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Nuclear Physics, Neutron Physics and Nuclear Energy

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Nuclear Physics, Neutron Physics and Nuclear Energy INIS-tnf—13944 PROCEEDINGS OF THE X INTERNATIONAL SCHOOL ON NUCLEAR PHYSICS, NEUTRON PHYSICS AND NUCLEAR ENERGY Varna, Bulgaria October 14-19, 1991 Institute for Nuclear Research and Nuclear Energy Sofia s5>.;ii_-_ 5., » PROCKISDINGS OF THE X INTERNATIONAL SCHOOL ON NUCLEAR PHYSICS, NEUTRON PHYSICS AND NUCLEAR ENERGY Varna, Bulgaria October 14-19, 1991 Editors: W. Andrejtscheff D. Elenkov Institute for Nuclear Research and Nuclear Energy Sofia Preface The history of the International School on Nuclear Physics, Neutron Physics and Nuclear Energy ("Varna School") goes back to the year 1973. Since that time it has been carried out in the fall of every other year in the Conference Center of the Bulgarian Academy of Sciences at the Black Sea coast near Varna. In a time of limited international contacts, the lectures and personal discussions with active scientists from all over the world played an important role in the professional career of many nuclear scientists from Bulgaria and Easteii Europe. It was mainly this tradition which gave us the motivation to start organizing the School in the difficult year 1991. The X School look place from Oct. 1<) to Oct. 19, 1991 at its traditional site. The organizers from the Institute for Nuclear Research and Nuclear !:!iicru,y and IVoui tin.' Faculty of Physics ;it Sofia University are particularly indebted to the lecturers and guests who came from different countries. This year, the organization of the Scliool required extraordinary efforts from tin-1 scientific secretary Dr. Dantcho Elenkov as well as from Prof. Chavdar Stoy- anov, Mr. Maurice Grinberg and Mr..Damian Damianov. Solia, June 1992 Wenzeslav Andrejtscheff Chairman TENTH INTERNATIONAL SCHOOL ON NUCLEAR PHYSICS, NEUTRON PHYSICS AND NUCLEAR ENERGY, OCTOBER 14-19, 1991 VARNA Contents 1. MICROSCOPIC STUDY OF ELECTROMAGNETIC PROPERTIES OF NUCLEI 1 I. Hamamoto 2. THE MICROSCOPIC THEORY OF NUCLEAR COLLECTIVE STATES 32 D. J. Rowe 3. LOW-LYING COLLECTIVE QUADRUPOLE STRENGTHS IN EVEN-EVEN NUCLEI 52 | S. Raman 1. A SIMPLE MODEL FOR THE DESCRIPTION OF TWO-QUASIPARTICLE STATES IN EVEN - A NUCLEI fill R.V. Jolos and M.M. Michailova 5. SYSTEMATIC NUCLEAR STRUCTURE STUDIES OF Z=53,55 ISOTOPES 71 D.B. Fossan 6. ELEMENT FORMATION IN RED GIANT STARS 106 F. Kappeler 7. MOMENTUM DISTRIBUTIONS, OCCUPATION NUMBERS AND NATURAL ORB1TALS IN NUCLEI WITHIN THE GENERATOR COORDINATE METHOD 129 A.N. Antonov 8. SELF CONSISTENT THEORY OF THE COLLECTIVE EXCITATIONS OF ATOMIC NUCLEI 148 B.I. Barts 9. MODELING OF RESONANCE CROSS SECTIONS IN THE UNRESOLVED ENERGY REGION 171 A. Lukyanov, M. Alami, N. Koyumdjieva, N. Janeva 10. RADIATIVE STRENGTH FUNCTION DETERMINATION IN THE (n,2g) REACTION FOR SOFT PRIMARY TRANSITION IN HEAVY NUCLEI 200 A.M. Sukhovuj 11. COLLECTIVE NUCLEAR POTENTIAL WITHIN THE MICROSCOPIC Sp(6,ll) MODEL 213 A.L. Blokhin V>. RELATION BETWEEN INTERACTING VECTOR BOSON MODEL AND SOME VERSIONS OF THE INTERACTING BOSON APPROXIMATIONS 223 R.M. Asherova, D.V. Fursa, A.L Gcorgiova, Yu. F. Smirnov 13. SHAPE COEXISTENCE IN Pb and Pb 242 C. Baldsiefen, H. Htbcl, D. MeliU, H.V.T. Rao, U. BirkenUl, G. Frohlingsclorf, M. Ncffgen, N. Nenoff, S.C. Pancholi, N. Singh, W. Schmitz, K. Tlieinc, P. Willsau, H. Grawe, J. Heese, II. Kluge, K.H. Maier, M. Schramm, R. Schubart, II.J. Main- ! !. Mri.TIPLE BREAK-UP OF NMU'LEl: EXPERIMENTS WITH ARGUS AT THIS HAHN-MEITNER-INSTITUT BlvRLIN 251 II. IMICIIS, 11. Homeyer, G. Pauscli, W. Terlau, C. Scliwarz, A. Siwek, A. Sourell, B. Bochev, VV. WagiuM-, A. Budzanowski, W. Kan lor 15. NEUTRON DEPOLARIZATION STUDY OF STATIC MAGNETIC CHARACTERISTICS OF AMORPHOUS FERROMAGNETIC ALLOYS 261 K. Kirahov, V. Lilkov, P. Konstantinov MICROSCOPIC STUDY OF ELECTROMAGNETIC PROPERTIES OF NUCLEI IKUKO HAMAMOTO Department of Mathematical Physics University of Lund Lund, Sweden Abstract The following two subjects are chosen to be discussed: (a) The properties of low-lying 1+ states in deformed even-even nuclei, which carry relatively strong magnetic-dipole (Ml) strength, (b) Electromagnetic properties ob- served in the high-spin yrast epectroscopy, which are drastically different from those in the traditional nuclear spectroscopy at low-energy and low-spins. 