Sum rules for nuclear collective excitations

Characterizations of the response function and of integral properties of the strength function via a moment expansion are discussed. Sum rule expressions for the moments in the RPA are derived. The validity of these sum rules for both density independent and density dependent interactions is proved. For forces of the Skyrme type, analytic expressions for the plus three energy weighted sum rules are given for isoscalar monopole and quadrupole operators. From these, a close relationship between the monopole and quadrupole energies is shown and their dependence on incompressibility and effective mass is studied. The inverse energy weighted sum rule is computed numerically for the monopole operator, and an upper bound for the width of the monopole resonance is given. Finally the reliability of moments given by the RPA with effective interactions is discussed using simple soluble models for the hamiltonian, and also by comparison with experimental data.     

双奇核174Re中的准粒子形状驱动效应

对双奇核174Re的在束γ谱学实验数据作了仔细分析, 提取出了带间与带内E2 γ跃迁分支比, 并导出了其约化跃迁概率的比值。用带混合理论对约化跃迁概率的比值进行了分析, 得到带间相互作用强度及转动带形变的信息。发现不同组态的转动带其跃迁电四极矩具有明显的差异。与相邻奇A核的结构特征类似,这种跃迁电四极矩的差异很可能是由于1/2-[541]准质子或1/2-[521] 准中子对原子核的形状驱动效应造成的。 By analyzing carefully the in beam γ spectroscopy data of odd-odd 174Re, we have extracted the branching ratios of the interband and intraband E2 γ transitions from the two rotational bands of different configurations in 174Re.The ratios of the reduced transition probabilities B(E2) have been deduced and analyzed using a band mixing theory. Information on the band interaction and deformation have been obtained. Apparent differences of transition quadrupole moments are found in the two configurations. A likely reason for the differences in the transition quadrupole moments is the shape driving effects of 1/2-[541] quasi proton or 1/2-[521] quasi neutron, which has been proposed in the oddA neighbors of 174Re.     

Nuclear vibrations and rotations of like nucleons in the same shell in even-even nuclei

The vibrational and rotational motions in even nuclei are considered. A microscopic study of these motions leads to a relation between the vibrational motion in spherical nuclei and the rotational motion in deformed nuclei. Nuclei with like nucleons in the same shell are considered. The quadrupole two-body interactions are used in the large singlej-shell of even nuclei. The energies and transition operators of nuclei in the nuclear rotational region are calculated using this microscopic method. Quadrupole moments are also calculated. These calculations are compared with the rotational model of the aligned coupling scheme. The present calculations are in good agreement with previous calculations.     

The nuclear scissors mode in a solvable model

The coupled dynamics of the scissors mode and the isovector giant quadrupole resonance is studied in a model with separable quadrupole–quadrupole residual interactions. The method of Wigner function moments is applied to derive the dynamical equations for angular momentum and quadrupole moment. Analytical expressions for energies, B(M1)- and B(E2)-values, sum rules and flow-patterns of both modes are found for arbitrary values of the deformation parameter. Some predictions for the case of superdeformation are given. The subtle nature of the phenomenon and its peculiarities are clarified.     

Generating functions and sum rules for quantum oscillator

Generating functions and sum rules are discussed for transition probabilities between quantum oscillator eigenstates with time-dependent parameters.     

Tests of a Deformable Core Plus Few-Nucleon Model

We formulate a core plus few-nucleon model allowing for a rotational excitation of the core. Three and four-body systems including a ¹²C core nucleus are studied using an explicitly correlated Gaussian basis. Effects of the core excitation are tested by investigating energy levels and electric quadrupole transition probabilities. Though some improvements are obtained, we realize that the Pauli principle for the nucleon-deformable core motion has to be appropriately defined for better understanding.     

Multipole moments and spin-dependent sum rules and their applications to f72 and s-d shell nuclei

Matrix elements of multipole operators, defined separately for neutrons and protons, are related to spin-dependent sums of spectroscopic factors. A clarification of their relation to the matrix elements of single-particle operators enables the overlap representation to be formally extended to a stripping form for J ≠ 0 operators. Multipole moments obtained from $\text{f}{}_{\mathrm{<mtext>7</mtext><mtext>2</mtext>}}$ transfer data are found to be dominated by the quadrupole moments when the final nucleus is odd-odd.A previously found (2J + 1) rule for spectroscopic sums, which arises when the odd-J multipole moments vanish, is shown to lead to approximate sum rules which apply separately to stripping and pickup data. The sum rules are generally well satisfied for transfers leading to odd-odd nuclei in the s-d shell.     

Experimental transition probabilities for lines arising from the 4d5p and 4d5d configurations of ZrIII

Relative transition probabilities for 120 lines arising from the 4d5p and 4d5d configurations of ZrIII were determined from measurements of emission-line intensities in a laser-produced plasma. The experiment was carried out with Cu-Zr alloy with a Zr content lower than 13% in order to have an optically thin plasma. Transition probabilities were placed on an absolute scale by using theoretical lifetimes, line-strength sum rules and Boltzmann plot. Comparison of the present experimental results with the available theoretical data is made.     

Quadrupole Transitions in the Bound Rotational-Vibrational Spectrum of the Hydrogen Molecular Ion

The three-body Schrödinger equation of the ${{\rm H}_{2}^{+}}$ hydrogen molecular ion is solved in perimetric coordinates using the Lagrange-mesh method. Energies and wave functions of the four lowest vibrational bound or quasibound states for total orbital momenta from 0 to 40 are calculated with high accuracy. A simple calculation using the associated Gauss quadrature provides accurate quadrupole transition probabilities per time unit between those states over the whole rotational bands.     

