Expressions for the number of J=0 pairs in even-even Ti isotopes
- Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08855-8019 (United States)
- Instituto de Estructura de la Materia, Consejo Superior de Investigaciones Cientificas, Serrano 123, E-28006 Madrid (Spain)
- Department of Physics and Institute of Natural Sciences, Kyung Hee University, Suwon, KyungGiDo (Korea, Republic of)
- Department of Theoretical Physics and Mathematics, Bucharest University, P.O. Box MG11 (Romania)
We count the number of pairs in the single-j-shell model of {sup 44}Ti for various interactions. For a state of total angular momentum I, the wave function can be written as {psi}={sigma}{sub J{sub P}}{sub J{sub N}}D(J{sub P}J{sub N})[(j{sup 2}){sub J{sub P}}(j{sup 2}){sub J{sub N}}]{sub I}, where D(J{sub P}J{sub N}) is the probability amplitude that the protons couple to J{sub P} and the neutrons to J{sub N}. 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 {sup 44}Ca. 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{center_dot}Q interaction. We are also able to obtain simplified formulas for the number of J=0 pairs for the I=0 states in {sup 46}Ti and {sup 48}Ti by noting that the unique state with isospin vertical bar T{sub z} vertical bar+2 is orthogonal to all the states with isospin vertical bar T{sub z} vertical bar.
- OSTI ID:
- 20695998
- Journal Information:
- Physical Review. C, Nuclear Physics, Vol. 71, Issue 3; Other Information: DOI: 10.1103/PhysRevC.71.034317; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2813
- Country of Publication:
- United States
- Language:
- English
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