arXiv subjects

P. Schuck

Publications and source records attributed to P. Schuck.

At least 55 records · Page 3Linked to original sources

arXiv2011

Isoscalar monopole excitations in $^{16}$O: $α$-cluster states at low energy and mean-field-type states at higher energy

Isoscalar monopole strength function in $^{16}$O up to $E_{x}\simeq40$ MeV is discussed. We found that the fine structures at the low energy region up to $E_{x} \simeq 16$ MeV in the experimental monopole strength function obtained by the $^{16}$O$(α,α^{\prime})$ reaction can be rather satisfactorily reproduced within the framework of the $4α$ cluster model, while the gross three bump structures observed at the higher energy region ($16 \lesssim E_{x} \lesssim 40$ MeV) look likely to be approximately reconciled by the mean-field calculations such as RPA and QRPA. In this paper, it is emphasized that two different types of monopole excitations exist in $^{16}$O; one is the monopole excitation to cluster states which is dominant in the lower energy part ($E_{x} \lesssim 16$ MeV), and the other is the monopole excitation of the mean-field type such as one-particle one-hole ($1p1h$) which {is attributed} mainly to the higher energy part ($16 \lesssim E_{x} \lesssim 40$ MeV). It is found that this character of the monopole excitations originates from the fact that the ground state of $^{16}$O with the dominant doubly closed shell structure has a duality of the mean-field-type {as well as} $α$-clustering {character}. This dual nature of the ground state seems to be a common feature in light nuclei.

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arXiv2011

Suppression of Superfluidity upon Overflow of Trapped Fermions. Quantal and Thomas-Fermi Studies

Two issues are treated in this work: (i) the generic fact that if a fermionic superfluid in the BCS regime overflows from a narrow container into a much wider one, pairing is much suppressed at the overflow point. Physical examples where this feature may play an important role are discussed (ii) A Thomas-Fermi (TF) approach to inhomogeneous superfluid Fermi-systems is presented and shown that it works well in cases where the Local Density Approximation (LDA) breaks down.

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arXiv2011

Spin Scissors Mode and the Fine Structure of M1 States in Nuclei

The coupled dynamics of low lying modes, including the scissors mode, and various giant quadrupole resonances are studied with the help of the Wigner Function Moments method generalized to take into account spin degrees of freedom. Equations of motion for collective variables are derived on the basis of Time Dependent Hartree-Fock equations in the model of harmonic oscillator with spin orbital mean field potential plus quadrupole-quadrupole residual interaction. Introducing spin allows one to consider new types of nuclear collective motion where the nucleons with spin 'up' oscillate against nucleons with spin 'down'.

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arXiv2011

Thomas-Fermi approximation to pairing in finite Fermi systems. The weak coupling regime

We present a new semiclassical theory for describing pairing in finite Fermi systems. It is based on taking the $\hbar \to 0$, i.e. Thomas-Fermi, limit of the gap equation written in the basis of the mean field (weak coupling). In addition to the position dependence of the Fermi momentum, the size dependence of the pairing force is also taken into account in this theory. Along isotopic chains the Thomas-Fermi gaps average the well known arch structure shown by the quantal gaps. This structure can be almost recovered in our formalism if some shell fluctuations are included in the level density. We point out that at the drip line nuclear pairing is strongly reduced. This fact is illustrated with the behavior of the gap in the inner crust of neutron stars.

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arXiv2011

Comment on "Fermi-Bose Mixtures near Broad Interspecies Feshbach Resonances"

In a recent Letter (Phys. Rev. lett. 105, 195301 (2010)), Song et al. introduced a new variational approach to treat strong attractive boson-fermion (BF) correlations in BF atomic mixtures. The proposed theory predicts a first order phase transition to a condensate of composite BF pairs with center of mass momentum Q=0 as opposed to a composite fermionic molecular Fermi gas. We show in this comment that their approach is incorrect and moreover, by resorting to an exactly solvable model we demonstrate that there cannot be more than one correlated Q=0 BF pair in complete contradiction with their conclusions.

