The investigation of the 2<Emphasis Type="Italic">νββ</Emphasis> decay by Pyatov method within quasiparticle random phase approximation formalism

The violated commutation condition between the total shell model Hamiltonian and Gamow-Teller operator (GT) has been restored by Pyatov method (PM). The considered nuclear model Hamiltonian in PM includes the separable GT residual interaction in ph and pp channels and is differentiated from the traditional schematic model by h ₀(restoration term). The influence of the h ₀ effective interaction on the 2νββ decay of ⁴⁸Ca, ⁷⁶Ge, ⁸²Se, ⁹⁶Zr, ¹⁰⁰Mo, ¹¹⁶Cd, ^128,130Te and ¹³⁶Xe is investigated. All the calculations have been done within the framework of standard QRPA. The results obtained by PM are compared with those of other approaches and experimental data. The influence of the restoration term on the stability of the 2νββ decay nuclear matrix elements is analysed.      

Rotational structures in 123Cs

High-spin states in ¹²³Cs, populated via the ¹⁰⁰Mo ( ²⁸Si, p4n) fusion-evaporation reaction at E _lab = 130 MeV, have been investigated employing in-beam γ-ray spectroscopic techniques. Rotational bands, built on πg _7/2, πg _9/2 and the unique-parity πh _11/2 orbitals, have been extended and evolve into bands involving rotationally aligned ν(h _11/2)² and π(h _11/2)² quasiparticles. A three-quasiparticle band based on the high-K πh _11/2 ⊗ νg _7/2 ⊗ νh _11/2 configuration has also been observed. Total Routhian Surface (TRS) calculations have been used to predict the nuclear shape parameters ( β₂, β₄, γ) for the various assigned configurations. The assigned configurations have been discussed in the framework of a microscopic theory based on the deformed Hartree-Fock (HF) and angular-momentum projection techniques.     

Rotational bands in the doubly odd 130Cs nucleus

The band structures built on the 5^- isomeric state ( T _1/2 = 3.46 m) in the doubly odd ¹³⁰Cs nucleus have been established up to I = 24? via the ¹²⁴Sn(¹¹B, 5n)¹³⁰Cs reaction. The previously observed bands based on the πh _11/2⊗νh _11/2, πg _7/2⊗νh _11/2 and πd _5/2⊗νh _11/2 configurations and a positive-parity side band with multiple connections to the α = 0 signature partner of the yrast πh _11/2⊗νh _11/2 band have been extended to higher spins. A new band based on the πh _11/2⊗νg _7/2 configuration is observed. The yrast πh _11/2⊗νh _11/2 band exhibits anomalous signature splitting whose magnitude decreases up to spin 15 and then increases without restoring the normal signature splitting. Received: 20 February 2001 / Accepted: 9 May 2001     

The electric quadrupole interaction of 111Cd in ZrZn2 and Zn in the samples prepared at 8 GPa

The perturbed angular correlation (PAC) measurements with the ¹¹¹In-¹¹¹Cd nuclear probe embedded into the lattice of the cubic (C15) Laves compound ZrZn₂ showed that ¹¹¹Cd nuclei experienced an axially symmetric electric quadrupole interaction with a frequency ν _Q  = 132.4 MHz at room temperature. The samples were synthesized and doped with the probe at a pressure 8 GPa. The temperature dependence of ν _Q was shown to be linear: ν _Q (T) = 147(1 − 0.033 T) MHz. Since the value of ν _Q is very close to that known for ¹¹¹Cd in the lattice of Zn, we have checked if it could be assigned to residual Zn metal in the sample. For the Zn sample melted and doped with ¹¹¹In at 8 GPa we have obtained ν _Q  = 117.3 MHz at 300 K and 127 MHz at 80 K – both values considerably lower than that for ¹¹¹In doped Zn samples prepared at an ambient pressure. These data, and the fact that ν _Q (T) in Zn is known to follow the T ^3/2 law, allow to attribute the ν _Q value quoted above to ¹¹¹Cd nuclei at the substitutional sites with tetrahedral symmetry in the Zn sublattice of ZrZn₂.     

