresponding irrep of the rotor algebra. Thus, we show that strongly coupled spin-SU(3) bands behave like strongly coupled rotor bands with properties that approach those of irreducible representations of the rigid-rotor algebra in the limit of large SU(3) quantum numbers. Moreover, we determine that the low angular-momentum states of a strongly coupled band of states of half-odd integer angular momentum behave to a high degree of accuracy as if they belonged to an SU(3) irrep. These are the quasispinor SU(3) irreps referred to in the title.

Elastic electron scattering from state-selected molecules

Electronically elastic, electron scattering cross sections are calculated for molecules in particular rotational states in order to establish the sensitivity of the scattering pattern to the quantum state. For the examples of diatomic molecules and symmetric tops considered here, the scattering pattern provides a unique fingerprint of the quantum state if one measures the scattered intensity for different orientations of the scattering vectors. The structure in the scattered intensity reflects the anisotropy of the square of the rotational wavefunction. Even for low angular momentum states which have diffuse rotational wavefunctions, very large differences in intensity are the result at certain scattering angles for states whose quantum numbers differ even by only one unit.

Classical model for angular momentum mixing of Rydberg states.

A classical model for l mixing of Rydberg states in atomic collisions is described. The primary assumption of the model is that l changing occurs in a single hard-sphere collision between the Rydberg electron and the perturbing atom which is represented by the zero-energy scattering length L. Predictions of the model, which are in the form of cross sections as functions of principal quantum number n, are compared with data for l mixing of Na(nd) and Rb(nf) by rare-gas atoms. Agreement is, in most cases, quite good, comparable with that of other, more sophisticated, models. It is shown that, because the calculation must be carried out in the reference frame of the ion core, the energy deficit between low angular momentum states and the nearest hydrogenic manifold can be made up in a single collision between the Rydberg electron and the perturbing atom, an effect that is analogous to the gravitational slingshot effect used to alter the orbits of a spacecraft under the influence of the Sun's gravitational field. Comparison of data for l mixing by ground-state Rb atoms with model calculations in which L is treated as a free parameter leads to an estimate of 10 a.u. for the zero-energy scattering length of Rb.

Isomer ratios of86,87Y and84Rb in the alpha induced reaction on85Rb

Isomer ratios for87Y,86Y and84Rb from α-induced reactions on85Rb in the energy range between 20 and 60 MeV have been measured. The data show a characteristic increase followed by a decrease with the increase in bombarding energy. The fall in the isomer ratio values are explained on the basis of enhanced angular momentum depletion by the precompound particles and thereby leaving the compound system at low angular momentum states. A different reaction mechanism has been proposed for the low yield of the high spin isomer in the /α, αn/ reaction in85Rb.

Rotational alignment in soft nuclei

Abstract It is shown that in transitional odd-A nuclei, where the rotation-aligned coupling scheme usually takes place, the low collective angular momentum states of the decoupled band are not completely aligned due to core softness. This is illustrated on the example of La-nuclei.

Rotation-vibration excitation using the infinite order sudden approximation for rotational transitions: Li+–N2

The rotational transitions in a collision of Li+ with N2 at 4.23 eV (center of mass) have been treated in the infinite order sudden approximation while treating the vibrational transitions in close coupling. A number of new problems were encountered and solved. The solution of the close coupling equations for the long range ion–molecule interaction was facilitated by use of an asymptotic ending technique. Due to the high energy of the collision and the extent of the potential, as many as 10 000 relative angular momentum states were required. Solutions for the high angular momentum states were obtained by means of a Born-like approximation. Intermediate angular momentum states were treated in the WKB approximation. Many low angular momentum states were obtained by solving the vibrationally close coupled equations, and a technique was developed by which it was possible to interpolate the magnitude and phase of the S-matrix elements between relative angular momentum states, permitting the solution of the close coupling equations for far fewer angular momentum states than would otherwise be required. Since the phase of the S matrix varies rapidly with diatom orientation, the integration of the S matrix over molecular orientation requires a large number of Gauss integration points. To avoid this problem we used Filon quadrature which allows integration over several periods of the phase with just a few integration points. A fit to an a priori interaction potential for Li+–N2 was made. The calculations of integral and differential cross sections were made over a range of angles which covered the experimentally measured cross sections. The results of the calculation do not agree with the experiment.

