DECEA - Departamento de Ciências Exatas e Aplicadas
URI permanente desta comunidadehttp://www.hml.repositorio.ufop.br/handle/123456789/551
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15 resultados
Resultados da Pesquisa
Item Numerical simulation of GUE two-point correlation and cluster functions.(2021) Sargeant, Adam JamesNumerical simulations of the two-point eigenvalue correlation and cluster functions of the Gaussian unitary ensemble (GUE) are carried out directly from their definitions in terms of deltas functions. The simulations are compared with analytical results which follow from three analytical formulas for the two-point GUE cluster function: (i) Wigner’s exact formula in terms of Hermite polynomials, (ii) Brezin and Zee’s approximate formula which is valid for points with small enough separations and (iii) French, Mello and Pandey’s approximate formula which is valid on average for points with large enough separations. It is found that the oscillations present in formulas (i) and (ii) are reproduced by the numerical simulations if the width of the function used to represent the delta function is small enough and that the non-oscillating behaviour of formula (iii) is approached as the width is increased.Item Attenuation of the intensity within a superdeformed band.(2001) Sargeant, Adam James; Hussein, Mahir Saleh; Pato, Mauricio Porto; Takigawa, Noboru; Ueda, MasahitoThe attenuation of the intra-band 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.Item Evaluation of effective astrophysical S factor for non-resonant reactions.(2001) Ueda, Masahito; Sargeant, Adam James; Pato, Mauricio Porto; Hussein, Mahir SalehWe derived analytic formulas of the effective astrophysical S factor, Seff, for a non- resonant reaction of charged particles using a Taylor expansion of the astrophysical S factor, S(E), and a uniform approximation. The formulas will be able to generate more accurate approximations to Seff than previous ones.Item Symmetrisation in the semiclassical theory of Coulomb excitation.(1997) Sargeant, Adam James; Johnson, R. C.; Tostevin, J. A.Corrections to the Alder and Winther semiclassical cross section for first order Coulomb excitation are considered through the Sukumar and Brink systematic expansion of the propagator in inverse powers of Sommerfeld's parameter, r/. The zeroth order term is that provided by unsymmetrised Alder-Winther theory and it is shown that to order 1/~7 the only type of correction is one corresponding to energy symmetrisation.Item Saturation of the width of the strength function(2000) Sargeant, Adam James; Hussein, Mahir Saleh; Pato, Mauricio Porto; Ueda, MasahitoThe strength function of a single state ud& is studied using the deformed Gaussian orthogonal ensemble. In particular we study the dependence of the spreading width of ud& on the degree of mixing.Item Effective astrophysical S factor for nonresonant reactions.(2000) Ueda, Masahito; Sargeant, Adam James; Pato, Mauricio Porto; Hussein, Mahir SalehWe have made an asymptotic expansion of the effective S factor, Seff , for nonresonant reactions of charged particles. The resulting analytic formulas can generate approximations to Seff which contain derivatives, with respect to the center of mass energy E, of the astrophysical S factor, S(E), up to any desired order. Thus our approximation incorporates better the center-of-mass energy dependence in S(E) than previous approximations which included only the first or second derivatives. The range of applicability of the method is discussed. We numerically investigate our expressions for the reaction 7Be(p,g )8B.Item Energy averages and fluctuations in the decay out of superdeformed bands.(2002) Sargeant, Adam James; Hussein, Mahir Saleh; Pato, Mauricio Porto; Ueda, MasahitoWe derive analytic formulas 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: G#/GS , GN /d, and GN /(GS1G#). Here G# is the spreading width for the mixing of a superdeformed ~SD! state u0& with the normally deformed ~ND! states uQ& whose spin is the same as u0&’s. The uQ& have mean lever spacing d and mean electromagnetic decay width GN whilst u0& has electromagnetic decay width GS. The average decay intensity may be expressed solely in terms of the variables G#/GS and GN /d or, analogously to statistical nuclear reaction theory, in terms of the transmission coefficients T0(E) and TN describing transmission from the uQ& to the SD band via u0& 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 GN /(GS1G#)5(d/2p)TN /(GS1G#). This suggests that analysis of an experimentally determined variance could yield the mean level spacing d as does analysis of the cross section autocorrelation function in compound nucleus reactions. We compare our results with those of Gu and Weidenmu¨ller.Item Variance of the decay intensity of superdeformed bands.(2004) Hussein, Mahir Saleh; Sargeant, Adam James; Pato, Mauricio Porto; Ueda, MasahitoWe present analytic formulae for the energy average and variance of the intraband decay intensity of a superdeformed band.Item Addendum : attenuation of the intensity within a superdeformed band.(2004) Sargeant, Adam James; Hussein, Mahir Saleh; Pato, Mauricio Porto; Takigawa, Noboru; Ueda, MasahitoWe investigate a random matrix model [Phys. Rev. C 65, 024302 (2002)] for the decay-out of a superdeformed band as a function of the parameters: G# /GS, GN/D, GS /D, and D/D. Here G# is the spreading width for the mixing of a superdeformed (SD) state u0l with a normally deformed (ND) doorway state udl, GS and GN are the electromagnetic widths of the SD and ND states, respectively, D is the mean level spacing of the compound ND states and D is the energy difference between u0l and udl. The maximum possible effect of a transition from ordered to chaotic states is inferred from analytical and numerical calculations of the decay intensity in the limiting cases for which the ND states obey Poisson and GOE statistics. Our results show that the sharp attenuation of the decay intensity cannot be explained solely by a transition from ordered to chaotic states.Item Resonances and the thermonuclear reaction rate.(2004) Hussein, Mahir Saleh; Ueda, Masahito; Sargeant, Adam James; Pato, Mauricio PortoWe 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 12C(p,γ)13N.