INTERACTING BOSON FERMION APROXIMATION FOR NUCLEAR STRUCTURE

Principal Investigators: 
	V.Paar, Croatian Academy of Arts and Sciences
	R.A.Meyer, U.S. Department of Energy
	W.B.Walters, University of Maryland

Project description and plan of work

The interacting boson model (IBM) by Arima and Iachello has been remarkably successful in the description of nuclear structure phenomena in medium heavy and heavy even-even nuclei. Its extension to the boson-fermion systems by Iachello and Scholten7,8 referred to as the interacting boson-fermion model (IBFM), was successfully applied to description of odd-even nuclei. This approach was further extended by Paar and collaborators to odd-odd nuclei, with coupled bosons, odd proton and odd neutron fermions; this model is referred to as the interacting boson-fermion-fermion model (IBFFM). The Hamiltonian of interacting boson-fermion-fermion Hamiltonian (IBFFM) reads: 
H = HIBFM () + HIBFM () - HIBM + HRES ( )          (1)
where HIBFM () and HIBFM () denote the IBFM Hamiltonian for the neighboring odd-even and even-odd nuclei, respecitvely, HIBM denotes the IBM Hamiltonian for the even-even core nucleus and HRES ( ) denotes the residual proton-neutron interaction. IBFFM calculations have been performed for several odd-odd nuclei and rather good agreement with experiment was obtained. There has been recently renewed interest in the study of high-spin states in nuclei. In the framework of IBM two features play a major role in the physics of high-spin states: (i) the breaking of correlated Cooper pairs that build the low-lying part of the spectrum and (ii) the promotion of particles from the closed shells to the valence shells that lead to the large deformations observed experimentally. It was pointed out by Iachello that a special role is played by dynamic symmertries of the SU(3) type in superdeformed bands. At large angular momenta in nuclei there appears the phenomenon of breaking the correlated pairs of IBM into their fermionic constituents. Therefore, in order to describe high-spin states, the model space corresponding to the susccessive breaking of (s,d) pairs was introduced, formed by the set of states with zero, one and two broken pairs in addition to states of the boson condensate. Energy and wave functions in such description are obtained by diagonalizing the Hamiltonian 
H=HB+HF+VBF+VMIX         (2)
within the model space. The first three terms in the Hamiltonian describe the bosons, ferrmions and boson-fermion interactions, respectively and have the standard form of the interacting boson-fermion model. The new ingredient for description of high-spin states is the pair breaking interactions, VMIX, that mixes states with different number of broken pairs. The study of high-spin states in nuclei within the framework of Eq. (2) was initiated with the work of Gelberg and Zemel, Morrison, Faessler and Lima, Yoshida, Arima and Otsuka, Chuu and Hsieh and Alonzo, Arias and Lozano, who considered a model space with zero and one broken pair. In a further extension of the interacting boson model, Vretenar, Paar, Bonsignori and Savoia have enlarged the model space to include two broken pairs. As a first example of these calculations the transitional nucleus 194Hg was considered by Iachello and Vretenar. For 194Hg a considerable amount of experimental information is available. The calculation reproduced the observed features of the first and second pair breaking. As was pointed out by Iachello and Iachello and Vretenar the advantages of this method are that it is straightforward, contains no additional free parameters (since all parameters can be determined from the low-lying states and that the corresponding calculations are done in the laboratory frame (thus allowing a direct comparison with experiment). The disatvantage, on the other hand, is that, as more and more pairs are broken, the dimension of the configuration space rapidly increases. The method is therefore useful for transitional nuclei, where the total number of bosons is relatively small. The same approach was successfully applied to high-spin states in several other nuclei. Iachello, Gelberg von Brentano and Casten and Paar, Sunko and Vretenar have pointed out possible applications of the framework of interacting boson model to description of superdeformed states. Within this framework one can treat superdeformation in heavy nuclei by introducing the model space where each successive term has two bosons (one particle boson and one hole boson) more than the preceding term. In this case the energy levels can be obtained by diagonalizing the Hamiltonian 
H = HB(s,d) + HB (s', d') + VB (s,d; s', d') + VMIX     (3)
where the first three terms describe particle and hole bosons and their interaction and VMIX is the new ingredient. The model of Eq. (3) has been previously applied by Duval and Barrett, and Sambataro to the study of excited configurations in several nuclei including up to 2p-2h excitations, and Iachello has pointed out that the same method may be applied to the study of superdeformed bands, with the use of Casten's NN scheme to estimate the value of total boson number in the superdeformed bands. An alternative method of analysis is that of describing the situation directly in terms of two shells. Superdeformed bands are suitable to look for dynamic symmetries. Dynamic symmetries in odd-A nuclei were previously introduced within the framework of the interacting boson-fermion model and discussed by Warner, Vervier, Bijker and Kota. Iachello