Microscopic foundation of the interacting boson model in thes d-shell nuclei

Starting from an isospin invariant shell-model hamiltonian, we describe a method for deriving microscopically the IBM-hamiltonian appropriate to lights d-shell nuclei. The key ingredients of our approach are:a) the Belyaev-Zelevinsky-Marshalek (BZM) bosonization procedure;b) two successive unitary transformations that extract the “maximally decoupled” collective bosons with angular momentaJ=0(s _ππ ⁺ ,s _νν ⁺ ,s _πν ⁺ ) andJ =2(d _ππ ⁺ ,d _νν ⁺ ,d _πν ⁺ (T=0),d _πν ⁺ (T=1)). The method is applied to obtain the low-energy spectra and the electron scattering form factors for the 0 ₁ ⁺ →2 ₁ ⁺ transitions in²⁰Ne and²⁴Mg. Good agreement with the exact shell-model results is achieved. The inclusion of proton-neutron bosons (s _πν ⁺ ,d _πν ⁺ (T=1),d _πν ⁺ (T=0)), as well as the renormalization of boson parameters due to the non-collective degrees of freedom, are shown to play a crucial role.     

Particle-rotor model for doubly odd transitional nuclei of the Tl-region

A model has been investigated describing a situation in which two noninteracting high-j Nilsson-BCS quasiparticles move in the deformed field of an axially and reflection symmetric rotor. According to the positions of thej-shells with respect to the proton and neutron Fermi surfaces structures of different character emerge referred to as semi- and doubly-decoupled. In particular, strongly Coriolis-distorted bands recently reported in doubly odd Tl nuclei are discussed. Also \(\tilde \pi h_{9/2} \) bands in neighbouring odd mass Tl isotopes are analysed on the same footing. It is shown that the pronounced odd even staggering of the transition energies can be understood as a specific quantal feature associated with the Coriolis interaction.     

A simple model for doublet bands in doubly odd nuclei

Nuclear structure of doublet bands in doubly odd nuclei with mass A ∼ 130 is investigated within the framework of a simple model where the even-even core couples with a neutron and a proton in intruder orbitals through a quadrupole-quadrupole interaction. The model reproduces quite well the energy levels of doublet bands and electromagnetic transitions. The staggering of the ratios B(M1;I → I - 1)/B(E2;I → I - 2) of the yrast bands turns out to be described by the chopsticks-like motion of two angular momenta of the unpaired neutron and the unpaired proton when they are weakly coupled with the core.-1 An erratum to this article is available at .     

Quasiparticle-phonon model calculations on doubly even Zn and Ge nuclei

The doubly even isotopes of Zn and Ge have been investigated in a model in which two quasiparticle excitations, constructed in a (0f _7/2), 1p _3/2, 0f _5/2, 1P _1/2, 0g _9/2 configuration space, are coupled with quadrupole vibrations of the core, viz.⁴⁰Ca or⁵⁶Ni. The 0f _7/2 orbit is excluded in case of a⁵⁶Ni core. The spectra, except for low-lying excited 0⁺ states, could be reproduced reasonably well. The calculatedE2 strengths and quadrupole moments are in fair agreement with experiment.     

Collective bands in doubly even Sn nuclei

Starting from a simplified picture treating proton two-particle two-hole excitations coupled with spherical quadrupole vibrations, in interaction with the low-lying quadrupole vibrational states in the doubly even Sn nuclei, we are able to account for a regular ΔJ = 2 band structure on top of excited J^π = 0⁺ states. We compare in some detail results for ¹¹⁶Sn concering energy spectra and E2 transition rates.     

Ground state energies of doubly even nuclei

Ground state energies of doubly even nuclei which are assumed to be composed of rigid and structureless alpha-particles are calculated. The alpha-particles are assumed to be interacting through a potential composed of a hard core followed by a square well potential in one set of calculations and a Gaussian potential in another set of calculations. Our calculations support the existence of the hard core in the alpha-alpha potential, and suggest the existence of the alphaclustering in doubly even light nuclei.From the graph betweenE ₀/N and we find thatE ₀/N is minimum at =2·57×10³⁷ particles cm^–3. This means that in the surface region an assembly of alpha-particles with = = 2·57×10³⁷ particles cm^–3 is the most stable one.We are greatly indebted to Professors R. Tamagaki, M. Harada and F. Iwamote for making very useful suggestions and for making a few points clear to us. Thanks are also due to Professors P. C. Sood, S. Duttamazumdar and M. K. Pal for many helpful discussinos, and to the Indian National Science Academy, New Delhi for giving financial assistance. Thanks are also due to Shri A. N. Phukan for drawing the graphs.     

