Redundancy-free single-particle equation-of-motion method for nuclei: (I). Intermediate coupling calculations for odd-mass near-spherical nuclei
Abstract
The problem of coupling an odd nucleon to the collective states of an even core is considered in the intermediate-coupling limit. It is now well known that such intermediate-coupling calculations in spherical open-shell nuclei necessitate the inclusion of ground-state correlation or backward coupling which gives rise to an overcomplete basic set of states for the diagonalization of the hamiltonian. In a recent letter1), we have derived a technique to free the single-particle equation-of-motion method of redundancy. Here we shall apply this redundancy-free equation-of-motion method to intermediate-coupling calculations in two regions of near-spherical odd-mass nuclei where forward coupling alone has not been successful. It is shown that qualitative effects of backward coupling previously reported are not spurious effects of double counting, although they are significantly modified by the removal of redundancy. We also discuss what further modifications of the theory will be needed in order to treat the dynamical interplay of collective and single-particle modes in nuclei self-consistently on the same footing.
References (17)
- A. Goswami et al.
Nucl. Phys.
(1970) - A.K. Kerman et al.
Phys. Lett.
(1962) - A. Klein
Phys. Rev.
(1984) - M. Baranger
Phys. Rev.
(1960) - A. Goswami et al.
Phys. Lett.
(1984) - A. de Shalit
Phys. Rev.
(1953) - D.C. Choudhury
Mat. Fys. Medd. Dan. Vid. Selsk.
(1954)S.T. BelayevMat. Fys. Medd. Dan. Vid. Selsk.
(1959) - L.S. Kisslinger et al.
Rev. Mod. Phys.
(1963)
Cited by (9)
Nuclear data sheets for A = 75
2013, Nuclear Data SheetsThe experimental nuclear spectroscopic data for known nuclides of mass number 75 (Fe, Co, Ni, Cu, Zn, Ga, Ge, As, Se, Br, Kr, Rb, Sr) have been evaluated and presented together with Adopted properties for levels and γ rays. New high-spin data are available for 75Ga, and 75Rb; and lifetime data for high-spin states in 75Br and 75Kr. For ΔJ =1, M1+E2 transitions in two rotational bands in 75Kr, several B(E2)(W.u.) values are anomalously high, deviating by 2–3 σ values from currently accepted RUL(E2) = 300. In the opinion of the evaluators, there is need to remeasure level lifetimes and multipole mixing ratios in 75Kr to resolve this serious discrepancy. New precise single-particle transfer cross section data are available for 75Ga, 75Ge, 75As and 75Se from several different reactions (2009Ka06,2008Sc03); these data give information for occupancy of valence neutron orbitals in the ground states of target nuclides: 76Ge, 76Se and 78Se. No significant new data since the 1999 NDS for A = 75 have been reported for 75As and 75Se. No data are yet available for excited states in 75Co, 75Ni and 75Sr. For 75Fe, only the isotopic identification is made with one observed event. The radioactive decay schemes of 75Co and 75Ni are unknown while those for 75Rb and 75Sr are incomplete. This work supersedes the data presented in the previous NDS evaluation of A = 75 published by 1999Fa05.
Nuclear Data Sheets for A = 77
2012, Nuclear Data SheetsThe experimental nuclear spectroscopic data for known nuclides of mass number 77 (Ni, Cu, Zn, Ga, Ge, As, Se, Br, Kr, Rb, Sr, Y) have been evaluated and presented together with adopted properties for levels and γ rays. New high-spin data are available for 77Ga, 77Br and 77Kr. New precise single-particle transfer cross section data are available for 77Ge, 77As, 77Se and 77Br from eight different reactions (2009Ka06,2008Sc03); these data give information for occupancy of valence neutron orbitals in the ground states of target nuclides: 76Ge, 76Se and 78Se. No significant new data since the 1997 NDS for A = 77 (1997Fa12) have been reported for 77Rb and 77Sr. No data are yet available for excited states in 77Ni, 77Cu and 77Y. Level schemes from the radioactive decays of 77Ni to 77Cu and 77Y to 77Sr are unknown, while those for the decays of 77Cu to 77Zn and 77Ga to 77Ge are incomplete. Detailed gamma-ray data for 77Ge from thermal-neutron capture in 76Ge, together with extensive gamma-ray data from 77Ge decay to 77As have become available from 2012Me04. This work benefited from earlier evaluations (1997Fa12,1989Fa07,1980Si05,1973Ur02) of A = 77 nuclides, however, the data presented here supersede those in above evaluations.
