Isotopic effects in the 7Li + 10, 11B elastic and inelastic scattering

Angular distributions of the ⁷Li + ¹⁰B elastic and inelastic scattering were measured at the energy E _lab (¹⁰B) = 51 MeV (21 MeV c.m.). These and previously measured ⁷Li + ¹⁰B elastic-scattering data known at the ⁷Li-beam energies 24 MeV (14.1 MeV c.m.) and 39 MeV (22.94 MeV c.m.) were analyzed within the optical model and coupled-reaction channels method to determine the energy dependence of the parameters of the scattering potential and find the difference of these parameters from that of ⁷Li + ¹¹B scattering. It was found that the ⁷Li + ¹¹B potential parameters fail to describe the ⁷Li + ¹⁰B scattering data. The biggest difference is observed between the depths of the imaginary potentials that describe these scatterings.     

Some considerations on the restoration of Galilei invariance in the nuclear many-body problem

The effects of the restoration of Galilei invariance in the nuclear many-body problem on the energies of simple bound states are investigated. As examples we consider the oscillator ground states of ⁴He, ¹⁶O and ⁴⁰Ca as well as the various hole states with respect to these reference configurations. Density-independent as well as density-dependent interactions are studied. It turns out that the full restoration of Galilei-invariance yields considerable contributions on top of the trivial 1/A effect resulting from removing the center-of-momentum part of the Hamiltonian. Received: 20 February 2001 / Accepted: 10 May 2002     

Electric dipolarizability of <Superscript>7</Superscript>Li

We calculate the electric dipolarizability of ⁷Li nucleus within the cluster model and estimate a value of about 0.0188 fm³. We also discuss the possibility of observing this in the scattering of ⁷Li from a ²⁰⁸Pb target at energies about 30 MeV.      

Resonance states in 12C and α-particle condensation

The states with J^π = 0⁺, 2⁺, and 4⁺ of ¹²C with excitation energies less than about 15 MeV are investigated with the alpha condensate wave function with spatial deformation and by using the method of ACCC (analytic continuation in the coupling constant) which is necessary for a proper treatment of resonance states. The calculated energy and width of the recently observed 2₂⁺ state are found to be well reproduced. The obtained 2₂⁺ wave function has a large overlap with a single condensate wave function of 3α gas-like structure. The density distribution is shown to be almost the same as that of the 0₂⁺ state that is regarded as a 3α Bose-condensed state, if the energy of the 2₂⁺ state is scaled down to the same value as the one of the 0₂⁺ state. Furthermore, the kinetic energy, nuclear interaction energy, and Coulomb interaction energy of the calculated 2₂⁺ state are shown to be very similar to those of the 0₂⁺ state. We conclude that the 2₂⁺ state has a structure similar to the 0₂⁺ state of Bose-condensate character with a dilute 3α gas-like structure. In addition, the resonance states, 0₃⁺, 0₄⁺, 4₂⁺, are also discussed.     

Ising models on hyperbolic graphs

We consider Ising models on a hyperbolic graph which, loosely speaking, is a discretization of the hyperbolic planeH ² in the same sense asZ ^d is a discretization ofR ^d . We prove that the models exhibit multiple phase transitions. Analogous results for Potts models can be obtained in the same way.     

Mass splitting of neutral <Emphasis Type="Italic">B</Emphasis><Stack><Subscript><Emphasis Type="Italic">d,s</Emphasis></Subscript><Superscript>0</Superscript></Stack> mesons in the framework of the minimal supersymmetric model

The effects of a minimal supersymmetric model with the Yukawa sector of the second type and explicit violation of CP invariance in the Higgs potential occurring during the mixing of physical states in systems of neutral B _d,s ⁰ mesons are considered. The mixing parameter Δm _LS is calculated in the limit of four-fermion approximation with the exchange of charged Higgs bosons (H ^±). This study specifies data presented in [1] and establishes new constraints on \(m_{H^ \pm } \) in this model.     