Improved calculations of quark distributions in hadrons: the case of the pion

The earlier introduced method of calculation of quark distributions in hadrons, based on QCD sum rules, is improved. The imaginary part of the virtual photon forward scattering amplitude on some hadronic current is considered in the case, when initial and final virtualities of the current , and are different, . The operator product expansion (OPE) in , is performed. The sum rule for quark distribution is obtained using double dispersion representation of the amplitude on one side in terms of calculated in QCD OPE and on the other side in terms of physical states contributions. Double Borel transformation in , is applied to the sum rule, killing background non-diagonal transition terms which deteriorated the accuracy in previous calculations. The case of the valence quark distribution in the pion is considered, which was impossible to treat by the previous method. OPE up to dimension 6 operators is performed and leading order perturbative corrections are accounted. Valence u-quark distribution in was found at intermediate x, , and normalization point . These results may be used as input for evolution equations. Received: 14 July 1999 / Published online: 6 March 2000     

Optical Thomas-Reiche-Kuhn sum rules

The Thomas-Reiche-Kuhn sum rule is a fundamental consequence of the position-momentum commutation relation for an atomic electron and it provides an important constraint on the transition matrix elements for an atom. Analogously, the commutation relations for the electromagnetic field operators in a magnetodielectric medium constrain the properties of the dispersion relations for the medium through four sum rules for the allowed phase and group velocities for polaritons propagating through the medium. These rules apply to all bulk media including the metamaterials designed to provide negative refractive indices. An immediate consequence of this is that it is not possible to construct a medium in which all the polariton modes for a given wavelength lie in the negative-index region.     

The calculation of the matrix element for proton decay

Matrix elements and proton decay probabilities are calculated in the SU(5) model of grand unification with the help of the matrix element of the proton transition into three quarks, found previously by the QCD sum rules. The results show that an increase of the existing experimental lower limit for the proton lifetime by a factor of 3–4 would rule out the standard SU(5) model.     

Evidence for nontermination of rotational bands in 74Kr

Three rotational bands in 74Kr were studied up to (in one case one transition short of) the maximum spin I(max) of their respective single-particle configurations. Their lifetimes have been determined using the Doppler-shift attenuation method. The deduced transition quadrupole moments reveal a modest decrease, but far from a complete loss of collectivity at the maximum spin I(max). This feature, together with the results of mean field calculations, indicates that the observed bands do not terminate at I = I(max).     

类铍离子磁四极M2 2s2 1S0—2s2p3P2 (Z=10—103)禁戒跃迁

利用全相对论多组态Dirac-Fock方法系统地计算了高离化类铍离子的磁四极M2 2s²¹S₀—2s2p³P₂ (Z=10—103)自旋禁戒跃迁的能级间隔、跃迁概率和振子强度，计算中考虑了重要核的有限体积效应，Breit修正和QED修正，所得结果和最近的实验数据以及理论值进行了比较，结果表明：高原子序数的高电荷离子(Z≥70)磁四极M2自旋禁戒跃迁几乎可以和中性原子的光学允许跃迁相比拟，不仅在天体等离子体中，在ICF和MCF高温激光等离子体中，磁四极自旋禁戒跃迁和其他自旋禁戒跃迁（磁偶极、电四极）一样不容忽视，在双电子复合、不透明度、自由程等理论计算中应该考虑其影响. 关键词： 磁四极M2 能级间隔 跃迁概率 振子强度     

Probability sum rules and consistent quantum histories

An example shows that weak decoherence is more restrictive than the minimal logical decoherence structure that allows probabilities to be used consistently for quantum histories. The probabilities in the sum rules that define minimal decoherence are all calculated by using a projection operator to describe each possibility for the state at each time. Weak decoherence requires more sum rules. They bring in additional variables, that require different measurements and a different way to calculate probabilities, and raise questions of operational meaning. The example shows that extending the linearly positive probability formula from weak to minimal decoherence gives probabilities that are different from those calculated in the usual way using the Born and von Neumann rules and a projection operator at each time.     

Spin-isospin sum rules based on the quark model

The response of nuclei to zero momentum transfer spin-isospin operators like the magnetic dipole and the Gamow-Teller operator are considered. On the basis of a non-relativistic quark model hamiltonian we derive energy-weighted sum rules for these operators. Ground-state correlations in the nucleus are treated in the random-phase approximation with a schematic baryon-baryon interaction. It is found that within reasonable limits of the coupling strength the sum rules are stable and thus can be termed model independent.     

Effect of γ-vibration on high-j rotational bands of odd-A nuclei

A γ-vibrational degree of freedom is incorporated into the particle-symmetric rotor model. The effects of γ-vibration on a high-j rotational band are studied. A characteristic signature splitting of the energy spectra is found to favor the presence of the interaction with the γ-vibration. E2 and M1 intraband transition probabilities of a high-j rotational band are better reproduced in a strongly deformed nucleus when the interaction with the γ-vibration is taken into account. It is found that the interaction with the γ-vibration induces a similar signature-dependent oscillation in E2 transition probabilities to that of the triaxial rotor-particle model.     

QCD sum rules for nucleon-nucleon and hyperon-nucleon interactions

The QCD sum rules for spin-dependent nucleon-nucleon (N N) and hyperon-nucleon (Y N) interactions are formulated and their physical implications are clarified. A dispersion integral around the nucleon threshold can be identified as a measure of interaction strength. Calculating the operator product expansion (OPE) of the correlation function, we have found that the spin-dependent operators are related to the axial and tensor charges. The obtained sum rules relate the interaction strengths to the nucleon matrix elements of the quark-gluon operators. The spin-dependent parts are smaller than the spin-independent parts in the N N and the Y N channels. The spin-independent N N interaction strength is greater than the spin-independent Y N interaction strengths. The results are consistent with the empirical result in the N N channel.