Random Interactions in Nuclei and Extension of 0+ Dominance in Ground States to Irreps of Group Symmetries

  • random one plus two–body hamiltonians invariant with respect to o(n_1)o(n_2)symmetry in the group–subgroup chains u(n )u(n_1)u(n_2)o(n_1)o(n_2)and u(n )o(n )o(n_1)o(n_2) of a variety of interacting boson models are used to investigate the probability of occurrence of a given(ω_1ω_2)irreducible representation(irrep)to be the ground state in even–even nuclei;[ω_1] and [ω_2] are symmetric irreps of o(n_1) and o(n_2) respectively. employing a 500 member random matrix ensemble for n boson systems (with n=10–25),it is found that for n_1,n_2≥3 the (ω_1ω_2)=(00) irrep occurs with~50% and (ω_1ω_2)=(n0) and (0n) irreps each with~25% probability. similarly,for n_1≥3,n_2=1,for even n the ω_1=0 occurs with~75% and ω_1=n with~25% probability and for odd n,ω_1=0 occurs with~50% and ω_1=1,n each with~25% probability. an extended hartree–bose mean–field analysis is used to explain all these results.
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  • [1] .Johnson C W, Bertsch G F,Dean D J. Phys. Rev.Lett. , 1998, 80: 27492. Bijker R,Frank A. Phys. Rev. Lett . , 2000, 84: 4203. Kota V K B. Phys. Rep. , 2001, 347: 2234. Zelevinsky V, Volya A. Phys. Rep. , 2004, 391: 3115. ZHAO Y M, Arima A,Yoshinaga N. Phys. Rep. , 2004, 400: 16. Kota V K B, Kar K. Phys. Rev. E, 2002, 65: 026130; Pluhar Z, Weidenm..ller H A. Ann. Phys. ( N. Y. ) , 2002, 297: 344; Chau P H-T et al . Phys. Rev. C, 2002, 66: 0613027. Daley H J, Iachello F. Ann. Phys. (N.Y. ) , 1986, 167: 738. Iachello F, Arima A. The Interacting Boson Model . Cambridge. Cam..bridge University Press, 19879. Rowe D J and Iachello F. Phys. Lett. B, 1983, 130: 23110. Kota V K B et al. J. Math. Phys. , 1987, 28: 1644; Devi Y D, Kota V K B. Z. Phys. A, 1990, 337: 1511. Engel J, Iachello F. Phys. Rev. Lett. , 1985, 54: 1126; Kusnezov D. J.Phys. A, 1990, 23: 5673; JI H Y et al. Nucl. Phys. A, 1999, 658: 19712. LONG G L et al. Science in China A, 1998, 41: 129613. Bijker R, Iachello F, Ann. Phys. (N.Y. ) , 2002, 298: 33414. Kota V K B. Ann. Phys. (N.Y. ) , 1998, 265: 10115. Kota V K B. Ann. Phys. ( N. Y. ) , 2000, 280: 1,Van Isacker P, Warner D D. Phys. Rev. Lett. , 1997, 78: 326616. Kota V K B. Pramana..J. Phys. , 2003, 60: 5917. Kusnezov D. Phys. Rev. Lett. , 2000, 85: 377318. Bijker R, Frank A. Phys. Rev. , 2001, C64: 061303; Phys. Rev. ,2002 C65: 04431619. Kota V K B. J. Math. Phys. , 1997, 38: 663920. Bijker R. preprint, 2003, nucl-th/030306921. Dukelsky J et al . preprint, 2003, nucl-th/031003122. Leviatan A. Ann. Phys. ( N. Y. ) , 1987, 179: 201; Dukelsky J et al. Nucl . Phys. , 1984, A425: 9323. Kota V K B. In: Proc. of the Symp. on Symmet ries in Science XIII.eds. Gruber B,Marmo G, Yoshinaga N. Dordrecht (The Netherlands) .Kluwer Academic publishers, 2004,P. 265;Van Isacker P. Rep. Prog.Phys. , 1999, 62: 1661
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V.K.B.Kota. Random Interactions in Nuclei and Extension of 0+ Dominance in Ground States to Irreps of Group Symmetries[J]. Chinese Physics C, 2004, 28(12): 1307-1312.
V.K.B.Kota. Random Interactions in Nuclei and Extension of 0+ Dominance in Ground States to Irreps of Group Symmetries[J]. Chinese Physics C, 2004, 28(12): 1307-1312. shu
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Received: 2003-11-29
Revised: 1900-01-01
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Random Interactions in Nuclei and Extension of 0+ Dominance in Ground States to Irreps of Group Symmetries

    Corresponding author: V.K.B.Kota,
  • Physical research laboratory,ahmedabad 380009,india

Abstract: random one plus two–body hamiltonians invariant with respect to o(n_1)o(n_2)symmetry in the group–subgroup chains u(n )u(n_1)u(n_2)o(n_1)o(n_2)and u(n )o(n )o(n_1)o(n_2) of a variety of interacting boson models are used to investigate the probability of occurrence of a given(ω_1ω_2)irreducible representation(irrep)to be the ground state in even–even nuclei;[ω_1] and [ω_2] are symmetric irreps of o(n_1) and o(n_2) respectively. employing a 500 member random matrix ensemble for n boson systems (with n=10–25),it is found that for n_1,n_2≥3 the (ω_1ω_2)=(00) irrep occurs with~50% and (ω_1ω_2)=(n0) and (0n) irreps each with~25% probability. similarly,for n_1≥3,n_2=1,for even n the ω_1=0 occurs with~75% and ω_1=n with~25% probability and for odd n,ω_1=0 occurs with~50% and ω_1=1,n each with~25% probability. an extended hartree–bose mean–field analysis is used to explain all these results.

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