TY - JOUR
T1 - Symmetries and structure in the fp shell and g9/2 shell
AU - Zamick, Larry
AU - Escuderos, Alberto
N1 - Funding Information:
We thank Shadow Robinson for his help and Yu-Min Zhao for his hospitality. A. E. acknowledges support from the Secretaría de Estado de Educación y Universidades (Spain) and the European Social Fund. We would also like to thank Noemie Koller, Gertfried Kumbartzki, Yitzhak Sharon, Ben Bayman and Igal Talmi for stimulating discussions and interactions.
PY - 2006/11
Y1 - 2006/11
N2 - First in a single-j-shell calculation (j = f7/2) we discuss various symmetries, e.g., two to one in 44Ti vs 43Ti. We note that the wave function amplitudes for T(higher) states are coefficients of fractional parentage, and that orthogonality of T(higher) and T(lower) states leads to useful results. Then we consider what happens if T = 0 two-body matrix elements are set equal to zero. We find a partial dynamical symmetry with several interesting degeneracies. It is noted that some formulae developed for identical particles also apply to different (companion) problems involving mixed systems of protons and neutrons. In the g9/2 shell, where one can have for the first time seniority violation for identical particles, we find some interesting yet unproven results.
AB - First in a single-j-shell calculation (j = f7/2) we discuss various symmetries, e.g., two to one in 44Ti vs 43Ti. We note that the wave function amplitudes for T(higher) states are coefficients of fractional parentage, and that orthogonality of T(higher) and T(lower) states leads to useful results. Then we consider what happens if T = 0 two-body matrix elements are set equal to zero. We find a partial dynamical symmetry with several interesting degeneracies. It is noted that some formulae developed for identical particles also apply to different (companion) problems involving mixed systems of protons and neutrons. In the g9/2 shell, where one can have for the first time seniority violation for identical particles, we find some interesting yet unproven results.
UR - http://www.scopus.com/inward/record.url?scp=33846264591&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33846264591&partnerID=8YFLogxK
U2 - 10.1142/S021830130600540X
DO - 10.1142/S021830130600540X
M3 - Article
AN - SCOPUS:33846264591
SN - 0218-3013
VL - 15
SP - 1681
EP - 1694
JO - International Journal of Modern Physics E
JF - International Journal of Modern Physics E
IS - 8
ER -