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arXiv2011

Nuclear Alpha-Particle Condensates

The $α$-particle condensate in nuclei is a novel state described by a product state of $α$'s, all with their c.o.m. in the lowest 0S orbit. We demonstrate that a typical $α$-particle condensate is the Hoyle state ($E_{x}=7.65$ MeV, $0^+_2$ state in $^{12}$C), which plays a crucial role for the synthesis of $^{12}$C in the universe. The influence of antisymmentrization in the Hoyle state on the bosonic character of the $α$ particle is discussed in detail. It is shown to be weak. The bosonic aspects in the Hoyle state, therefore, are predominant. It is conjectured that $α$-particle condensate states also exist in heavier $nα$ nuclei, like $^{16}$O, $^{20}$Ne, etc. For instance the $0^+_6$ state of $^{16}$O at $E_{x}=15.1$ MeV is identified from a theoretical analysis as being a strong candidate of a $4α$ condensate. The calculated small width (34 keV) of $0^+_6$, consistent with data, lends credit to the existence of heavier Hoyle-analogue states. In non-self-conjugated nuclei such as $^{11}$B and $^{13}$C, we discuss candidates for the product states of clusters, composed of $α$'s, triton's, and neutrons etc. The relationship of $α$-particle condensation in finite nuclei to quartetting in symmetric nuclear matter is investigated with the help of an in-medium modified four-nucleon equation. A nonlinear order parameter equation for quartet condensation is derived and solved for $α$ particle condensation in infinite nuclear matter. The strong qualitative difference with the pairing case is pointed out.

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arXiv2010

Semi-Classical Description of the Average Pairing Properties in Nuclei

We present a new semi-classical theory for describing pairing in finite Fermi systems. It is based in taking the $\hbar \to 0$, i.e. Thomas-Fermi, limit of the gap equation written in the basis of the mean field (weak coupling). In addition to the position dependence of the Fermi momentum, the size dependence of the matrix elements of the pairing force is also taken into account in this theory. An example typical for the nuclear situation shows the improvement of this new approach over the standard Local Density Approximation. We also show that if in this approach some shell fluctuations are introduced in the level density, the arch structure displayed by the quantal gaps along isotopic chains is almost recovered. We also point out that in heavy drip line nuclei pairing is strongly reduced.

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arXiv2010

Cooper pair sizes in superfluid nuclei in a simplified model

Cooper pair sizes are evaluated in a simple harmonic oscillator model reproducing the values of sophisticated HFB calculations. Underlying reasons for the very small sizes of 2.0-2.5 fm of Cooper pairs in the surface of nuclei are analysed. It is shown that the confining properties of the nuclear volume is the dominating effect. It is argued that for Cooper pair sizes LDA is particularly inadapted.

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arXiv2010

Coexistence of 'alpha+ 208Pb' cluster structures and single-particle excitations in 212Po

Excited states in 212Po have been populated by alpha transfer using the 208Pb(18O,14C) reaction at 85MeV beam energy and studied with the EUROBALL IV gamma multidetector array. The level scheme has been extended up to ~ 3.2 MeV excitation energy from the triple gamma coincidence data. Spin and parity values of most of the observed states have been assigned from the gamma angular distributions and gamma -gamma angular correlations. Several gamma lines with E(gamma) < 1 MeV have been found to be shifted by the Doppler effect, allowing for the measurements of the associated lifetimes by the DSAM method. The values, found in the range [0.1-0.6] ps, lead to very enhanced E1 transitions. All the emitting states, which have non-natural parity values, are discussed in terms of alpha-208Pb structure. They are in the same excitation-energy range as the states issued from shell-model configurations.

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arXiv2010

Energy density functional on a microscopic basis

In recent years impressive progress has been made in the development of highly accurate energy density functionals, which allow to treat medium-heavy nuclei. In this approach one tries to describe not only the ground state but also the first relevant excited states. In general, higher accuracy requires a larger set of parameters, which must be carefully chosen to avoid redundancy. Following this line of development, it is unavoidable that the connection of the functional with the bare nucleon-nucleon interaction becomes more and more elusive. In principle, the construction of a density functional from a density matrix expansion based on the effective nucleon-nucleon interaction is possible, and indeed the approach has been followed by few authors. However, to what extent a density functional based on such a microscopic approach can reach the accuracy of the fully phenomenological ones remains an open question. A related question is to establish which part of a functional can be actually derived by a microscopic approach and which part, on the contrary, must be left as purely phenomenological. In this paper we discuss the main problems that are encountered when the microscopic approach is followed. To this purpose we will use the method we have recently introduced to illustrate the different aspects of these problems. In particular we will discuss the possible connection of the density functional with the nuclear matter Equation of State and the distinct features of finite size effects proper of nuclei.