has pointed out that the Class II Bose-Fermi symmetries can provide an explanation of the peculiar experimental discovery of identical moments of inertia in neighboring nuclei. Gelberg, von Brentano and Casten have proposed an interpretation of the identical superdeformed bands in 152Dy and 151Tb as a consequence of U(6/12) supersymmetry which was investigated by Iachello, Iachello and Kuyucak, Balantekin, Bars, Bijker and Iachello, and Van Isacker, Frank and Sun. Paar, Sunko and Vretenar have pointed out that in the framework of the interacting boson-fermion model there exists a limit where no polarization is induced by the addition of an odd fermion to the SU(3) boson core. A possible extension of boson-fermion dynamical symmetries to odd-odd nuclei was first considered by Bars, who noted that the existence of the U(6/4) and U(6/12) supersymmetries to the nuclei in the supermultiplet (194Pt, 195Pt, 196Pt*,...) implies the possibility of having a larger supersymmetry describing the odd-odd nucleus 196Au as well. The simplest of such schemes incorporating both U(6/4) and U(6/12) chains have been investigated. An alternative symmetry chain for odd-odd system was introduced by Balantekin and Paar. The U(6/12) symmetry Hamiltonian has been related to the Hamiltonian of the interacting boson-fermion model. For odd-odd systems it was shown that an exact equivalence is established by adequately revising the exchange term of the IBFFM Hamiltonian. The framework of the interacting boson model has been also used to study the features of quantum chaos.

The plan of the work

The plan of the work on the proposed project includes further investigations in the framework of interacting boson model in relationship to most recent experimental data. In particular, the plan includes the following topics: 
	Croatian participants:

V.Paar, full professor (Croatian Academy of Sciences and Arts, and Faculty of Science) 
S.Brant, associated professor (Faculty of Science) 
V.Lopac, full professor (Faculty of Technology) 
D.K.Sunko, assistant professor (Faculty of Science)
Lj.Simicic, assistant (Faculty of Science)
N.Pavin, graduate student (Faculty of Science)
R.Pezer, graduate student (Faculty of Science)

	Senior American participants:

R.A.Meyer (Department of Energy), Co-principal investigator
W.B.Walters (University of Maryland), Co-principal investigator
F.Iachello (Yale University)
R.F.Casten (Brookhaven National Laboratory)
R.Chrien (Brookhaven National Laboratory)
P.Chowdhury (Yale University)
Y.Alhassid (Yale University)
C.J.Lister (Yale University)

Previous collaboration

Scientific collaboration between V.Paar and R.A.Meyer was initiated and gradually extended to a collaboration with a number of distinguished American scientists: F.Iachello (Yale University), R.F.Casten (Brookhaven National Laboratory), R.Chrien (Brookhaven National Laboratory), B.D.Kern (University of Kentucky), R.G.Lanier (LLNL), S.J. Robinson (Tennessee Technical University), W.R.Daniels (Los Alamos Scientific Laboratory), A.B. Balantekin (Oak Ridge National Laboratory), E.R.Flynn (Los Alamos Scientific Laboratory) and others. The cooperation of Zagreb group with American scientists was intensified during last few years by a fruitful participation of D.Vretenar in theoretical research at Yale University in collaboration with F.Iachello, Y.Alhassid, C.J.Lister and collaborators. Significant contributions have been also made by S.Brant, V.Lopac, D.K.Sunko and D.Vorkapi} from the Zagreb group. On several occasions R.A.Meyer has visited Croatia for shorter periods in the framework of previous U.S.-former Yugoslavia joint projects or using Fulbright and NATO fellowships. In 1986 R.A. Meyer was, together with V.Paar, Chairman and Co-organizer of a large International Conference on Nuclear Structure, Reactions and Symmetries in Dubrovnik, which has resulted in three books of proceedings (published by World Scientific and Harwood Academic Publishers). V.Paar has visited USA eight times in the framework of previous joint projects, with shorter stays at various U.S. institutions (Lawrence Livermore National Laboratory, Oak Ridge National Laboratory, Lawrence Berkeley Laboratory, Iowa State University, University of Pennsylvania, Yale University, Brookhaven National Laboratory, University of Maryland) and delivered talks at several international conferences in USA. Also, V.Paar and S.Brant have been working in USA on a project of U.S. Department of Defense. The collaboration was supported by U.S. National Science Foundation in the framework of three previous joint projects (Principal investigator: V.Paar, Co-principal investigator: R.A.Meyer): "The study of nuclear structure in the Cluster-vibration model and Vibration models in the region of medium-heavy nuclei" (1980-1983); "Study of nuclear structure in the cluster-vibration model and quasicluster-vibration model in the region of medium-heavy nuclei" (1985-1987); and "Spin distribution, level density, IBFFM and quantum chaos" (1991-1993). The main scientific results of previous collaboration between Croatian and U.S. scientists are presented in the following publications published in coauthorship of American and Croatian coauthors (denoted by ** and *, respectively):
  1. Broglia, R.A., Landowne, S.**, Paar, V.*, Nilsson, B., Bes, D.R., Flynn, E.R.**: Coupling between inelastic and pair transfer degrees of freedom. The 208Pb(t,p)210Pb(3-) reaction analyzed in the coupled channel Born approximation. Phys.Lett. 36B (1971) 541-546.
