Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

Adopted values for the reduced electric quadrupole transition probability, B(E2)↑, from the ground state to the first-excited 2+ state of even–even nuclides are given in Table I. Values of τ, the mean life of the 2+ state; E, the energy; and β, the quadrupole deformation parameter, are also listed there. The ratio of β to the value expected from the single-particle model is presented. The intrinsic quadrupole moment, Q0, is deduced from the B(E2)↑ value. The product E×B(E2)↑ is expressed as a percentage of the energy-weighted total and isoscalar E2 sum-rule strengths.

Table II presents the data on which Table I is based, namely the experimental results for B(E2)↑ values with quoted uncertainties. Information is also given on the quantity measured and the method used. The literature has been covered to November 2000.

The adopted B(E2)↑ values are compared in Table III with the values given by systematics and by various theoretical models. Predictions of unmeasured B(E2)↑ values are also given in Table III.

Transition probability from the ground to the first-excited 2^+ state of even-even nuclides

Progress in particle and nuclear physics

We carry out state-of-the-art optimization of a nuclear energy density of Skyrme type in the framework of the Hartree-Fock-Bogoliubov theory. The particle-hole and particle-particle channels are optimized simultaneously, and the experimental data set includes both spherical and deformed nuclei. The new model-based, derivative-free optimization algorithm used in this work has been found to be significantly better than standard optimization methods in terms of reliability, speed, accuracy, and precision. The resulting parameter set unedf0 results in good agreement with experimental masses, radii, and deformations and seems to be free of finite-size instabilities. An estimate of the reliability of the obtained parameterization is given, based on standard statistical methods. We discuss new physics insights offered by the advanced covariance analysis.

Nuclear Energy Density Optimization

Progress in Nuclear Physics Vol. 5. Edited by Prof. O. R. Frisch. (Progress Series.) Pp. vii + 325. (London and New York: Pergamon Press, Ltd., 1956.) 80s. net; 12.50 dollars.

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Advances in Nuclear Physics

The nucleus-nucleus interaction potentials in heavy-ion fusion reactions are extracted from the microscopic time-dependent Hartree-Fock theory for the mass symmetric reactions ${}^{16}\mathrm{O} + {}^{16}\mathrm{O}$, ${}^{40}\mathrm{Ca} + {}^{40}\mathrm{Ca}$, and ${}^{48}\mathrm{Ca} + {}^{48}\mathrm{Ca}$ and the mass asymmetric reactions ${}^{16}\mathrm{O} + {}^{40, 48}\mathrm{Ca}$, ${}^{40}\mathrm{Ca} + {}^{48}\mathrm{Ca}$, ${}^{16}\mathrm{O} + {}^{208}\mathrm{Pb}$, and ${}^{40}\mathrm{Ca} + {}^{90}\mathrm{Zr}$. When the c.m. energy is much higher than the Coulomb barrier energy, potentials deduced with the microscopic theory identify with the frozen density approximation. As the c.m. energy decreases and approaches the Coulomb barrier, potentials become energy dependent. This dependence indicates dynamical reorganization of internal degrees of freedom and leads to a reduction of the ``apparent'' barrier felt by the two nuclei during fusion of the order of 2--3% compared to the frozen density case. Several examples illustrate that the potential landscape changes rapidly when the c.m. energy is in the vicinity of the Coulomb barrier energy. The energy dependence is expected to have a significant role on fusion around the Coulomb barrier.

Energy dependence of the nucleus-nucleus potential close to the Coulomb barrier

Multi reference calculations along the lines of the generator coordinate method or the restoration of broken symmetries within the nuclear energy density functional (EDF) framework are becoming a standard tool in nuclear structure physics. These calculations rely on the extension of a single-reference energy functional, of the Gogny or the Skyrme types, to nondiagonal energy kernels. There is no rigorous constructive framework for this extension so far. The commonly accepted way proceeds by formal analogy with the expressions obtained when applying the generalized Wick theorem to the nondiagonal matrix element of a Hamilton operator between two product states. It is pointed out that this procedure is ill defined when extended to EDF calculations as the generalized Wick theorem is taken outside of its range of applicability. In particular, such a procedure is responsible for the appearance of spurious divergences and steps in multi reference EDF energies, as was recently observed in calculations restoring particle number or angular momentum. In the present work, we give a formal analysis of the origin of this problem for calculations with and without pairing, i.e., constructing the density matrices from either Slater determinants or quasiparticle vacua. We propose a method to regularize nondiagonal energy kernels such that divergences and steps are removed from multi reference EDF energies. Such a removal is a priori quasiparticle-basis dependent. A special feature of the method we use to proceed to the actual regularization is that it singles out one basis among all possible ones. The regularization method is applicable to calculations based on any symmetry restoration or generator coordinate but is limited to EDFs depending only on integer powers of the normal and anomalous density matrices. Eventually, the method is formally illustrated for particle-number restoration and is specified to configuration mixing calculations based on Slater determinants.