Rotational structures in the 125Cs nucleus

The collective band structures of the ¹²⁵Cs nucleus have been investigated by in-beam γ-ray spectroscopic techniques following the ¹¹⁰Pd ( ¹⁹F, 4n) reaction at 75MeV. The previously known level scheme, with rotational bands built on πg_7/2, πg_9/2 and πh_11/2 orbitals, has been extended and evolves into bands involving rotationally aligned ν(h_11/2)² and π(h_11/2)² quasiparticles. A strongly coupled band has been reassigned a high-K πh_11/2 ⊗ νg_7/2 ⊗ νh_11/2 three-quasiparticle configuration and a new side band likely to be its chiral partner has been identified. Configurations assigned to various bands are discussed in the framework of Principal/Tilted Axis Cranking (PAC/TAC) model calculations.     

Low Temperature Phase Diagrams¶of Fermionic Lattice Systems

We consider fermionic lattice systems with Hamiltonian H=H ^{(0)}+λH _Q , where H ^{(0)} is diagonal in the occupation number basis, while H _Q is a suitable “quantum perturbation”. We assume that H ^{(0)} is a finite range Hamiltonian with finitely many ground states and a suitable Peierls condition for excitations, while H _Q is a finite range or exponentially decaying Hamiltonian that can be written as a sum of even monomials in the fermionic creation and annihilation operators. Mapping the d dimensional quantum system onto a classical contour system on a d+1 dimensional lattice, we use standard Pirogov–Sinai theory to show that the low temperature phase diagram of the quantum system is a small perturbation of the zero temperature phase diagram of the classical system, provided λ is sufficiently small. Particular attention is paid to the sign problems arising from the fermionic nature of the quantum particles. As a simple application of our methods, we consider the Hubbard model with an additional nearest neighbor repulsion. For this model, we rigorously establish the existence of a paramagnetic phase with commensurate staggered charge order for the narrow band case at sufficiently low temperatures. Received: 23 December 1996/ Accepted: 7 April 1999     

The exponent λ (x, Q2) of the proton structure functionF2(x, Q2) at lowx

The exponent λ of the structure function F₂ ∼x ^−λ is calculated using the solution of the DGLAP equation for gluon at lowx reported recently by the present authors. The quantity λ is calculated both as a function ofx at fixedQ ² and as a function ofQ ² at fixedx and compared with the most recent data from H1     

Minimum Polynomial for Single-Mode Parabose Parasupercharge and Hamiltonian

We calculate the minimum polynomial φ(x,y) of parasupercharge Q and Hamiltonian H for single-mode parabose parasupersymmetry (P-PSUSY). Suppose that φ(x,y) satisfies the homogeneity ∀ λ∈ℝ,φ(λ x,λ ² y)=λ ⁿ φ(x,y), then the parafermionic order p _f is restricted to either 1, 2, or 4. Under the P-PSUSY, the homogeneity of the φ(x,y) is equivalent to the parasuperconformality of Q and H. The physical meaning of the parasuperconformality is discussed, in connection with the spin of the elementary particle.     

Observation of a πh9/2 ⊗ νi13/2 oblate band in 188Tl

Excited states in ¹⁸⁸Tl have been studied experimentally using the ¹⁵⁷Gd (³⁵Cl, 4n) reaction at a beam energy of 170MeV. A rotational band built on the πh _9/2 ⊗ νi _13/2 configuration with oblate deformation has been established for ¹⁸⁸Tl. Based on the structure systematics of the oblate πh _9/2 ⊗ νi _13/2 bands in the heavier odd-odd Tl nuclei, we have tentatively proposed spin values for the new band in ¹⁸⁸Tl. The πh _9/2 ⊗ νi _13/2 oblate band in ¹⁸⁸Tl shows low-spin signature inversion, and it can be interpreted qualitatively by the two-quasiparticle plus rotor model including a J-dependent p-n residual interaction.     

Precise Nuclear Quadrupole Moments of 8B and 13B

The electric quadrupole coupling constants eqQ/h of ⁸B (, T _1/2 = 769 ms) and ¹³B (, T _1/2 = 17.4 ms) in single crystal TiO₂ have been precisely measured by the β-NQR technique. The ratios of these Q moments to Q(¹²B) were determined as ∣Q(⁸B)/Q(¹²B)∣ = 4.882(32) and ∣Q(¹³B)/Q(¹²B)∣ = 2.768(24).     