  2. Balantekin, A.B.**, Paar, V.*: Realization of the parabolic rule in the Bose-Fermi symmetry schemes for odd-odd nuclei. Phys.Lett. 169B (1986) 9-13.
  3. Scholten, O.**, Brant, S.*, Paar, V.*: A microscopic approach to the U (6/4)>Spin (6) Hamiltonian of the interacting boson-fermion model. Phys.Lett. 171B (1986) 335-338.
  4. Flynn, E.R.**, Igo, G.J.**, Broglia, R.A., Landowne, S.**, Paar, V.*, Nilsson, B.:
  5. An experimental and theoretical investigation of the structure of 210Pb. Nucl. Phys. A195 (1972) 97-118.
  6. Paar, V.*, Brant, S.*, Canto, L.F., Leander, G.**, Vouk, M.*: SU(6) quadrupole phonon model for even and odd nuclei and the SU(3) limit. Nucl.Phys. A378 (1982) 41-76.
  7. Tokunaga, Y., Seyfarth, H., Schult, O.W.B., Brant, S.*, Paar, V.*, Vretenar, D.*, Boerner, H.G., Barreau, G., Faust, H., Hofmeyr, Ch., Schreckenbach, K., Meyer, R.A.**: A study of 75Se by neutron capture and the SU(3) - SU(5) transition in the quadrupole phonon representation. Nucl.Phys. A430 (1984) 269-300.
  8. Kern, B.D.**, Fenyes, T., Krasznahorkay, A., Dombradi, Zs., Brant, S.*, Paar, V.*: Excited states of 96Nb from 96Zr (p,n) 96Nb reaction. Nucl.Phys. A340 (1984) 301-319.
  9. Tokunaga, Y., Seyfarth, H., Meyer, R.A.**, Schult, O.W.B., Boerner, H.G., Barreau, G., Faust, H.R., Schreckenbach, K., Brant, S.*, Paar, V.*, Vouk, M.*, Vretenar, D.*: Low-lying levels of 77Se studied through thermal neutron capture and evidence for a new term in the E2 operator of TQM (IBM). Nucl. Phys. A439 (1985) 427-455.
  10. Mayerhofer, U., Egidy, T. von, Dürner, P., Hlawatsch, G., Klora, J., Lindner, H., Brant, S.*, Seyfarth, H., Paar, V.*, Lopac, V.*, Kopecky, J.**, Warner, D.D.**, Chrien, R.E.**, Pospisil, S.: Nuclear structure of 198Au studied with (n,g) and (d,p) reactions and interpreted with the IBFFM. Nucl. Phys. A492 (1989) 1-22.
  11. Dragulescu, E., Ivascu, M., Petrache, C., Popescu, D., Semenescu, G., Gurgu, I., Ionescu - Bujor, M., Iordachescu, A., Pascovici, G., Meyer, R.A.**, Lopac, V.*, Brant, S.*, Paar, V.*, Vorkapi}, D.*, Vretenar, D.*: Nuclear structure and high - spin states of 137Pr. Nucl. Phys. A458 (1992) 435-452.