1. Introduction Under the present title I would liko to talk about the following two subjects: (a) Low-lying magnetic-dipole (Ml) strengths in deformed even-even nuclei (in sect. 2); and (b) Electromagnetic properties studied in the yrast specroscopy (in sect. 3). In the present lecture I do not intend to show numerical calculations which beau- tifully reproduce experimental data. I would rather prefer to reviewing how far we have understood the phenomena and what are the remaining problems to be understood. I always try to keep a close connection with available experimental informations. In standard textbooks on the spectroscopy of axially symmetric deformed nuclei one can find the formulae for rotational energies, B(E2)- and B(M1)- values within a given rotational band (with 1% = K as a good quantum number) as EROT - ( 2 = -^-t'Ql < I1K20\ItK > (1) loir which have been so successful in the analysis of low-energy nuclear spectroscopy. (See, for example, ref. 1.) The formulae (1) are obtained for an 7£-invariant axially- symmetric intrinsic shape, assuming that the intrinsic structure is not disturbed by rotation. In ref. 1 it was pointed out that in the low-energy electric-dipolc (El) transitions the leading-order intensity relation for the El matrix elements, which could be derived in the same approximation as the one used in obtaining the expressions (1), did not explain the characteristic feature of observed data. The reason is that the leading-order matrix elements of low-energy El transitions are usually very much hindered due to the relevant nuclear shell-structure and, thus, relatively small admixed components in the wave functions could make a sizable contribution to the total El matrix elements. An example of the analysis can be found on p. 110 of ref. 1. In the calculation of Ml transitions in sect. 2 I use the approximation employed in the derivation of the expressions (1), since I discuss the properties of 1-f states, in which the rotational perturbation is small because the states are the band-head states. In contrast, in the recent high-spin yrast spectroscopy (sect. 3), in which the Coriolis and centrifugal forces produce major modifications in the particle motion, the expressions which are totally different from those in (1) must be applied, as I explain in sect. 3. The central issue of the subject (a) is to discuss to what extent the low-lying Ml strengths, which are detected by (e, e') reactions2'3 or (7,7') reactions4'6, can be. understood in terms of a classical picture, socalled "scissors" mode. The "scissors" mode may be a good normal mode, if in the nuclear many-particle system the Ml transition operator consists of only the orbital angular momentum of particles and the response function of the Ml operator has only one frequency (with a number of degeneracy). These conditions are almost fullfilled in the case of the ddormed oscillator model, in which there are no spin-orbit potential, no spin contributions to the Ml transition operator, and only one peak in the low-energy region of the two-quasipartide (2qp) response function of the Ml operator. However, in nuclear physics the importance of the presence of the spin-orbit potential is well known since the nuclear shell model was proposed in 1949 by M.G. Mayer and J.H.D. Jensen6. Together with the fact that the nuclear one-body potential with a relatively well- defined surface favours the orbits of higher orbital angular momentum compared with the sequence in an oscillator potential, the nuclear spin-orbit potential leads to a unique-parity "high-j" orbit in each major-shell of the one-particle spectrum. The crucial role played by high-j orbits in the nuclear spectroscopy of both spherical and deformed nuclei is by now well established. (For example, see ref. 1.) In addition, the spin contribution to the low-lying Ml strengths is not at all negligible, though the repulsive n&ture of the ipin- and isoipin-dependent residual interaction in the nuclear system shifts a considerable amount of the spin-dependent part of the Ml strengths to a region of higher excitation energy1. Furthermore, when one employs one-particle spectra in a realistic deformed nuclear potential, one clearly observes a couple of different (namely, non-degenerate) low-lying strong peak* in the 2qp response function, even in the case that only the orbital part of Ml operator is used. And, the lowest-lying strong Ml strength, which comes from the tvvo-quasiproton high-j configuration, is clearly separated from the higher-lying strong Ml strengths by, in most cases, several hundreds keV7. The presence and the position of this 3 lowest-lying excitation consisting of quasiproton high-j (i.e. (hu/2) in the case of rare-earth nuclei) configurations have recently been nicely confirmed in the case of 164Dy by a (t, a) reaction8. We note that the nucleus 1MDy is a very lucky case in which the (t,a) reactions could be used to detect the proton (/in/j)2 excitations, because of the availability of the target odd-Z nuclei '"Ho, of which the ground state has an An/j configuration. The form factor measured in (e, e') scatterings is a nice tool to identify the configurations involved in the excitation process, in contrast to having just aB(Ml)- vr.lue, which is just a single number and may easily be reproduced by adjusting some parameters if one wants. Since 1984 we keep saying7'9 that the (e,e;) form-factor of the lowest-lying excitation coming from the high-j orbits, which should carry a relatively large B(M1) value, is quite different from the one coming from the normal-parity orbits and that the measured (e, e') form factor at Eex « 3.1 MeV in even-even rare-earth nuclei has a clearly different shape from the calculated form factor of the proton high-j excitations.
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