The next-to-leading order (NLO) gluon distribution from DGLAP equation and the logarithmic derivatives of the proton structure functionF 2(x, Q 2) at lowx

At lowx, an analytic solution of the DGLAP equation for gluon in the next-to-leading order (NLO) is obtained by applying the method of characteristics. Its compatibility with double leading logarithmic approximation (DLLA) asymptotics is discussed and comparison with the exact ones like GRV98NLO is made. The solution is then utilized to calculate the derivatives∂F ₂ (x,Q ²)/∂ lnQ ² and ∂ lnF ₂(x,Q ²)/∂ ln (1/x) and compared with the recent HERA data. Our solution is found to reproduce most of the essential features of the data on the derivatives.     

Solution of approximate gluon evolution equation for small-x at fixed ‘ρ’

A simple method has been applied to solve the approximate gluon evolution equation for small-x at fixedρ(≡√ln(x ₀/x)/ln[ln(Q ²/Λ²)/ln(Q ₀ ² /Λ²)]. Numerical comparison is made with the predictions from ‘double asymptotic scaling’ and fit. Better agreement is found between our solution and fit nearρ=1. The solution gives approximate double scaling in this region having ‘hard’ pomeron with small contamination.     

Super-Diffusivity in a Shear Flow Model¶from Perpetual Homogenization

This paper is concerned with the asymptotic behavior solutions of stochastic differential equations dy _t =dω _t −∇Γ(y _t ) dt, y ₀=0 and d=2. Γ is a 2 &\times; 2 skew-symmetric matrix associated to a shear flow characterized by an infinite number of spatial scales Γ₁₂=−Γ₂₁=h(x ₁), with h(x ₁)=∑ _{n =0} ^∞γ _n h ⁿ (x ₁/R _n ), where h ⁿ are smooth functions of period 1, h ⁿ (0)=0, γ _n and R _n grow exponentially fast with n. We can show that y ^t has an anomalous fast behavior (?[|y ^t |²]∼t ^1+ν with ν > 0) and obtain quantitative estimates on the anomaly using and developing the tools of homogenization. Received: 1 June 2001 / Accepted: 11 January 2002     

Gluon distributions in real and virtual photon and the photon structure function

Gluon distributions in real and virtual photons are calculated using evolution equations in the NLO approximation. The quark distributions in the photon determined on the basis of the QCD sum rule approach in [1] are taken as an input. It is shown that gluon distribution in the photon can be reliably determined up tox=0.03÷0.05, much lower than the corresponding values in the case of quark distributions. Two variants of the calculations are considered: (1) it is assumed that there are no intrinsic gluons in the photon at some low normalization pointQ ²=Q ₀ ² ∼1GeV²; (2) it is assumed that gluonic content of the photon at lowQ ₀ ² is described by gluonic content of vector mesonsρ, ω, ϕ. The gluon distributions in these two variants appear to be different. This fact permits one to clarify the origin of nonperturbative gluonic content of the photon by comparing the results with experiment. Structure functionsF ₂(x) for real and virtual photon are calculated and it is shown that in the regionx≥0.2 where QCD approach is valid, there is a good agreement with experiment.     

Measurement and QCD analysis of the diffractive deep-inelastic scattering cross section at HERA

A detailed analysis is presented of the diffractive deep-inelastic scattering process ep→eXY, where Y is a proton or a low mass proton excitation carrying a fraction 1-x_IP>0.95 of the incident proton longitudinal momentum and the squared four-momentum transfer at the proton vertex satisfies |t|<1 GeV². Using data taken by the H1 experiment, the cross section is measured for photon virtualities in the range 3.5≤Q²≤1600 GeV², triple differentially in x_IP, Q² and β=x/x_IP, where x is the Bjorken scaling variable. At low x_IP, the data are consistent with a factorisable x_IP dependence, which can be described by the exchange of an effective pomeron trajectory with intercept α_IP(0)=1.118±0.008(exp.)^+0.029 _-0.010(model). Diffractive parton distribution functions and their uncertainties are determined from a next-to-leading order DGLAP QCD analysis of the Q² and β dependences of the cross section. The resulting gluon distribution carries an integrated fraction of around 70% of the exchanged momentum in the Q² range studied. Total and differential cross sections are also measured for the diffractive charged current process e⁺p→ν̄_eXY and are found to be well described by predictions based on the diffractive parton distributions. The ratio of the diffractive to the inclusive neutral current ep cross sections is studied. Over most of the kinematic range, this ratio shows no significant dependence on Q² at fixed x_IP and x or on x at fixed Q² and β.     