  12. Kern, J., Raemy, A., Beer, W., Dousse, J.C., Schwitz, W., Balodis, M.K., Prokofjev, P.T., Kramer, N.D., Simonova, L.I., Hoff, R.W.**, Gardner, D.G.**, Gardner, M.A.**, Casten, R.F.**, Gill, R.L.**, Eder, R., Egidy, T. von, Hagn, E., Hungerford, P., Scheerer, H.J., Schmidt, H.H., Zech, E., Chalupka, A., Murzin, A.V., Libman, V.A., Konenko, I.V., Coceva, C., Giacobbe, P., Kondurov, I.A., Loginov, Yu.E., Sushkov, P.A., Brant, S.*, Paar, V.*: Nuclear levels in 192Ir. Nucl.Phys. A534 (1991) 77-127.
  13. Meyer, R.A.**, Marsh, K.V.**, Brenner, D.S.**, Paar, V.*: Cluster vibrational-field model for 95Mo and levels populated in the decay of 95Tcm,g. Phys.Rev. C16 (1977) 417-426.
  14. Meyer, R.A.**, Fontanilla, J.E.**, Smith, N.L.**, Smith, C.F.**, Ragaini, R.C.**, Paar, V.*: Level properties of 85Rb from the decay of the 85Kr and 85Sr isomers and the cluster-vibration model. Phys.Rev. C21 (1980) 2590-2599.
  15. Petkov, P., Andrejtscheff, W., Robinson, S.J.**, Mayerhofer, U., Egidy, T. von, Brant, S.*, Paar, V.*, Lopac, V.*: Electromagnetic transition strengths in the transitional doubly odd nucleus 198Au. Nucl.Phys. A554 (1993) 189-208.
  16. Chrien, R.E.**, Koene, B.K.S., Stelts, M.L.**, Meyer, R.A.**, Brant, S.*, Paar, V.*, Lopac, V.*: Neutron capture gamma-ray study of levels in 135Ba and description of nuclear levels in interacting boson-fermion model. Phys.Rev. C47 (1993) 1-9.
  17. Hicks, H.G.**, Landrum, J.H.**, Henry, E.A.**, Meyer, R.A.**, Brant, S.*, Paar, V.*: Population of 133I from the beta decay of fission product 133Te and the cluster-vibration model. Phys.Rev. C27 (1983) 2203-2216.
  18. Brant, S.*, Paar, V.*, Vretenar, D.*, Meyer, R.A.**: Anomaly in spectra of 105Pd and 103Ru. Phys. Rev. C34 (1986) 341-344.
  19. Balantekin, A.B.**, Paar, V.*: Bose-Fermi symmetry chain for the description of odd-odd nuclei. Phys. Rev. C34 (1986) 1917-1919.
  20. Meyer, R.A.**, Nagle, R.J.**, Brant, S.*, Frle`, E.*, Paar, V.*, Hopke, P.K.**: Interacting boson fermion model description for the levels of 71Ge populated in the beta decay of 65.30-h 71As. Phys. Rev. C41 (1990) 686-696.
  21. Meyer, R.A.**, Marsh, K.V.**, Seyfarth, H., Brant, S.*, Bogdanovi}, M., Paar, V.*: Interacting-boson-fermion-fermion model description of 140La and comparison with levels populated by beta decay and neutron capture. Phys. Rev. C41 (1990) 1172-1183.
  22. Meyer, R.A.**, Scholten, O., Brant, S.*, Paar, V.*: Mixed-symmetry states in 144Nd: Semi-microscopic accounting within the cluster vibration model and its mapping into the interacting boson model. Phys. Rev. C41 (1990) 2386-2396.
  23. Rogowski, J., Alstad, J., Brant, S.*, Daniels, W.R.**, Frenne, D.De, Heyde, K., Jacobs, E., Kaffrell, N., Paar, V.*, Skanemark, G., Trautmann, N.: Intruder states in odd-mass Ag isotopes. Phys. Rev. C42 (1990) 2733-2736.
  24. Paar, V.*, Meyer, R.A.**: A possible semimicroscopic mechanism to generate two 0+ bands and their band mixing: 110Cd as an example. J.Phys. G5 (1979) 75-78.
  25. Paar, V.*, Brant, S.*, Meyer, R.A.**, Kyrchev, G.: New term in L=0 Two-Particle Transfer Operator of TQM-IBM. Z. Physik (Short Note) A319 (1984) 357-358.
  26. Lopac, V.*, Brant, S.*, Paar, V.*, Schult, O.W.B., Seyfarth, H., Balantekin, A.B.**: Odd-Odd Nucleus 198Au as First Test of IBFFM(OTQM). Z. Physik (Short Note) A323 (1986) 491-492.
