Particle-hole Configurations Research Articles

Generalized particle-hole state densities within the equidistant spacing model

We present an improved mathematical method to compute particle-hole state densities, with high numerical accuracy, for an arbitrary single particle level scheme. For the simplest case, the equidistant spacing model (ESM), we compare our exact particle-hole state density calculations with several existing and new analytical formulae. The latter are derived using the method of Berger and Martinot and lead to a generalization of the Obložinský formula for the two-component particle-hole state density. Our new formulae, which include correction terms up to any order, are discussed for various particle-hole configurations over a broad energy range.

Renaissance of the Nilsson-model approach to light nuclei: The case of the A = 26 system

The farthest reaching interpretation of a light nuclear system in terms of the Nilsson-model is obtained for A = 26. The T = 1 and T = 0 levels of either parity in 26Mg and/or 26Al are shown to be grouped in more than 35 rotational bands together containing some 55 levels in 26Mg and 170 in 26Al. The Nilsson-model configurations and deformations of bands are deduced from measured spectroscopic factors and electromagnetic transition rates. The experimental data are amended by shell-model calculations in the complete s-d basis space based on the universal s-d Hamiltonian. The rotational structure of positive-parity states is completely contained in the shell-model results. The Nilsson diagram gives a natural explanation of all bands. An important facet is the observation of particle-hole configurations with large K which arise from the complete alignment of particle and hole angular momenta along the major axis of deformation.

Giant resonances as collective states with dissipative coupling

Giant resonances manifest themselves as broad bumps in the nuclear spectra above the neutron emission threshold. It has been established that the structure of these states consists of a large number of relevant particle-hole configurations, all of them contributing in phase to the excitation process. Be- cause of this, giant resonances are the most collective vibra- tional states in nuclei. Alternatively, given the strong collectivity of the giant resonances and the many degrees of freedom that influence their properties, one may consider that a statistical modeling of the formation and decaying processes including concepts like mean values and variances is an appropriate path to at- tact this difficult problem. In this paper, we adopt such a point of view. We consider a collective coordinate q and its vibrational modes determined by a harmonic oscillator po- tential. That is, we consider that the giant resonance corre- sponds to the first excitation of the harmonic oscillator, with energy \v 0, and the GR2 to the second excitation, with two quantum oscillations and energy 2\v 0 . Besides these exci- tations, we distinguish an ''environment'' of all the other excitations. In Sec. II we derive Lindblad's quantum master equation using physical concepts, since the original derivation @15# is rather abstract. We also derive a form of this equation which includes friction and diffusion @16,17#. It has been shown that this equation gives very accurate descriptions of pro- cesses in optics @18# as well as in nuclear physics @19,20# .I n Sec. III we obtain the energy mean value and width of the giant resonance and of the GR2. The corresponding equa- tions turn out to be analytically integrable. The decay spec- trum of the giant resonances is presented in Sec. IV and a summary and conclusions are in Sec. V.

The method of time-ordered graph decoupling and its application to the description of giant resonances in magic nuclei

A microscopic approach to analyzing the excited states of magic nuclei is described. It is based on the systematic use of the method of quantum Green functions. When applied to the theory of giant multipole resonances, the approach explicitly includes the three principle mechanisms of resonance formation in a finite nucleus: decay via particle–hole configurations of the discrete spectrum, decay via particle–hole configurations with a particle in the continuum, and decay via more complicated configurations of the particle–hole⊗phonon type. The results of a numerical realization of this approach for describing giant resonances in magic stable and unstable nuclei are discussed.

Preequilibrium proton decay in40Ca

The proton spectra of the giant quadrupole resonance decay in ${}^{40}$Ca is analyzed. The decay mechanism of this excitation is studied by the inclusion of the semidirect, preequilibrium, and statistical modes through the chaining evolution of the particle-hole configurations. Strong evidence for the contribution of preequilibrium decay of the giant resonance is established.

Enhanced E0 and E2 transition rates in the midshell Xe isotopes.

New measurements for lifetimes of excited ${0}^{+}$ and ${2}^{+}$ levels in $^{120}\mathrm{Xe}$ following $\ensuremath{\beta}$ decay of $^{120}\mathrm{Cs}$ isomers are reported. From these data, $E0$ and $E2$ transition rates are derived which exceed values calculated from models assuming only a limited valence nucleon space. The observed collectivity can be described by the inclusion of additional valence protons associated with particle-hole intruder configurations involving the $\ensuremath{\pi}{g}_{\frac{9}{2}}$ orbital.

Microscopic study of a C4-symmetry hypothesis in A~150 superdeformed nuclei: Deformed Woods-Saxon mean field.