High-spin states of rotational bands built upon νi13/2 in 166Lu

High-Spin states of odd-odd ¹⁶⁶Lu were populated using the ¹³⁹La(³⁰Si,3nγ)¹⁶⁶Lu at a beam energy of 120 MeV. Twelve new γ-rays were placed on top of the previously known two rotational bands built upon πg _7/2⊗νi _13/2 and πh _11/2⊗νi _13/2. Extending high-spin states up to 21⁺ and 25⁻ for each band, we have observed the onset of band crossing near ħω _c ≈ 0.35 MeV. The band crossing frequency of the yrast πh _11/2⊗νi _13/2 band is consistent with the neutron BC band crossing observed in lighter odd-odd Lu isotopes.     

The Asymptotic Limits of Zero Modes of Massless Dirac Operators

Asymptotic behaviors of zero modes of the massless Dirac operator H = α · D + Q(x) are discussed, where α = (α₁, α₂, α₃) is the triple of 4 × 4 Dirac matrices, , and Q(x) = (q _jk (x)) is a 4 × 4 Hermitian matrix-valued function with | q _jk (x) | ≤ C 〈x〉^−ρ, ρ > 1. We shall show that for every zero mode f, the asymptotic limit of |x|² f (x) as |x| → + ∞ exists. The limit is expressed in terms of the Dirac matrices and an integral of Q(x) f (x).      

Quadrupole moment measurement of the highly deformed πg 9/2⊗νh 11/2 band in 130Pr

The quadrupole moment for the πg _9/2⊗νh _11/2 band in the ^130>Pr nucleus has been measured using the Doppler-shift attenuation method. A centroid shift analysis was carried out and a value of Q₀=6.1±0.4 eb, corresponding to an axial prolate deformation of β₂=0.35(3), has been determined. This is the first direct experimental confirmation of the deformation-driving character of the πg _9/2 orbital in an odd-odd nucleus in the A≃135 superdeformed region. Received: 23 April 1998     

Solutions of independent DGLAP evolution equations for the gluon distribution and singlet structure functions in the next-to-leading order at low x

We present a set of independent formulas to extract the gluon distribution and the singlet structure function from its derivatives with respect to lnQ ² in the next-to-leading order of perturbation theory at low x based on a hard Pomeron exchange. In this approach, both singlet quarks and gluons have the same high-energy behavior at small x. This approach requires the QCD input parameterizations for independent DGLAP evolutions, which we calculated numerically and compared with the MRST, GRV, and DL models. The Pomeron has a hard nature. Its evolution gives a good fit to the experimental data. The values obtained are in the range 10⁻⁴ ≤ x ≤ 10⁻² at Q ² = 20 GeV². The text was submitted by the author in English.     

Wave mechanics of two hard core quantum particles in A 1-D box

The wave mechanics of two impenetrable hard core particles in a 1-D box is analyzed. Each particle in the box behaves like an independent entity represented by a macro-orbital (a kind of pair waveform). While the expectation value of their interaction, 〈 V _HC (x) 〉, vanishes for every state of two particles, the expectation value of their relative separation, 〈 x 〉, satisfies 〈 x 〉≥λ/2 (or q ≥ π/d, with 2d=L being the size of the box). The particles in their ground state define a close-packed arrangement of their wave packets (with 〈 x 〉= λ/2, phase position separation Δϕ = 2π and momentum |q _o| = π/d) and experience a mutual repulsive force (zero point repulsion) f _o =h ²/2md ³ which also tries to expand the box. While the relative dynamics of two particles in their excited states represents usual collisional motion, the same in their ground state becomes collisionless. These results have great significance in determining a correct microscopic understanding of widely different many-body systems.