Microscopic study of the low-energy3H(d,n)4He reaction

We have studied the³H(d, n)⁴He reaction at low energies within a multi-channel resonating-group calculation based on many-bodyn+ andd+³H configurations and pseudo-states as well as on an effective nucleonnucleon interaction containing central, spin-orbit, and tensor components. The low-energy fusion cross section is excellently reproduced within our approach.Dedicated to Prof. Erich Schmid on the occasion of his 60th birthday     

Reaction cross sections in the ten-nucleon system

The properties of the 10-nucleon system are investigated with a multiconfiguration resonating-group method, which consists of +⁶Li,d+⁸Be,d+⁸Be^*, and +⁶Li^* cluster configurations, where⁶Li^* and⁸Be^* represent the rotational excited-states of⁶Li and⁸Be with orbital angular momentum equal to 2. The results show that, among reactions initiated from the +⁶Li incident channel, the inelastic-scattering process⁶Li(,)⁶Li^* dominates. The -transfer reactions⁶Li(,d)⁸Be and⁶Li(,d)⁸Be^* have smaller cross sections, but still contribute, on the average, to about one-third of the +⁶Li total reaction cross sections in the centre-of-mass energy region between 12 and 24 MeV. The calculated +⁶Li total reaction cross section at 27 MeV is equal to around 70% of the empirical value obtained by analyzing +⁶Li differential scattering cross-section data. This is a respectable amount, considering the complexity of the problem and that no adjustable parameters are involved in the calculation. Based on the findings of this and previous investigations, some general criteria which govern the importance of cluster-transfer processes in light nuclear systems have also been obtained. These criteria should be very useful in qualitatively understanding the behaviour of other systems that have hitherto not been studied with the multi-configuration resonating-group method.     

The low-energyD(α, γ)6Li and6Li+208Pb→D+α+208Pb cross sections

We have calculated theE1 andE2 contributions to the low-energyD(,)⁶Li fusion and to the⁶Li+²⁰⁸Pb D++²⁰⁸Pb Coulomb dissociation cross sections within a multichannel Resonating Group calculation based on many-body deuteron+ configurations and pseudo-states. For both reactions experimentally determined cross sections are reasonably well reproduced. We find that dipole capture contributes noticeably to the fusion cross sections atE500 keV, while it is negligible in the Coulomb dissociation data.     

Resonating-Group Study of Three-Nucleon Bound State and p+d Scattering

The multi-configuration resonating-group method is employed to study the properties of the three-nucleon system. The model space is spanned by p+d, p+d', n+ 2p, and a large number of their associated pseudo-inelastic configurations. The nucleon-nucleon potential used is the Minnesota potential which contains nuclear central, Coulomb, and spin-orbit components. The results show that the calculated p+d complex phase shifts agree well with the values obtained by an empirical analysis of experimental data. Differential scattering and total reaction cross sections in the p+d system are calculated at centre-of-mass energies up to 32 MeV. Without adjusting any parameter, it is found that the agreement between calculation and experiment is quite satisfactory. The effects of successively enlarging the model space have also been examined. Here the finding is that, in order to obtain reliable results, all three types of cluster configurations must be included in the calculation. Received March 11, 1994; revised June 17, 1994; accepted for publication August 6, 1994     

A Rigorous Derivation of a Linear Kinetic Equation of Fokker–Planck Type in the Limit of Grazing Collisions

We rigorously derive a linear kinetic equation of Fokker–Planck type for a 2-D Lorentz gas in which the obstacles are randomly distributed. Each obstacle of the Lorentz gas generates a potential V( ), where V is a smooth radially symmetric function with compact support, and >0. The density of obstacles diverges as ^– , where >0. We prove that when 0< <1/8 and =2+1, the probability density of a test particle converges as 0 to a solution of our kinetic equation.     

Gauge Fields with Generic Singularities

Let Mbe an n-dimensional manifold equipped with an Abelian Yang–Mills field with connection form . We consider an external potential function Vand examine the existence and regularity of the vortex lines of the form +Vdtwhich define the motion of a particle weakly coupled to the Yang–Mills field on M. These curves are smooth unless the curvature form d is singular and in this paper we treat this singular case from a generic aspect. The problem reduces to the division properties for smooth functions and differential forms, the development of which constitutes the main part of the work presented here.     