  27. Pfeiffer, B., Brant, S.*, Kratz, K.L., Meyer, R.A.**, Paar,V.*: The K=3/2+ Side-Band in 99Y and its Description by the IBFM-PTQM Model. Z. Physik A325 (1986) 487-488.
  28. Meyer, R.A.**, Monnand, E., Pinston, J.A., Schussler, F., Pfeiffer, B., Paar, V.*: Pseudo-bands in Non-SU(3) Odd-Mass Nuclei and Coherent State Structure of Quadrupole Phonons. Z. Physik A327 (1987) 393-396.
  29. Seyfarth, H., Güven, H.H., Kardon, B., Lauppe, W.D., Lhersonneau, G., Sistemich, K., Brant, S.*, Kaffrell, N., Maier-Komor, P., Vonach, H.K., Paar, V.*, Vorkapi}, D.*, Meyer, R.A.**: Structure of the triplet of low-lying states in 101Mo. Z.Phys. A339 (1991) 269-278.
  30. Mayerhofer, U., Egidy, T. von, Jolie, J. Boerner, H.G., Colvin, G., Judge, S. Krusche, B., Robinson, S.J.**, Schreckenbach, K., Brant, S.*, Paar, V.*: The experimental structure of 199Au and the interacting boson-fermion model. Z. Phys. A341 (1991) 1-8.
  31. Paar, V.*, Sunko, D.K.*, Brant, S.*, Mustafa, M.G.**, Lanier, R.G.**: Gaussian polynomial method for spin-dependent level density and new formula for spin-distribution. Z. Phys. A345 (1993) 343-358.
  32. Hamilton, W., Croft, W.**, Brantley, W.**, Rayburn, L.**, Girit, I.**, Brant, S*, Paar, V.*: Gamma-ray multipole mixing ratios in 71Ge. Phys.Rev. C47 (1993) 1042-1047.
  33. Meyer, R.A.**, Kaffrell, N., Lawin, H., Lhersonneau, G., Monnand, E., Paar, V.*, Pfeiffer, B., Pinston, J.A., Ragnarsson, I., Schussler, F., Schmitt, A., Seo, T., Sistemich, K., Trautmann, N.: Symmetric deformation in A=100 odd and odd-odd nuclei and its influence on fission product beta-decay rates. Proc. Meet. on Fission Product Data, Brookhaven National Laboratory (1983).
  34. Balantekin, A.B.**, Huebsch, T.*, Paar, V.*: Boson-Fermion Symmetries and Dynamical Supersymmetries for Odd-Odd Nuclei. In: Nuclei Off the Line of Stability. R.A. Meyer and D.S. Brenner, Eds., American Chemical Society, Washington D.C. (1986) 14-19.
  35. Meyer, R.A.**, Brant, S.*, Paar, V.*: The N=59 isotones as a test of fermion-boson models. Inst. Phys. Conf. Ser. 88 (1988) 454-457.
  36. Brant, S.*, Sistemich, K., Seyfarth, H., Ohm, H., Stolzenwald, M.L., Paar, V.*, Vretenar, D.*, Vorkapi}, D.*, Lopac, V.*, Meyer, R.A.**, Lhersonneau, G., Kratz, K.L., Pfeiffer, B.: IBM and IBFFM approach to nuclei in the A=100 region. In: Nuclear structure of the zyrconium region, Springer Verlag, Berlin (1988) 199-214.
  37. Vretenar, D.*, Paar, V.*, Iachello, F.**, Bonsignori, G., Savoia, M.: Two- and four-quasiparticle states in the interacting boson model. Description of high spin states. In: Understanding the variety of nuclear excitations, ed. A.Covello (World Scientific, Singapore, 1991) 661-671.
  38. Kern, J., Balodis, M.K., Beer, W., Brant, S.*, Casten, R.F.**, Chalupka, A., Coveca, C., Dousse, J.-Cl., Eder, R., Egidy, T. von, Gardner, D.G.**, Gardner, M.A.**, Giacobbe, P., Gill, R.L., Hagn, E., Hoff, R.W., Hungerford, M.A., Kondurov, I.A., Konenko, I.V., Kramer, N.D., Libman, V.A., Loginov, Yu.E., Murzin, A.V., Paar, V.*, Prokofjev, P.T., Raemy, A., Scheerer, H.J., Schmidt, H.H., Schwitz, W., Simonova, L.I., Sushkov, P.A., Zech, E.: Intrinsic Excitations in 192Ir. American Institute of Physics Conference Proceedings 238 (1991) 263-270.