Nucleon momentum distributions in doubly closed shell nuclei

The momentum distributions in nuclei like⁴He,¹⁶O and⁴⁰Ca are explicitly calculated within a phenomenological model which includes dynamical short range and tensor correlation effects. The common behaviour of such distributions in the high momentum region, already established in light nuclei, is extended to the medium weight region. Comparison with existing calculations is discussed and, for completeness, also form factors are evaluated within the same framework.     

High spin states in doubly even pf-shell nuclei

High spin states of the yrast band in ⁵⁰Ti, ⁵²Cr, ⁵⁴ and ⁴⁶Ti are investigated in a microscopic approach allowing a coupling of rotations, vibrations and quasiparticle excitations. The lowering of the 6⁺ state in N = 28 nuclei is shown to originate mainly from proton K = 0 two-quasiparticle excitations. Using as a basis the entire pf-shell 8⁺ and 10⁺ states can be predicted for ⁵⁰Ti and ⁵⁴Fe.     

Electromagnetic transitions in some doubly odd deformed nuclei

Nanosecond lifetimes of excited states in doubly odd deformed nuclei have been determined by in-beam measurements applying the method of delayed γ-γ coincidences as well as by experiments in the radioactive decay with the method of delayed γ-ce coincidences, respectively. Analysing the time distributions and delayed γ-ray spectra, the following half-lives of isomeric states could be obtained for the first time: $\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(63.7}\text{keV in}{}^{160}\text{Tb}\text{) = 60 ± 5}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(138.7}\text{keV in}{}^{160}\text{Tb}\text{) = 5.7 ± 0.5}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(82.0}\text{keV in}{}^{156}\text{Ho}\text{) = 1.25 ± 0.20}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(87.2}\text{keV in}{}^{156}\text{Ho}\text{) = 58.5 ± 3.5}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(139.2}\text{keV in}{}^{158}\text{Ho}\text{) = 1.85 ± 0.10}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(38.3}\text{keV in}{}^{162}\text{Ho}\text{) = 1.2 ± 0.2}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(179.9}\text{keV in}{}^{162}\text{Ho}\text{) = 8.7 ± 0.2}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(342.8}\text{keV in}{}^{164}\text{Ho}\text{) = 2.6 ± 0.2}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(295.1}\text{keV in}{}^{166}\text{Ho}\text{) = 1.10±0.15}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(44.6}\text{keV in}{}^{162}\text{Tm}\text{) = 1.40±0.15}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{,(163.4}\text{keV in}{}^{162}\text{Tm}\text{) = 1.1 ± 0.1}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(220.1}\text{keV in}{}^{178}\text{Ta}\text{) = 8.5 ± 1.0}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(289.5}\text{keV in}{}^{178}\text{Ta}\text{) = 2.0 ± 0.5}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(392.8}\text{keV in}{}^{178}\text{Ta) ≈ 1 ns, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(316.5}\text{keV in}{}^{186}\text{Re}\text{) = 0.20 ± 0.10}\text{ns}\text{, T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(300.2}\text{keV in}{}^{188}\text{Re}\text{) = 1.5 ± 0.2}\text{ns and}\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(482.2}\text{keV in}{}^{188}\text{Re}\text{) = 0.26 ± 0.10}\text{ns}$. Furthermore, upper limits for the half-lives of fifteen excited states in ¹⁶⁰Tb, ^{164, 166}Ho and ^{186, 188}Re have been estimated. For eight isomeric levels in ^{186, 188}Re, the lifetimes earlier determined have been remeasured. Unlike previous studies, the existence of isomeric states at 87.2 keV in ¹⁵⁶Ho and at 179.9 keV in ¹⁶²Ho is suggested. Absolute γ-ray transition probabilities are deduced and compared with single-particle estimates according to Weisskopf and Nilsson, the latter also including pairing correlations. The K-, Ω- and f-forbidden transitions can qualitatively be explained in terms of configuration mixings. Experimental El, ΔK= 1 transition matrix elements in odd-odd deformed nuclei are supposed to be appreciably influenced by higher-order vibrational admixtures coupled via RPC and p-n interaction mixings.     