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arXiv2010

Microscopic study of 4-alpha-particle condensation with proper treatment of resonances

The 4-alpha condensate state for ^{16}O is discussed with the THSR (Tohsaki-Horiuchi-Schuck-Roepke) wave function which has alpha-particle condensate character. Taking into account a proper treatment of resonances, it is found that the 4-alpha THSR wave function yields a fourth 0^+ state in the continuum above the 4-alpha-breakup threshold in addition to the three 0^+ states obtained in a previous analysis. It is shown that this fourth 0^+ ((0_4^+)_{THSR}) state has an analogous structure to the Hoyle state, since it has a very dilute density and a large component of alpha+^{12}C(0_2^+) configuration. Furthermore, single-alpha motions are extracted from the microscopic 16-nucleon wave function, and the condensate fraction and momentum distribution of alpha particles are quantitatively discussed. It is found that for the (0_4^+)_{THSR} state a large alpha-particle occupation probability concentrates on a single-alpha 0S orbit and the alpha-particle momentum distribution has a delta-function-like peak at zero momentum, both indicating that the state has a strong 4-alpha condensate character. It is argued that the (0_4^+)_{THSR} state is the counterpart of the 0_6^+ state which was obtained as the 4-alpha condensate state in the previous 4-alpha OCM (Orthogonality Condition Model) calculation, and therefore is likely to correspond to the 0_6^+ state observed at 15.1 MeV.

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arXiv2010

Octupole deformation properties of the Barcelona-Catania-Paris energy density functionals

We discuss the octupole deformation properties of the recently proposed Barcelona-Catania-Paris (BCP) energy density functionals for two sets of isotopes, those of radium and barium, where it is believed that octupole deformation plays a role in the description of the ground state. The analysis is carried out in the mean field framework (Hartree- Fock- Bogoliubov approximation) by using the axially symmetric octupole moment as a constraint. The main ingredients entering the octupole collective Hamiltonian are evaluated and the lowest lying octupole eigenstates are obtained. In this way we restore, in an approximate way, the parity symmetry spontaneously broken by the mean field and also incorporate octupole fluctuations around the ground state solution. For each isotope the energy of the lowest lying $1^{-}$state and the $B(E1)$ and $B(E3)$ transition probabilities have been computed and compared to both the experimental data and the results obtained in the same framework with the Gogny D1S interaction, which are used here as a well established benchmark. Finally, the octupolarity of the configurations involved in the way down to fission of $^{240}$Pu, which is strongly connected to the asymmetric fragment mass distribution, is studied. We confirm with this thorough study the suitability of the BCP functionals to describe octupole related phenomena.

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arXiv2010

Open Problems in $α$ Particle Condensation

$α$ particle condensation is a novel state in nuclear systems. We briefly review the present status on the study of $α$ particle condensation and address the open problems in this research field: $α$ particle condensation in heavier systems other than the Hoyle state, linear chain and $α$ particle rings, Hoyle-analogue states with extra neutrons, $α$ particle condensation related to astrophysics, etc.

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arXiv2010

Two-particle spatial correlations in superfluid nuclei

We discuss the effect of pairing on two-neutron space correlations in deformed nuclei. The spatial correlations are described by the pairing tensor in coordinate space calculated in the HFB approach. The calculations are done using the D1S Gogny force. We show that the pairing tensor has a rather small extension in the relative coordinate, a feature observed earlier in spherical nuclei. It is pointed out that in deformed nuclei the coherence length corresponding to the pairing tensor has a pattern similar to what we have found previously in spherical nuclei, i.e., it is maximal in the interior of the nucleus and then it is decreasing rather fast in the surface region where it reaches a minimal value of about 2 fm. This minimal value of the coherence length in the surface is essentially determined by the finite size properties of single-particle states in the vicinity of the chemical potential and has little to do with enhanced pairing correlations in the nuclear surface. It is shown that in nuclei the coherence length is not a good indicator of the intensity of pairing correlations. This feature is contrasted with the situation in infinite matter.