Evaluation of certain statistical sums

Summary Certain statistical ensembles,e.g. open chemical systems with randomly varying number of particles, are characterized by partition functions of the type ,n being a natural number anda _j ’s generalized temperatures. The state of the system is well defined if one knows the dependence ofa _j ’s on ensemble averages 〈n ^j 〉. For making the equations 〈n ^j 〉=〈n ^j 〉 (a ₁, ...,a _s) at least more accessible for numerical calculations a transformation of the partition function to a series of Fourier integrals is proposed. In the special case of the integrals can be calculated analytically transforming the statistical sum into a series of error functions.     

Are the New Physics Contributions from the Left-Right Symmetric Model Important for the Indirect CP Violation in the Neutral B Mesons?

No Heading Several works analyzing the new physics contributions from the Left-Right Symmetric Model to the CP violation phenomena in the neutral B mesons can be found in the literature. These works exhibit interesting and experimentally sensible deviations from the Standard Model predictions but at the expense of considering a low right scale υ_R around 1 TeV. However, when we stick to the more conservative estimates for υ_R, which say that it must be at least 10⁷ GeV, no experimentally sensible deviations from the Standard Model appear for indirect CP violation. This estimate for υ_R arises when the generation of neutrino masses is considered. In spite of the fact that this scenario is much less interesting and says nothing new about both the CP violation phenomenon and the structure of the Left-Right Symmetric Model, this possibility must be taken into account for the sake of completeness and when considering the see-saw mechanism that provides masses to the neutrino sector. ¹ Associate researcher of the Centro Internacional de Física, Ciudad Universitaria, Bogotá D.C., Colombia.     

Extension of the spectroscopic Monte Carlo method to realistic effective interactions

We propose an extension of the spectroscopic Monte Carlo method to realistic effective interactions. The scheme is applied to the recently introduced GXPF1 interaction for fp nuclei for the ground state of ⁶⁰Fe, ⁵⁶Ni, ⁶⁴Ni and ⁶⁰Zn. The method hinges on the use of Hartree-Fock-Bogoliubov wave functions (properly projected before variation) and on a reformulation of the effective interaction so that it is a sum of negative squares of Hermitian one-quasi-particle operators, so the application of the Hubbard-Stratonovich transformation to the elementary propagator exp[- ] gives a functional integral over a Hermitian propagator. Limitations and difficulties encountered in the calculation are discussed.     

Pion radiative weak decays in nonlocal chiral quark models

We analyze the radiative pion decay π⁺→e⁺νeγ${\pi }^{+}\to e^{+}{\nu }_e\gamma$ within nonlocal chiral quark models that include wave function renormalization. In this framework we calculate the vector and axial-vector form factors FV$F_V$ and FA$F_A$ at q²=0$q^2=0$ — where q²$q^2$ is the e⁺νe$e^{+}{\nu }_e$ squared invariant mass — and the slope a   of FV(q²)$F_V(q^2)$ at q²→0$q^2\to 0$. The calculations are carried out considering different nonlocal form factors, in particular those taken from lattice QCD evaluations, showing a reasonable agreement with the corresponding experimental data. The comparison of our results with those obtained in the (local) NJL model and the relation of FV$F_V$ and a   with the form factor in π⁰→γ^?γ${\pi }^0\to {\gamma }^{?}\gamma$ decays are discussed.     

Optical potential analysis of proton elastic scattering from <Superscript>12</Superscript>C based on the <Emphasis Type="Italic">α</Emphasis>-particle model

Based on an α-particle model of ¹²C, an optical potential for intermediate-energy proton- ¹²C scattering is presented in the framework of the KMT theory. The parameterized proton- ⁴He amplitude, the required basic input for constructing the optical potential, is obtained by fitting the proton- ⁴He scattering data. The differential cross-sections and analyzing powers of the proton- ¹²C elastic scattering at incident energies ranging from 0.2 to 1.0GeV have been calculated by using the obtained optical potential. The main features of the measured angular distributions of the cross-section and the analyzing power can be satisfactorily described. The proton- ¹²C total cross-sections have also been calculated, and the results are in good agreement with the experimental data at energies below 0.6GeV but underestimate the data about 6% at higher energies.     