  39. Paar, V.*, Brant, S.*, Sunko, D.K.*, Mustafa, M.G.**, Lanier, R.G.**: New Formula for Spin-Dependent Level Density, American Institute of Physics Conference Proceedings 238 (1991) 672-684.
  40. Meyer, R.A.**, Paar, V.*: Nuclear Structure, Reactions and Symmetries, Volume I. (World Scientific, Singapore, 1986) 1-564.
  41. Meyer, R.A.**, Paar, V.*: Nuclear Structure, Reactions and Symmetries, Volume II. (World Scientific, Singapore, 1986) 567-1170.
  42. Meyer, R.A.**, Paar, V.*: Symmetries and Nuclear Structure (Harwood Academic Publishers, Chur, 1987) 1-620.
  43. Alhassid, Y.** and Vretenar D.* : Chaos in nuclei with broken pairs, Phys.Rev. C46 (1992) 1334-1338.
  44. Chowdhury, P.**, Lister, C.J.**, Vretenar, D.*, Winter, Ch.**, Janzen, V.P., Andrews, H.R., Blumenthal, D.J., Crowell, B., Drake, T., Ennis, P.J., Galindo-Urbarri, A., Horn, D., Johanson, J.K., Omar, A., Pilotte, S., Prevost, D.,Radford, D., Waddington, J.C., Ward, D.: Large B(M1) staggering at high spins in 86Zr: Broken boson paris in the four-quasiparticle regime, Phys.Rev.Lett. 67 (1991) 2950-2953.
  45. Lister,C.J.**, Chowdhury, P.**,Vretenar, D.*: The extension of the IBM to high spin, Nucl.Phys. A557 (1993) 361-371.
  46. Chisthi, A.A.**, Chowdhury, P.**, Blumenthal, D.J.**, Ennis, P.J.**,Lister, C.J.**, Winter, Ch.**, Vretenar, D.*, Bonsignori, G., Savoia, M.: Collectivity in light zirconium isotopes: Evolution with neutron number and angular momentum, Phys.Rev.C48 (1993) 2607-2616.
  47. Iachello, F.**, Vretenar, D.*: Phys.Rev. C43 (1991) 945-948.
The list of coauthors from U.S. institutions, according to the affiliation given in these publications, is as follows:
  1. Meyer, R.A., Lawrence Livermore National Laboratory, Livermore, California; U.S. Department of Energy, Washington, D.C.
  2. Iachello, F., Center for Theoretical Physics, Yale University, New Haven, Connecticut
  3. Balantekin, A.B., Oak Ridge National Laboratory, Oak Ridge, Tennessee
  4. Casten, R.F., Brookhaven National Laboratory, Upton, New York
  5. Gill, R.L., Brookhaven National Laboratory, Upton, New York.
  6. Scholten, O., Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan
  7. Flynn, E.R., Los Alamos Scientific Laboratory, Los Alamos, New Mexico
  8. Igo, G.J., Los Alamos Scientific Laboratory, Los Alamos, New Mexico
  9. Landowne, S., Argonne National Laboratory, Argonne, Illinois
  10. Kern, B.D., Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky
  11. Fontanilla, J.E., Lawrence Livermore National Laboratory, Livermore, California
  12. Smith, N.L., Lawrence Livermore National Laboratory, Livermore, California
  13. Smith, C.F., Lawrence Livermore National Laboratory, Livermore, California
  14. Ragaini, R.C., Lawrence Livermore National Laboratory, Livermore, California
  15. Hicks, H.G., Lawrence Livermore National Laboratory, Livermore, California
  16. Landrum, J.H., Lawrence Livermore National Laboratory, Livermore, California
  17. Henry, E.A., Lawrence Livermore National Laboratory, Livermore, California
  18. Chrien, R.E., Brookhaven National Laboratory, Upton, New York
  19. Brenner, D.S., Clark University, Worcester, Massachusetts
  20. Stelts, M.L., Brookhaven National Laboratory, Upton, New York
  21. Mustafa, M.G., Lawrence Livermore National Laboratory, Livermore, California
  22. Lanier, R.G., Lawrence Livermore National Laboratory, Livermore, California
  23. Hoff, R.W., Lawrence Livermore National Laboratory, Livermore, California
  24. Gardner, D.G., Lawrence Livermore National Laboratory, Livermore, California
  25. Gardner, M.A., Lawrence Livermore National Laboratory, Livermore, California
  26. Marsh, K.V., Lawrence Livermore National Laboratory, Livermore, California
  27. Casten, R.F., Brookhaven National Laboratory, Upton, New York
  28. Gill, R.L., Brookhaven National Laboratory, Upton, New York
  29. Robinson, S.J., Tennessee Technical University, Cookville, Tennessee
  30. Nagle, R.J., Lawrence Livermore National Laboratory, Livermore, California
  31. Hopke, P.K., Department of Chemistry, Cora and Bayard Clarkson Science Center, Clarkson University, Potsdam, New York