Noble-gas broadening of the sodium D lines measured by photon echoes

Noble-gas-induced relaxation of photon echo signals is used to determine the broadening rates of the Na D lines. Since echo signals are 'Doppler free', precision measurements are possible at low perturber-gas pressures (<or=1 Torr), and are sensitive to the previously inaccessible central lineshape. Interestingly, the authors results disagree with other recently published broadening rates. The equivalence of linewidth measurements and echo measurements on transitions between states of low electronic angular momentum is discussed.

Proton-proton potential models obtained from the Virginia phase-shift analysis

The results of a recent phase-shift analysis of the experimental data have been used to construct equivalent local potential models for the low angular momentum states of the proton-proton system. The equivalent local potential for the 1S0 state is found to be quite different from that obtained from the Livermore phase-shifts and to be an improvement on the Reid 1S0 potential at intermediate distances. The difficulties experienced with the previous 3P0 and 3P1 phase-shifts are not encountered with the new data. The triplet tensor potential differs from most other phenomenological results but is similar to that of the Paris potential and thus reflects the effects of omega exchange. A simple nonlocal potential for the set of even states 1S0, 1D2 and 1G4 and one for the set of odd states 3P0, 3P1, 3P2-3F2, 3F3 and 3F4-3H4 are presented.

On the exact solution of the harmonic quadrupole collective hamiltonian

Explicit expressions for the eigenfunctions of the harmonic quadrupole collective Hamiltonian both in the lab and intrinsic systems of references are given. Two alternative approaches, the technique of projective coherent states and the theory of harmonic polynomials in collective coordinates, are used. Symmetry properties and recursive formulae for the internally labelled wave functions are established. Applications to the yrast states as well as to the low angular momentum states in the case of the asymmetric rotor Hamiltonian are also presented.

Generalized shells in nuclei: Hartree-Fock calculations for bubble nuclei

Hartree-Fock calculations in the bubble degree of freedom have been performed on a variety of spherical nuclei. Of particular importance are incipient bubble configurations in 36Ar, 68Se, 84Se, 100Sn, 116Ce, 138Ce and 200Hg, each of which possesses a binding energy which is comparable to that of the normal spherical closed-shell configuration. The densities of the above nuclei display strong deviations from a uniform shape, and give rise to depletions in the nuclear interior. These nonuniformities are due both to the absence of low angular momentum states in otherwise normally occupied spherical shells, and also to strong self-consistency effects. The nonuniformities in the mass density are further enhanced for nuclei whose neutron and proton densities have depressions or peaks at approximately the same distance from the center of the nucleus. A depression of the central density is most pronounced in the nuclei 36Ar, 138Ce and 200Hg. Interior depletions of the density are associated with the relatively higher energies of low angular momentum single-particle levels as compared to high angular momentum single-particle levels. This effect can give rise to moderately large gaps at the Fermi surface. Finally, it is shown that in a bubble configuration, the spin-orbit splitting of low lying doublets is sometimes reversed, and that this effect is especially pronounced for levels with low angular momentum.

Low Angular Momentum States Populated in the Decay of 178Lu

The low angular momentum states in 178Hf populated in the beta decay of the low spin state (T1/2 = 30 min) of 178Lu are investigated with both high resolution and high efficiency Ge(Li) detectors as well as a NaI(Tl)–Ge(Li) (γ,γ) coincidence system. The sources of 178Lu were produced through the 178Hf(n,p) and 181Ta(n,α) reactions on natural targets of hafnium and tantalum, respectively, using 14.8 MeV neutrons. Sixteen gamma transitions in the energy range 1090.8 to 1730.0 keV have been found to decay with the 30 min period of 178Lu. A decay scheme of 178Lu has been proposed with the excited levels in 178Hf at 93.17(2+), 306.59(4+), 1309.7(0+, 1±), 1362.7(0+, 1±, 2+), 1434.2(0+), 1442.9(0+), 1496.7(2+), 1514.2(2+), 1562.0(2+), 1772.1(0+, 1±, 2+), and 1823.2(0+, 1±, 2+) keV. The weak β-branching ratios and their log ft values are deduced from the observed γ-ray intensities and results thus obtained are discussed.