Growth velocity and the topography of Ni-Zn binary alloy electrodeposits

We show that the electrodeposition of Ni-Zn alloys at the lowest growth velocities, v < 0.5μm/s, exclusively proceeds from an abnormal co-deposition phenomenon. The growth process in this v region greatly depends on the initial [Co²⁺] concentration of the film deposition bath. A theoretical approach of this process including the role of the saturation surface roughness of the alloy, , leads to an estimation of the transport properties of the ad-atoms involved during the deposit formation. Their surface diffusion coefficient varying between 1.76×10^-10 and 2.40×10^-8 cm^-2/s exhibits a minimal value, D _s = 2.10×10^-10 cm^-2/s located between v = 0.17 and 0.35μm/s. The spatial scaling analysis of the local roughness, σ, examined according to the power-law σ≈L ^α reveals that the resulting roughness exponents concurs with the Kardar-Parisi-Zhang dynamics including the restricted surface diffusion. Two main v regions leads to different fractal textural features of the alloy film surface. Below 0.10 μm/s, the roughness exponent obtained is α≈ 0.6, depicting a limited ad-atom mobility. Over v = 0.30μm/s, this exponent stabilises at α≈ 0.82, indicating an increase of the surface diffusion. Received 16 August 2000 and Received in final form 20 June 2001     

Optical reaction cross-sections for light projectiles

The optical reaction cross-sections forn, p,²H,³He,³He and⁴He for several global optical potentials available in the literature have been parametrized in terms of simple empirical expressions which are smooth functions of the target mass number and the projectile energy. The empirical forms are 5–10% accurate over the periodic table and energy-range upto 50 MeV. They can be conveniently used in calculations where the optical reaction cross-sections are required as input. The calculation of proton spectra in the (n, p) reaction at 14 MeV is discussed.     

Determination of the calcium ground state scattering length by photoassociation spectroscopy at large detunings

Photoassociation spectroscopy was used to determine the s-wave scattering length of ⁴⁰Ca atoms in their electronic ground state. Vibrational levels were observed in an extended range of up to 182 GHz below the dissociation limit 4s^{2 1}S₀–4s4p ¹P₁. Thus, the frequency interval was nearly tripled, in which photoassociation was observed compared to previous measurements. The spectra were analyzed by means of quantum mechanical simulations. With the new data it was possible to resolve the discrepancy concerning the ground state scattering length presented in earlier publications [Phys. Rev. A 67, 043408 (2003); Eur. Phys. J. D 26, 155 (2003)]. An improved dipole-dipole coupling constant C₃ ^Σ = 0.52306(20) ×10³ cm^-1 nm³ is obtained.     

Cubic potential models for cluster radioactivity

Cluster radioactivity is a process by which nuclei equal and heavier than the α-particle is emitted spontaneously. The clusters usually emitted in this process are the α-particle, carbon, oxygen, neon, magnesium, silicon etc. When the mass of the cluster becomes comparable with the mass of the daughter, symmetric fission takes place. Thus the cluster radioactivity is an intermediate process between the well known α-decay and the spontaneous fission. In earlier years such cluster radioactivity was found mostly in actinide nuclei like radium, uranium etc. Very recently it has been predicted that such decays are possible in a new region around ¹¹¹Ba. There has been an exciting experimental detection of the emission of ¹²C from ¹¹¹Ba leading to ¹⁰²Sn, which is attracting a lot of attention recently. To study the phenomenon of cluster radioactivity there are various theoretical models in vogue. The existing models generally fall under two categories: the unified fission model (UFM) and the preformed cluster model (PCM). The physics of the UFM and the PCM are completely different. The UFM considers cluster radioactivity simply as a barrier penetration phenomenon in between the fission and the α-decay without worrying about the cluster being or not being preformed in the parent nucleus. In the PCM clusters are assumed to be preborn in a parent nucleus before they could penetrate the potential barrier with a given Q-value. The basic assumption of the UFM is that heavy clusters as well as the α-particle have equal probability of being preformed. In PCM, clusters of different sizes have different probabilities of their being preformed in the parent nucleus. We have developed three fission models during the last decade using the cubic potential for the pre-scission region. The use of these models in the study of cluster radioactivity in both the actinide and barium regions will be discussed in this talk in comparison with the other existing theories.     