Spectroscopic parameters of theJ π=1+,T=0 excited6Li level

An analysis of thed- coincidence spectra of the⁷Li(³He, d)⁴He reaction at incident energy of 5.0 MeV and at various detector angles has been carried out. The values of the spectroscopic parameters of theJ =1⁺,T=0⁶Li state at excitation energy of 5.65 MeV have been deduced. The results, considering the experimental errors, do not appear to be dependent on the geometry and are in line with the ones adopted in literature.     

Anisotropic singlet superconductivity for systems with strongly correlated electrons

The periodic Anderson model extended by pairing interactions amongf- and conduction electrons is investigated in the context of the singlet-like superconductivity. We evaluate the transition temperatureT _c and the ratios of superconducting order parameters atT _c as functions of an effective parameter which describes the correlation off-electrons. The relative stability of thes- andd -superconductivity depends on the values of the Fermi wave vector and on the magnitude of . Due to the absence of on-site pairing forf-electrons, the increase of Coulomb correlations makes thes-like superconductivity more favourable than thed -superconductivity. This behaviour is accompanied by crossover effects: with the increase of Coulomb correlations amongf-electrons the superconductivity is taken over by conduction electrons.Supported by PAN, CPBP 01.12     

Solution of the Semi-Infinite Toda Lattice for Unbounded Sequences

The semi-infinite Toda lattice is the system of differential equations d _n (t)/dt = _n (t)(b _n+1(t) – b _n (t)), db _n (t)/dt = 2( _n ²(t) – _n–1 ²(t)), n = 1, 2, ..., t > 0. The solution of this system (if it exists) is a pair of real sequences _n (t), b _n (t) which satisfy the conditions _n (0) = _n ,, b _n (0) = b _n , where _n > 0 and b _n are given sequences of real numbers. It is well known that the system has a unique solution provided that both sequences _n and b _n are bounded. When at least one of the known sequences _n and b _n is unbounded, many difficulties arise and, to the best of our knowledge, there are few results concerning the solution of the system. In this letter we find a class of unbounded sequences _n and b _n such that the system has a unique solution. The results are illustrated with a typical example where the sequences _i (t), b _i (t), i = 1, 2, ... can be exactly determined. The connection of the Toda lattice with the semi-infinite differential-difference equation d²/dt ² log h _n = h _n+1 + h _n–1 – 2h _n , n = 1, 2, ... is also discussed and the above results are translated to analogous results for the last equation.     

Zero value of the Schwarzschild mass for an asymptotically Euclidian system of gravitational waves

A class of the asymptotically Euclidian space-times is shown to exist for which the Schwarzschild mass is equal to zero. The coordinate atlases of these space-times satisfy two additional conditions: _k (-gg ^0k )=0 and _ik ⁰ _0g ^ik - _ik ^k _0g ⁰ⁱ =0. In aT-orthogonal metricgs ²=g ₀₀ dt ² -g dx dx these conditions take a simple form: ₀(detg )=0 and (₀ g )(₀ g )=0.     

On the oxygen isotope effect and apex anharmonicity in high-T c cuprates

Emphasis is put on aprecise knowledge of the oxygen isotope shift exponent _O is the so far synthesized high-T _c superconductors in order to elucidate the basic mechanism. The known data, see _a in Table 6, indicate the presence of a presumably anharmonic coupling of pyramidal apex oxygen motion along thec-axis in these highly in-plane correlated superconductors. _a is computed from _O=r _a , based on the conjecture that the ratior of apex to total oxygen-ion content per unit cell is relevant. The related experimental and theoretical literature is reviewed.     

Final-state interactions and repulsive Coulomb effects ind+3He→3H+p+p reaction

Differential cross sections of the reactiond+³He³H+p+p have been measured atE _d =23.083 MeV in two different kinematical configurations. A gas target was used in order to obtain absolute differential cross sections and two E–E telescopes allowed a very good identification of the various particles coming from thed+³He reaction. The role of the finalstate interactions and repulsive Coulomb effects appears rather distinctly.     

