Application of Self-Consistent Field Methods to Rotational Motion in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>sd</mml:mi></mml:math>Shell Nuclei

Kelson, I.; Levinson, C. A.

doi:10.1103/physrev.134.b269

Cited by 123 publications

(11 citation statements)

References 8 publications

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“…9 These difficulties are compounded by the uncertainties associated with the related "core" parameters themselves: Present evidence delimits h 2 /2I to +0.24+0.02 MeV for Ne 20 and +0.19±0.03 MeV for Ne 22 (note also that h 2 /2I= +0.21±0.O2 for Mg 24 ). The present uncertainty associated with the appropriate value for the spin-orbit coupling parameter K in the Nilsson-model description of I = 11 nuclear systems will FIG.…”

Section: Introductionmentioning

confidence: 81%

“…In situations where branching occurs from state i to two lower lying states j and /, respectively, the total transition probability associated with the gamma radiations from state i is given by the relation T^Tij+Tv, (9) and the pertinent branching ratio is expressed as B.R. = 2V/ZV (10) In the presentation to follow, the states i, j, and/or f involved are labeled as the &th member of the rotational band (k= 1, 2, 3 ...) as identified in Table I.…”

Section: Electromagnetic Transitionmentioning

confidence: 99%

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Collective Representation of Lower Lying States inNe21,Na21, an

1965

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Employing model parameters deduced from the observed static properties of the nuclear systems Ne 21 , Na 21 , and Na 28 , both total and partial gamma-ray transition probabilities involving relevant states in the ground-state rotational bands are computed within the Nilsson strong-coupling collective-model framework and compared with the respective observed values; agreement within a factor of 2 is noted for all cases with the exception of the first-excited to ground-state Ne 21 transition. Similar comparisons of relative total gamma-ray transition probabilities involving postulated § + members of these same rotational bands are also presented. The relative phases of coherently interfering magnetic-dipole and electric-quadrupole radiation amplitudes are predicted for the pertinent intraband transitions; agreement with the observed relative phases is found in three of the four cases available for unambiguous comparison. Model-predicted values for beta-ray transition probabilities involving the ground states of these three nuclei are in good agreement with observations. These comparisons provide striking support for the model validity for the description of these nuclei; prolate deformations corresponding to 77^-{-4.0 are indicated by these comparisons and in addition by examination of the total nuclear binding energy calculated as a function of deformation.

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Section: Introductionmentioning

confidence: 81%

Section: Electromagnetic Transitionmentioning

confidence: 99%

Collective Representation of Lower Lying States inNe21,Na21, an

1965

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“…(1) leads to the following equations for Cij and Siji CI/(P) = -(hj/p) 1 LCi J (p)ni(p)ji(p)-Si J (p)nt i (p)'2…”

Section: General Formalismmentioning

confidence: 99%

Influence of Electromagnetic Interaction on Neutron Scattering from Nuclei

Hogan

Seyler

1969

Phys. Rev.

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The influence of the interaction between the magnetic moment of a neutron and the Coulomb field of a target nucleus is investigated. A formalism is developed whereby the interaction can be treated exactly in optical-model calculations. Calculations performed at energies of 0.5, 1.0, 7.0, 14.5, and 24 MeV for Al, Mn, Nb, and Bi indicate that this electromagnetic interaction can be adequately treated in the Born approximation. Whereas the influence on the differential cross section is confined to scattering angles less than 2°, the influence on the polarization extends to larger angles corresponding to minima in the cross section. 6

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“…In nuclear structure physics the Hartree-Fock (HF) approach [1] is usually considered as a method to extract out of the total nuclear Hamiltonian the optimal average single particle field each of the nucleons feels due to its interactions with all the others. This so-called "selfconsistent potential" is derived by a variational principle for the total energy of the system demanding a minimum for the expectation value of the total Hamiltonian using as test-wave function a single Slater determinant.…”

Section: Introductionmentioning

confidence: 99%

Variational equations for the solution of the Hartree-Fock problem with angular momentum projection before the variation

Schmid

Grümmer

1979

Z Physik A

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A variational principle is used to determine the optimal angular momentum projected one determinant approach to the N-nucleon yrast-wave function for a given total spin value. The solution is given in terms of a set of coupled nonlinear equations. Besides an orthonormality constraint for the occupied orbits and a normalization condition for the total wave function, this set consists out of a matrix equation taking care of the fact that the spin-projected wave function does not depend on the orientation of the intrinsic determinant it is based on, and a second subset of equations, which can be considered as a Thouless theorem for the spin-projected N-nucleon state, and describes the diagonalization of the total Hamiltonian in the subspace of linear independent N-nucleon shell model configurations contained in the test-determinant. Furthermore, a numerical method for the solution of these equations is proposed and an extension of the theory for the description of excited bands is given. Finally, the consistency of the equations is checked by solving them for a simple example analytically.

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Application of Self-Consistent Field Methods to Rotational Motion insdShell Nuclei

Cited by 123 publications

References 8 publications

Collective Representation of Lower Lying States inNe21,Na21, an

Collective Representation of Lower Lying States inNe21,Na21, an

Influence of Electromagnetic Interaction on Neutron Scattering from Nuclei

Variational equations for the solution of the Hartree-Fock problem with angular momentum projection before the variation

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