Molecular-orbital structure in neutron-rich Be and C isotopes

The structure of Be and C isotopes are investigated based on the molecular-orbit (MO) model. The low-lying states are characterized by several configurations of valence neutrons, which are constructed as combinations of basic orbits. In ¹⁰Be, all of the observed positive-parity bands and the negative-parity bands are described within the model. The second 0⁺ state of ¹⁰Be has a large α-α cluster structure, and this is characterized by a (1/2⁺ _σ)² configuration. An enlargement of the α-α distance due to two-valence neutrons along the α-α axis makes their wave function smooth and reduces the kinetic energy drastically. Furthermore, the contribution of the spin-orbit interaction due to coupling between the S _z = 0 and the S _z = 1 configurations, is important. In the ground state of ¹²Be, the calculated energy exhibits similar characteristics, that the remarkable α clustering and the contribution of the spin-orbit interaction make the binding of the state with (3/2^- _π)²(1/2⁺ _σ)² configuration properly stronger in comparison with the closed p-shell (3/2^- _π)²(1/2^- _π)² configuration. This is related to the breaking of the N = 8 (closed p-shell) neutron magic number. Also, the molecule-like structure of the C isotopes is investigated using a microscopic α+α+α+n+n+ ^{. . .} model. The combination of the valence neutrons in the π- and the σ-orbit is promising to stabilize the linear-chain state against the breathing and bending modes, and it is found that the excited states of ¹⁶C are the most promising candidates for such structure. Received: 1 May 2001 / Accepted: 4 December 2001     

No Zero Energy States for the Supersymmetric x 2 y 2 Potential

We show that the positive supersymmetric matrix-valued differential operator H = p _x ² + p _y ² + x ² y ² + x₃ + y₁ has no zero modes, i.e., H = 0 implies = 0. The result depends on a virial type argument for the corresponding supercharge. The model may be regarded as a simple relative of dimensional reductions of supersymmetric Yang–Mills theories.     

Mechanism of the 12C(11B,15N)8Be reaction and 8Be + 15N optical-model potential

Angular distributions of the ¹²C( ¹¹B, ¹⁵N) ⁸Be reaction were measured at the energy E_lab(¹¹B) = 49 MeV for the transitions to the ground and 2.94 MeV (2⁺) excited state of ⁸Be and to the ground and 5.270 MeV (5/2⁺) + 5.299 MeV (1/2⁺), 6.324 MeV (3/2^-), 7.155 MeV (5/2⁺) + 7.301 MeV (3/2⁺), 7.567 MeV (7/2⁺) excited states of ¹⁵N. The data were analyzed by the coupled-reaction-channel method. The elastic, inelastic scattering and one- and two-step transfers were included in the coupling scheme. The data of the ¹²C( ¹¹B, ⁸Be) ¹⁵N reaction at E_cm = 9.4-17.8 MeV known from the literature, were also included in the analysis. The mechanism of the ¹²C( ¹¹B, ¹⁵N) ⁸Be reaction and the optical-model potential parameters for the ¹⁵N + ⁸Be channel were deduced. The energy dependence of the optical-model parameters for the ¹⁵N + ⁸Be channel was obtained.