  32. Daniels, W.R., Los Alamos National Laboratory, Los Alamos, New Mexico
  33. Iachello, F., Center for Theoretical Physics, Yale University, New Haven, Connecticut
  34. Croft, W.L., Mississippi State University, Mississippi State, Mississippi.
  35. W.H.Brantley, Furman University, Greenville, South Carolina.
  36. L.A.Raybarn, Oak Ridge Associated Universities, Oak Ridge, Tennessee
  37. I.C.Girit, Oak Ridge Associated Universities, Oak Ridge, Tennessee
  38. Y.Alhassid, Center for Theoretical Physics, Yale University, New Haven, Connecticut.
  39. P.Chowdhury, A.W.Wright Nuclear Structure Laboratory, Yale University, New Haven, Connecticut
  40. C.J.Lister, A.W.Wright Nuclear Structure Laboratory, Yale University, New Haven, Connecticut
  41. Ch.Winter, A.W.Wright Nuclear Structure Laboratory, Yale University, New Haven, Connecticut
  42. P.J.Ennis, A.W.Wright Nuclear Structure Laboratory, Yale University, New Haven, Connecticut
  43. D.J.Blumenthal, A.W.Wright Nuclear Structure Laboratory, Yale University, New Haven, Connecticut
  44. A.A.Chishti, A.W.Wright Nuclear Structure Laboratory, Yale University, New Haven, Connecticut

Bibliography

  1. F. Iachello and A. Arima, The Interacting Boson Model, Cambridge University Press, Cambridge (1987).
  2. A. Arima and F. Iachello, Phys. Rev. Lett. 35 (1975) 1069.
  3. A. Arima and F. Iachello, Adv. Nucl. Phys. 13 (1984) 139.
  4. A. Arima and F. Iachello, Ann. Phys. 99 (1976) 253; 111 (1978) 201; 123 (1979) 468.
  5. R.F. Casten, Nuclear Structure from a Simple Perspective, Oxford University Press, Oxford (1990).
  6. A. Arima and F. Iachello, Ann. Rev. Nucl. Part. Sci. 31 (1981) 75.
  7. F. Iachello and O. Scholten, Phys. Rev. Lett. 43 (1979) 679.
  8. O. Scholten, Prog. Part. Nucl. Phys. 14 (1985) 189.
  9. V. Paar, In: In-beam nuclear spectroscopy, Vol. 2, eds. Zs. Dombradi and T. Fenyes (Akademiai Kiado, Budapest, 1984), p. 675; in: Capture gamma-ray spectroscopy, Proc. AIP Conf. 125 (American Institute of Physics, New York, 1985), p. 70.
  10. S. Brant, V. Paar and D. Vretenar, Z. Physik, A319 (1984) 351.
  11. V. Paar, D.K. Sunko and D. Vretenar, Z. Physik A327 (1987) 291.
  12. V. Lopac, S. Brant, V. Paar, O.W. B. Schult, H. Seyfarth and A.B. Balantekin, Z. Phys. A323 (1986) 491.
  13. U. Mayerhofer, T. von Egidy, P. Duerner, G. Hlawatsch, J. Klora, H. Lindner, S. Brant, H. Seyfarth, V. Paar, V. Lopac, J. Kopecki, D.D. Warner, R.E. Chrien and S. Pospisil, Nucl. Phys. A492 (1989)1.
  14. J. Kern et al., Nucl. Phys. A534 (1991) 77.
  15. R.A. Meyer, K.V. Marsh, H. Seyfarth, S. Brant, M. Bogdanovi} and V. Paar, Phys. Rev. C41 (1990) 1172.
  16. J. Timar, T.X. Quang, T. Fenyes, Zs. Dombradi, A. Krasznahorkay, J. Kumpulainen, R. Julin, S. Brant, V. Paar and Lj. Simicic, Nucl. Phys. A573 (1994) 61.
