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Expressions for the number of J=0 pairs in even-even Ti isotopes

AuthorsZamick, L.; Escuderos, Alberto; Lee, S. J.; Mekjian, A. Z.; Moya de Guerra, Elvira ORCID; Raduta, A. A.; Sarriguren, Pedro CSIC ORCID
Keywords[PACS] Relation with nuclear matrix elements and nuclear structure
[PACS] Nuclear structure models and methods
[PACS] Properties of specific nuclei listed by mass ranges: 39 ≤ A ≤ 58
Issue Date28-Mar-2005
PublisherAmerican Physical Society
CitationPhysical Review C 71(3): 034317 (2005)
AbstractWe count the number of pairs in the single-j-shell model of 44Ti for various interactions. For a state of total angular momentum I, the wave function can be written as Ψ=∑JPJND(JPJN)[(j2)JP(j2)JN]I, where D(JPJN) is the probability amplitude that the protons couple to JP and the neutrons to JN. For I=0 there are three states with (I=0, T=0) and one with (I=0, T=2). The latter is the double analog of 44Ca. In that case (T=2), the magnitude of D(JJ) is the same as that of a corresponding two-particle coefficient of fractional parentage. In counting the number of pairs with an even angular momentum J, we find a new relationship is obtained by diagonalizing a unitary nine-j symbol. We are also able to get results for the “no-interaction” case for T=0 states, for which it is found, e.g., that there are fewer (J=1, T=0) pairs than on the average. Relative to this no-interaction case, we find that for the most realistic interaction used there is an enhancement of pairs with angular momentum J=0,2,1, and 7, and a depletion for the others. Also considered are interactions in which only the (J=0, T=1) pair state is at lower energy, interactions where only the (J=1, T=0) pair state is lowered, interactions where both are equally lowered, and the Q·Q interaction. We are also able to obtain simplified formulas for the number of J=0 pairs for the I=0 states in 46Ti and 48Ti by noting that the unique state with isospin |Tz|+2 is orthogonal to all the states with isospin |Tz|.
Description8 pages, 3 tables, 1 appendix.-- PACS nrs.: 23.40.Hc; 21.60.-n; 27.40.+z.-- ArXiv pre-print available at:
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