Level density for doubly odd deformed nuclei

The level density for doubly odd deformed nuclei near B_n is calculated within the framework of the semi-microscopic approach. The calculated values are found to be in good agreement with the experimental ones. It is shown that for the I ? 1 states it is important to take into account rotational motion.     

Theory of deuteron stripping on doubly even nuclei

Using the method of quantum Green functions we derive a rigorous formula for the deuteron stripping on a doubly even nucleus. Starting from this formula we discuss the distorted-wave Born approximation, some additional assumptions usually made in numerical calculations and the high-energy case. In addition to this we show that the formfactor can be calculated using a model for the nucleon self energy.     

Multiparticle production of doubly charged fragments in the fragmentation of relativistic nuclei

Features of angular distributions of events involving two or more doubly charged fragments of relativistic nuclei ²²Ne, ²⁴Mg, ¹⁴N, ¹¹B, and ¹⁰B in photoemulsions are studied. It is found that, in all cases, with the exception of the case of the intermediate-state decay ⁸Be → 2α, the fragments in these events are independent of one another. The inclusive angular distributions of fragments of relativistic nuclei ²²Ne for events in which the number of particles ranges between one and five are identical. Thus, the emission angle of each fragment of a relativistic nucleus does not depend either on other fragments or on the presence or absence of product particles and target-nucleus fragments in an event.     

Long-range orders in the doubly degenerate Hubbard model

The doubly degenerate Hubbard model is studied in the CPA alloy analogy approximation corrected by Lacroix-Lyon-Caen and Cyrot. The static susceptibility method is used. In the strong scattering limit, a ferromagnetic instability for 1 < N < 2 and 2 < N < 3 is confirmed. It is proved that there is no antiferromagnetic or charge-order instability for any N.     

Configuration interaction in the hyperfine structure of 4d-shell atoms

Fusion and deep inelastic cross sections for the system¹³²Xe+⁵⁶Fe within the Gross-Kalinowski friction model are in good agreement with radiochemical measurements and in contradiction to counter experiment data. This casts doubts on the latter and the need for a new damping mechanism in this system.     

Alloy analogy of the doubly degenerate Hubbard model

The doubly degenerate Hubbard model is studied in the CPA alloy analogy approximation. In the strong coupling limit, a ferromagnetic instability occurs when 1 < N < 2 and 2 < N < 3. We compare this approximation with other approximations and with the exact results.     

Properties of doubly heavy baryons in the relativistic quark model

Mass spectra and semileptonic decay rates of baryons consisting of two heavy (b or c) and one light quark are calculated in the framework of the relativistic quark model. The doubly heavy baryons are treated in the quark-diquark approximation. The ground and excited states of both the diquark and quark-diquark bound systems are considered. The quark-diquark potential is constructed. The light quark is treated completely relativistically, while the expansion in the inverse heavy-quark mass is used. The weak transition amplitudes of heavy diquarks bb and bc going, respectively, to bc and cc are explicitly expressed through the overlap integrals of the diquark wave functions in the whole accessible kinematic range. The relativistic baryon wave functions of the quark-diquark bound system are used for the calculation of the decay matrix elements, the Isgur-Wise function, and decay rates in the heavy-quark limit.     

Calculated isospin-mixing corrections to Fermi β-decays in 1s0d-shell nuclei with emphasis on A = 34

Corrections to the Fermi matrix element due to analogue symmetry breaking are evaluated for the superallowed β-decays of ²²Mg, ³⁴Cl, and ³⁴Ar by considering the effects of Coulomb and other isospin-nonconserving potentials. Analogue symmetry breaking is calculated within the shell-model formalism by considering: (i) the deviations from unity of the radial overlap between the proton and neutron single-particle wave functions, and (ii) isospin mixing between states within the 0d$\text{5}\text{2}$0d$\text{3}\text{2}$0d$\text{1}\text{2}$ shell. The radial-overlap corrections for several cases of interest in the sd shell are evaluated with single-particle wave functions obtained from a self-consistent Hartree-Fock calculation. The sd-shell isospin-mixing corrections are calculated with an isospin-non-conserving potential which reproduces the experimental isobaric mass shifts. Comparisons with previous calculations are made. The Fermi matrix elements for the isospin-forbidden (β-decays of ³⁴Cl and ³⁴Ar to excited 0⁺ states are also calculated.