Some exact solutions to the sine-Gordon equations

We present some new exact (solitary and traveling) solutions to the sine-Gordon equationsc ²u_xx–u_tt = sinu andcu _xt+ u_tt = sinu, and the dissipative sine-Gordon equationc ²u_xx–u_tt–u_t=₁ sinu+ ₂ sin(2u). Here,, ₁, and ₂ are the coupling constants, real numbers;c is theintrinsic speed of the propagating wave determined by the system; and is the damping factor. The physical implication is briefly discussed.     

α-relaxation near the glass transition — a local time process

The empirical Cole-Cole and Cole-Davidson expressions for the -relaxation part of the susceptibility (z)=o/[z ^b +1] ^a are analyzed within a general framework of diffusion processes. It is found that (z) represents a Green function for such a process, and the corresponding relaxation function can be expressed in terms of a local time processF(t)=1–E ₀[(t)]. This latter process describe an intermittent relaxation process occurring on a Cantor like visiting time-setJ _o. The exponentsa andb are fractal dimensions of such sets. It is argued that, in caseb1, the underlying diffusion process is related to the experimentally observed -process which then triggers the -process on the time-setJ _o.     

Critical exponents for the self-avoiding random walk in three dimensions

We compute by direct Monte Carlo simulation the main critical exponents, , ₄, andv and the effective coordination number for the self-avoiding random walk in three dimensions on a cubic lattice. We find both hyperscaling relationsdv=2– anddv– 2 ₄+=0 satisfied ind = 3.     

Translation group and spectrum condition

Let {A, ^d ,} be aC*-dynamical system, where ^d is thed-dimensional vector group. LetV be a convex cone in ^d and its dual cone. We will characterize those representations ofA with the properties (i) _a ,a ^d is weakly inner, (ii) the corresponding unitary representationU(a) is continuous, and (iii) the spectrum ofU(a) is contained in .     

Spouge's Conjecture on Complete and Instantaneous Gelation

We investigate the stochastic counterpart of the Smoluchowski coagulation equation, namely the Marcus–Lushnikov coagulation model. It is believed that for a broad class of kernels, all particles are swept into one huge cluster in an arbitrarily small time, which is known as a complete and instantaneous gelation phenomenon. Indeed, Spouge (also Domilovskii et al. for a special case) conjectured that K(i, j)=(ij) , >1, are such kernels. In this paper, we extend the above conjecture and prove rigorously that if there is a function (i, j), increasing in both i and j such that _j=1 1/(j(i, j))< for all i, and K(i, j)ij(i, j) for all i, j, then complete and instantaneous gelation occurs. Evidently, this implies that any kernels K(i, j)ij(log(i+1)log(j+1)) , >1, exhibit complete instantaneous gelation. Also, we conjuncture the existence of a critical (or metastable) sol state: if lim _i+j ij/K(i, j)=0 and _{i, j=1} 1/K(i, j)=, then gelation time T _g satisfies 0<T _g<. Moreover, the gelation is complete after T _g.     

Seven basic regimes of steady crystal growth in two dimensions

Using a Markov rate-process model, exact expressions are found for the steady growth rate of an edge of a two-dimensional crystal in terms of the numberM of particles along the edge, the height difference (or number of permanent steps)K along the edge, the nucleation rate , and the speed + of movement of steps. The familiar growth regimes can be identified with asymptotic regimes for the parametersK, (v/)^1/2, andM. From a mathematical viewpoint, there are seven basic regimes, of which the known physical regimes are special cases.     

An Alternative Approach to Study the Dynamical Group for the Modified Pöschl–Teller Potential

The properties of the modified Pöschl–Teller potential are outlined. The ladder operators are constructed directly from the wave functions without introducing any auxiliary variable. It is shown that these operators are associated to the SU(2) algebra. Analytical expressions for the functions sinh(x) and (1/)cosh(x)d/dx are evaluated from these ladder operators. The harmonic limit for this system is discussed. The expansion of the coordinate x and the momentum p from the operators of the SU(2) are also obtained.