  17. F. Iachello, in: Understanding the Variety of Nuclear Excitations, ed. A. Covello, World Scientific (1991) p. 647.
  18. A. Gelberg and A. Zemel, Phys. Rev. C22 (1980) 937.
  19. J. Morrison, A. Faessler and C. Lima, Nucl. Phys. A372 (1981)13.
  20. N. Yoshida, A. Arima and T. Otsuka, Phys. Lett. 114B (1982) 86.
  21. D.S. Chuu and S.T. Hsieh, Phys. Rev. C38 (1988) 960; D.S. Chuu, S.T. Hsieh and H.C. Chiang, Phys. Rev. C40 (1989) 382.
  22. C.E. Alonso, J.M. Arias and M.Lozano, Phys. Lett. 177B (1986) 130
  23. D. Vretenar, V. Paar, G. Bonsignori and M. Savoia, Phys. Rev. C42 (1990) 993
  24. D. Vretenar, G. Bonsignori and M. Savoia, Phys. Rev. C47 (1993) 2019.
  25. A. Chishti, C. Choudhury, D. Blumenthal, P. Ennis, C. Lister, C. Winter, D. Vretenar, G. Bonsignori and M. Savoia, Phys. Rev. C48 (1993) 2607; P. Choudhury, C.J. Lister, D. Vretenar et al., Phys. Rev. Lett. 67 (1991) 2950.
  26. D. Vretenar, V. Paar, F. Iachello, G. Bonsignori and M. Savoia, in: Understanding the Variety of Nuclear Excitations, ed. A. Covello, World Scientific, Singapore (1991), p. 661.
  27. D. Vretenar, V. Paar, M. Savoia and G. Bonsignori, Phys. Rev. C44 (1991) 223.
  28. F. Iachello, Nucl. Phys, A522 (1991) 83.
  29. A. Gelberg, P. von Brentano and R.F. Casten, J. Phys. G16 (1990) L 143.
  30. V. Paar, D.K. Sunko and D. Vretenar, J. Phys. G18 (1992) L 191; D.K. Sunko and V.Paar, Phys. Lett. 146 B (1984) 279.
  31. P. Duval and B.R. Barrett, Nucl. Phys. A376 (1982) 283.
  32. M.Sambataro, Nucl.Phys. A380 (1982) 365; M.Sambataro and G.Molnar, Nucl.Phus. A376 (1982) 283..
  33. R.F. Casten, Nucl. Phys. A443 (1985)1.
  34. T. Otsuka, in: Understanding the Variety of Nuclear Excitations, ed. A. Covello, World Scientific (1991), p. 321.
  35. F. Iachello, in: Progress in Nuclear and Particle Physics, Vol. 9, D. Wilkinson, ed., Pergamon Press (1983), p. 5.
  36. D.D. Warner, Phys. Rev. Lett. 52 (1984) 259.
  37. J. Vervier, Rivista Nuovo Cimento 10 (1987) No 9.
  38. R. Bijker and V.K.B. Kota, Ann. Phys. 187 (1988) 148.
  39. F. Iachello, Phys. Rev. Lett. 44 (1980) 772.
  40. F. Iachello and S. Kuyucak, Ann. Phys. 136 (1981) 168.
  41. A.B. Balantekin, J. Bars, R. Bijker and F. Iachello, Phys. Rev. C27 (1983) 1761.
  42. P. Van Isacker, A. Frank and H.Z. Sun, Ann. Phys. 157 (1984) 183.
  43. I. Bars, in Bosons in Nuclei, ed. D.H. Feng, S. Pittel and M. Vallieres, World Scientific, Singapore, 1984, p. 155.
  44. P. Van Isacker, J. Jolie, K. Heyde and A. Frank, Phys. Rev. Lett. 54 (1985) 653.
  45. T. Huebsch, V. Paar and D. Vretenar, Phys. Lett. 151 B (1985) 320.
  46. A.B. Balantekin and V. Paar, Phys. Rev. C34 (1986) 1917.
  47. R. Bijker and O. Scholten, Phys. Rev. C32 (1985) 591.
  48. O. Scholten, S. Brant and V. Paar, Phys. Lett. B171 (1986) 335.
  49. V. Paar, D. Vretenar, C. De Coster, K. Heyde and O. Scholten, Phys. Rev. C45 (1992) 284.
  50. Y. Alhassid, A. Novoselsky and N. Whelan, Phys. Rev. Lett. 65 (1990) 2971.
  51. V. Lopac, S. Brant and V. Paar, Phys. Rev. A45 (1992) 3503.
  52. Y. Alhassid and D. Vretenar, Phys. Rev. C46 (1992) 1334.