arXiv subjects
Publications and source records attributed to M. P. Pato.
We present an approximate analytic expression for thermonuclear reaction rate of charged particles when the cross section contains a single narrow or wide resonance described by a Breit-Wigner shape. The resulting expression is uniformly valid as the effective energy and resonance energy coalesce. We use our expressions to calculate the reaction rate for $^{12}$C(p,$γ$)$^{13}$N.
We derive analytic formulae for the energy average (including the energy average of the fluctuation contribution) and variance of the intraband decay intensity of a superdeformed band. Our results may be expressed in terms of three dimensionless variables: $Γ^{\downarrow}/Γ_S$, $Γ_N/d$, and $Γ_N/(Γ_S+Γ^{\downarrow})$. Here $Γ^{\downarrow}$ is the spreading width for the mixing of a superdeformed (SD) state $|0>$ with the normally deformed (ND) states $|Q>$ whose spin is the same as $|0>$'s. The $|Q>$ have mean level spacing $d$ and mean electromagnetic decay width $Γ_N$ whilst $|0>$ has electromagnetic decay width $Γ_S$. The average decay intensity may be expressed solely in terms of the variables $Γ^{\downarrow}/Γ_S$ and $Γ_N/d$ or, analogously to statistical nuclear reaction theory, in terms of the transmission coefficients $T_0(E)$ and $T_N$ describing transmission from the $|Q>$ to the SD band via $|0\angle$ and to lower ND states. The variance of the decay intensity, in analogy with Ericson's theory of cross section fluctuations depends on an additional variable, the correlation length $Γ_N/(Γ_S+Γ^{\downarrow})=\frac{d}{2π}T_N/(Γ_S+Γ^{\d ownarrow})$. This suggests that analysis of an experimentally obtained variance could yield the mean level spacing $d$ as does analysis of the cross section autocorrelation function in compound nuclear reactions. We compare our results with those of Gu and Weidenmüller.
It is shown that several effects are responsible for deviations of the intensity distributions from the Porter-Thomas law. Among these are genuine symmetry breaking, such as isospin; the nature of the transition operator; truncation of the Hilbert space in shell model calculations and missing transitions
We derived analytic formulas of the effective S astrophysical S factor,S^eff for a non-resonant reaction of charged particles using a Taylor expension of the astrophysical S factor and a uniform approximation.The formulas will be able to generate generate more accurate approximation to S^eff than previous ones.
We derive an exact general formalism that expresses the eigenvector and the eigenvalue dynamics as a set of coupled equations of motion in terms of the matrix elements dynamics. Combined with an appropriate model Hamiltonian, these equations are used to investigate the effect of the presence of a discrete symmetry in the level curvature distribution. An explanation of the unexpected behavior of the data regarding frequencies of acoustic vibrations of quartz block is provided.
The attenuation of the intraband intensity of a superdeformed band, which results from mixing with normally deformed configurations, is calculated using reaction theory. It is found that the sharp increase of the attenuation is mostly due to the tunnelling through a spin dependent barrier and not to the chaotic nature of the normally deformed states.
It is shown how initial conditions can be appropriately defined for the integration of Lorentz-Dirac equations of motion. The integration is performed \QTR{it}{forward} in time. The theory is applied to the case of the motion of an electron in an intense laser pulse, relevant to nonlinear Compton scattering.
The strength function of a single state $|d>$ is studied using the deformed Gaussian orthogonal ensemble. In particular we study the dependence of the spreading width of $|d>$ on the degree of mixing.
It is shown that an operator can be defined in the abstract space of random matrices ensembles whose matrix elements statistical distribution simulates the behavior of the distribution found in real physical systems. It is found that the key quantity that determines these distribution is the commutator of the operator with the Hamiltonian. Application to symmetry breaking in quantum many-body systems is discussed.
A multifractal analysis is performed on the universality classes of random matrices and the transition ones.Our results indicate that the eigenvector probability distribution is a linear sum of two chi-squared distribution throughout the transition between the universality ensembles of random matrix theory and Poisson .
We study the postacceleration of charged fragments in reactions with unstable nuclear beams. For elastic breakup processes we show that the postaceleration effect can be well understood in terms of closed analytical forms derived in a quantum mechanical formulation. This gives theoretical support to the effect experimentally observed in the breakup of Li-11 projectiles at intermediate energies.
A Deformed Gaussian Orthogonal Ensemble (DGOE) which interpolates between the Gaussian Orthogonal Ensemble and a Poissonian Ensemble is constructed. This new ensemble is then applied to the analysis of the chaotic properties of the low lying collective states of nuclei described by the Interacting Boson Model (IBM). This model undergoes a transition order-chaos-order from the $SU(3)$ limit to the $O(6)$ limit. Our analysis shows that the quantum fluctuations of the IBM Hamiltonian, both of the spectrum and the eigenvectors, follow the expected behaviour predicted by the DGOE when one goes from one limit to the other.