Nuclear Data Sheets for A = 97
2010, Nuclear Data SheetsThe 1993 evaluation of A = 97 (1993Ar09) was updated using data available prior to Nov. 19, 2009.
Nuclear data sheets for A = 75
1999, Nuclear Data SheetsThe experimental nuclear spectroscopic data for known nuclides of mass number 75 (Co, Ni, Cu, Zn, Ga, Ge, As, Se, Br, Kr, Rb, Sr) have been evaluated and presented together with adopted properties for levels and γ rays. No data are yet available for excited states in75Co,75Ni,75Cu,75Zn and75Sr. Since the 1990 evaluation (90Fa07), new high-spin data are available for75Se,75Br,75Kr and75Rb; and new nuclides of75Co,75Ni and75Sr are now identified. No significant new data, since 1990, have been reported for75Ga and75As. The nuclide75Fe has not yet been identified but half-life calculations are reported by 85Bu27 (also 71Pe16 and 97Mo25). This evaluation supersedes earlier evaluations (90Fa07,81Ek02,75Ho17) of A = 75.
Nuclear data sheets for A = 77
1997, Nuclear Data SheetsAbstract:The experimental nuclear spectroscopic data for known nuclides of mass number 77 (Nl, Cu, Zn, Ga, Ge, As, Se, Br, Kr, Rb, Sr, Y) have been evaluated and presented together with adopted properties for levels and γ rays. New high-spin data are available for77As,77Se,77Br,77Kr,77Rb and77Sr. No significant new data (since the 1989 Nuclear Data Sheets for A=77) have been reported for77Zn,77Ga, and77Ge. No data are yet available for excited states in77Nl,77Cu and77Y. This work supersedes earlier evaluations (89Fa07,80Si05,73Ur02) of A=77 nuclides.Cutoff Date:Literature available up to July 15, 1997, has been consulted.General Policies and Organization of Material:See the January issue of Nuclear Data Sheets.Acknowledgments:The evaluators are indebted to Prof. Ali Al-Shamlan and Prof. Adnan Al-Ageel for their help and encouragement. We thank A. Kestelman for mending data on77Ge β−decay (52.9 s) prior to publication, K.P. Lieb and A. Jungelaus for sending a preprint of their high-spin study of77Rb, and M.J. Martin for a detailed and constructive review of this evaluation.General Comments:The statistical analysis of γ-ray data and deduced level schemes is carried out through computer codes available at data centers in Berkeley and Brookhaven. The methodology and procedures for some of these codes are described by 86BrZQ and 86Br21. A general 3% uncertainty is assumed in quoted theoretical internal conversion coefficients taken mainly from 68Ha53.
Nuclear Data Sheets Update for A = 79
1993, Nuclear Data SheetsNuclear spectroscopic information for known nuclides of mass numer 79 (Cu, Zn, Ga, Ge, As, Se, Br, Kr, Rb, Sr, Y) have been evaluated and presented together with adopted energies and Jπ of levels in these nuclei. No data are yet available for excited states in 79Cu and 79Zn. This evaluation represents a revision of earlier ones (82Si21, 75Ur03). No data are available for 79Ni, but calculations of %β−n and T1/2(g.s) using RPA method have been reported by 89Kr02. The half -life of 79Se has been quoted as ≤6.5×104 y since 1949 (work by 49PaZZ). But a recent analysis (93HeZW) suggests that the half-life maybe longer by a factor of 10. A remeasurement of this half-life would be desirable since this isotope is of importance in reactor-irradiated fuel composition.