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arXiv2009

Cooper pair sizes in 11Li and in superfluid nuclei: a puzzle?

We point out a strong influence of the pairing force on the size of the two neutron Cooper pair in $^{11}$Li, and to a lesser extent also in $^6$He. It seems that these are quite unique situations, since Cooper pair sizes of stable superfluid nuclei are very little influenced by the intensity of pairing, as recently reported. We explore the difference between $^{11}$Li and heavier superfulid nuclei, and discuss reasons for the exceptional situation in $^{11}$Li.

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arXiv2009

Concepts of alpha-particle condensation

Certain aspects of the recently proposed antisymmetrised alpha particle product state wave function, or THSR alpha cluster wave function, for the description of the ground state in 8Be, the Hoyle state in 12C, and analogous states in heavier nuclei, are elaborated in detail. For instance, the influence of antisymmetrisation in the Hoyle state on the bosonic character of the alpha particles is studied carefully. It is shown to be weak, so that bosonic aspects are predominant. The de Broglie wave length of alpha particles in the Hoyle state is shown to be much larger than the inter-alpha distance. It is pointed out that the bosonic features of low density alpha gas states have measurable consequences, one of which, that is enhanced multi-alpha decay properties, likely already have been detected. Consistent with experiment, the width of the proposed analogue to the Hoyle state in 16O at the excitation energy of E_x=15.1 MeV is estimated to be very small (34 keV), lending credit to the existence of heavier Hoyle-like states. The intrinsic single boson density matrix of a self-bound Bose system can, under physically desirable boundary conditions, be defined unambiguously. One eigenvalue then separates out, being close to the number of alpha's in the system. Differences between Brink and THSR alpha cluster wave functions are worked out. No cluster model of the Brink type can describe the Hoyle state with a single configuration. On the contrary, many superpositions of the Brink type are necessary, implying delocalisation towards an alpha product state. It is shown that single alpha particle orbits in condensates of different nuclei are almost the same. It is thus argued that alpha particle antisymmetrised product states of the THSR type are a very promising novel and useful concept in nuclear physics.

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arXiv2009

Microscopic-Macroscopic Approach for Binding Energies with Wigner-Kirkwood Method

The semi-classical Wigner-Kirkwood $\hbar$ expansion method is used to calculate shell corrections for spherical and deformed nuclei. The expansion is carried out up to fourth order in $\hbar$. A systematic study of Wigner-Kirkwood averaged energies is presented as a function of the deformation degrees of freedom. The shell corrections, along with the pairing energies obtained by using the Lipkin-Nogami scheme, are used in the microscopic-macroscopic approach to calculate binding energies. The macroscopic part is obtained from a liquid drop formula with six adjustable parameters. Considering a set of 367 spherical nuclei, the liquid drop parameters are adjusted to reproduce the experimental binding energies, which yields a {\it rms} deviation of 630 keV. It is shown that the proposed approach is indeed promising for the prediction of nuclear masses.

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arXiv2009

A novel manifestation of $α$-clustering: new '$α$ + $^{208}$Pb' states in $^{212}$Po revealed by their enhanced E1 decays

Excited states in $^{212}$Po were populated by $α$ transfer using the $^{208}$Pb($^{18}$O, $^{14}$C) reaction and their deexcitation $γ$-rays were studied with the Euroball array. Several levels were found to decay by a unique E1 transition (E$_γ<$ 1 MeV) populating the yrast state with the same spin value. Their lifetimes were measured by the DSAM method. The values, found in the range [0.1-1.4] ps, lead to very enhanced transitions, B(E1) = 2$\times10^{-2}$ - 1$\times10^{-3}$ W.u.. These results are discussed in terms of an $α$-cluster structure which gives rise to states with non-natural parity values, provided that the composite system cannot rotate collectively, as expected in the '$α$ + $^{208}$Pb' case. Such states due to the oscillatory motion of the $α$-core distance are observed for the first time.

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