Microscopic description of rotational spectra including band-mixing. - I. Formulation in a microscopic basis

Within the framework of the projection theory of collective motion, a microscopic description of the rotational energy with band-mixing is formulated using a method based on an inverse power perturbation expansion in a quantity related to the expectation value of the operator Jy2. The reliability of the present formulation is discussed in relation to the difference between the individual wave functions obtained from the variational equations which are established before and after projection. In addition to the various familiar quantities which appear in the phenomenological energy formula, such as the moment of inertia parameter, the decoupling factor and the band-mixing matrix element for |0394K| = 1, other unfamiliar quantities having the factors with peculiar phases, (1)J+1 J(J + 1), (1)J+3/2(J 1/2) (J + 1/2) (J + 3/2), (1)J+1/2(J + 1/2) J(J + 1), (1)J J(J + 1) (J 1) (J + 2) and [J(J + 1)]2 are obtained. The band-mixing term for |0394K| = 2 is also new. All these quantities are expressed in terms of two-body interactions and expectation values of the operator Jym, where m is an integer, within the framework of particle-hole formalism. The difference between the moment of inertia of an even-even and a neighbouring even-odd nucleus, as well as the effect of band-mixing on the moment of inertia are studied. All results are put into the forms so as to facilitate comparisons with the corresponding phenomenological terms and also for further application. J. Physique 43 (1982) 1575-1595 NOVEMBRE 1982,

[1]  B. Biran.  Trace anomaly for gauge theories in a conformally flat space , 1983 .

[2]  N. Ullah.  On the distribution of the angular momentum coefficients , 1979 .

[3]  S. Jang,et al.  Application of the projected Hartree--Fock method to rotational motion in 1p-shell odd-A nuclei , 1976 .

[4]  B. Ward.  Spin sum rules for inelastic (anti) neutrino-nucleon scattering , 1973 .

[5]  F. Villars,et al.  Collective Energies from Momentum– and Angular Momentum–Projected Determinantal Wavefunctions , 1971 .

[6]  P. Ring,et al.  Symmetry-conserving Hartree-Fock-Bogolyubov-theory and its application to collective nuclear rotation , 1970 .

[7]  J. Christensen.  Doctoral thesis , 1970 .

[8]  I. P. Johnstone,et al.  Application of the projected Hartree-Fock model to 21Ne , 1969 .

[9]  K. L. Bhatia,et al.  Decoupling Parameter in Light Nuclei , 1969 .

[10]  N. Onishi.  Hartree-Bogoliubov theory with projection method , 1968 .

[11]  A. Kamlah,et al.  An approximation for rotation-projected expectation values of the energy for deformed nuclei and a derivation of the cranking variational equation , 1968 .

[12]  J. C. Parikh,et al.  INVESTIGATION OF GROUND-STATE CORRELATIONS FOR A MODEL HAMILTONIAN OF THE NUCLEUS. , 1968 .

[13]  J. Svenne,et al.  Parity Mixing in Nuclear Hartree-Fock Calculations , 1967 .

[14]  I. Kelson.  Collective and spherical states in O16 , 1965 .

[15]  Chi-yu Hu.  The influence of the Pauli exclusion principle on the moment of inertia of strongly deformed nuclei , 1965 .

[16]  D. Rowe.  A calculation of some ΔK = ±2 band-mixing effects in the odd-mass nucleus W183 , 1965 .

[17]  I. Kelson,et al.  Application of Self-Consistent Field Methods to Rotational Motion in sd Shell Nuclei , 1964 .

[18]  B. Verhaar.  ODD-EVEN SHIFT AND MOMENTS OF INERTIA FOR K=0 ROTATION BANDS OF ODD NUCLEI , 1963 .

[19]  D. Thouless,et al.  Variational approach to collective motion , 1962 .

[20]  D. Thouless.  Stability conditions and nuclear rotations in the Hartree-Fock theory , 1960 .

[21]  R. Peierls,et al.  THE COLLECTIVE MODEL OF NUCLEAR MOTION , 1957 .

[22]  D. R. Inglis.  Particle Derivation of Nuclear Rotation Properties Associated with a Surface Wave , 1954 .