One-meson-exchange contributions to nucleon-nucleon scattering below 400 MeV and relation to scattering at higher energies

Nucleon-nucleon scattering is studied from the standpoint of meson resonances. The 0 to 400 MeV p-p and n-p data is fit by a sum of ρ, ω, π and ε Born contributions in the geometric-unitarization model, with the S-wave phase-shift parameters searched phenomenologically as in phase-shift analysis. The correspondence of this model with ordinary phase-shift analysis, which incorporates just the pion pole term, is brought out. Evidence for multi-uncorrelated meson exchange effects is indirectly obtained in that the ρ, ω and ε masses, when freed in the search, take on low values, much as the ρ and ω masses take on low values in single-pole fits to the nucleon electromagnetic form factors. However the π-mass, when freed, remains close to the physical mass. Thus a verification of the pion pole contribution to N-N scattering is provided by the lower partial waves. It is concluded that the muiti-pole, geometric-unitarization model correctly depicts the major features of the N-N interaction but must be augmented by uncorrelated meson-exchange contributions. Nucleon-nucleon scattering in the range 400 to 800 MeV is briefly touched upon. Several predictions are pointed out for high-energy, high orbital angular momentum states due to meson-exchange models which fit low-energy, low angular momentum states. A plea is made for experimental measurements to test time-reversal invariance and conservation of isotopic spin.

Electric-Field-Induced Spectra: Theory and Experimental Study of Formaldehyde

An experiment is described which measures the modulation, produced by an applied electric field, of the absorption coefficient of the rovibronic spectrum of a gaseous sample. Phase-sensitive detection provides for measurement of 0.01% modulation at a spectral resolution of 0.1 cm− 1 in the near ultraviolet. A theoretical development of the electric-field-induced spectral line shape and intensity as an expansion in powers of the applied field is presented. The important molecular parameters are the ground-state and excited-state dipole moments and rotational constants; measurement of the excited-state moment is discussed. The dependence of line intensity on quantum numbers is predicted to be such as to emphasize transitions to states of low angular momentum; observation of this emphasis is of importance in assigning spectra. The correspondence between field-induced and absorption spectra in a single experiment lends great confidence to assignments of specific absorption features. Experimental study of formaldehyde confirms many of the predictions of the theory. Assignments are obtained for the low-K subbands in the 3390-, 3430-, and 3520- Å bands, and the asymmetry parameters are presented. Effects of asymmetry on the EFS are shown. A method of determination of the excited-state dipole moment based on measurement of ratios of intensities of EFS in different polarizations is presented. The dipole moment of HCHO in the A 1A″ state is determined to be 1.4 ± 0.1 D.

The photodisintegration of molybdenum

Cross sections for the reactions Mo 100(γ, n + γ, p), Mo 98(γ, np), Mo 97(γ, p), Mo 92(γ, n) and Mo 92(γ, 2n + γ, np) have been determined by activation methods for photon energies up to 33 MeV. The photoproton cross section, which exhibits a maximum at 21 MeV, accounts for some ten percent of the total absorption and is about equal to the sum of the cross sections for the measured multiple reactions. The results are discussed in terms of competition between direct nucleon emission and the formation of a compound nucleus, and it is argued that the high proton yield derives from transitions between shell model states of low angular momentum. The data are consistent with the existence of an E1 “overtone” in the region above 20 MeV.

Electronic wave functions round a vacancy in a metal

A calculation of the wave functions round a vacancy in a metal has been carried out for a simple model. This corresponds to the case of a finite number of particles in a free-electron metal, with the boundary condition that the wave functions vanish on the surface of the spherical metal. Calculations are reported for particle numbers of approximately 2 x 10 2 , 2 x 10 3 and 10 6 . The density fluctuations in the unperturbed metal are found to be serious for the first two cases, but by consideration of the difference between the electronic density distributions in the perturbed and the unperturbed cases, extrapolation from the case of a relatively small number of particles to obtain results valid for very large numbers is shown to be feasible in the region surrounding the vacancy. The possibility of obtaining an accurate density difference by consideration only of states of low orbital angular momentum is exploited. Comparison is made between the finite metal results, existing Thomas–Fermi calculations, and a self-consistent von Weizsäcker calculation which is also reported here. By examination of the solutions of Poisson’s equation, it is shown that the total charge density obtained by summing the squares of the normalized wave functions for the assumed Thomas–Fermi potential in the 10 6 particle case is such as to make this potential self-consistent to a good approximation. Our calculations also reveal long-range oscillations in the total perturbed electron density for finite metals. Although the amplitude of these oscillations decreases with increasing volume, extrapolation to the case of an infinite metal does not seem justified here. However, our calculations should provide an upper bound to the amplitude for the assumed potential, and the oscillations are small. Finally, brief reference is made to applications of the present results.