Configuration mixing within the energy density functional formalism: Removing spurious contributions from nondiagonal energy kernels

We discuss the origin of pathological behaviors that have been recently identified in particle-number-restoration calculations performed within the nuclear energy density functional framework. A regularization method that removes the problematic terms from the multi reference energy density functional and that applies (i) to any symmetry-restoration- and/or generator-coordinate-method-based configuration mixing calculation and (ii) to energy density functionals depending only on integer powers of the density matrices was proposed in [D. Lacroix, T. Duguet, and M. Bender, Phys. Rev. C 79, 044318 (2009)] and implemented for particle-number-restoration calculations in [M. Bender, T. Duguet, and D. Lacroix, Phys. Rev. C 79, 044319 (2009)]. In the present article, we address the viability of noninteger powers of the density matrices in the nuclear energy density functional. Our discussion builds on the analysis already carried out in [J. Dobaczewski et al., Phys. Rev. C 76, 054315 (2007)]. First, we propose to reduce the pathological nature of terms depending on a noninteger power of the density matrices by regularizing the fraction that relates to the integer part of the exponent using the method proposed in [D. Lacroix, T. Duguet, and M. Bender, Phys. Rev. C 79, 044318 (2009)]. Then, we discuss the spurious features brought about by the remaining fractional power. Finally, we conclude that noninteger powers of the density matrices are not viable and should be avoided in the first place when constructing nuclear energy density functionals that are eventually meant to be used in multi reference calculations.

Particle-number restoration within the energy density functional formalism: Nonviability of terms depending on noninteger powers of the density matrices

We give a detailed analysis of the origin of spurious divergences and finite steps that have been recently identified in particle-number-restoration calculations within the nuclear energy density functional framework. We isolate two distinct levels of spurious contributions to the energy. The first one is encoded in the definition of the basic energy density functional itself, whereas the second one relates to the canonical procedure followed to extend the use of the energy density functional to multi-reference calculations. The first level of spuriosity relates to the long-known self-interaction problem and to the newly discussed self-pairing interaction process that might appear when describing paired systems with energy functional methods using auxiliary reference states of Bogoliubov or BCS type. A minimal correction to the second level of spuriosity to the multi-reference nuclear energy density functional proposed in [D. Lacroix, T. Duguet, and M. Bender, Phys. Rev. C 79, 044318 (2009)] is shown to remove completely the anomalies encountered in particle-number-restored calculations. In particular, it restores sum rules over (positive) particle numbers that are to be fulfilled by the particle-number-restored formalism. The correction is found to be on the order of several hundreds of keVs up to about 1 MeV in realistic calculations, which is small compared to the total binding energy but often accounts for a substantial percentage of the energy gain from particle-number restoration and is on the same energy scale as the excitations one addresses with multi-reference energy density functional methods.

Particle-number restoration within the energy density functional formalism

The effect of pairing correlation on transfer reaction below the Coulomb barrier is investigated qualitatively and quantitatively using a simplified version of the time-dependent Hartree-$\mathrm{Fock}+\mathrm{BCS}$ approach. The effect of particle-number symmetry breaking on the description of reaction and dedicated methods to extract one- and two-nucleon transfer probabilities (${P}_{1n}$ and ${P}_{2n}$) in a particle-number symmetry breaking approach are discussed. The influence of pairing is systematically investigated in the ${}^{40}\mathrm{Ca}+{}^{40,42,44,46,48,50}\mathrm{Ca}$ reactions. A strong enhancement of the two-particle transfer probabilities owing to initial pairing correlations is observed. This enhancement induces an increase of the ratio of probabilities ${P}_{2n}/{({P}_{1n})}^{2}$ compared to the case with no pairing. It is shown that this ratio increases strongly as the center-of-mass energy decreases with a value that could be larger than ten in the deep sub-barrier regime. An analysis of the pair transfer sensitivity to the type of pairing interaction, namely surface, mixed, or volume, used in the theory is made. It is found that the pair transfer is globally insensitive to the type of force and depends mainly on the pairing interaction strength.

Denis Lacroix

Papers

Energy dependence of the nucleus-nucleus potential close to the Coulomb barrier

Configuration mixing within the energy density functional formalism: Removing spurious contributions from nondiagonal energy kernels

Particle-number restoration within the energy density functional formalism: Nonviability of terms depending on noninteger powers of the density matrices

Particle-number restoration within the energy density functional formalism

Effect of pairing on one- and two-nucleon transfer below the Coulomb barrier: a time-dependent microscopic description