Microscopic analysis of the quantum (shell) effects related to the presence of the hexadecapole (${\mathit{Y}}_{4\mathrm{\ensuremath{\mu}}}$; \ensuremath{\mu}=0,2,4) components in the nuclear mean field is performed for the superdeformed nuclei in the mass A \ensuremath{\sim} 150 region using the deformed Woods-Saxon potential. No shell effects favoring the ${\mathit{C}}_{4}$-symmetry are found. The calculations indicate, however, the existence of the ${\mathrm{\ensuremath{\alpha}}}_{44}$-deformation driving orbitals whose occupation might induce an ${\mathrm{\ensuremath{\alpha}}}_{44}$-polarization effect. For $^{149}\mathrm{Gd}$ and $^{153}\mathrm{Dy}$ nuclei, in which the existence of the ${\mathit{C}}_{4}$-symmetry effects is suspected, properties of several excited particle-hole configuration are analyzed.

A Microscopic, Coupled-Channel Theory of Pion Scattering

We develop a new and comprehensive coordinate-space theory of pion-nucleus scattering to facilitate disentangling the conventional aspects of pion scattering from the non-conventional ones relevant to issues of hadron dynamics. We work in coordinate space in order to both unify and extend the relatively extensive and successful analyses of exclusive pion-nucleus reactions previously made within a similar framework. We construct the optical potential microscopically in a shell-model framework by summing particle-hole pair configurations, leading naturally to a coupled-channel formulation. The theory includes a complete treatment of all spin-isospin components of the pion-nucleon scattering amplitude, and Fermi averaging is done explicitly. We present numerical results showing the significance of Fermi motion and spin dependence on charge-exchange angular distributions: Single and double spin flip are shown to play dominant and generally unappreciated roles in charge-exchange reactions, and corrections for Fermi motion are shown to be needed in order to quantitatively separate medium effects from conventional multiple scattering.

Width of the 3841-keV level in 17O.

The width of 3841-keV level in $^{17}\mathrm{O}$ was precisely measured in nuclear resonance fluorescence experiments performed at the Stuttgart Dynamitron facility. The result of \ensuremath{\Gamma}(3841 keV)=(92\ifmmode\pm\else\textpm\fi{}6) meV is compared with upper limits quoted in the literature. Possible particle-hole configurations of the 3841-keV level are discussed.

On the quenching of the (e, e′) form factor of the M1 transition to the 10.23 MeV state in 48Ca

The form factor of the process (e, e′) 48Ca(1 +; 10.23 MeV) is analyzed in the framework of the random-phase approximation. As in previous calculations the obtained wavefunction is dominated by the neutronic ( 1 f 5 2 1 f 7 2 −1 particle-hole configuration, but it is shown that the role of the small (non-dominant) components is not negligible. A quenching factor independent of the momentum transfer is found. The effect of the meson-exchange currents is also considered. Experimental data can be explained by the additional consideration of second order core polarization and tensor correlations effects.

Transient fieldg-factor measurement of the first 3− state in144Sm

The g-factor of the octupole vibrational state 3− at 1810 keV in144Sm has been measured to be 0.76(9) by means of the transient field technique. The state has been Coulomb excited by 217 MeV58Ni beam. The obtained value agrees with the predictions of RPA calculations and confirms the dominance of the proton particle-hole configuration π(1h11/2−2d5/2−1)

Two-nucleon excitations in 66 148 Dy82 from Gamow-Teller decay of the 67 148 Ho81 6? isomer

Two-particle excitations in the two-proton nucleus148Dy populated inβ-decay of 10-s 148Ho(6−) were investigated throughγ-ray measurements following on-line mass separation. Theπh 11/2s1/2 two-proton doublet and the (vh 9/2 s 1 2/−1 )5− neutron particle hole configuration are firmly identified, and theπh 11/2 d 5 2/−1 and πh11/2D3/2 multiplets are also observed. The results suggest dominantπh 11/2vs 1 2/−1 character for the148Ho 6−-isomer.

Sharing of collective multipole strength in the nuclear particle-hole model.

A procedure is given for defining explicitly the noncollective states of the degenerate schematic model for nuclear particle-hole configurations. The method is based on the view that the degenerate model is an approximation to the nondegenerate particle-hole model. In the collective-noncollective basis with a single force type, the separable particle-hole Tamm-Dancoff Hamiltonian matrix is transformed into one which is diagonal except for the row and column of the one collective state. The multipole strength of any noncollective state of the nondegenerate problem is given in perturbation theory in terms of the collective-noncollective matrix elements, which are expressed in terms of the parameters of the assumed separable multipole interaction. Application of the sharing formulas is made to Landau damping of the collective state due to mixing with the noncollective states. The relative contribution to the width due to the nondegeneracy and the nonseparable nature of the interaction are examined. Another application examines the random-phase-approximation energy distribution of isospin shared by the isoscalar and isovector collective states with the noncollective states over the giant quadrupole resonance region in $^{118}\mathrm{Sn}$.

Dynamical symmetries in even-even Te nuclides.

The structure of the even-even Te nuclides with 114A134 is shown to consist of features that can be associated with underlying low-energy collective excitations, as well as particle-hole intruder and two-quasiparticle configurations. Energy level positions and branching ratios from new and existing measurements can be reasonably well fitted with a proton-neutron interacting boson model calculation that includes particle-hole configuration mixing. After identifying levels that have large particle-hole intruder admixtures, little evidence for structures closely resembling those of the O(6) or SU(5) dynamical limits can be found.

Multireference coupled-cluster methods using an incomplete model space: Application to ionization potentials and excitation energies of formaldehyde

A recent fully linked multireference coupled-cluster method using an incomplete model space is applied to the direct calculation of the difference energies of formaldehyde. For the calculation of excitation energies (EE) use is made of a reference space composed of particle-hole excited configurations built from a set of active orbitals. Ionization potentials are obtained from a model space of singly ionized configurations. Results are compared with experiment and previous calculations.

High spin states in 208Pb.

Proton cross sections for $^{208}\mathrm{Pb}$ have been measured for elastic and inelastic scattering to the ${12}^{+}$, 6.10 MeV, ${12}_{1}^{\mathrm{\ensuremath{-}}}$, 6.43 MeV, ${12}_{2}^{\mathrm{\ensuremath{-}}}$, 7.06 MeV, and ${14}^{\mathrm{\ensuremath{-}}}$, 6.74 MeV states at ${E}_{\mathrm{p}=318}$ MeV. We analyze the inelastic transitions in the distorted wave impulse approximation and use the previously published electron scattering results to constrain the wave functions in the unnatural parity calculations. A ${13}^{\mathrm{\ensuremath{-}}}$ state is discussed as an unresolved ``contaminant'' to the ${12}_{1}^{\mathrm{\ensuremath{-}}}$, 6.43 MeV state. Mixing between the ${12}^{\mathrm{\ensuremath{-}}}$ neutron and proton particle-hole configurations is found to reduce substantially the differences reported previously in observed proton and electron quenching factors. This results in greater quenching for the ${12}_{2}^{\mathrm{\ensuremath{-}}}$, 7.06 MeV state, and less quenching for the ${12}_{1}^{\mathrm{\ensuremath{-}}}$, 6.43 MeV state than was previously reported in (e,e') analyses.

Particle-hole multiplets in146Gd from in-beam studies of non-yrast levels

Non-yrast levels of146Gd have been investigated by in-beamγ-ray and conversion electron spectroscopy following the144Sm(α, 2n) reaction at 25.7 MeV, an energy which was determined to provide optimum population of levels above the yrast line. The detailed146Gd level scheme includes twenty-one newly identified levels, many of which can be characterized in terms of specific proton particle-hole configurations. Several twoparticle-twohole states involving the 3− phonon have also been identified.

Stretched states in 26Mg from the 25Mg( alpha,3He) reaction at 81 MeV.

The $^{25}\mathrm{Mg}$(\ensuremath{\alpha}, $^{3}\mathrm{He}$${)}^{26}$Mg reaction was used at 80.9 MeV to investigate the stretched ${6}^{\mathrm{\ensuremath{-}}}$ states from the (${d}_{5/2}^{\mathrm{\ensuremath{-}}1}$,${f}_{7/2}$) particle-hole configuration, which had been identified by inelastic electron scattering. The summed spectroscopic factors for the T=1 ${6}^{\mathrm{\ensuremath{-}}}$ states are only about 27% of the expected strength and are to be compared to 85% of the extreme single model strength found in inelastic electron scattering. The T=1 ${6}^{\mathrm{\ensuremath{-}}}$ spectroscopic strength is considerably more fragmented in the mass 26 system than it is in mass 28.

Direct neutron decay of the giant quadrupole resonance in 92Zr and its particle-hole structure.

The $^{92}\mathrm{Zr}$(\ensuremath{\alpha},\ensuremath{\alpha}'n${)}^{91}$Zr reaction through the giant quadrupole resonance in $^{92}\mathrm{Zr}$ was studied with \ensuremath{\alpha}'-n correlation measurements. Three groups of fast neutrons decaying from the giant quadrupole resonance were found, which leave single-neutron-hole states of (i) 2d${(5/2)}^{\mathrm{\ensuremath{-}}1}$, (ii) 1g${(9/2)}^{\mathrm{\ensuremath{-}}1}$, and (iii) 2${p}^{\mathrm{\ensuremath{-}}1}$ and 1${g}^{\mathrm{\ensuremath{-}}1}$ in the residual $^{91}\mathrm{Zr}$ nucleus. They indicate the microscopic particle-hole configuration of the giant quadrupole resonance. The direct fast decay branch is about 16%.

Isospin dependence of two-component particle-hole state densities for nuclei

A simple expression is derived for the two-component particle-hole state densities for nuclei with a specified isospin quantum number. In spite of the lack of a one-to-one correspondence between the particle-hole configurations in different members of the same isospin multiplet, the density of T = T/sub z/+1 states in a nucleus may be simply related to the density of states of this isospin in the neighboring nucleus, where T is the ground state isospin. Thus results similar to those for other types of isospin dependent state densities are obtained, but important differences are also noted.